Fifth Conference Proceedings Tokyo 11-15 November 1974

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Fifth Conference Proceedings Tokyo 11-15 November 1974

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V

Fifth Conference Proceedings

Tokyo

11-15 November 1974

INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, 1 975


Cover picture showing CLEO stellarator at Culham Laboratory

by permission of the

United Kingdom Atomic Energy Authority


PLASMA PHYSICS

AND CONTROLLED

NUCLEAR FUSION RESEARCH

1974


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The Agency's Statute was approved on 23 October 1956 by the Conference on the Statute of the IAEA

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Printed by the IAEA in Austria

June 1975


PROCEEDINGS SERIES

PLASMA PHYSICS

AND CONTROLLED

NUCLEAR FUSION RESEARCH

1974

PROCEEDINGS OF THE

FIFTH INTERNATIONAL CONFERENCE ON PLASMA PHYSICS

AND CONTROLLED NUCLEAR FUSION RESEARCH

HELD BY THE

INTERNATIONAL ATOMIC ENERGY AGENCY

IN TOKYO, 11-15 NOVEMBER 1974

In three volumes

VOL.1

INTERNATIONAL ATOMIC ENERGY AGENCY

VIENNA, 1975


PLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION RESEARCH 1974

IAEA, VIENNA, 1975

STI/PUB/381

ISBN 92-0-030075-8


FOREWORD

Substantial progress towards the demonstration of the scientific feasibility of controlled

fusion and towards the design and construction of the first controlled thermonuclear power

reactor is shown in the three volumes of these Proceedings of the Fifth IAEA Conference on

Plasma Physics and Controlled Nuclear Fusion Research.

The Conference, held in Tokyo from 11 to 15 November 1974, was organized by the

Agency with the assistance and cooperation of the Japanese Government and the Japan Atomic

Energy Research Institute. Nearly 500 participants from 24 countries and three international

organizations attended. A total of 187 papers was presented on research ranging from plasma

physics to the design of fusion reactors. The papers are published here in the original language;

English translations of the Russian papers will be published in a Special Supplement of the

Nuclear Fusion Journal.

By regularly organizing conferences on controlled nuclear fusion and by holding seminars

and specialists' meetings on selected topics the Agency promotes the close international collaboration

among plasma physicists of all countries. These activities will, we hope, contribute to

the rapid use of this new source of energy by mankind.


EDITORIAL NOTE

The papers and discussions have been edited by the editorial staff of the International

Atomic Energy Agency to the extent considered necessary for the reader's assistance. The views

expressed and the general style adopted remain, however, the responsibility of the named authors

or participants. In addition, the views are not necessarily those of the governments of the

nominating Member States or of the nominating organizations.

Where papers have been incorporated into these Proceedings without resetting by the Agency,

this has been done with the knowledge of the authors and their government authorities, and their

cooperation is gratefully acknowledged. The Proceedings have been printed by composition

typing and photo-offset lithography. Within the limitations imposed by this method, every effort

has been made to maintain a high editorial standard, in particular to achieve, wherever practicable,

consistency of units and symbols and conformity to the standards recommended by competent

international bodies.

The use in these Proceedings of particular designations of countries or territories does not

imply any judgement by the publisher, the IAEA, as to the legal status of such countries or

territories, of their authorities and institutions or of the delimitation of their boundaries.

The mention of specific companies or of their products or brand names does not imply any

endorsement or recommendation on the part of the IAEA.

Authors are themselves responsible for obtaining the necessary permission to reproduce

copyright material from other sources.


TOKAMAK EXPERIMENT I (Session I)

CONTENTS OF VOLUME 1

The JFT-2 tokamak experiment (IAEA-CN-33/A 1-1) 3

TV. Fujisawa, A. Funahashi, S. Kunieda, M. Maeno, N. Suzuki, T. Matoba, S. Kasai,

S. Itoh, T. Takeda, K. Toi, T. Sugawara, T. Shoji, T Kawakami, TV. Toyoshima,

T. Ohga, T. Arai, K Yokokura, T. Tani, T. Shiina, M. Ohta, S. Matsuda, S. Yano,

H. Shirakata, K. Takahashi, T. Tazima, M. Nagami, M. Yoshikawa, S. Mori

Research on a tokamak with an axisymmetric divertor and impurity problems in

tokamak devices (IAEA-CN-33/A 1-2) 17

M. Yoshikawa, T. Tazima, Y. Shimomura, A. Kitsunezaki, H. Maeda, K. Inoue,

T. Nagashima, T. Tokutake, H. Ohtsuka, M. Nagami, M. Tanaka, S. Kunieda,

A. Funahashi, T. Kawakami, K. Takahashi, T. Matoba, M. Azumi, T. Shoji, K. Anno,

K Kumagai, S. Kasai, T. Ohga, H. Takeuchi, T Tani, T Arai, S. Mori

Discussion on papers IAEA-CN-33/A 1-1, A 1-2 31

Bo3MymeHHJi MarHHTHoro no/ia npH HeycTOHMHBOCTH cpbiBa

B ycTaHOBKe ToKaMaK-6 (IAEA-CN-33/A 2-1) 33

B.C.BnaceHKOB, B.M . JleoHOB, B.T.MepeacKHH , B. C.MyxoBaTOB

(Perturbation of a magnetic field during the break-up instability in Tokamak-6:

V.S. Vlasenkov et al.)

B/iHHHHe ro$pHpoBKH npofloJibHoro MarHHTHoro no;ifl Ha HOHHyio

KOMnoHeHTy n/ia3Mbi B TOKawiaKax (IAEA-CN-33/A 2-2) 43

M .11 .IleTpOB

(The effect of corrugation of the longitudinal magnetic field on the ion component

of plasma in tokamaks: M.P. Petrov)

Discussion on papers IAEA-CN-33/A 2-1, A 2-2 53

Radiation from plasmas in the ST-Tokamak (IAEA-CN-33/A 3-1) 55

TV. Bretz, D. Dimock, A. Greenberger, E. Hinnov, E. Meservey, W. Stodiek,

S. Von Goeler

Wave generation and heating in the ST-Tokamak at the fundamental and harmonic

ion cyclotron frequencies (IAEA-CN-33/A 3-2) 65

J. Adam, M. Chance, H. Eubank, W. Getty, E. Hinnov, W. Hooke, J. Hosea, J. Jobes,

F. Perkins, R. Sinclair, J. Sperling, H. Takahashi

Discussion on papers IAEA-CN-33/A 3-1, A 3-2 75

Neutral-beam heating in the adiabatic toroidal compressor (IAEA-CN-33/A 4-1) 77

K. Bol, J.L. Cecchi, C.C. Daughney, R.A. Ellis, Jr., H.P. Eubank, H.P. Furth,

R.J. Goldston, H. Hsuan, E. Mazzucato, R.R. Smith, RE. Stott

Experiments on the adiabatic toroidal compressor (IAEA-CN-33/A 4-2) 83

K. Bol, J.L. Cecchi, C.C. Daughney, F. DeMarco, R.A. Ellis, Jr., H.P. Eubank,

HP. Furth, H. Hsuan, E. Mazzucato, R.R. Smith

Discussion on papers IAEA-CN-33/A 4-1, A 4-2 99

Plasma confinement in the Ormak device (IAEA-CN-33/A 5-1) 101

L.A. Berry, J.D. Callen, J.F. Clarke, R.J. Colchin, E.C. Crume, J.L. Dunlap,

PH. Edmonds, G.R. Haste, J. T. Hogan, R.C. Isler, G.L. Johns, N.H. Lazar, J.F. Lyon,

M. Murakami, R. V. Neidigh, W.R. Wing

Neutral beam injection experiments in Ormak (IAEA-CN-33/A 5-2) 113

L.A. Berry, C.E. Bush, J.L. Dunlap, P.H. Edmonds, T.C. Jernigan, J.F. Lyon,

M. Murakami, W.R. Wing

Discussion on papers IAEA-CN-33/A 5-1, A 5-2 125


Neutres atomiques et impuretes dans TFR (IAEA-CN-33/A 6-1) 127

EQUIPE TFR

Decharges a fort courant dans TFR (IAEA-CN-33/A 6-2) 135

EQUIPE TFR

Discussion on papers IAEA-CN-33/A 6-1, A 6-2 145

3>opMa nonepeMHOro ceqeHHH nna3MeHHoro uiHypa B nepcxeHbKOBOM

TOKaMaKe (IAEA-CN-33/A 7-2) 147

A.B.BOPTHHKOB, H.H.BpeBHOB, C.H.repacHMOB, B.T. )KyKOBCKHH,

K).C.MaKCHMOB, B.H.IlepraMeHT, M . K. PoMaHOBCKHH

(The shape of the transverse cross-section of a plasma column in the finger-ring

tokamak: A. V. Bortnikov et al.)

Relaxation of toroidal discharges to stable states and generation of reverse magnetic

fields (IAEA-CN-33/PD-1) 161

J.B. Taylor

TOKAMAK EXPERIMENT II (Session II)

Electron runaway in LT-3 (IAEA-CN-33/A 8-1) 171

J.D. Strachan, R.L. Dewar

Well-centred discharges in the Pulsator-I Tokamak (IAEA-CN-33/A 8-2) 179

0. KliXber, S. Corti, J. Gernhardt, F. Karger, G. Lisitano, D. Meisel, S. Sesnic

Electron cyclotron emission from a tokamak plasma: experiment and theory

(IAEA-CN-33/A 8-3) 185

A.E. Costley, R.J. Hastie, J.W.M. Paul, J. Chamberlain

High- and low-current-density plasma experiments within the M.I.T. Alcator programme

(IAEA-CN-33/A 8-4) 191

U. Ascoli-Bartoli, G. Bosia, G. Boxman, P. Brossier, B. Coppi, I. De Kock, B. Meddens,

B. Montgomery, A. Oomens, L. Ornstein, R. Parker, L. Pieroni, S. Segre, R. Taylor,

P. Van der Loan, R. Van Heyningen

Discussion on papers IAEA-CN-33/A 8-1, A 8-2, A 8-3, A 8-4 205

Influence of resonant helical fields on tokamak discharges (IAEA-CN-33/PD-2) 207

F. Karger, H. Wobig, S. Corti, J. Gernhardt, O. KliXber, G. Lisitano, K. McCormick,

D. Meisel, S. Sesnic

Discussion on paper IAEA-CN-33/PD-2 215

HarpeB ruia3Mbi a3HMyTa;i&H0 HecHMMexpHMHOH HOHHO-U.HK;IOTPOHHOH

BO/IHOH B ycxaHOBKe ToxaMaK TM-l-BH (IAEA-CN-33/A 9-1) 217

B. JI.B,2IOBHH, B. JI.PycaHOB, H .B. HlanoTKOBCKHH

(Plasma heating with an azimuthally non-symmetrical ion cyclotron wave in

Tokamak TM-l-HF: V.L. Vdovin et al.)

The Frascati turbulent tokamak experiment (T.T.F.) (IAEA-CN-33/A 9-2) 227

R. Luppi, M. Martone

SKcnepMMeHThi no BbicoKonacTOTHOMy HarpeBy n/ia3MBi

Ha TOKaMaKe «S>T-1 (IAEA-CN-33/A 9-3) 231

B.E.ro;iaHT, H.Il.rjiaflKOBCKHH, B.B.£bHHeHKO, M .M . JIapHOHOB,

JI.C. JleBHH, E. A.MHxafiJiOB, B.B. PoacnecTBeHCKHH ,

r. A.CepeSpeHbiH, O.H.HIep6nHHH

(High-frequency plasma heating experiments in the Tokamak FT-1:

V.E. Golant et al.)

Hccne,ziOBaHHe $yHKiJHH pacnpe^eneHHH a^eKTpOHOB no SHeprHHM

H ee H3MeHeHHH B npoiiecce HarpeBa Ha sjieKTpoHHO-UHKJioTpoHHOM

pesoHaHce (IAEA-CN-33/A 9-4) 241

B.B. A/iHKaeB, r. A.EOSPOBCKHH, B.H.I1O3HHK,

K .A.Pa3yMOBa, K). A.COKOTIOB

(Investigation of the electron energy distribution function and its variation during

electron cyclotron resonance heating: V. V. Alikaev et al.)


MarHHT03ByK0B0H HarpeB rma3Mbi B ToKaMane TO-1

(IAEA-CN-33/A 9-5) 255

H . B. HBaHOB, H. A. KoBaH

(Magnetoacoustic heating of plasma in Tokamak TO-1: N. V. Ivanov and LA. Kovan)

Discussion on papers IAEA-CN-33/A 9-1, A 9-2, A 9-3, A 9-4, A 9-5 265

IIoxtyMeHHe HOHHO-ropHHefl naa3Mbi Ha HHacHeM :TH6PH,ZIHOM pe30HaHce

H H3MepeHHe ee napaMeTpoB (IAEA-CN-33/C-5) 267

B.M .TJiaroneB , A.r.,H;io6aH/tOB , H. A. KpHBOB,

B. B.MapTBiHeHKO, K). B. CKOCbipeB

(Production of a hot ion plasma at the lower hybrid resonance and measurement

of its parameters: V.M. Glagolev et al.)

Studies of non-circular cross-section toroids in the Doublet II and IIA device

(IAEA-CN-33/A 10-1) 281

T. Ohkawa, C.C. Baker, N.H. Brooks, MingSheng Chu, J.C DeBoo, R.K. Fisher,

R.L. Freeman, Chung Lih Hsieh, T.H. Jensen, M. Mahdavi, K. Matsuda,

A.A. Schupp, Jr., T. Tamano, V. Vanek,J.C. Wesley

A tokamak-divertor experiment in the dc Octopole (IAEA-CN-33/A 10-2) 291

R. Prater, R.L. Freeman, Y. Hamada, C. Moeller, T. Ohkawa, T. Tamano

Discussion on papers IAEA-CN-33/A 10-1, A 10-2 297

OPEN CONFINEMENT SYSTEMS (Session III)

Stabilizing mechanisms for loss-cone modes (IAEA-CN-33/D 1-1) 301

D.E. Baldwin, H.L. Berk, L.D. Pearlstein, T. Kammash, T. Uckan

Theoretical studies of plasma confinement in magnetic mirrors (IAEA-CN-33/D 1-2) .... 311

M.E. Rensink, T.K. Fowler, R.P. Freis, J. Killeen, A.A. Mirin, R.W. Moir,

L.D. Pearlstein, R.F. Post, C.G. Tull, L.S. Hall, B. McNamara, J.K. Boyd,

C.A. Finan, III, D. Fuss, C.A. Wilgus

Discussion on papers IAEA-CN-33/D 1-1, D 1-2 321

Plasma containment in 2XII (IAEA-CN-33/D 2-1) 323

H. Coensgen, W.F. Cummins, A.W. Molvik, W.E. Nexsen, Jr., T.C. Simonen,

B. W. Stallard

Intense-neutral-beam research and development (IAEA-CN-33/D 2-2) 329

W.R. Baker, K.H. Berkner, W.S. Cooper, K.W. Ehlers, W.B. Kunkel, R. V. Pyle,

J.W. Stearns

Discussion on papers IAEA-CN-33/D 2-1, D 2-2 339

y^ep^aHHe nn&3Mbi B JiOByiiiKe IIP-7 (IAEA-CN-33/D-3) 341

K).B.roTT,M.C.Ho(|)$e, B.H.KaHaeB, A.r.MoTViHq,

B.n.IlacTyxoB, P. H.Co6o;ieB

(Plasma confinement in a PR-7 trap: Yu. V. Gott et al.)

YaepxaHne n/ia3Mbi B npocroH npo6oMHofi noByuiKe OrPA-3

B npHCyTCTBHH MHOrOSJieMeHTHOH CHCTeMM o6paTHOH CBH3H

(IAEA-CN-33/D-4) ~ 355

B. A.)KH;ibiiOB, B.X. JlHXTeHniTeHH, R. A.ITaHOB, n.M. KocapeB,

B. A.HyjiHOB, A.r.IIIep6aKOB

(Plasma confinement in the Ogra-3 simple mirror trap in the presence of a multielement

feedback system: V.A. Zhil'tsov et al.)

Discussion on paper IAEA-CN-33/D-4 369

Etude du plasma a electrons chauds dans la configuration magnetique a minimum B Circe

(IAEA-CN-33/D 5-1) 371

R. Bardet, P. Briand, L. Dupas, C. Gormezano, G. Melin, F. Werkoff

Plasma production and confinement in the Baseball II mirror experiment

(IAEA-CN-33/D 5-2) 379

O.A. Anderson, D.H. Birdsall, C.C. Damm, J.H. Foote, A.H. Futch, R.K. Goodman,

F.J. Gordon, G.W. Hamilton, EB. Hooper, A.L. Hunt, J.E. Osher, G.D. Porter


Laser-initiated target experiment (LITE) (IAEA-CN-33/D 5-3) . 391

A.F. Haught, W.B. Ard, W.J. Fader, R.A. Jong, A.E. Mensing, D.H. Polk,

R. G. Tomlinspn, J. T. Woo

Discussion on papers IAEA-CN-33/D 5-1, D 5-2, D 5-3 399

TOKAMAK THEORY I (Session IV)

Equilibre, perturbation et evolution d'un systeme plasma-vide du type Tokamak

(IAEA-CN-33/A 11-1) 403

C. Mercier, Soubbaramayer

Free-boundary MHD-equilibria (IAEA-CN-33/A 11-2) 411

Y. Suzuki, A. Kameari, H. Ninomiya, M. Masuzaki, H. Toyama

3>HKcaiiHH XapaKTepHbix ToneK KaK MeTOfl noa^ep^aHHH aa^aHHofl

Tono^orHH paBHOBecHOH n/ia3MeHHOH KOH


TOKAMAK THEORY II (Session V)

Extraction des impuretes d'une configuration Tokamak (IAEA-CN-33/A 15-1) 563

R. Dei-Cas, A. Samain

Action de forces exterieures sur la migration des impuretes dans une configuration

toroidale (IAEA-CN-33/A 15-2) 571

T. Consoli, R. Le Gardeur, G.F. Tonon

Electrostatic trapping of high-Z impurity ions, and alpha-particle diffusion in

tokamak reactors (IAEA-CN-33/A 15-3) 589

R.D. Hazeltine, A.A. Ware, D.J. Sigmar, S.P. Hirshman, J.E. McCune, E.C. Crume,

J.T. Hogan.J.F. Clarke

The effects of impurities and magnetic divertors on high-temperature tokamaks

(IAEA-CN-33/A 15-4) 605

D.M. Meade, HP. Furth, P.H. Rutherford, F.G.P. Seidl, D.F. Duchs

Discussion on papers IAEA-CN-33/A 15-1, A 15-2, A 15-3, A 15-4 621

The distortion of the plasma ion distribution during neutral injection heating

(IAEA-CN-33/A 16-1) 623

J.G. Cordey

Excitation of ion cyclotron harmonic waves by injection of a 10-keV ion beam into

a plasma (IAEA-CN-33/A 16-2) 633

A. Goede, P. Massmann, H.J. Hopman, J. Kistemaker, G.J. Brakenhoff

Neutral beam injection into tokamaks (IAEA-CN-33/A 16-3) 645

J.D. Callen, R.J. Colchin, R.H. Fowler, D.G. McAlees, J.A. Rome

Onpe^ejieHHe AOJIH y6eraK>uiHx 9JieKTpoHOB B ToponaajibHOM

pa3pH.qe no cneKTpy peHTreHOBCKoro H3;iyHeHH3 ropHMen

HeMaKCBe;i/iOBCKOH n;ia3Mbi (IAEA-CN-33/A 16-4) 659

B. A. ASpaMOB

(Determination of the fraction of runaway electrons in a hot non-Maxwellian toroidal

plasma from the X-ray spectrum: V.A. Abramov)

Discussion on papers IAEA-CN-33/A 16-1, A 16-2, A 16-3, A 16-4 667

Neoclassical diffusion and the influence of a-particles on the energy balance in large

tokamaks and fusion reactor plasmas (IAEA-CN-33/A 17-1) 669

D.F. Duchs, D. Pfirsch

Etude numerique de quelques proprietes d'un plasma confine dans un Tokamak

de grande dimension (IAEA-CN-33/A 17-2) 681

J.-P. Girard, D.A. Marty, P. Moriette

Two-dimensional simulation of a fluid model for tokamak (IAEA-CN-33/A 17-3) 697

G.H. Tut tie, D.E. Potter, M.G. Haines

Chairmen of Sessions, and Secretariat of the Conference 711


Session I

TOKAMAK EXPERIMENT I


Chairman: K. HUSIMI (Japan)

Papers A 1,-1 and A 1-2 (JFT-2, JFT-2a) were presented

by M. YOSHIKAWA as Rapporteur

Papers A 2-1 and A 2-2 (T-6, T-4) were presented

by K.A. RAZUMOVA as Rapporteur

Papers A 3-1 and A3-2 (Princeton ST) were presented

by W. HOOKE as Rapporteur

Papers A 4-1 and A 4-2 (ATC) were presented

by E. MAZZUCATO as Rapporteur

Papers A 5-1 and A 5-2 (ORMAK) were presented

by M. MURAKAMI as Rapporteur

Papers A 6-1 and A 6-2 (TFR) were presented

by J. TACHON as Rapporteur


THE JFT-2 TOKAMAK EXPERIMENT

N. FUJISAWA, A. FUNAHASHI, S. KUNIEDA, M. MAENO,

N. SUZUKI, T. MATOBA, S. KASAI, S. ITOH* T. TAKEDA,

K. TOI* T. SUGAWARA** T. SHOJI, T. KAWAKAMI,

N. TOYOSHIMA, T. OHGA, T. ARAI, K. YOKOKURA,

T. TANI, T. SHIINA, M. OHTA, S. MATSUDA, S. YANO >; ° : ° : ;

H. SHIRAKATA, K. TAKAHASHI, T. TAZIMA, M. NAGAMI,

M. YOSHIKAWA, S. MORI

Japan Atomic Energy Research Institute, Tokai, Naka, Ibaraki,

Japan

Abstract

IAEA-CN-33/A 1-1

THE JFT-2 TOKAMAK EXPERIMENT.

This paper reports recent experimental results on the plasma confinement and the dynamic limiter

experiments in the JFT-2 tokamak.

Radial profiles of electron temperatures in hydrogen plasma were measured by the Thomson scattering

method. The electron temperatures reach peak values of 250 - 450 eV at the centre. The electron

densities and temperatures start to decrease before the peak of a plasma current. Ion temperatures, measured

by charge-exchanged neutral particles, reach peak values of 210 eV.

Radial profiles of the ionization rate, the neutral particle density and the particle diffusion coefficient

are deduced from detailed measurements of the photon flux of the Hot-line.

The dynamic limiter is composed of two molybdenum plates which are set parallel to each other inside

the vacuum vessel and can be derived upwards and downwards pneumatically. The average and maximum

speeds of the dynamic limiter are 5 m/s and 9 m/s, respectively. The results of the measurements of the

radial density profile and the radial Ha-photon flux profile show that the density near the plasma boundary

' diffuses together with the dynamic limiter, but that the region of the hot core of the plasma does not expand.

1. INTRODUCTION

In previous publications [1,2], several features of the JFT-2 tokamak

plasma have been deduced from diamagnetic measurements. In the present

paper, the radial profiles of electron density and temperature are

described. Moreover, the radial profiles of the neutral-particle density

have been determined from detailed measurements of the photon flux of

the Hor-line. These profiles-lead to the determination of the properties

of particle and energy confinement.

It is very important to investigate experimentally how the plasma

behaves when the limiter is removed in a tokamak device. The effect of

the limiter current on the equilibrium has been investigated experimentally

by Mukhovatov [3], and it has been shown that the limiter current plays

a relatively unimportant role. The experiment has, however, been

carried out on the fixed limiter of T-5 tokamak and it has not been concluded

definitely whether the material limiter is indispensable in sustaining

* Present address: Institute of Plasma Physics, Nagoya University, Nagoya, Japan.

>io ' ; On leave from Research and Development Center, Tokyo Shibaura Co. Ltd., Kawasaki, Japan.

*** present address: Kobe University of Mercantile Marine, Kobe, Japan.

3


4 FUJISAWA et al.

the equilibrium and stability of a tokamak discharge or not. In the JFT-2

tokamak, the plasma behaviour can be investigated by removing a dynamic

limiter at any time during the discharge.

2. JFT-2 DEVICE

The dimensions of the JFT-2 tokamak are shown in Table I. Figure 1

presents a plan view of the JFT-2 tokamak with the location of the various

diagnostic instruments: the Ohmic heating current (from a Rogowski coil)

and the loop voltage (measured on the inner surface of the aluminium shell);

diamagnetic loops and pick-up coils; a ruby-laser Thomson-scattering

apparatus for the measurement of the electron-temperature distributions

on a plasma cross-section; a 4-mm microwave interferometer for the

determination of electron line densities; a neutral-particle energy analyser

for determining the energy spectrum of the ions via resonant chargeexchange

processes; a 25-cm visible monochrometer for the determination

of the absolute intensities of the lines of hydrogen gas; a 50-cm

normal-incidence VUV monochrometer for the determination of ultraviolet

radiation intensities of impurity ions; a Si(Li) semiconductor

detector for the determination of the energy spectrum of soft X-ray

radiation; and a hard X-ray monitor.

TABLE I. DIMENSIONS OF JFT-2

Major Radius

Minor Radius

Vacuum Vessel

Shell

Thickness

Liner

Shell

Fixed Limiter

Radius of L

M

S

Dynamic Limiter

Minimum Distance

Maximum Distance

Maximum Speed

90

30

36

0.06

3

25

20

16.3

25

51

9

cm

cm

cm

cm

cm

cm

cm

cm

cm

cm

m/s


VACUUM PUMPING MANIFOLD

IAEA-CN-33/A 1-1 5

FIG. 1. Plan view of JFT-2 tokamak showing locations of various diagnostic instruments.

The plasma boundary can be limited by a molybdenum aperture limiter

or by a molybdenum dynamic rail limiter. The former is located at the

pumping box b2, and the latter is located at the dynamic limiter box b3.

The axis of the fan-shaped toroidal magnetic field coils is shifted outwards

by 10 cm from that of the aluminium shell in order to minimize the nonuniformity

of the toroidal magnetic field at the outer surface of the plasma.

3. PLASMA CONFINEMENT EXPERIMENT

3.1. Experimental conditions

The experimental conditions under which the plasma confinement

was studied are listed in Table II. The direction of the toroidal magnetic

field is counterclockwise as viewed from above, and the plasma current

flows in the direction opposite to the toroidal magnetic field.

Since discharge behaviour fluctuates considerably during the initial

stage of the operation, the 2000 - 3000 discharge shots were intentionally

used for the purpose of conditioning. An ultimate pressure of 1.2 X 10" 7 Torr

was obtained. Purified hydrogen is continuously introduced into the vacuum

vessel through a palladium film as working gas, the pressure of which is

adjusted to 3.3 X 10 -4 Torr. At filling pressures above 3.5 X 10" 4 Torr,

the plasma tends to display so-called disruptive instabilities. At filling


6 FUJ1SAWA et al.

TABLE II. EXPERIMENTAL CONDITIONS

Toroidal Field

Vertical Field

Horizontal Field

Filling Pressure

Ohmic Heating Energy

ECRH Preionization

Limiter Radius

Plasma Current

9

65

8

-4

3.3xlC

400 + 10400

10

1

25

75

+ 1.7

kG

G

G

Torr H

pressures below 3.3 X 10 " 4 Torr, hard X-ray radiation which seems to

be due to runaway electrons increases gradually with the decrease of

pressure.

Electron temperatures obtained from Thomson-scattering measurements

rise with increasing plasma current from 50 kA to 80 kA, but remain

constant above it. This confinement experiment is carried out with a

maximum plasma current of 75 kA, which corresponds to qa = 4.3, where

qa is the value of q calculated at the limiter.

3.2. Experimental data

The time behaviour of various parameters under the abovementioned

conditions is shown in Fig.2.

The condenser banks for Ohmic heating consist of two kinds of banks

as is shown in Table II; the first bank is fired at 6 ms. After the second

bank fired at 26 ms, the plasma current reaches its peak value of 75 kA

at 60 ms as is shown in Fig.2a.

The displacements of the plasma axis from the shell axis are determined

from the magnetic probes. The time behaviour of the horizontal

and vertical displacements is shown in Fig.2b. The former is 1 - 2 cm

inwards in the time interval from 30 ms to 100 ms. The latter is well

centred within 1 cm. The vertical displacement can be adjusted by an

external horizontal field which compensates an error field generated by

the toroidal coils.

The electron densities are measured by a 4-mm microwave interferometer.

The density at R = 90 cm averaged over the microwave path parallel

to the major axis is shown in Fig.2c. The time behaviour of the density

from 10 ms to 20 ms cannot be measured because of the large fluctuations

in the plasma. The density in the time interval from 20 ms to 3 5 ms

increases, but after 35 ms it decreases monotonically.

Figure 2d shows the plasma temperatures. The ion temperatures are

determined from the energy spectrum of the charge-exchanged neutral

PF

kV

kW

cm

kA


1AEA-CN-33/A 1-1 7

FIG. 2. Time behaviour of a discharge in hydrogen under conditions presented in Table II.

(a) It; Ohmic heating current including the liner current (< 1 kA; t >25 ms) and Vloop; loop voltage

measured on the inner surface of the aluminium shell, and the loop voltage obtained by the simulation (....).

(b) Vertical and horizontal displacements of the plasma from pick-up coils, (c) Electron line density from

a 4-mm microwave interferometer, (d) Temperature; ion temperature (x) measured from energy spectrum

of charge-exchanged neutral particles, electron temperature (o) from Thomson-scattering measurements,

electron temperature (A) from energy spectrum of soft X-ray radiation, conductivity temperature ( ),

and electron and ion temperatures obtained by the simulation (....). (e) Time behaviour of carbon and

oxygen ion light emissions measured with the 50-cm normal-incidence VUV monochrometer. (f) Magnetic

field oscillations and mode number m.

particles, which presumably give the ion temperature in the hot region of

the plasma. The electron temperatures at the centre of the vacuum vessel

deduced from the Thomson-scattered light show a large spread, although

the discharges are highly reproducible from shot to shot in all macroscopic

respects such as the plasma current and the loop voltage. The electron

temperatures are also determined from the energy spectrum of soft X-ray

radiation. The electron conductivity temperature is calculated by using

the plasma current, the loop voltage, the plasma displacement and the

diamagnetic signal, assuming that the effective charge is 1.0. It should

be noted that the time of the maximum electron-conductivity temperature

coincides with that of the maximum plasma current.

A detailed view of the time behaviour of the carbon and oxygen light

intensities is presented in Fig.2e. The intensities of these lines were

measured with the 50-cm normal-incidence VUV monochrometer on a

horizontal midplane of the torus at the dynamic limiter box. The time


8 FUJISAWA et al.

FIG. 3. Time evolution of radial profiles of electron densities from a 4-mm microwave interferometer,

(a) 30 ms, (b) 40 ms, (c) 50 ms, (d) 60 ms, (e) 70 ms, (f) 100 ms.

behaviour of these light intensities is consistent with the abovementioned

electron temperatures.

The time evolution of the mode number of the low-frequency oscillations

is measured by magnetic pick-up coils and is shown in Fig.2f. The

low-frequency oscillations are characterized by magnetic-field perturbations

with mode structures exp [i(m&-n$)] where m ranges from 6 to 2

and n = 1. It may be noted that m = 2 modes appear even at qa = 5, and

that the m = 2 modes seem to be associated with the decrease of the

electron density. The direction of the mode rotation is in the electron

diamagnetic direction, and its frequency is 1 - 5 kHz.

The horn of the 4-mm microwave interferometer can be moved

horizontally at intervals of 6 cm. Figure 3 shows the time evolution of

the electron density profiles obtained by inverse transformation of the

electron line density on the assumption of zero density at the liner surface.

The peak of the density profile is shifted 2-4 cm inward from the vacuum

vessel centre. It should be noted that this displacement of the density

profile agrees with that of the plasma axis determined from the magnetic

probes. It should be emphasized that the density profile is rather peaked.

The profile at 30 ms coincides with that of

and after 40 ms the profiles fit

n(?) = n(0) (l-? 2 ); ? = r/aliner

n(5) = n(0) (l-? 2 ) 2

Figure 4 shows the electron temperature profile determined from the

Thomson-scattering measurement at 30 ms. The reproducibility of the


300

.200

100

IAEA-CN-33/A 1-1

- I ...-.

A

/

'-->

. ,/1

/ 1 1

' ! ' i '

\ i

\

1 ]

i

h

-30 -20 -10 10 20 30

( cm )

FIG. 4. Vertical profile of electron temperatures at R = 90 cm measured from Thomson-scattered light

at 30 ms. Broken line indicates the profile of (1 - 5 ) .

0 10 20 (cm)

Radius

FIG. 5. Time evolution of radial profiles of neutral-particle densities from Ha photon flux,

(a) 30 ms, (b) 40 ms, (c) 50 ms, (d) 60 ms, (e) 70 ms, (f) 100 ms.

electron temperature is not good, as previously mentioned. The temperature

profile can be described by

Te(?) = Te(0)(l-?2)2

3.3. Particle confinement time and diffusion coefficient

To determine the ionization rate, we measured the vertical distribution

of Hor photon flux. This Ua photon flux was measured with both the

25-cm visible monochrometer at b3 observation box and the spectrometer

.


10 FUJISAWA et al.

of the Thomson-scattering apparatus at bl as shown in Fig.l. The

measurement at the b3 box was subject to the strong influence of the

dynamic limiter which was composed of two rails separated vertically

by 51 cm. In this paper, the Ha photon flux obtained at the bl observation

box is assumed to he the uniform component along the torus. Figure 5

shows the radial profile of the neutral-particle density as a function of

time, which is calculated from the collisional-radiative theory and the

radial profile of the Ha photon flux obtained by inverse transformation.

It should be emphasized that the neutral-particle density increases with

time, while the radial profile remains almost constant.

The particle confinement time rp, defined as

-7— = > (ionization rates) - — ; N = total electron number

is shown in Fig.6. The particle confinement time, which is 10 ms at 30 ras,

drops monotonically to 3 ms at 100 ms.

100 (ms)

FIG. 6. Particle confinement time from Ha photon flux and electron density ( ) and gross energy

confinement time obtained by the simulation (....).

( cm )

FIG. 7. Time evolution of radial profiles of diffusion coefficients calculated from electron density

profiles and ionization rates, (a) 30 ms, (b) 40 ms, (c) 50 ms, (d) 60 ms, (e) 70 ms, (f) 80 ms.


IAEA-CN-33/A 1-1 11

The electron particle flux r can be calculated from the radial profile

of the ionization rate. The diffusion coefficient D, defined as

r = - DVn + (Ware pinch)

is shown in Fig.7. It should be noted that the radial profile of the diffusion

coefficients is similar to that of the Pfirsch-Schliiter type, and that their

absolute values increase from 100 X DP at 30 ms to 400 X DP S at 100 ms,

where DP S is the Pfirsch-Schliiter diffusion coefficient for Zeff = 1.

3.4. Simulation of energy confinement

To interpret the energy confinement, a numerical model is used.

The input data of the model are the total plasma current and the time

behaviour of the radial profiles of tike electron density and the neutral

particle density, and the transport coefficients are adjusted so that the

simulation results are in good agreement with the measured temperatures

and the loop voltage. However, the abovementioned model cannot explain

the measured ion temperature because the charge-exchange loss and the

thermal-convection loss decrease the ion temperature. To reduce the

ion-energy loss, the computations have been carried out on the assumption

that the photon flux of the Ha line is one third of the measured photon flux.

The best fitting of the simulation with the experimental results can be

obtained with the following transport coefficients: the thermal conductivity

of electrons


12 FUJISAWA et al.

of the runaway current to the total plasma current is chosen to increase

from 0 at 30 ms to 0.3 at 80 ms.

The results of the simulation are represented in Figs 2a and 2d.

The gross energy confinement time TE is shown in Fig.6. Figure 8 shows

the radial variations of the electron and ion local power balances at 60 ms.

The electron power balance shows that the thermal conduction loss is the

dominant electron loss process in the centre, whereas near the edge the

convection loss is the main loss process. The ion power balance indicates

that the dominant loss processes are convection loss and charge-exchange

loss.

4. DYNAMIC LIMITER EXPERIMENT

4.1. Experimental conditions

The dynamic rail limiter is composed of two molybdenum plates

which are set parallel to each other inside the dynamic limiter box b3

as is shown in Fig.l and can be driven pneumatically upward and downward

with average and maximum speeds of 5 m/s and 9 m/s, respectively.

The experiments were carried out for three operation modes of the

dynamic limiter: the open, closed and dynamic modes. In the open and

closed operation modes, the two molybdenum plates are fixed at distances

of 51 cm and 25 cm, respectively. In the dynamic operation mode, the

dynamic limiter plates were triggered to move at 50 ms as is shown in

Fig.9. The experimental conditions are as follows: the toroidal magnetic

field is 10 kG, the vertical magnetic field is 35 G and the filling pressure

is 2.5 X 10" 4 Torr H2.

o

30.0

20.0

: / A

-h io.o

o 40 60 80 100

( ms )

FIG. 9. Half distance between limiter plates after the dynamic limiter is triggered at 50 ms.

4.2. Results

The time behaviour of various parameters for the abovementioned

three operation modes is shown in Fig. 10. The value of qa for the closed

operation mode is chosen to be above 3. Figure 10c indicates that the


IAEA-CN-33/A 1-1 13

I , , , . • , • • • . -\ ~". , I l — , — , — , — , — i — . — . — , — , i , >__ , _ l

O 50 100 150 o 50 100 , 150

( ms) < ms >

FIG. 10. Time behaviour of discharges for three operation modes of dynamic limiter experiment,

(a) Loop voltages, (b) Plasma currents, (c) Plasma displacements, (d) Temperatures, (e) Magneticfield

perturbations. Solid line, broken line and dotted line indicate dynamic operation mode, open

operation mode and closed operation mode, respectively.

horizontal displacement of the plasma axis for the dynamic operation

mode coincides with that of the closed operation mode before the dynamic

limiter is triggered (t < 50 ms) and that of the open operation mode after

the dynamic limiter is almost fully open (t > 70 ms).

The electron and ion temperatures are determined from Thomson

scattering and the charge-exchanged neutral-particle measurements,

respectively. It should be noted that both temperatures have large error

bars. The time evolutions of the low-frequency-oscillation mode number

for three operation modes are shown in Fig.lOe. The m = 2 modes appear

in all operation modes.

Figure 11 shows the electron density profiles for three operation

modes. The displacements of the density-profile peak coincide with those

of the plasma axis determined from the magnetic probes. In the case of

the dynamic operation mode, the density profile approaches that of the

open operation mode after the dynamic limiter is triggered, and it is

probable that the density near the plasma boundary diffuses with the

dynamic limiter.

The radial profiles of the Hor photon flux for three operation modes

are shown in Fig. 12. It is reasonable that the plasma column for the closed

operation mode is limited by the dynamic limiter, while it may be understood

from Fig. 12a that the radius of the hot core of the plasma for the

open operation mode is within 10 cm. The cooling by the neutral particles


FIG. 11. Time evolution of density profiles for three operation modes of dynamic limiter experiment.

(A) Open operation mode. (B) Closed operation mode. (C) Dynamic operation mode,

(a) 50 ms, (b) 60 ms, (c) 70 ms, (d) 80 ms, (e) 100 ms.


e T

A

FIG. 12. Time evolution of Ha photon flux profiles for three operation modes of the dynamic limiter

experiment. (A) Open operation mode. (B) Closed operation mode. (C) Dynamic operation mode,

(a) 40 ms, (b) 50 ms, (c) 60 ms, (d) 70 ms, (e) 80 ms, (f) 90 ms, (g) 100 ms.


16 FUJISAWA et al.

seems to be one of the probable explanations. Figure 12c shows that the

peak of the Efo photon flux moves outward with the dynamic limiter. It is

very difficult to conclude from this figure whether the region of the plasma

hot core expands with the dynamic limiter or not. The Thomson-scattering

measurement suggests that the region of the hot core does not expand. It

is likely that the displacement of the peak of the Ha photon flux is due to

the diffusion of the density at the plasma boundary.

REFERENCES

[1] 1TOH, S., et al., in Toroidal Plasma Confinement (Proc. 3rd Int. Symp. Garching, March 1973) B-4.

[2] ITOH, S., et al., JAERI-M 5385 (1973).

[3] MUKHOVATOV, V. S., in Plasma Physics and Controlled Nuclear Fusion Research (Proc. 2nd Int.

Conf. Culham, 1965) 2, IAEA, Vienna (1966) 577.


IAEA-CN-33/A 1-2

RESEARCH ON A TOKAMAK WITH

AN AXISYMMETRIC DIVERTOR AND

IMPURITY PROBLEMS IN TOKAMA.K DEVICES

M. YOSHIKAWA, T. TAZIMA, Y. SHIMOMURA, A. KITSUNEZAKI,

H. MAEDA, K. INOUE, T. NAGASHIMA, T. TOKUTAKE,

H. OHTSUKA, M. NAG AMI, M. TANAKA, S. KUNIEDA,

A. FUNAHASHI, T. KAWAKAMI, K. TAKAHASHI, T. MATOBA,

M. AZUMI, T. SHOJI, K. ANNO, K. KUMAGAI, S. KASAI,

T. OHGA, H. TAKEUCHI, T. TANI, T. ARAI, S. MORI

Japan Atomic Energy Research Institute, Tokai, Naka, Ibaraki,

Japan

Abstract

RESEARCH ON A TOKAMAK WITH AN AXISYMMETRIC DIVERTOR AND IMPURITY PROBLEMS IN TOKAMAK

DEVICES.

Experimental and theoretical research work on impurity problems in tokamak plasma confinement carried

out at JAERI is described. Initial experiments in a tokamak with an axisymmetric divertor indicate that a

positionally stable plasma equilibrium enclosed in a separatrix magnetic surface is obtained and that the gross

behaviour of the plasma is rather similar to that of conventional tokamak plasmas. Theoretical studies on

impurity problems are made in impurity density distributions, radiation losses, and time evolution of impurity

content; they indicate that the relevant problems have to be studied seriously before a large tokamak device

of the next generation can be designed.

1. INTRODUCTION

It has been recognized that one of the aspects in tokamak plasma confinement

requiring further investigation is plasma interaction with wall and

limiters. Finding practicable methods of reducing the impurity content in

plasmas becomes all the more pressing as we come to envisage future

tokamak devices with higher temperatures and longer duration of confinement.

The JFT-2a (DIVA) Tokamak is a device for studying the effect of a

divertor in reducing the impurity levels and for investigating the confinement

of a plasma with non-circular cross-section. The device was designed

in 1972-73 and constructed in 1973-74. Experiments were started in

September 1974.

Theoretical studies on impurity problems in tokamak devices were

carried out in co-operation with the JFT-2 and JFT-2a (DIVA) experimental

programmes. Emphasis was recently placed on impurity problems relevant

to design studies of a large tokamak of the next generation.

2. JFT-2a (DIVA) EXPERIMENTAL RESEARCH (M. Yoshikawa,

Y. Shimomura, A. Kitsunezaki, H. Maeda, T. Nagashima, T. Tokutake,

H. Ohtsuka, M. Nagami, S. Kunieda, A. Funahashi, T. Kawakami,

K. Takahashi, T. Matoba, T. Shoji, K. Anno, K. Kumagai, S. Kasai,

T. Ohga, H. Takeuchi, T. Tani3 T. Arai)

17


18 YOSHIKAWA et al.

2.1. Research objectives

(1) Effect of a divertor on plasma confinement [1, 2j.

A possibility of lowering the impurity content is provided by a divertor

guiding the plasma ions to a burial chamber and also acting as a substitute

for limiters. Studies are to be made in plasma equilibrium, stability,

transport, and basic operational characteristics of the divertor.

(2) Plasma confinement in a Tokamak with a non-circular crosssection

[3].

A tear-drop-like, cross-section was chosen for the device. It allows

straightforward accommodation of the divertor and provides larger magnetic

well and shear than other cross-sections, depending on the plasma parameters.

For example, the current density limit to stabilize a local

instability is higher in cases of flat current distribution and of parabolic

distribution at low j3.

2.2. Description of the device [2, 3]

The basic machine parameters are shown in Table I. The crosssectional

and the plan view of the device are shown in Figs 1 and 2, respectively.

Since most of the components shown are self-explanatory, a brief

description is given only of those features which are uncommon in standard

tokamaks.

Shell: The plasma is encased in a copper shell divided into four

sector pieces. Its surface is iron-plated with gold to reduce gas adsorption.

Part of the shell — the movable shell — can be moved vertically to vary the

width of the opening connecting the plasma to the divertor.

Divertor hoop: A four-turn coil enclosed in a vacuum-tight stainless -

steel tube. A pair of divertor plates made of titanium intersects the

separatrix magnetic surface. The surfaces of the divertor plates and other

nearby surfaces are coated with titanium between shots.

Limiters: Three gold-clad molybdenum pieces 1 mm in thickness,

manually retractable for experiments with the divertor in operation.

Gas feeders: The gas can be introduced into the device through fast

gas valves or a variable leak valve.

TABLE I. BASIC PARAMETERS OF JFT-2a

Toroidal magnetic field

Vertical magnetic field

Magnetic flux of iron core

[ Major radius

Shell i Inner minor radius

[ Thickness

Maximum divertor hoop current

1.0 T

1.2 x 10" 2 T

0.3 V-s

600 mm

105 x 140 mm

20 mm

60 kA


Ti-ALLOY WIRE

ELECTROSTATIC PROBE

ELECTRON GUN

FOR PRQ0MZAT10N

FAST GAS VALVE

DIAGNOSTIC PORT-

MICROWAVE

INTERFEROMETER

SOFT X-RAY ANALYSE

ROGOWSKI COIL -

MAGNETIC PROBES

FAST GAS VALVE

MICROWAVE NTERFEROMETER

FAST PRESSURE GAUGE

ECRH HORN FOR PREIONIZATION

GAS INLET

IAEA-CN-33/A 1-2 19

FIG. 1. Cross-section of vacuum chamber.

ELECTROSTATIC PROBE

IMITER

FAST GAS VALVE

MOVABL

LIMITER '

80

R (cm)

DIAGNOSTIC PORT

NEUTRAL ANALYSER

OPTICAL SPECTROMETER

FAST GAS VALVE

THOMSON SCATTERING APP

DIAGNOSTIC PORT

OPTICAL SPECTROMETER

FAST GAS VALVE

FIG.2. Plan view of the device.


20 YOSHIKAWA et al.

0 10 20 30

t (ms)

(A) (B)

FIG.3. Oscillograms of sum of plasma current Ip and divertor hoop current ID, ID, loop voltage V, line

density measured by a microwave interferometer at R = 63 cm, light intensities of La and CIV lines, and

neutral particle pressure P0 at R = 80 cm and Z = -7 cm at a gap of neighbouring shell sectors. Case A is

for Ij_)/Ip = 0 and Case B for Ip/Ip = 0.9. The operation condition is By = 0 and the filling pressure

= 1.3x 10" 4 Torr.

2.3. Early experimental results

(1) Operation conditions

The operation conditions for the experiments described below are as

follows. The toroidal field is fixed at 1 T, the vertical field varied up to

2 x 10" 3 T, and the horizontal field was adjusted so as to locate the plasma

on the median plane. The divertor hoop current is varied approximately

up to the level of the plasma current. The movable shell is in open position,

the limiters extend 1 cm from the shell, and no titanium is flushed. The

base pressure is below 2 x 10~ 7 Torr after 50 h of baking at 100°C. Hydrogen

gas of (0.8 - 3) x 10" 4 Torr is introduced through a variable leak. The data

shown are taken after about 3000 shots of preceding discharges.

(2) Typical discharges at 2 0 kA

Figure 3 shows oscillograms of typical discharges at about 2 0 kA, which

gives a q-value of about 5 in a circular-cross-section tokamak with a major


45 51 57 63 69

R (cm)

(A)

IAEA-CN-33/A 1-2 21

45 51 57 63 69

R (cm)

FIG.4. Line density measured by a microwave interferometer. The operation conditions are the same as in

Fig. 3.

Is

(A)

0.6

0.4

0.2

0

(B)

(A)

\ — (B)

\ (R=68cm)

\3ms

5~20\„ ,= \

-7 -8

Z (cm)

FIG. 5. Double probe current versus vertical distance from the median plane. Direction of electron drift

is antiparallel to Z-axis. The operation condition is the same as in Fig. 3.


22 YOSHIKAWA et al.

FIG.6. Poloidal-magnetic-field distribution on the inner surface of the shell measured by magnetic probes

for Ir)/Ip = 0«9> Curves show calculated results for equilibria with a uniform current distribution. The

operation condition is the same as in Fig. 3.

radius of 60 cm and a minor radius of 10 cm. On the left-hand side, oscillograms

without a divertor hoop current (Case A) are shown and on the righthand

side, we see oscillograms with a divertor hoop current (Case B). Their

gross behaviour is rather similar, except that the discharge with a divertor

hoop current lasts longer. The resistivity temperature is about 70 eV at

13 ms assuming Z = 2 and the average density measured by a zebra-stripe

4-mm microwave interferometer is about 1.4 x 10 13 cm" 3 at R = 63 cm.

The pressure measured by a fast ionization gauge placed 10 cm from the

plasma in the gap between neighbouring shell sectors shows a drop of the

filling pressure from 1.3 x 10" 4 Torr to a plateau of 2.5 x 10" 5 Torr.

Negative spikes intermittently appear in the loop voltage during the discharge,

accompanied by a sudden increase in the Laline, in the CIV line (1548 A),

and in the electron density. A simultaneous magnetic probe measurement

shows rapid inward shift of the plasma.

The density distribution is measured by the microwave interferometer

for the bulk of the plasma (Fig. 4) and by double probes for plasma

"outskirts" (Fig. 5). The density profile near the divertor hoop measured

by scanning a double probe at R = 40 cm shows a peak at Z = -3 cm,

suggesting the presence of plasma extending towards the divertor near the

separatrix magnetic surface. The electron temperature is about 10 eV,

the maximum plasma density is about 1 x 10 12 cm" 3 at 13 ms. Figure 6

shows the magnetic-field distribution measured by magnetic probes placed

on the inner shell surface. For comparison, also shown in the figure are

the calculated distributions for a uniform current distribution for two values

of j3p[l].

(3) Typical discharges at lower and higher currents

When the plasma current is reduced to about 10 kA, disruptive fluctuations

in the loop voltage, electron density, and line radiation are greatly

reduced. The resistivity temperature is 20-30 eV. The density distribution

near the divertor hoop at R = 40 cm is similar to that shown in Fig. 5.

It was, furthermore, observed that the position of the density peak moves


IAEA-CN-33/A 1-2 23

closer to the median plane as the divertor hoop current is reduced as is

expected from the calculation of magnetic configurations.

With plasma currents above 20 kA, the plasma tends to be unstable.

Large positive spikes are observed in the loop voltage at about 30 kA. and,

in some cases, the current does not increase appreciably even when the

charging voltage of the capacitor bank is raised.

(4) Conclusions

Preliminary measurements indicate that a positionally stable plasma

enclosed in a separatrix magnetic field is produced. The plasma extending

towards the divertor hoop near the separatrix magnetic field has a density

an order of magnitude lower than that of the confined plasma. In the gross

behaviour of the plasma, there are no startling differences whether or not

the plasma is enclosed in a separatrix magnetic surface.

3. THEORETICAL STUDIES OF IMPURITY PROBLEMS [4] (T. Tazima,

K. Inoue, M. Tanaka, M. Azumi, M. Yoshikawa)

3.1. Diffusion of impurity ions in a tokamak plasma

A numerical study is made on the density distributions of impurities

in a cylindrical plasma taking into account the diffusion across the magnetic

field and the successive ionization-recombination processes. A. set of

MHD-equations for the impurity ion densities

- ~ £:( rr k) + n eK-l n k-l - «lftc) - n e^k-i n k - ^VW = °

fc = 2, 3, .. . , M (1)

is solved under the boundary conditions; dnk/dr = 0 at r = 0 (axis) and

nj< = 0 at r = rp (boundary). Here ne and n^ are the densities of electrons

and impurity ions with a charge (k-1), respectively, and a^ and j?k are the

ionization and radiative recombination rates given in Ref. [5] , respectively.

The particle flux of impurity ions Tkis given on the assumption that

the ion temperature of hydrogen is equal to those of the impurities and

neglecting the effect of ion temperature gradients as [6]

dn, k-1 dn.

r k = ~ D kt^r - (— -[jrH], k = 2, 3, ..., M (2)

where Dk is the Pfirsch-Schliiter diffusion coefficient for impurity ions and

ni is the hydrogen ion density. Because of a difficulty encountered in

numerically solving Eqs (1) and (2), we shall neglect the second term in the

square bracket of Eq. (2), i. e. the flux of impurity ions due to the pressure

gradient of the plasma.

The density distribution of impurity neutrals nx(r) is expressed by a

slab model, assuming that the neutrals enter the plasma at the mean thermal

velocity V^ at a temperature of 5 eV

ni(r) = nx(rp)[ exp(- •— / a^dr') + exp(- -~- / ar^dr' - ~ / ar^dr 1 )] (3)

o


24 YOSHIKAWA et al.

"c"

5

4

3

10

2

10

1

10' _

0

-1

_C

-

_

-

-

/ I

7

6 /v

/ / i

/ /V^

////

//// -

/

-2

10

o-o 5^5 O o.gs

r/rn

Tft

FIG.7. Density distributions of carbon ions. Parameters are major radius 3 m, minor radius rD = 1 m,

toroidal magnetic field 5 T, and q(rp) = 2.5. Assumed are iy = 7.5x 10 19 [l-(r/rp) 4 ] + 10 18 ,

Te = 2 x f e [l-(r/rp) 2 ] + 10 eV, and Tj = 2 x Ti [l-(r/rpf] + 5 eV with Ti = Te = 5 x 10 3 eV. Numbers

shown correspond to the ion charge plus unity.

10'

10 J _

10< -

10' _

•0

-

~

-_—^^

-

10'

10

10 -2 1 •

/

•0 0-E> 0.9 0.95 1.0

9

\

111

1 ¥

h-lL

/ /Jr /t

/ n

"7rn

FIG. 8. Density distributions of oxygen ions. Otherwise, similar to Fig.7.

-

-

_

_

:

-


0.0 (Hs" Cp9 0795 TTO~

r/rn

vP- 10

cf"" 3

10 ;

10'

10"

10"

10"


-

-

-

-

FP

18 A

,7 \^77 Al

16^S/ k

1A \ Iff

15 \TMf

130f/f|

120rffl

11-Cmif

10 ^4j|f

//I/

0-0 0-5 0-9 0-95 1.0

17 rn

FIG. 9. Density distributions of iron ions. Otherwise, similar to Fig.7.

-

.

10"

10'

io-

io £ r

10 l

10

26 /

J5JX27N

:Fe \

24/

-23/

22/

,-2

0 'O.S

/

11 21/ /V

/ V 20/ A

' l\H \

D.9 0.95 1.0

r/rn

-


-

-


26 YOSHIKAWA et al.

The numerical model is slightly different from the previous one [7] which

has been successfully tested by computing a case obtained in the STexperiment

[8].

Figures 7-9 show the computed density distributions of impurity ions,

carbon, oxygen, and iron in a large tokamak. Apparent in the figures is

a shell-like structure of the radial distribution for each charge state, with

more highly-ionized ions closer to the axis.

3.2. Energy losses caused by impurities

Energy losses caused by impurities, such as ionization loss Pj(r),

bremsstrahlung loss pBR(r), and excitation loss pEX(r), are calculated using

the stationary distributions of impurity ions obtained in the previous section.

The ionization and bremsstrahlung losses are approximately expressed by

BR

M-l

1.6 x lO' 19 ) [nenkakxk + (3/2)nenk+1/3kTe

k=l

1.5 x 10" 38 Z n 2 Tl/2

e e (4)

where x, and T are the ionization potential of impurities and the electron

temperature, respectively, in eV. The expressions for the excitation loss

by carbon and oxygen impurities are taken from fief. [9]. Since no

literature is available on the excitation loss by iron impurities, its approximate

expression is formulated [10] considering the collisional excitation

by electrons, using atomic data compiled by Tucker and Koren [11] , and

by Lotz [12].

Figure 10 shows the total losses, i.e. the abovementioned losses

integrated over the plasma volume. These energy losses amount to several

MW at the concentration of 5% carbon or oxygen, and of 0.5% iron.

5 10

Te=Tj (KeV)

F?(0.5%Fe)

f|R(5 %0)

&(Q5%Ffe)

;C4-f=x(0.5%Fe)

&(5%C)

f? (5 %0)

f?(5 %C)

f|x(5%0)

f^x(5%C)

FIG. 10. Total energy losses caused by impurities; excitation loss Pgy, bremsstrahlung loss PBR, and

ionization loss Pj.


,„„„>„„„„„„,,„J,^

diffusion \ ^_

IAEA-CN-33/A 1-2 27

FIG. 11. Recycling processes of impurities.

FIG. 12. Accumulation of metallic impurities.


28 YOSHIKAWA et al.

FIG. 13. Accumulation of gas impurities.

3.3. Recycling processes of impurities [13]

Influx of impurities may result from the vaporization of limiter materials,

the sputtering of limiter and first-wall materials, and the gas desorption

from the limiter and first wall. These processes and other processes

related to impurity production are schematically shown in Fig. 11. A

simplified model which considers the sputtering due to hydrogen and impurity

ions and hot neutrals generated through charge exchange between hydrogen

ions and cold neutrals., gives the following equation for impurity accumulation:

dN7 N 7 Nn

z

dt -r,1(l-Sl)--£ + r,1(T:-)

r T.

where N and Nz are the total numbers of hydrogen and impurity ions,

respectively, T and T2 are their respective particle confinement times,

r)1 and r)2 are their respective sputtering yields, and ^ and £2 are their

respective divertor efficiencies, y is the number of hot neutral particles

escaping from the plasma for each incident cold neutral particle. Figures

12 and 13 show the accumulation of metallic and gas impurities, respectively,

for typical sets of parameters. It can be seen that the impurity concentration

reaches the permissible level within a few T without a divertor.

N7

TZ

^Z

JT Z

(5)


3.4. Summary

IAEA-CN-33/A 1-2 29

The permissible level of impurities in a large tokamak of the next

generation is of the order of 1% for light gas impurities and 0.1% for heavy

metallic impurities if the heating should be kept below 10 MW or so. Such

a level will be reached in a few Tp without divertor.

In an advanced tokamak device with a high efficiency divertor and low

influx of cold neutral particles, the impurity concentration may be suppressed

below the permissible level. However, if the divertor pumps hydrogen, the

hydrogen has to be supplied to keep the density constant. A method of fuel

supply as the neutral beam and the pellet injection inevitably leads to the

production of hot neutral particles and the increase in impurity influx through

wall bombardment.

ACKNOWLEDGEMENTS

The authors wish to thank K. Mori (Institute of Physical and Chemical

Research) for valuable discussions on the impurity problem. We also thank

M. Yamamoto who made a special effort in the fabrication of fast gas valves.

REFERENCES

[1] KITSUNEZAKI, A., MAEDA, H., SHIMOMURA, Y., Nucl. Fusion^ 5 (1974).

[2] YOSHIKAWA, M., SHIMOMURA, Y., MAEDA, H., KITSUNEZAKI, A., in Controlled Fusion and

Plasma Physics (Proc. 6th Europ. Conf. Moscow, 1973) 173.

[3] KITSUNEZAKI, A., MAEDA, H.,SHIMOMURA,Y., YOSHIKAWA, M. , 3rd Int. Symp. Toroidal

Plasma Confinement (Garching, 1973) Paper G-2.

[4] TAZIMA, T., INOUE, K., to be reported in detail.

[5] HINNOV, E., MATT-777 (1970).

[6] TUDA, T., TANAKA, M., JAERI-M 5376 (1973).

[7] TAZIMA, T., TANAKA, M., YOSHIKAWA, M., INOUE, K., Nucl. Fusion_14 (1974) 517.

[8] DIMOCK, D., et al., in Plasma Physics and Controlled Nuclear Fusion Research (Proc. 4th Int. Conf.

Madison, 1, IAEA, Vienna (1971) 451.

[9] DUCHS, D., GRIEM, H.R., Phys. Fluids_9 (1966) 1099.

[10] INOUE, K., TAZIMA, T., to be reported in detail.

[11] TUCKER, W.H., KOREN, M., Astrophys. J. ^168 (1971) 283.

[12] LOTZ, W., J. Opt. Soc. Am. J56 (1967) 873.

[13] DUCHS, D., HAAS, G., PFIRSCH, D., VERNICKEL, H., IAEA Workshop on Fusion Reactor Design

Problems (Culham, 1974)409.


DISCUSSION

ON PAPERS IAEA-CN-33/A 1-1, A 1-2

F. WAELBROECK: In the DIVA device (paper A 1-2) the divertor plates

and burial chamber are located directly inwards of the confined plasma in a

region of higher magnetic field. What happens then to the non-buried escaping

ionized particles or to ionized impurities released from the plates? Will

they not fall back — as a result of VB effect and other drift motions — towards

the scrape-off layer, in the immediate vicinity of the confined plasma? In

other designs such as D-shaped axisymmetrical divertors, or the Princeton

Reference Design, the divertor plates are located to the side. Was the

choice of location governed by technological reasons or some other

considerations?

M. YOSHIKAWA: The divertor is placed inwards for MHD resgns. In

the present device the loss of ions on the divertor magnetic surface's is the

mirror loss and does not depend greatly on the mirror ratio. Details of the

design considerations can be found in Ref. [2] of the paper.

D.M. MEADE: Perhaps I can add a comment on this matter. The motion

of impurities parallel to the magnetic field in the scrape-off region of a

divertor is determined mainly by the electrostatic field generated by the

outflowing proton plasma. For typical tokamak divertor experiments, this

electrostatic field sweeps impurities into the divertor with a parallel energy

of the order of 3ZkTe. Moreover, the impurities are usually collisional in

the divertor scrape-off region so that the mirroring effects are reduced

even further.

M.S. KAMINSKY: Your paper shows density distrubtions for impurity

ions of C, O and Fe. I note, however, that your plasma is encased in a

gold-plated copper shell and that you used gold-clad molybdenum limiters.

Why did you not observe high-Z impurity gold ions since gold sputters more

readily than Fe, and your device appears to have rather large gold covered

surfaces?

M. YOSHIKAWA: So far we have not tried to measure metal impurities.

I should also point out that the plasma will be isolated from the limiters in

the final divertor experiments.

R. BEHRISCH: Did you observe a decrease in plasma density, as would

be expected if the divertor works?

M. YOSHIKAWA: We have not yet operated the titanium evaporator.

Your assumption is correct, however, and I am looking forward to doing

the measurements that would be involved. At the moment the plasma is

not separated from the limiter and wall and is in reasonable contact with

them in the particle balance.

31


IAEA-CN-33/A2-1'

B03MymEHHfl MArHHTHOrO IIOJI5I IIPH

HEYCTOHHHBOCTH CPLIBA B YCTAHOBKE

TOKAMAK-6

B.C.BJIACEHKOB, B.M.JIEOHOB,

B.T.MEPE3KKHH, B .C .MYXOBATOB

HHCTHTyT aTOMHofi 3HeprHH HM . H .B .KypnaTOBa,

MocKBa,

COK>3 CoBeTCKHX CouuajiHCTKHecKHX Pecny6^HK

Abstract- Amo-ramm

PERTURBATION OF A MAGNETIC FIELD DURING THE BREAK-UP INSTABILITY IN TOKAMAK-6.

In the present paper the results of measuring perturbations in a poloidal field during the development

of the break-up instability in Tokamak-6 are presented. The following discharge parameters were applied:

plasma current I ~ 50 kA, longitudinal magnetic field strength Hg = 5-6 kOe, 2q < (a) < 3. It was

demonstrated that the break-up instability was accompanied by large-scale perturbations in the magnetic

field, associated with distortion in the shape of the plasma column. In the vicinity of the discharge chamber

walls, the amplitude was ~2CP/o of that of the unperturbed field. It was also shown that the structure of

these perturbations underwent substantial changes during the development of the instability.

B03MYIIIEHHH MArHHTHOrO nOJIfl nPH HEYCTOHMHBOCTH CPblBA B YCTAHOBKE

TOKAMAK-6.

B pa6oTe H3;io>KeHbi pe3y/ibTaTbi H3MepeHHH B03MyiueHnii ncnoHflajibHoro nojia B npoijecce

pa3BHTHH HeycToflHHBOCTH cpbiBa B ycTaHOBKe ToKaMaK-6 npH crceflyiomHX napaMeTpax pa3pa.ua:

TOK B n;ia3Me I~50KA, HanpnxceHHOCTb npoaonbHoro MarHHTHoro nonn HQ = 5 -r 6 K3,2q


34 BJIACEHKOB H ap.

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MeHHoro uiHypa, aocTHraeT ~20% OT Be^HMHHbi HeB03MymeHHoro MarHHT-

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Hoe n3MeHeHH€ cxpyKTypbi B03MymeHnii.

nOCTAHOBKA3AflAHH. METO^HKA

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ceMeHHH ruia3MeHHoro uiHypa.

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c nocTOHHHOfi BpeMeHH ~100 MC . Ha Bxoflbi HHTerpwpyiomHX ycH/iHTe/iefi

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Pnc.1. CxeMaTHMecKoe H3o6pa>tceHHe pa3paaHOH KaMepti H pacno/ioaceHHe flHarwodHKH,


IAEA-CN-33/A2-1 35

6Hpajiacb TaKOH, MTO6BI HenocpeacTBeHHO nepea pa3BHTHeM HeycTOHMHBOC-

TH CpHBa pa3HOCTHHH CHTHaTI COCTaBMn He 6o;iee 2 -r 3 % OT Be./IH4HHbI

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f ~

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2jr

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o

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30H£bi.

PE3yJIBTATbI SKCnEPHMEHTOB

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(A


36 BJIACEHKOB H ap•

PHC.2. OcuH^i^orpaMMbi HanpnaceHHfl Ha o6xofle Topa U(t), TOKa B njiasMe I(t) H cpeflHefl

n^OTHOCTH 3;ieKTpoHOB B njia3Me ne (t). H = 5,5 K3, PQ = 1,4 • 10" MM pT .CT. q(a) = 2,4 .

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IAEA-CN-33/A2-1 37

5QMKC

PHC.3. H3MeHeHHe HanpaaceHHOCTH nonoHflanbHoro MarHHTHoro no/iH Hu (t) Ha pa^wyce pacnojio7K.ennH

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IAEA-CN-33/A2-1 39

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BpeMeHH, yKa3aHHux cTpe/iKaMH.


IAEA-CN-33/A2-1 41

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m ' wO v

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B03MymeHHH MarHHTHoro nonn B cpeaHeft MacTH cpbiBa ^ocTHraeT ~20%

OT BejiHMHHbi HeB03MymeHHoro no/ia. HapacTaHHe STHX B03MymeHHH npo-

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MymeHHH.

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TaKxe HecoBepmeHCTBO MeTOflHK, Hcno/ib30BaHHbix B pa6oTax [6,7], npHBe-

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CH CHJIbHO pa3BHTOH BHHTOBOH HeyCTOHMHBOCTblO nM3MeHHOrO UIHypa .

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MH HeycTofiMHBOCTHMH. TeopHH, B npHHqHne, He npoTHBopeMHT 3TOMy [8].

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42 BJIACEHKOB H ap.

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aKcnepnivieHTOB H JI .JX .CHHHLiHHy 3a noMomb B o6pa6oTKe pe3y/ibTaT0B H3-

MepeHHH.

JIHTEPATYPA

[1] VLASENKOV, V.S. etal., 6th European Conf. Controlled Fusion and Plasma Physics,

(Proc. Conf. Moscow, 1973)1^, Moscow (1973) 55.

[2] MHPHOB, C.B., ATOMHaa SHeprwH J/7 (1964) 209 .

[3] TOPByHOB, E.n., PA3YMOBA, K.A., AxoMHaa 3neprm _15 (1963) 363 .

[4] APUHMOBHH, JI.A., MHPHOB, C.B., CTPEJIKOB, B.C., ATOMHaa SHeprra

r7(1964) 170.

[5] BHHOrPAflOBA, H.fl., PA3VMOBA, K.A., Plasma Physics and Controlled Nuclear

Fusion Res. IAEA, Vienna 2 (1966) 617.

[6] MHPHOB, C .B ., CEMEHOB, H .B ., AT0MH3H SHeprHH 30 (1971) 20 .

[7] BOL, K. et al., 6th European Conf. Controlled Fusion and Plasma Physics (Proc.

Conf. Moscow, 1973) 1_ Moscow (1973) 18.

[8] KADOMTSEV, B.B., POGUTSE, O.P., 6th European Conf. Controlled Fusion and

Plasma Physics (Proc. Conf. Moscow, 1973) ^Moscow (1973) 59.


IAEA-CN-33/A2-2

BJIH^HHE rOSPHPOBKH nPO^OJIbHOrO

MATHHTHOrO IIOJI5I HA HOHHYK) KOMnOHEHTY

IIJIA3MBI B TOKAMAKAX

M.n.nETPOB

$H3HKO-TeXHHMeCKHH HHCTHTyT HM . A . . MO(|> 1 keV) is evidently associated with the

drift of ions trapped in the corrugations of the longitudinal magnetic field in the tokamaks. By comparison of

experimental and theoretical data it is shown that, in tokamaks with a relative field corrugation 6 Z \%

(averaged over the plasma column section), the ions trapped in the corrugations (so-called locally trapped ions)

entrain an appreciable fraction of the energy from the ion component of the plasma.

BJIHHHHE rO*PHPOBKH rtPOflOJIbHOrO MArHHTHOrO IIOJLH HA HOHHyK) KOMnO-

HEHTY IUIA3MbI B TOKAMAKAX.

B noKnajxe npHBe,neHbi sxcnepHMeHTa/ibHbie pe3y;ibTaTM no H3MepeHH» pacnpeae/ieHHH

noTOKa aTOMOB nepe3apaaKH no ceneHHio njia3MeHHoro HiHypa Ha ycTaHOBKax ToKaMaK-3,

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BMCOKHX 3HeprHH (E£ 1 KaB) CBflaaHa, no-BHflHMOMy, c flpeftcffOM HOHOB, 3anepTwx B ro$pax

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6£ 1% (ycpe^HeHHOH no ceMeHHio njia3MeHHoro nmypa) HOHU, 3anepTbie B ro


44 nETPOB

—I 1 1 1 1 1 1 1 1 1 •

1 0,8 0,6 0,4 0,2 0 0,2 0,4 0,6 0,8 1 r/a

BHYTPb HAPyWY

PHC.1. 3aBHCHM0CTb r;iy6nHbi Moay/wuHH npoaonbHoro MarHHTHoro no^a OT paccroHHHH flo OCH

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HHTHHX noBepxHOCTeH 3a cnex TopoHflantHoro #peH


IAEA-CN-33/A2-2

njia3MH B TOKaMaKax. CneayeT 3aMeTHTb, MTO STO cepbe3Hoe npeaynpe*aeHHe

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sjieKTpuMecKoro nojw Ha flpeH$ «OKa^bHO-3anepTUxqacTHq 3aTpyflHeH

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H3 pa3/iHHHbix 06/iacTeH ceieHHa n/ia3MeHHoro uiHypa TOKaMaKa.

II . PACIIPE,HEJIEHHE nOTOKOB ATOMOB nEPE3AP5IflKH nO CEHE-

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aTOMHbix MacxHq, KOTOpbie pacnonaraiarcji O6BIHHO B sKBaTOpnaiibHOH njioc-

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(~10^ 20"). 3TH aTOMW noHB^aioTCH npn nepesapH^Ke HOHOB C OTHOineHH-

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aTOMHbix nacTHU. 1- ueHTp noBopoxa OCH aHa;iH3aTopa (iBTpHxnyHKTHpHwe ;IHHHH - KpaftHHe

no/ioaceHHH OCH aHa;iH3aTopa), 2- TopoHaa/ibHaa KaMepa TOKaMaxa, 3- rpaHHua naa3MU,

4- panpeae^eHHe KOHueHTpaqHH aTOMOB BO«opo«a no ceieHWO nna3MeHHoro niHypa B TOKaMaKax.

45


46 nETPOB

200 sB

OlOOOaB

0,6 0,4 0,2 0 0,2 0,4 0,6 r/a

06 0,4 0,2

500 3 B

1300aB

4000sB ^ 25003B

0,2 0,4 0,6 r/a

2003B

O 1300sB

0,6 r/a

Pnc.3. PacnpeaejieHHH noTOKa aTOMOB Boaopoaa pa3Hwx SHeprvift no ce^ieHHio naa3MeHHoro

umypa B TOKaMaxax: a) ToKaMaK-3 . PexHM pa3p«aa: H = 25 K3, I =55KA, na= 1013 CM" 3

6) ToxaMaK-4. Pe*HM pa3pa«a: H = 27,5 K3, 1= 137 KA, na = 2-10 13 CM-3 (aefiTepHfl)

B) ToKaMaK-6. PexHM pa3pHfla: H = 10 K3, 1=45 KA, na= 10 CM" 3 .


IAEA-CN-33/A2-2 47

eM COCTaBJIfllOmHX CKOpOCTH V„ /^ ~ (3 -r 5)'10" 3 (3flecb V„ H Vx — COCTaB-

/ifliomHe CKOPOCTH ^acxHU, HanpaBjieHHbie napa;i;ie.7ibHo H nepneHflHKy/iapHO

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3KcnepHMeHTa/ibHO 3a;1000 aB) pe3KO acHM-

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BbipaaceHa crca6o HJIH BOo6me oxcyxcxByex ; 6) neraapHoexb acHMMex-

PHH cooTBeTCTByeT HanpaB/ieHHio TopoH^a^bHoro npevifya HOHOB ; B) acHM-

MeTpwH MeHaeTca Ha o6paTHyro npn nepewieHe HanpaBjieHHfl npo,zio;ibHoro

MarHHTHoro no/ia ; HanpaBjieHHe TOKa paspa^al He B^waeT Ha (£opMy p'acnpeaejieHHH.

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IOXCH no xapaKxepy ox pacnpe,ne;ieHHH, OXHOCHHIHXCH K T-3 H T-4. B SXOM

craynae He o6Hapy«.eHO 3aMexHOH acHMMexpnn AJIH axoMOB 6ojibiuoH 3Hep-

THH (E= 1300 sB), H 3acpHKCHpOBaHa c;ia6ast acHMMeTpHH RJW. axoMOB MajioPi

aHeprHH (E = 200 sB).

IlpHBefleHHbie Ha pnc.3 SKcnepHMeHxa^bHbie KpHBbie xopomo corjiacyioTCH

c MonenbK) flpeficpa jioKajibHo-3anepTbix HOHOB, pa3BHT0H B pa6o-

Tax 11], 12]. Ha6jiK>aaeMaH acHMMeTpHH pacnpeaejieHHH MOKei 6wxb

CB«3aHa co CMemeHHeM pacnpeae/ieHHH n^oTHOCTH jioKaabHO-3anepxbix

HOHOB no ceneHHio njia3MeHHoro iimypa 3a CMex HX xopoH^ajibHoro npeRcjia .

5peH$OBoe cMemeHHe ;iOKa;ibHO-3anepxbix HOHOB 3a BpeMa Mesjiy HOH-

HOHHblMH CTOJIKHOBeHHSMH, BblBOflH IUHMH HOHbl H3 COCXOHHHH 3anepTOCXH

B roi|)pe, onpefle/iaexcH Bbipa*eHHeM:

Ar~Vg^ (1)

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HHX cxo/iKHOBeHHH B n/ia3Me. PaccMHxaHHbie no QopMyne (1) flpeHOBbie

CMemeHHH ^OKajibHO-3aciepTbix HOHOB c SHeprHeH E> 1 KSB Ana Hccjie^OBaH-

HblX pejKHMOB yCTaHOBOK T-3 H T-4 (6~6% H 3%, COOTBeTCXBeHHO) COCxaB/iaiox

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Ka^bHO-3anepxbix HOHOB c SHeprneft E>, 1000 aB Ha ycTaHOBKax T-3 H T-4


48 I1ETPOB

Ha Be^HMHHbi nopH^Ka pa,ziHyca"a". HTO KacaeTCH HOHOB Ma;ibix SHeprnH

( E = 200 -r 500 aB) B 3THX ycTaHOBKax, TO HX ^peH


13ioB 2003B

1 1 1 1 ^-

10' 10 2 10 3 10 4

Die"'

IAEA-CN-33/A2-2 49

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MOCTH OT HOHHOH HaCTOTbl CTO;lKHOBeHHH .

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50 nETPOB

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npoH3BOflHnHcfc 3KcnepHMeHTa/ibHbie H3MepeHHH. Pnc.4a noKa3BiBaeT,

HTO SKcnepHMeHTa^bHO Mcc/ieflOBaHHbiH ^Hana30H nacTOT V[ , noKasaHHbifi

OTpe3KOM npHMOfi, HB/ifleTcfl nepexo^HHM H3 o6^acTeH 6o/ibinHx vi , rue

B^HHHHe ^0Ka^ibH0-3anepTbix HOHOB Ha yHOc Ten/ia npeHe6pe»HMO Ma/10,

B 06/iacTH Ma/iwx vi , vj\e /ioKa;ibHO-3anepTbie HOHH nrpaior onpeaeyijuomyio

po;ib B noTepax SHeprHH. SKcnepHMeHTbi no H3MepeHHK> pacnpeae/ieHHH

noTOKa aTOMOB c SHepraaMH B STOM flwana30He IA o6Hapy>KHBaioT COOT-

BeTCTByromwH nepexoa OT cHMMeipwiHtix K pe3K0 acHMMexpHHHbiM pacnpeaeaeHHHM.

TaKHM o6pa30M, CTeneHb acHMMeTpHH 3KcnepnMeHTa^bHO H3-

MepeHHHbix pacnpefle^eHHH HacTHU. onpefleyieHHOH SHeprnn MOseT 6biTb

KpHTepneM BJIHHHHH /iOKa^bHO-3anepTbix HOHOB cooTBeTCTByiomeH SHeprnn

Ha yHOC Ten/ia H3 nw3Mti.

2) ToKaMaK-4 (pHc.46). 3TOT pHcyHOK cooxBeTCTByeT pe*HMy T-4

c HaHBbicmeH 3aperHCTpHpOBaHHofi HOHHOH xeMnepaxypofi BO/iopo/iHOH nna3-

MW (T. ** 700 sB) [6], Koxopofi cooxBexcxByex H3o6pa»eHHaa Ha pncyHKe

xoHKa Aj . H3 rpa$HKa BH^HO, HTO y*e B STOM pe«HMe T-4 jioKanbHO-

3anepTbie HOHM yHOCHT H3 HOHHOH KOMnoHeHTbi nna3Mbi npHMepHO no;ioBHHy

sHeprHH, TepaeMOH eio (apyran nojioBHHa yHOCHTcn KJiaccHHecKofi 6eccTo/iK-

HOBHTe/ibHoft HOHHOH Ten/ionpoBO^HOCTbio). 5ICHO, HTO npH aa;ibHeHiiieM

HarpeBe nna3MM H cooTBeTcTByiomeM yMeHbineHHH v. jiOKa;ibHO-3anepTbie

HOHW 6y#yT yHOCHTb Bee 6o;ibiiiyio,zio/noTen;ia, H He yaacTCH aocTHHb cyMMapnoH

HOHHOH Ten^onpoBoaHOCTH, cymecTBeHHO MeHbiueH, MeM Ten^onpoBO^HOcTb

H3 06/iacTH njiaTO (ypOBeHb cnnoiUHOH npHMOH X; B npaBOH nacTH rpa$HKa) .

3) ToKaMaK-6 (PHC.4B). Oipe3KOM npHMoft y OCH a6cuHcc 3/iecb,

KaK H B craynae pHc.4a, noKa3aH anana30H nacTOT v^ , cooTBeTcTByiomHH

anana30Hy SHeprHH npH H3MepeHHH pacnpeae/ieHHH noTOKa aTOMOB no ce-

MeHHio njia3MeHHOro iiiHypa (PHC.3B). B craynae T-6, KaK yKa3biBa/iocb BBIine,

TaKHe pacnpeae^eHHH noKa3a/in OTcyTCTBHe npoHB^eHHH #peHT, HTO H3-3a ^pe3BBmaHHO Marion ropH-

POBKH nO/Ifl H BJIHHHHe JI0Ka/IbH0-3anepTbI X HOHOB B HCCJieflOBaHHOM flHana30He

SHeprHH 200 -r 1300 aB Ha yHoc Ten/ia H3 n/ia3MH npeHe6pe»HMo

Mano. CornacHO pacneTawt STO BjiHHHHe B cnynae T-6 MOKex npoHBHTbcn

numb npH 3HeprHH HOHOB n^a3Mbi He MeHee 10-f 15 KS-B.

4) ToKaMaK-10 (pnc .4r). ToHKa A2 , H3o6pa»eHHan Ha pncyHKe,

cooxBeTCTByeT no nacTOxaM cTOJiKHOBeHHfi npe^no/iaraeMOMy pe>KHMy STOH

cTponmeiicH ycTaHOBKH (HOHHaH TeMnepaTypa ~3KSB). BHAHO, HTO B STOM

peatHMe, KaK H B c/iynae T-4, /ioKa;ibHO-3anepTbie HOHH MoryT yHOCHTb

3HaMHTe/ibHyio norno Tenna OT o6mero KonHiecTBa Ten^a, TepaeMoro HOHHOH

KOMnoHeHTOH nuasMbi^ B03MOXHO, HTO B c/iynae T-10 H3~3a 3aMeTHOH

ro


IAEA-CN-33/A2-2 51

Tbix HOHOB, Heo6xoflHMO yMHTtiBaTb npH o6pa6oTKe SHepreTHMecKHX pacnpefle/ieHHH

STOMOB c u,enhK> nonynemix H3 HHX HH^opMaqwH o HOHHOH TeMnepaType

n;ia3Mbi. B ycrcoBHHx TOKaMaxoB c 6o/ibmoH roeKTHBHOH HOHHOH Ten^onpoBOflHocTbio, cymecTBeHHO

MeHbiiien, MeM K/iaccHHecKaH Ten/ionpoBOflHOCTb Ha ypoBHe n/iaTO. IlpHMH-

Ha 3Toro 3aK^K)MaeTcs( B cymecTBeHHOH POJIH ;ioKa/ibHO-3anepTMX HOHOB B

yHoce Ten^a H3 n;ia3Mbi TaKHX TOKaMaKOB.

ABTOP npHHOCHT HCKpeHioio 6;iaro4apHOCTb B .C . MyxoBaTOBy 3a MHOroMHC/ieHHbie

o6cy»aeHHH H KOHcy^bTatiHH no npe^MeTy aaHHOH pa6oTbi.

JIHTEPATYPA

fl] ANDERSON, O.A., FURTH, H.P., Nucl. Fusion K2 (1972) 207.

[2] STRINGER, T.E., Nucl. Fusion 12 (1972)689.

13] TAJIEEB, A.A., CAT^EEB, P.3., )K3T* 53_ (1967) 348.

14] APU.HMOBHH, JI.A., TJIYXOB, A.B., nETPOB, M.n., nwcbMa B 5K3T* 1J_(1970)449.

[5] STODIEK, W., 5th European Conf. Controlled Fusion and Plasma Physics

(Grenoble, 1972) £ (1972)1.

[6] GORBUNOV, E.P., ZAVER.TAEV, V.S., PETROV, M.P., 6th European Conf.

Controlled Fusion and Plasma Physics (Moscow, 1973) 2 (1973) 1.

[7] BHHOrPAflOBA,H.fl.H flp., 4th Int. Conf. Plasma Physics and Controlled

Nuclear Fusion Research (Proc. Conf. Madison, 1971)£, IAEA, Vienna (1971)441.


DISCUSSION

ON PAPERS IAEA-CN-33/A 2-1, A 2-2

O. KLUBER: Is the positive spike observed in the current trace during

disruption due to a real increase of the current or to electrical perturbations?

If it is a real current increase, what is the explanation for it?

K.A. RAZUMOVA: The increases seen in the plasma current during

disruption are due to a reduction in the inductance of the plasma column

brought about by an increase in the column's minor radius and a decrease in

its major radius. The amplitude of the current change depends on the electrotechnical

parameters of the primary circuit exciting the discharge.

R.J. TAYLOR: I should like to comment on this same question. One

more commonly observes a negative voltage spike accompanied by a steplike

increase in the current. At MIT we see this in all our tokamaks

(Alcator, Versator, Rector), with and without the copper shell, but with

air-core transformers.

53


RADIATION FROM PLASMAS

IN THE ST-TOKAMAK*

N. BRETZ, D. DIMOCK, A. GREENBERGER, E. HINNOV,

E. MESERVEY, W. STODIEK, S. VON GOELER

Plasma Physics Laboratory, Princeton University,

Princeton, N.J. ,

United States of America

Abstract

IAEA-CN-33/A 3-1

RADIATION FROM PLASMAS IN THE ST-TOKAMAK;

Quantitative vacuum ultraviolet (UV) measurements (A. £ 100 A) of various ST-Tokamak discharges show

that the atom density of metal impurities is about 0.1% to 1. 5% of the electron density and that the atom

density of oxygen is about 1% to lO^o. These concentrations yield an effective ionic charge, Z, consistent

with the measured current, voltage, and profiles of electron temperature. The radial distribution of high-Z

material is obtained from X-ray measurements in the range 1 A^K- 4 A; from these we conclude that there

is no extreme concentration of high-Z material in the centre, but cannot exclude variations within a factor

of 2. The X-ray spectrum is dominated by recombination; using bremsstrahlung and recombination calculations

the value of Z derived from X-ray intensity is comparable with the value from conductivity. An instrument is

described for making measurements in the extreme UV region (5 < k< 20 A). In this range strong emission has

been observed (radiated power about 10% of power input in the centre), which we attribute to line emission

from heavy-metal (Fe or Mo) ions which are produced only at an electron temperature above about 1200 eV;

the very narrow radial profile of observed intensity is consistent with measured temperature and density profiles.

Rough estimates of the concentration of heavy metals required to account for the radiated power are consistent

with vacuum UV and X-ray data.

1. INTRODUCTION

The concentration and spatial distribution of high-Z impurities

promises to be of very great importance to the temperature, power balance,

and stability of large tokamaks being built now or being planned for the

future. In particular, if metallic impurities (Fe, Mo, W, for example)

are present, the radiative power loss will be dominated by line radiation

even at rather high electron temperature; only in very pure plasmas can

one expect the limiting case of bremsstrahlung radiation balancing input

power.

In this paper we attempt to correlate information about radiation

intensities from ST Tokamak discharges as measured in x-ray, extreme ultraviolet

(UV) and vacuum UV regions by a variety of instruments and methods.

Aside from questions of mutual consistency of these measurements, the problem

of particular interest is the evidence for or against preferential

central concentration of heavy impurities, and, more generally, the importance

of various processes in the energy balance near the center of the

discharge.

The first section of the paper discusses analysis of measurements in

the vacuum UV (100 & S A < 1000 A), identification of ion species, and

quantitative determinations of average impurity concentration; most of the

"Work supported by USAEC Contract AT (ll-l)-3073.

55


56 BRETZ et al.

power radiated from the ST appears in this general region. The second section

of the paper discusses soft x-ray measurements (1


Ha PEAK

IAEA-CN-33/A 3-1 57

5 10 15 20 25

TIME (msec)

I

(IO l3 cnT 3 )

fi~e

0.5

FIG. 1. Time behaviour of photon emission rate for vacuum UV lines of various ions. Dashed line is electron

density from microwave interferometer data, averaged over a diameter.

If one further assumes that the radial motion of an ion is slow

(e.g., ^ plasma radius/mean particle containment time) then the state of

ionization can be calculated as a function of radius from the known profiles

T (r) and n (r). The observed plateau intensity then gives the rate

of ionization, as well as the concentration of the ion in the shell. Such

calculations show invariably that a) the oxygen concentration does not

vary appreciably in time during the discharge and probably not in space;

and b) the metallic impurities (for which the plateau measurement is

usually very difficult) may show a slow increase in time, at least in some

discharges.

From a set of such measurements, we can deduce the effective ionic

charge, Z = En.; Z?/£n.Z. , and compare it with values determined from elec-

I i i i

trical resistance. The agreement is good, with the resistivity Z-values

generally 0-30% higher. The discrepancy may be due to unobserved impurities,

such as tungsten (which cannot be measured at present because of the

complicated and largely unknown electron configuration of its ions). Typical

concentrations are: Oxygen, 3-10%; molybdenum and iron, 0.1-1.0%;

plus traces of chromium and nickel, probably appropriate to the stainless

steel wall composition. Generally there is a reciprocal relationship: with

continued machine operation oxygen concentration falls and those of metals

rise. The result is a gradual change in the radial profiles of T (r) and

other discharge parameters, but not necessarily of Z(r).

The highest states of ionization observed are close to, but slightly

lower than those expected on the basis of coronal equilibrium (collisional

ionization balanced by radiative and dielectronic recombination at measured

T ). Thus lithium-like and beryllium-like iron, and sodium-like and

magnesium-like molybdenum have been observed. The existence of these

states of ionization sets a lower limit to the ion confinement times,

which turn out to be comparable to the average particle confinement times.

On the important question of relative concentration of heavy impurities

toward the center (i.e., in the direction of electron density gradient)

/ the UV measurements in the absence of radial scans can give no

definite answer. However, plasmas with extreme concentration toward the

center can be ruled out from energy balance considerations. Such plasmas

would have high central resistivity, hence low current and power input


58 BRETZ et al.

density, and yet such large radiation losses that the steady-state temperature

could not be maintained._ On the basis of such considerations, a

peak-to-average variation of Z(r) much larger than a factor 1.5 could not

be maintained.

3. SOFT X-RAY DETERMINATION OF RADIAL DISTRIBUTION OF IMPURITIES

In order to look more closely at the question of the radial distribution,

and as a check on the UV measurements, we have made studies of the

radial distribution of x-rays emitted by the plasma in the 3-10 keV range.

This radiation is primarily recombination radiation of impurity ions plus

a small amount of bremsstrahlung and x-ray line emission. This work has

been discussed in detail elsewhere ; so we will give only a qualitative

discussion here.

The recombination spectrum of a given ion consists of a sum (over

final bound states) of bremsstrahlung-like spectra, each of which has a

low-energy cutoff at the ionization energy of the particular final state.

Since the measurements were performed above the cutoff, each ion species

appears simply to be radiating an enhanced bremsstrahlung spectrum. The

strength of this radiation depends greatly on the elements present, on

their states of ionization, and on the plasma temperature. For light

impurities (in our case mainly oxygen) relatively accurate predictions can

be made, because these elements become completely stripped in the central

region of the discharge. For high Z impurities (mainly iron and molybdenum

and/or tungsten) the ionization states must be calculated or measured. Both

have been attempted for iron.

The measurement of ionization state consists of an investigation of

the K -line shift of iron. The shift results from a reduction in shielding

of the nuclear charge as electrons are removed from the L-shell in the

process of ionization. Figure 2(a) shows a spectrum in the region 6.4 to

6.7 keV obtained in a discharge with 1200 eV central electron temperature.

The instrument used was a commercially available Bragg spectrometer with

a LiF crystal looking tangentially to the magnetic axis of the plasma. Its

resolution can be deduced from the neutral iron K -line—also plotted in

Fig. 2(a)—which was produced by fluorescence from an x-ray tube. The

indicated classification of the "satellites" follows that of Lie and Elton.

The figure shows that for ST conditions ionization takes place in the

L-shell, which contains 2 to 5 electrons at T = 1200 eV.

e

These measurements are compared with calculations balancing ionization

and recombination. The computations of Jordan 5 indicate that dielectronic

recombination is the dominant recombination process with a = 10 -11 to

3*10 * cm 3 /sec in the range of interest. These calculations, however,

refer to the solar corona; at the higher densities of the tokamak, dielectronic

recombination may be somewhat reduced. On the other hand, in the

tokamak, the lifetime of the ions is important. Typical values of 1/n T,

where T is the particle confinement time, are in the range 10" 11 to 10 -12 .

Probably somewhat larger values should be used in a comparison with the

recombination rate, because an ion recombines in the outer cooler plasma

regions rather than at the wall. In Fig. 2(b) is plotted the relative

population of various ionization states as calculated by Jordan. These

calculations probably overemphasize the population of helium and lithiumlike

states, which have smaller dielectric recombination and are probably

determined more by particle loss. The relative intensities of the K satellites

can be determined from the concentrations, if the excitation functions

are known. Assuming these all to be equal gives rough agreement with

the observed spectrum.


IAEA-CN-33/A 3-1

E/keV

Te=l200eV

743749

FIG. 2. Spectrum of iron Kft line structure, (a) Measured spectrum at central electron temperature

Te = 1200 eV (+); neutral KQ line showing resolution of Bragg spectrometer (•); line identification from

Ref. [4] . (b) Relative population of ionization states predicted by Jordan [5] for corona equilibrium at

T0 = 1200 eV.

Knowing the charge state of the ions, we can calculate the emitted

recombination radiation and can make a comparison between the amounts of

impurities deduced from the vacuum UV measurements and the x-rays. The

measurements agree within a factor of 2, the x-rays tending towards somewhat

higher concentrations than the vacuum UV.

Representative x-ray data are shown in Fig. 3. Figure 3(a) shows

Thomson scattering measurements of electron temperature and density profiles

taken at a time (70 msec) during the steady-state part of the discharge.

In Fig. 3(b) the crosses (x) show relative x-ray intensity (at

X = 3.1 k) observed along chords at three different radii; the circles (o)

are the corresponding relative radiation intensities calculated from the

temperature and density profiles, assuming a uniform distribution of

impurities. The normalizing factor for absolute intensity at the center is

50 times the Z = 1 bremsstrahlung intensity. Interpreted as recombination

radiation, these data give Z = 8, which agrees within the estimated accuracy

with the conductivity result (Z = 7) and the vacuum UV data; therefore

we conclude that the concentration of impurity is uniform to within a factor

of 2.

The x-ray measurements provide another kind of evidence about the

impurity distribution. Phase and amplitude measurements of fluctuations

in x-ray intensity 5 clearly show the presence of m = 1, n = 1 oscillations

in the central part of the plasma, extending out to a radius of 3 ±1/2 cm.

59


60 BRETZ et al.

FIG. 3. (a) Profiles of electron temperature and density versus radius, (b) Radiation intensities versus chord

radius. Calculations are shapes expected for Z = 1 bremsstrahlung. Intensity-normalizing factor is 50 for

soft X-ray at A. = 3.1 A (o) and 400 for diode array (extreme UV) range 0-15 A ( ).

The theory of the m = 1, n = 1 MHD kink mode shows that the radial extent

of these oscillations will be bounded by the q = 1 surface. Assuming the

loop voltage to be_independent of radius and using Spitzer conductivity, we

find the value of Z within the central 3-cm radius to be equal to Z for the

whole aperture within the experimental error of ±50%.

Our x-ray intensity profiles are similar to those in the T-4 Tokamak?

which are attributed to impurity peaking in the center. This explanation

does not apply in the ST plasmas. The difference is that the T-4 temperature

profile (determined from x-ray measurements) is much broader than the

ST profile (from Thomson scattering).

4. EXTREME UV RADIATION INTENSITY AND RADIAL PROFILE

Some data have been taken with a new diagnostic instrument designed to

complement the x-ray and vacuum UV data with measurements in the extreme

UV range (5-20 A). This instrument consists of a windowless version of a

commercially available self-scanned array 8 of 128 silicon diodes, each measuring

^ 0.005 x 0.040 cm. This array is placed behind a slit designed

for good space resolution; a set of thin metal filters arranged on a wheel

gives some crude spectral resolution. The output of the array consists of


2.6

IAEA-CN-33/A 3-1 61

\25M

V

TRANSMISSION VS WAVELENGTH

m

> \\s \

\l l\\ \

25/iAI

4.3/tAI

13/iBe

3fiS\02

l/iSi02

! \ * » •

\ ! \\\ \

I 2 4 6 10 c 20 40 60 100

WAVELENGTH ANGSTROMS

FIG. 4. Transmission curves for S1O2 (detector surface coating) and for Be an Al filters.

a repeated series of 128 pulses each of which represents the charging current

needed to replace the charge lost from a particular diode by exposure

to radiation since the last time it was charged. Each pulse is therefore

proportional to the integrated exposure of a diode for a period equal to

the time required for a complete readout cycle. A charge sample and hold .

circuit

u SiO layer that is needed to prevent

In addition, the array had a two-micron layer of SiO

9 provides a readable output for oscilloscope display. In our setup

the external connections limited the operating frequency so that a complete

cycle time was just under 1 msec.

o

The array was not expected to have much sensitivity beyond about 20 A,

since at longer wavelengths the radiation would be absorbed by the dead

layer of the diodes and by the 1

surface leakage.

for scratch protection. Transmission curves for SiO and for several

filters are shown in Fig. 4. These data are calculated from the tables of

Henke, Elgin, et al 1 . 0 (The SiO actually contains some phosphorus, which is

ignored in these calculations.) Because the SiO is in intimate contact

with the diodes, the transmission curve represents a lower limit to the

effective transmission, since in our geometry some photons resulting from

scattering and x-ray fluorescence go on to produce conduction charges in

the diodes. Also some of the energetic electrons produced in the SiO

reach the diodes; and there may also be a weak sensitivity at much longer

wavelengths, due to fluorescent conversion into the visible region of the

spectrum.

An approximate absolute calibration of the diode sensitivity was made

as follows. The sensitivity of the array was measured in the visible at

6200 A, using a standard lamp and a narrow-band interference filter. With

a photoefficiency of 80%, this can be converted to a sensitivity in terms

of volts per electron-hole pair per cm 2 per sec. Assuming that extreme UV

photons produce electron hole pairs with about the same efficiency as

somewhat harder x-rays (i.e., ^ 3.5 eV per pair) one has an energy calibration

of the array in the extreme UV region.

Typical results are shown in Fig. 3 with data taken after a fairly

extensive opening of the ST machine. Vacuum UV measurements for this

particular discharge are not available, but past measurements show that


62 BRETZ et al.

such a discharge has oxygen as its dominant impurity, ^ 10%, with smaller

amounts of iron, ^ 0.2%, and molybdenum, ^ 0.3%. The electrical behavior

of the discharge and the electron temperature and density profiles show the

character expected for this type of discharge.

In Fig. 3(b) the solid line shows the spatial distribution of the

emission plotted versus chord radius. The dashed line is calculated as

follows: from the electron temperature and density profiles, the Z = 1

bremsstrahlung intensity has been integrated from 0-15 K, integrated along

chords, and plotted against chord radius. This has been normalized to the

observed intensity at the center, requiring a normalization factor of 400.

The region of emission is extremely narrow, corresponding approximately

to the flattopped region in the temperature profile. As discussed

above, the x-ray measurements (1 < X < 4 A) indicate that this

strong peaking cannot be attributed to a concentration of high-Z material

in the center. The possibility that we are seeing visible light from a

reflection or incandescent spot on the vacuum wall is excluded, because

the entire signal was eliminated by inserting a 0.5 mm piece of polished

calcium fluoride, which cuts out the extreme UV and transmits the visible

over the entire region where the diodes have any sensitivity to visible

light.

The emission appears to be stronger and narrower than expected from

bremsstrahlung or recombination radiation. We assume therefore that we are

seeing line emission. Interpreting the observed radiation as line emission,

we can account for the strong intensity peaking by assuming that the particular

ion or ions we are observing occur only at temperatures above about

1200 eV. A crude determination of the energy of the emitted photons can

be obtained from the absorbing filters. The 0.0013 cm Be filter attenuates

the signal by a factor of 4, and the 0.0043 cm Al by a factor of 8. From

the Be transmission curve in Fig. 4 we may conclude that most of the radiation

we are seeing is to the long-wavelength side of 12 A. Of the radiation

transmitted by the Be filter, about half must lie in the region of

the Al K absorption band from 4 to 8 A.

In Figs. 5(a) and (b) are plotted, respectively, the diameter (full

width at half height) and relative peak intensity of the emission versus

time. It can be seen that at 30 msec the width is even less than that

shown in Fig. 3(b) and increases in time. The radiation first appears at

about the time when the center of the plasma reaches 1200 eV. At first

the profile width is about that of the 1200 eV contour; later it broadens

with time, but not as much as the 1200 eV contour; this might be

expected if the center intensity increases disproportionately because the

increased temperature in the center brings in more lines at shorter wavelength.

The increase in intensity with time is expected if the effective

diameter of the radiating source increases as the temperature increases.

The exact origin of this extreme UV radiation cannot be determined

without better spectral resolution; it is known, however, that L-shell

lines of iron and M-shell lines of molybdenum lie in this region. Some

L-shell iron lines in the range 10-17 A have been observed in solar flares 11

and identified with states of ionization that correspond approximately to

those deduced from the crystal spectrometer data of Fig. 2. No comparable

data are available for molybdenum.

A crude estimate of the power radiated in the 0-15 A region and of

the number density of the emitting species can be obtained as follows.

Using the known solid angle of the slit, we find that the peak emission is

approximately 0.45 W/cm 2 , i.e., 0.075 W/cm 3 , using 6 cm as the diameter of

the emitting column. This is a lower limit, since we know that most of the

energy is being radiated in a spectral region where the silica layer can


* 6

K 4

1.0

0.5

••-NO FILTER

x 13,/zBe

o 4.3/iAI

.-+-!200eV

IAEA-CN-33/A 3-1 63

^

n 1

20

1

40

oo

1

60

TIME (msec)

1

80

|

- ^ it)

..J....

100 120

FIG. 5. (a) Time variation of full width at half height of extreme UV signal from silicon detector array.

• no filter; x 13-/1 Be-filter; o 4. 3-M Al-filter; + 1200-eV contour diameter, (b) Relative peak intensity

for same conditions as (a).

be expected to give significant attenuation. If we assume that the observed

radiation is concentrated near 12 A and make the naive assumption that we

should correct for the full attenuation of the 3 p of silica, we get 0.5

W/cnr As noted above, the fact that the silica is in direct contact with

the diodes can be expected to reduce the attenuation, and 0.25 W/cm 3 can

be considered to be a reasonable estimate for the emission in the spectral

region 0 to 15 A.

Using this value of radiated power (^ 0.25 W/cm 3 ) and assuming a highly

allowed An = 1 transition (the 11.9 A line of Fe XXII, for example) we calculate

the number density of the emitting species to be ^ 2 x 10 11 cm" 3

(^ 1% of electron density). In view of the crudeness of the estimate, this

is a reasonable agreement with the vacuum UV and x-ray measurements.

Further development of the silicon diode technique, coupled with

crystal spectrometer measurements, can be expected to be very useful in

analyzing the radiation in this important extreme UV region.

REFE RENCES

[1] DIMOCK, D. L., et al. Nuclear Fusion _13_ (1973) 271.

[2] SPITZER, L., Jr., Ap. J. 116 (1952) 299.

[3] VON GOELER, S., et al., Princeton Plasma Physics Laboratory

MATT-1081 (1974).

[4] LIE, T. N. and ELTON, R

[5] JORDAN, C, Mon Not. R.

[6] VON GOELER, S., et al.,

MATT-1058 (1974).

, C, Phys. Rev. A _3 (1971) 865.

Astr. Soc. 148_ (1970) 17.

Princeton Plasma Physics Laboratory


64 BRETZ et al.

[7] VERSHKOV, V. A. and MIRNOV, S. V., Kurchatov Inst. Atomic Energy

Report IAE-2298 (Moscow, 1973); also PPPL MATT-TRANS-113 (1973).

[8] RL 128A/17,Reticon Corp., Mountain View, California.

[9] RS-2C/128A, Reticon Corp., Mountain View, California.

[10] HENKE, B. L., et al., "X-Ray Absorption in the 2-to-200 A Region,"

Nerelco Reporter XIV (No. 3-4):112, July-Dec. 1967.

[11] NEUPERT, W. M., et al., Ap. J. (Letters) 149 (1967) L79.


WAVE GENERATION AND HEATING

IN THE ST-TOKAMAK AT

THE FUNDAMENTAL AND HARMONIC

ION CYCLOTRON FREQUENCIES* 1 "

J. ADAM? M. CHANCE, H. EUBANK, W. GETTY**

E. HINNOV, W. HOOKE, J. HOSEA, F. JOBES,

F. PERKINS, R. SINCLAIR*,*!. SPERLING, H. TAKAHASHI

Plasma Physics Laboratory, Princeton University,

Princeton, N.J. ,

United States of America

Abstract

IAEA-CN-33/A 3-2

WAVE GENERATION AND HEATING IN THE ST-TOKAMAK AT THE FUNDAMENTAL AND HARMONIC ION

CYCLOTRON FREQUENCIES.

Theoretical and experimental investigations of wave generation and heating at the fundamental and the

first harmonic of the ion cyclotron frequency are reported. General theoretical considerations are followed

by a description of experiments on the ST-Tokamak designed to test the feasibility of this heating scheme for

providing the additional heating required for toroidal reactor operation. Two RF-coils were used in an enlarged

section of the ST vacuum vessel to allow operation up to ~1 MW of RF-power. Wave generation efficiencies

of ~90% have been computed from theory and observed experimentally. The ion cyclotron (slow) wave is

observed to be strongly damped, but the fast hydromagnetic wave is seen to propagate many times around the

machine so that standing toroidal eigenmodes are generated. The dependence of the eigenmode resonances

on the density and magnetic field agrees closely with a theory based on a cylindrical, cold-plasma model.

At w = 2 wjc, with relatively short RF-pulses, the ion temperature approximately doubles and increases by

~ 100 eV, corresponding to a heating efficiency of ~20 = o>iC, the ion temperature increases by only

25% under similar conditions. Longer RF-pulses lead to a neutral-particle influx which tends to constrict the

current channel and leads to MHD-instabilities. The impurity component of this influx also leads to enhanced

ion heating by decreasing the ion-electron equipartion time. The temperature increases quoted are for

conditions where the effect of this neutral influx was negligible.

1 - INTRODUCTION

The feasibility of employing wave heating at frequencies in the

vicinity of the ion cyclotron frequency and its harmonics to supplement

ohmic heating in future toroidal reactors is being investigated theoretically

and with experiments on the ST Tokamak. This work demonstrates that heating

by cyclotron absorption of fast magnetosonic waves is an efficient and

attractive supplementary method from the viewpoint of both physics and the

availability of high power rf generators.

Our initial experimental [l, 2] and theoretical [l, 3] work indicated

that wave generation and heating in the ion cyclotron frequency regime

would be effective, given an appropriate wave launching structure. In

Reference 3 it was emphasized that toroidal eigenmodes should exist for the

fast hydromagnetic wave which should be damped by linear processes at the

fundamental or first harmonic of the ion cyclotron frequency.

t Supported by USAEC Contract AT (II-l)-3073.

''" Centre d'Studes nuclSaires, Fontenay-aux-Roses, France.

:,


66 ADAMetal.

This first study on ST was conducted at modest wave powers (-20 kW)

and was directed toward ascertaining the wave generation properties for the

hot toroidal plasma. A single half-turn loop was used to generate a flat

axial spectrum of wave modes (k„) with minor azimuthal mode numbers m = 0

and/or ± 1. The dependence of coil loading resistance [R = P Dp/I|plon

ft = uw/u) . was found to be in qualitative agreement with the cylindrical

theory modified by the expected toroidal effects [l]. In this earlier work

the efficiency of wave generation deduced from the coil loading (power

going into waves as opposed to circuit losses) was 35-50 %.

Evidence of ion heating was also observed with CIV Doppler scans

and perpendicular charge exchange neutral detection [2]. These measurements

of T..revealed bulk heating near ft = 1 and 2 (a few tens of eV) and considerable

tail heating near ft = 2. However,the power level, and the uncertainty

of the Ti. spatial distribution precluded a reliable determination of the

ion heating efficiency.

Encouraged by the results of our initial study, we have modified

the coil system on ST in order to improve the wave generation efficiency,

to increase the wave power level, and to discriminate against heating the

exterior of the plasma. In addition, we have assembled a considerable array

of diagnostics to allow us to monitor the wave generation and heating and,

as well, the wave influence on the basic discharge characteristics ; e.g.,

equilibrium and stability.

2 - THEORY

This necessarily short section on theory outlines where our recent

work departs conceptually from previous approaches. To provide a basis for

comparison, we recall that most of the previous theory [l, 4, 5] concentrated

on calculating the radiation resistance R of a finite wave-launching

antenna. The radiation resistance resulted from the rate at which energy

propagated away from the antenna in the form of waves. The waves, in turn,

were strongly absorbed elsewhere. The principal new concept is that weakly

damped waves, which form toroidal eigenmodes in tokamak geometry, are more

effective at plasma heating than strongly absorbed waves. As a particular

example, let us consider the toroidal eigenmodes of the fast magnetosonic

wave in tokamak geometry.

The waves are weakly damped by ion-cyclotron damping at the fundamental

and second harmonic of the ion-cyclotron frequency and by transitmagnetic-pumping

on electrons and resistive wall (vacuum chamber) effects

at all frequencies in this range. The damping decrements have been calculated

to be [3, 6, 7]:

(R/a) (k£ T^Mqft^ ~ 10 5 sec '

(R/a) (qkJiyMft^ ~ 3>10 5 sec

k l T e /Mfi i ~ 3 ' 1()5sec

(c/5a) (w/a) 1/2 ~ 10 4 sec '

a) = ft.

w = 2fti

e-TTMP, to/k„~Y e

where q is the concentration of the resonant species and the numerical values

are typical of the ST experiments reported in the following sections.

The important point is this : Although the collisionless damping

decrements are small compared to the wave frequency, what really matters is

that they are large compared to the resistive losses in the wall and to the

typical energy loss rates (^ 10 2 sec -1 ). The first inequality guarantees

wall


IAEA-CN-33/A 3-2 67

that most of the wave energy goes into the plasma particles, while the second

inequality means that the wave energy density can be much smaller than the

thermal energy density and still achieve adequate heating. Indeed, using 2

second harmonic damping and the approximate dispersion relation to 2 = (2ft.)

= k 2 V 2 '

U V A '

= j6Bzj[

*> 10

'v 10

waves Bi Rfixu

plasma

-1 3 - 1

With T. = T-/T. ^ 10 sec . Such small wave intensities preclude any

nonlinear wave effects aside from heating.

Eigenmode heating has several - notable advantages : First, the

weak damping permits ready penetration of the energy to the center of even

a reactor plasma. Second, the roughly uniform distribution of wave amplitude

throughout the torus produces heating that is roughly uniform. This

contrast with the spatially localized heating associated with the resonances

of strongly absorbed waves. Third, both theory and the experiments reported

herein demonstrate that the loading resistance R increases substantially

for toroidal eigenmodes.

The principal disadvantage is the temporal variation of eigenmode

frequencies caused by density variations. Wave generation systems with

sufficient bandwidth to follow an eigenmode frequency [8] must be used.

A 10 % bandwidth should be entirely adequate for large devices such as PLT

or T-10 which will have many eigenmodes.

Let us next describe the mechanism of ion heating. In a tokamak,

the location of a surface where nft^(R) = OJ is a cylinder of constant major

radius. Each time an ion crosses this surface, it receives an increment in

perpendicular energy AE, whose sign depends on relative phase between waves

and particles. Hence ail circulating ions and many trapped ones can participate

in the heating process. Using the AEj_ one can derive a Fokker-Plank equation

governing the quasilinear evolution of the ion velocity distribution:

lt f < E 1- E ")= r n3Ej; E l T2 ""l4 f (E 1' E " )

where n = 1 ,2 correspond to fundamental and second harmonic heating^respectively;

the formulas for r are

2

where

r i = ft(r + r0)MT. ' E £l' 2

F 2 = 8(r + r0)ft 3 M z I VE £2l 2

r0 * (R/a) (yM) 172 ft." 1

k„ i 1/2

"£l 721 I'M

Vpi 2

3r' 2 E rl

Z denotes the plasma dispersion function:

1=1 Kw-^J/k,, 1.

(2m-l) 9_ F

r 8r rl

and E , E are the right-and left-hand electric field components,

: rl(m £ -l)


68

ADAM et al.

Computational solutions show that these quasi linear diffusion operators

yield high energy tails, the second harmonic operator producing a stronger

tai 1.

3 - EXPERIMENT

3.1. Coij[_system.

In upgrading the initial (Phase I) experiments to the present

level (Phase II) (Fig. 1) three principal modifications have been made in

the wave launching structure for the high power system : (i) two half-turn

coils, separated along the plasma colunmby 43 cm, are used in place of the

single coil launcher, (ii) the distance between the coils and the vessel

has been increased from ~ 1.3 cm to ~ 4 cm, and (iii) the coil entrance port

diameters have been enlarged from 3.5 cm to 7.6 cm. Alterations (i) and (ii)

are predicted to raise the maximum generation efficiency [Pwaves/(Pwaves

+ P circuit loss^ to > 80_9 ° $• Alteration (iii) provides for greater voltage

standoff which, coupled with the increased loading efficiency, permits

operation at wave powers up to ~ 1 MW. In Fig. 2 we show the relative position

of the R F coils and the diagnostics. The neutral detectors labeled

Tj_ /T„ measure energy distributions of particles with velocity components

primarily perpendicular/parallel to the toroidal magnetic field.

3.2. Qgil_loadingi_wave_generation_efficiencyi_ai]

Figure 3 gives a typical loading curve obtained for the new system.

The enhancement of Rs (= PRp/InF) in the vicinity of Q = w Jti. = 1 (2) due

to slow (fast) wave generation is ~ 10 times the circuit loss value, giving

a wave generation efficiency of - 90 % as predicted. Rs is found to depend

on plasma parameters (e.g., n ) as predicted by the cylindrical theory and

PHASE I

PHASE H

FIG. 1. The RF-coil configuration. The upper half of the figure represents the initial or Phase-I experiments.

Phase II, on the lower half, refers to the present experiment.


RF EXCITATION COILS [

IAEA-CN-33/A 3-2 69

ZRF

PROBES

M, N OR A

ATTENUATION

LENGTH

FIG. 2. Schematic representation of the ST-Tokamak showing the relative position of the RF-coils, magnetic

probes and charge-exchange neutral detectors.

Rs

(OHMS)

2P

1 i.o

- 0.8

- 0.6

-

- 0.4

- 0.2

-

" T — •

m = 0, + l

* *

* *

*

** m=

r

-

* * * * * #

-+

V

*

*

1 *•* 1—

m = 0, + l

**

1—

1.0 1.5

—1

2.0

h-

2.5

OMEGA= curf/ajc;

FIG. 3. Loading resistance, Rs, versus Q = w/wjc for helium. (I0h = 21 kA, ne = 10 13 cm" 3 , PRF = 10 kW,

w = 2JT-25 MHz).

is independent of RF power level. The magnitude of the circuit resistance

is indicated by the horizontal line at the 0.06 ohm level.

An array of 22 R F probes is used to identify the generated wave

modes and to monitor axial (major azimuthal) attenuation. The theoretically

predicted minor azimuthal modes are observed (Fig. 3). Axial attenuation

is large (A , ~ 1 m) for the slow waves but the fast waves propagate many

times arouna the machine. Toroidal eigenmodes are observed from loading and

magnetic probe measurements. These toroidal modes lead to large peaks in the

loading curves (Fig. 4) but are not seen in Fig. 3 because of the coarseness

of the magnetic field scan. The observed and computed dependence of these

modes on ft and time (density) is seen in Fig. 5. The left side of this dia-

-

-

-

-

;

-


70 ADAM et al.

FIG. 4

These

20 40

TIME (ms)

- 0.8

- 0.6

- 0.4

- 0.2

- 2.0

- 1.0

A.

m

J -

***** *

s*

mJH*

i 1—--9BB-I

1.0

OMEBA

Loading resistance versus time (density) and versus Q showing toroidal eigenmodes in a H-plasma.

traces represent input data for the Q -time plots in Fig. 5.

TOROIDAL MOOES

FIG. 5. Plots of the occurrence of eigenmodes in fi-time space; theoretical (R), experimental (L). The time

dependence comes from the density variation in Fig. 4.

R--3ERIE3

HHMS

- 0.9

- 0.7

-0.5

- o!V

- 0.1

' '

—i 1 r

0.283 KH

_L i-. i -1 1 L

HO 130 150

MSEC

170

0.7 1

0.5 -

0.3 -

0.1 -

-0.1 -

i

7

n = 9

-i 1 1 1 1—

MODE SPLITTING

CHANCE and PERKINS

(*2e)B 2. n m at

ne=l.04x!0"cm 5 3R 2 '

8

L^S~.22j L£J "e.

I ne H I nf

ATTENUATION LENGTH

d~l8.8 m

120 140 160 180 200 220

TIME (msec)

FIG, 6. Loading resistance versus time showing the characteristic double peaks; exp. (L), theor. (R).


iOO

200

Till e\

100

0

IAEA-CN-33/A 3-2 71

WITH RFv

j^O^^^

_^i RF u_

-H ON 1*-

/VTV

JVv

1 ^ ,

PRF=I60 kW

^V^^r^^^

/y/ 7 ^^

NO RF

i 1 i

30 40 50

TIME.ms

FIG. 7. Tjn versus time for a long RF pulse. The slow time response represents the effects of impurities

induced by the RF-energy.

FIG. 8. Tj|| versus time with no RF, but a pulse of neon gas affecting discharge equilibrium.

gram is a computer read-out such that the dark lines indicate experimentally

observed loading peaks, and the right side corresponds to a theory [9] which

assumes that these peaks occur when an integral number (n) of wavelengths

fit into the torus.

There is a tendency for these loading peaks to occur in pairs

(Fig. 6). The right side of Fig. 6 shows a theoretical calculation of the

load resistance wherein the splitting of the peaks is attributable to the

poloidal magnetic field influence on propagation.

3*3. Ion_heating_and_gyerall_discharge_res

We began our heating studies with relatively long (5-10 msec) R F

pulses. Charge-exchange neutral scans of T., revealed considerable ion

"body" (~ 100 eV) and "tail" heating (larg


72 ADAM et al.

0 E - KeV 4

FIG. 9. Perpendicular energy distribution showing the two-component Maxwellian induced at Q = 2.

rf ON A= 2.07

Mm\ W25KA

25 29 33 37

TIME (msec)

FIG. 10. Tj|) and Tj^ versus time from charge exchange neutral measurements in D2. The pulse is short

enough so impurity effects shown in Figs 8 and 9 are negligible (PRF (WAVE) a 70 kW. ne = 6 X 10 12 cm" 3 ,

U = 2.07).

At supplementary powers comparable to the ohmic heating power, we

expect and find significant perturbations of the equilibrium conditions.

These perturbations can be attributed to the ion heating and to an increase

in neutral influx. The neutral influx is troublesome in two respects.

First, it tends to constrict the current channel and can lead to

MHD instability. Secondly, impurity influx can increase the electron-ion

equipartition rate and thereby enhance the ohmic heating of the ions. Simulation

of the R F produced density increase with pulsed gas injection give

no additional ion heating for a D^ pulse but gives considerable ion heating

for Ne (Fig. 8) on a time scale of ~ 10 msec. In fact, most of the T.„ increase

for Q, ~ 1 is due to impurity influx for long R F pulse operation.

The influx has been markedly reduced by decreasing the machine base

pressure and by using shorter R F pulses. Removal of the influx effect on

ion temperature reveals that T.„ approximately doubles during an R F pulse

with P * 70 kW at Q. ~ 2 (Fig.9) but only increases a factor of ~ 1.25

wave

at Q, ~ 1. In both cases T.„ decays back to its initial value in ~ 2 msec.


IAEA-CN-33/A 3-2 73

The wave heating efficiency (AW. /AW ) at ft " 2 is ~ 20 % and

appears to be consistent with the observed containment time and energetic

ion tail orbit loss.

In Fig. 10 we show a typical ion energy distribution showing the

"tail" which occurs for ft = 2. The quoted temperatures in this paper always

refer to the temperature of the "body" of the distribution. The lower efficiency

at ft ~ 1 is thought to be due to the peculiarities of the slow wave

in a torus (which could result in considerable energy deposition in the surface

of the plasma).

4 - DISCUSSION

The experiments here demonstrate that the physical process involved

in wave generation and absorption in the ion cyclotron frequency regime

is understood, e.g., the magnitude of the coil loading, mode characteristics,

and the formation of high energy tails. In future, larger devices (PLT, PDX,

T-10, etc..) a variety of eigenmodes may be excited and fast wave generation

will be optimized. Because the plasma current will be roughly 40 times that

of the modest ST discharges studied here, the confinement of the ions and

especially the energetic ion tails will be dramatically improved. This should

result in higher heating efficiency and reduced neutral influx.

ACKNOWLEDGEMENTS

The authors appreciate the continued support of Drs. M. GOTTLIEB,

H. FURTH, and T. STIX ; the expert assistance of D. KNUTSEN, T. SIVO,

J. BOYCHUCK, V. C0RS0, and J. PERRON and his technical staff in designing

and making operational the wave heating system on ST ; and finally the aid

of Dr. E. MESERVEY in performing the ST conversion to Phase II.

REFERENCES

[ l] HOSEA, J.C., H00KE, W.M., Phys. Rev. Lett. 3J. (1973) 150.

[2] H00KE, W.M., HOSEA, J.C., Proc. 4 th Int. Conf. on Cont. Fus. & Plasma

Phys. (Grenoble, France, 1972) 107.

[3] PERKINS, F.W,, et a!., 3 rd Int. Sym. on Tor. Plasma Conf. (Garching

Germany (1973) B-8.

[4] STIX, T., Theory of Plasma Waves, Mc.Graw Hill, New York (1962) 99.

[5] HOSEA, J.C., SINCLAIR, R.M., Phys. Fluids. 13 (1970) 701.

f 6] ADAM, J., SAMAIN, A., Fontenay-aux-Roses, Report EUR-CEA-FC-579 (1971)

29.

[7] PERKINS., F., Symposium on Plasma Heating and Injection, Varenna,

Editrice, Compositori, Bologna (1972) 20.

[8] IVAN0V, M.V., K0VAN, I.A., LOS', E.V. , Zh. Eksp, Teor, Fiz., Pis'ma Red.

1± (1971) 212 [JETP Letters ^4 (1971) 138].

[9] ADAM, J., EUR-CEA-FC-711, Octobre 1973.

[10] HOSEA, J.C., BOBELDIJK, C., GROVE D.J., Proceedings of the Fourth

Conference on Plasma Physics and Controlled, Nuclear Fusion Research,

IAEC, Madison (1971) 425.


DISCUSSION

ON PAPERS IAEA-CN-33/A 3-1, A 3-2

E.K. MASCHKE: In regard to paper A 3-1 I should like to comment

that, theoretically, one can expect the equilibrium distribution of high-Z

impurities to be strongly peaked, but the experiments do not show such

peaking. Can one be sure that equilibrium distributions have been established

at the time the measurements are made?

W. HOOKE: I hesitate to answer on behalf of the authors but I think

an analysis of the impurity light plateaus indicates that a recycling equilibrium

is reached in a time which is much shorter than the pulse length of ~100 ms.

O. S. PAVLICHENKO: In connection with HF plasma heating you

mentioned that the heating efficiency was 20% (paper A 3-2). What is your

definition of heating efficiency, because in principle plasma heating is the

result of wave energy absorption and energy loss processes?

W. HOOKE: We defined efficiency as the observed increase in the

energy stored in the plasma divided by the net RF-energy transmitted to the

plasma. This is an appropriate definition for very short RF-heating pulses.

75


IAEA-CN-33/A 4-1

NEUTRAL-BEAM HEATING IN

THE ADIABATIC TOROIDAL COMPRESSOR*

K. BOL, J.L. CECCHI, C. C. DAUGHNEY, R.A. ELLIS, Jr.,

H.P. EUBANK, H.P. FURTH, R.J. GOLDSTON, H. HSUAN,

E. MAZZUCATO, R.R. SMITH, P. E. STOTTt

Plasma Physics Laboratory, Princeton University,

Princeton, N.J.,

United States of America

Abstract

NEUTRAL-BEAM HEATING IN THE ADIABATIC TOROIDAL COMPRESSOR.

Results are given for tangential injection into ATC of two 15-keV neutral beams with net power up to

100 kW. The ion temperature rise exceeds 100 eV, consistent with theoretical expectations. Fast-ion drag

rates and pitch-angle scattering have been measured, the latter to determine Zeff- With a single source we

have also injected at 83° and 97° to the plasma current. At 83° some ion heating is observed; at 97° the

heating is negligible. The fast-ion energy distributions, observed tangentially, show the severity of the

"loss-region" for counter-circulating particles.

We reported earlier 1 results derived from tangential injection into

ATC of two 14-15 keV beams of H° or D°, which yielded net input powers

captured by the plasma of up to *> 60 kW„ The observed ion temperature

increases resulting from beam heating were found to be reasonably consistent

with theoretical expectations for charge-exchange-limited energy

transport at neutral atom densities of = 10 9 cm" 3 . The saturation of ion

temperature T. with time was better accounted for by the ion energy confinement

time T . K T. -1 '^(consistent with charge-exchange losses) than by a

positive exponent of T..

More recently, we have, adapted our two Lawrence Berkeley Laboratory

ion sources with curved extraction grids that provide a one-dimensional

beam focus at 2 meters„ 2 For our rectangular beam ports, this allows

considerable improvement in injected power. We have thus extended the

earlier 60 kW input power results to 100 kW, producing the ion temperature

rise shown in Fig. 1„ Using a single source, at power input levels of

^ 60 kW, we have detected small toroidal rotational velocities * 5*10^

cm/sec. These rotational velocities are derived from frequency shifts of

the hydromagnetic kink modes, as measured by x-rays and magnetic loops.

It is worth noting that, as we have proceeded to higher input beam

power, a density increase related to beam energy has been observed, and

that the density rise is more pronounced with injection opposite to the

*Work supported by USAEC Contract AT (ll-l)-3073.

tOn leave of absence from Culham Laboratory, United Kingdom.

77


78

plasma current than with injection

parallel to the current. This seems

reasonable in view of the fact that

antiparallel injection does result in

a larger fraction of beam power impinging

on surfaces, due to somewhat

poorer confinement of the injected

hot ions. 3 ' 4 The results of Fig. 1

were obtained under conditions in

which the electron density rise during

the time of injection is 15%,

two-thirds of which is from the

beam opposing the current and onethird

from the parallel beam. We

find the heating efficiency for the

beams injected antiparallel to the

plasma current to be only 70-80% of

that for parallel injection.

FIG. 1. Ion temperature versus time for (a) no beam,

but with source valves open, and (b) two beams at

captured power of 100 kW. Beam is on for

20 ms < t < 30 ms.

BOLet al.

The ion energy distributions are

inferred from a measurement of the charge-exchange neutral flux emerging

perpendicular to the magnetic surfaces. A few milliseconds suffice to

degrade injected beam particles in energy and scatter them in angle so that

they produce an observable distortion in the high-energy tail of the

thermal ion distribution; for ATC conditions, the lowest energy to which

this effect could extend is E >_ 9 kT. or E > 2 keV. This is, in fact, just

the region where the measured distribution departs from Maxwellian. The

ion temperature values in Fig. 1 are derived from the slope of the unperturbed

region of the distributions.

We have also used helium beams for injection, just to reduce the

contribution of beam particles to the measured neutral flux. Helium quickly

becomes doubly ionized following capture and has a much lower probability

of charge-exchanging with hydrogen gas to become a fast neutral. Moreover,

the neutral-detector efficiency is reduced for helium relative to hydrogen.

There is a possibility of contaminating the helium by wall-occluded hydrogen;

nevertheless, we were able to reduce the beam contribution to the fastneutral

flux by an order of magnitude at 3 keV, and still achieve an

ion temperature rise comparable to that achieved with hydrogen or deuterium

beams. These results are quite similar to those obtained at Culham 5 except

for our apparently reduced hydrogen contamination in the helium beam.

The ratio of energetic-ion pressure to plasma pressure is typically

~ 0.25, and the corresponding poloidal field g-valves are ~ 0.06. These

numbers are similar to those of a DT-reactor alpha-particle population.

The present plasma ion heating rate of ~ 25 keV/sec would also be appropriate

for neutral-beam heating to ignition or subsequent alpha-particle heating,

in an appropriately larger device with T . ^ 1 sec. It is most encouraging

that in spite of the pronounced anisotropy of the injected population

(i.e., v„ > vx), the behavior of the fast ions appears to be entirely

classical. We find that fast H ions lose energy more rapidly than D ions,

320-

300-

260-

Tj(ev)

160-

0*,H +

Po=l00kW

ne- i.8'io ,3 /cm

140- 18 20 22 26 28 30 32

t(msec)


IAEA-CN-33/A 4-1 79

as expected; moreover, both H + and D + lose energy more rapidly when

injected against the toroidal electric field than when injected parallel

to it. The electric field manifests itself clearly in the decay of neutron

production, for D° injected into D + plasma, following beam turn-off., For

parallel injection the neutron decay times are 3-4 msec, whereas, for antiparallel

injection, the decay times are < 1 msec„ Both decay times are

accounted for by the observed fast-ion energy loss-rate The most important

point of these data on fast-ion deceleration is that no evidence of

anomalous energy loss has yet been observed. This result is of particular

importance to the feasibility of the "two-component reactor" approach. 5

With an ion source obtained from Oak Ridge National Laboratory, we

have extended the measurements of fast-ion slowing-down rates and neutron

production both parallel and antiparallel to the electric field, to 25 keV.

Again, the results appear classical„

Fast-ion slowing-down rates are relatively insensitive to Z ; pitchangle

scattering, on the other hand, depends strongly upon the impurity

ions, and measurements of scattering times can be used to determine Z «•

We have measured the 90° scattering times (actually, the effective scattering

angle is nearer 80°) for both tangentially injected beams and nearperpendicular

ly injected beams. Figure 2 shows the signal increase in time

for injection at 83° to the plasma

current and tangential viewing by

d

: INJ. SS'TOIpleOkAljBEAM.MkeV

FAST NEUTRALS -TANGENTIAL 0° INTO 0 +

t(ms)

!2keV

!3keV

the fast neutral detector. The shape

of these pitch angle scattering data

is clearly dependent upon chargeexchange

losses. With an analytic

approximation to the Fokker-Planck

equation we can reproduce the shape

of these scattering data quite well

for charge-exchange times T = 6-9

msec and Z = 4-6, the latter in

good agreement with laser temperatureresistivity

values but somewhat more

than spectroscopic values. The most

sensitive test for Z __ would have

been a measurement o *f i

: the absolute

flux. In any case, the important

point of these data is that 90° scattering

times are about the same magnitude

as charge-exchange and slowingdown

times. This implies that the

FIG. 2. Fast-neutral intensity versus time for

injection at 83° to the plasma current and tangential

viewing by the fast-neutral detector.

effects of the "loss-region" existing near the boundary between trapped

and counter-circulating particles can be very severe on small machines with

low poloidal magnetic field. 3 ' 4 Even with tangential injection of 14-15

keV D° beams, the fast neutral signal observed at 90° is, for antiparallel

injection, considerably reduced in both energy and intensity, from that

for parallel injection. For ATC, the trapped-particle-circulating-


80 BOL et al.

particle boundary (v„/v = /2 r/B) corresponds to an angle of about 60°

relative to the plasma current Loss region effects would, therefore, be

much more severe for near-perpendicular injection than for tangential

injectiono

We have used a single beam source to inject into ATC at 83° and 97°

relative to the plasma current, i0e0, a fixed beam line 7° off the perpendicular

for both directions of the plasma current. In this geometry, the

fraction of the neutral beam input which is captured by the plasma is

reduced relative to tangential injection as is that portion of the captured

beam which is initially on confined orbits. Taking into account

the beam composition at full,one

half and one third energies, we

calculate that fraction of the

neutral beam power captured on

initially confined orbits as 56%.

This compares to about 80% for

tangential injection„ As we

observe an ion temperature rise

in Fig„ 1 of ^ 1 eV/kW, we would,

on the basis of capture efficiency

coupled with the neutral

beam power of 70 kW, expect some

40 eV ion temperature rise in

Fig. 3. That we see a ion tem-

FIG. 3. Ion temperature increase due to beam

injection at 83° to the plasma current. The

effective beam power input is ~20 kW.

DEUTERIUM

/=70kA

J'JQ b-l'/of}

t(ms)

26 28

perature rise of only 20 eV, we take to imply that essentially one half of

the neutral beam energy otherwise directed to the ions has been carried

into the loss region„

For injection at 97° relative

Particle Orbits Which Hit the Limiter in ATC (Axes are

Labeled in kev)

to the plasma current, the heating

efficiency is considerably reduced

due both to bad initial orbits and to

the proximity of the "loss-region" at

the boundary between trapped and

counter-circulating particles. The

severity of this latter effect is

indicated by Fig. 4, which shows the

calculated loss-region boundary for

various particle energies and initial

radial positions Following the

procedure discussed above for 83°

FIG. 4. Loss-region computations for ATC

(Courtesy of J. A. Rome, ORNL) with initial point

of ionization, r/a, as the parameter. Particles

with Ex, E||, greater than the values indicated

by the solid lines,intersect the limiter.


injection we calculate, for 97°,

the fraction of neutral beam power

on initially confined orbits to

be 27%„ The neutral beam power of

70 kW and capture efficiency of

27% thus yields 19 kW input to the

plasma. Under these conditions

where AT. < 5 eV, it would appear

FIG. 5. Ion temperature versus time for injection

at 97° to the plasma current. Poor initial orbits

and the proximity of the loss-region at ~ 120° has

reduced ATj to £ 5 eV.

IAEA-CN-33/A 4-1 81

200

190

180

170

Tj(eV)

160

150-

140

130

—i 1

-*- HV = l4.5kV

-6- HV= 0

INJ. 97° TO Ip

D° INTO D*

20 22

t(ms)

HV 0N-

24 26 28 30

that the loss region has effectively removed some three quarters or more of

the energy which would, without loss regions, flow into the ions. In this

case we observed essentially no ion temperature increase, as shown by Fig, 5,

The difference in the fast-ion energy distribution for 83° and 97°

injection, as indicated by the neutral flux emerging tangentially, is shown

in Pig, 6, With 83° injection, ions scatter and emerge as neutrals with

energies up to and slightly above the injection energy. At 97°, the fast

neutrals can be followed only up to 12 keV, and the intensity is about 2

orders of magnitude below that for 83° injection.

Even under these conditions of somewhat more unfavorable velocity

distribution for the fast ions 7 (v^/v,, » 1) we have not observed any beamrelated

instabilities. The rather poor heating efficiency is, of course,

K)3

10 -

:

:

N(E)

_

;

-

-

"

_

-

r

-

1 1— — r T 1 1 1 I :

FAST ION ENERGY DISTRIBUTION :

E0M4.5keV ;

x ^ NX 0° INTO D +

X

^ ^>

\

+

\ \

\ \

> i

\

\

\ \ X

\ \ \83°T0Ip

\

X \

\

\

\ 97°T0Ip \

\ \ \ \

\ \ +

\

6 i 10 i 12 i 14 i J 16 18 i 20

EjUev)—•

a direct consequence of our low

poloidal field, coupled with the short

scattering times for Z z 5 plasmas.

Since the fractional hot-ion drift

excursions are, for fixed particle

momentum, inversely proportional to

plasma current, there is good reason

to think that near-perpendicular

injection will, for larger plasma

current, approach the efficiency for

heating attainable with parallel

injection.

FIG. 6. Fast-ion energy distribution observed

tangentially for the two near-perpendicular injection

paths at 83° and 97° to the plasma current.


82

BOL et al.

REFERENCES

{1} BOL, K., et al., Phys. Rev. Lett. 32 (1973) 661.

{2> COOPER, W. S., BERKNER, K. H., and PYLE, R. V., Bull. Am. Phys. Soc.

18^ (1973) 1321.

(3> STIX, T. H., Plasma Physics 14_ (1971) 367.

{4} ROME, J. A., et al., Sherwood Theory Meeting, University of

California, Berkeley, California, 1974 (to be published).

{5} CORDEY, J. G., et al., Nuclear Fusion 14_ (1973) 441.

{6> DAWSON, J. M., FURTH, H. P., and TENNEY, F. H., Phys. Rev. Lett. 26_

(1971) 1156.

{7} CORDEY, J. G. and HOUGHTON, M. J., Nuclear Fusion 13 (1973) 215.


EXPERIMENTS ON THE ADIABATIC

TOROIDAL COMPRESSOR*

t

K. BOL, J. L. CECCHI, C. C. DAUGHNEY, F. DeMARCO ,

R.A. ELLIS, Jr., H. P. EUBANK, H.P. FURTH, H. HSUAN,

E. MAZZUCATO, R. R. SMITH

Plasma Physics Laboratory, Princeton University,

Princeton, N.J.,

United States of America

Abstract

IAEA-CN-33/A 4-2

EXPERIMENTS ON THE ADIABATIC TOROIDAL COMPRESSOR.

Magnetic compressional heating of a tokamak discharge has been demonstrated successfully in the

Adiabatic Toroidal Compressor (ATC). In addition to these investigations of compressional heating, other

basic measurements have been made on ATC recently. These measurements are of interest because the ATC

incorporates an air-core transformer and dispenses with the usual copper shell, two features likely to be found

on future larger devices with smaller aspect ratios. The following topics will be discussed: (1) characteristics

of the uncompressed discharges in ATC, including the dependence of £p on discharge parameters, bolometric

measurements of the energy balance, measurements of the concentration of impurities; (2) MHD-behaviour

and attempts at stabilization of the m = 2 kink-tearing mode.

I. INTRODUCTION

Magnetic compressional heating involving a large change in major radius

has been successfully demonstrated in the Adiabatic Toroidal Compressor

(ATC). A general discussion of slow adiabatic compression has been given

by Furth and Yoshikawa-'- and the first experimental results obtained on ATC

have been published.2-4 Typical pre-and post-compression parameters are

listed in Table I. Two of the distinctive features of ATC, the use of an

air-core transformer and the absence of a conductive liner, are very likely

to be found on future larger devices with smaller aspect ratio, so that the

detailed investigation of the precompression plasma of ATC is of special

interest. The design of ATC has also permitted the study of plasma heating

by injection of high-powered neutral beams.^>6

In section II, the ATC device is described and compression results are

summarized. In Section III, some characteristics of the uncompressed ATC

discharges are considered including: the scaling of the poloidal beta, 3p ,

with discharge parameters; bolometric measurements of energy balance; and

the concentration of impurities. In section IV, the MHD behavior and

attempts to stabilize the kink-tearing mode are discussed.

II. THE ATC DEVICE

The major radius compression in ATC is produced by increasing the

vertical equilibrium field, Bv , in a time which should be long compared

with the particle collision time and short compared with the energy confinement

times. For a plasma assumed to obey infinite-conductivity MHD theory,

* Supported by USAEC Contract AT(ll-l)-3073.

T Present address: Laboratori Gas Ionizzati, Frascati (Italy).

83


84 BOLet al.

VERTICAL w '

'

PRE-

COMPRESSION

POST-

COMPRESSION

FIG. 1. Vertical equilibrium and Ohmic transformer field patterns.

-77 cm MAJOR RADIUS COILS TOROIDAL FIELO COILS

116cm ID ,142cm 0 0

38cm MAJOR —

RADIUS PLASM*

AFTER

COMPRESSION

90 cm MAJOR RADIUS

-PLASMA BEFORE

COMPRESSION

FIG. 2. Cross-section of ATC.

D OHMIC HEATING COILS

• i SHAPING AND COMPRESSION

COILS


IAEA-CN-33/A 4-2 85

FIG. 3. Time variation of major radius, plasma current, vertical field current, and Ohmic transformer

current during a compression discharge.

simple scaling laws have been derived which give the plasma behavior for

various modes of compression. The compression in ATC is carried out in a

static toroidal field for which the following relations hold if C = Ri/Rf ,

where R^ is the initial major radius, and Rf is the compressed major radius

and i and f denote the initial and compressed states, respectively,

Tf/Ti = C 4 ' 3 ; nf/ni = C 2 ; af/a± = C - - 1 -/ 2 ; and If/Ii = C where T, n, a,

and I denote temperature, density, minor radius, and plasma current

exclusive of skin current.

The magnetic field configurations of the vertical equilibrium (and

compression) field and of the ohmic transformer field are shown in Fig. 1

for the following states: just prior to the discharge; during the precompression

phase; and during the compression. The physical arrangement of

the poloidal field coils and a cross section of the vacuum vessel and of a

toroidal field coil are shown in Fig. 2. The standard tokamak diagnostic

systems are in routine use on ATC. The vacuum vessel is a stainless steel

bellows without an insulating break. Originally four pumps with a pumping

speed of * 2000 liters/sec produced a base pressure of 2-4 x10 Torr after

discharge cleaning with several thousand 2 msec 20 kA discharges in a mixture

of hydrogen and neon. It has proved possible to obtain satisfactory discharges

with only one pump although the base pressure increased as the

number of pumps was reduced. The limiters for most of the discharges

presented here were molybdenum top and bottom rails and inner and outer

segments which conformed to the shape of the vacuum vessel. Only the inner

limiter segments show significant erosion which occurs after compression

and is attributed mainly to the effect of the high densities and thermal

energies of compressed discharges which almost invariably terminate on the

inner limiters. Recently it has been possible to use stainless steel

limiters without any evidence of either excessive impurities in the

discharge or damage to the limiters.

Figure 3 illustrates the operating cycle of ATC. After preionization

by a 100 kHz oscillator, the transformer and vertical field windings are

energized by the currents IQK an d *v which respectively induce the plasma


86 BOLet al.

Major Radius R

Minor Radius a

Toroidal Field Bt

Plasma Current Ip

Ion Temperature T^

Electron Temperature Te

Average Electron Density ne

ION TEMPERATURE INCREASE

WITH COMPRESSION

TABLE I. Typical ATC Parameters

Before Compression After Compression

90 cm

17 cm

15 kG

60 kA

200 eV

1 keV

1-2 x 10 13 cm" 3

T C

10

9

8

7

6

5

4

T 0 3

2.5

2

38 cm

10 cm

46 kG

150 kA

600 eV

2 keV

10 14 cnr 3

i i l l —I—" T 1 1

ELECTRON TEMPERATURE J

INCREASE WITH COMPRESSION

o =THOMSON SCATTERING

• *BREMSSTRAHLUNG

: /©" :

r /f

/ / R o

/Y R <

1.5

1 A

6 7 8 r i .

2.5

, 1

3

i i 6 i 7 i 8

FIG. 4. Observed scaling of electron and ion temperatures.

current and determine the major radius. The transformer field becomes

large for R < 60 cm which requires that the transformer be current-biased

so that IQH is near zero at the time of compression, the precise value being

an important compression parameter. The IQH current waveform is determined

by the discharge of capacitor banks and the Iv waveform up to compression

is determined by an amplifier which also provides control of the major

radius of the plasma current by a feedback loop involving an array of magnetic

probes as position sensors. At a pre-determined time a capacitor bank

is discharged into the Bv windings, rapidly increasing Bv and causing the

compression. The compression field reaches a peak in about 2 msec and

slowly decays. The compressed plasma equilibrium is governed by the decay

of the currents in the Bv and OH windings, which are not controlled externally.

The discharge in Fig. 3 slowly decreased in major radius until it

terminated in a disruptive instability caused by contact with a limiter

protecting the inner surface of the vacuum vessel.

Table I summarizes typical parameters for uncompressed and compressed

discharges in ATC. The density and the ion temperature generally follow

the expected behavior (n - C^ ~ 5 , T, ~ C*/3

~ 3) whereas the electron

temperature tends to be directly proportional to the compression ratio.

Figure 4 shows that this difference in behavior also occurs for partial


-

(0)

1

IAEA-CN-33/A 4-2

>

"~~"—^v

Ip

20 , .30

Po * 3»l0 5 torr H2

FIG. 5. Typical behaviour of plasma current, Ip; loop voltage, V; average electron density < ne> ; and

peak electron temperature, T ax .

compressions. The difference presumably reflects the fact that the compression

time Te is intermediate with respect to the ion and electron energy

replacement times T^ and T£ , respectively: T i > T c ~ T e •

The total plasma current should ideally be such that the poloidal flux

linked by all of the plasma ring remains constant. Usually there is some

decrease in this external flux during compression, so that the total current

undergoes a somewhat smaller increase than would be expected in the ideal

case.

^"^

III. SOME CHARACTERISTICS OF THE ATC UNCOMPRESSED DISCHARGES

The time behavior of the loop voltage, plasma current, average density,

and peak electron temperature of a typical ATC discharge are shown in Fig.

5. The electron density continues to increase long after the ionization of

the filling gas, indicated by the break in the density curve shortly after

the start of the discharge. This is an indication of a large influx of gas

during the discharge which has been shown to be mainly hydrogen from the

vicinity of the limiter. Figure 6 shows two temperature and density profiles

which were taken (with Thomson scattering) during later portions of

the discharges when a quasi-steady state has been reached. The electron

temperature profile is always more narrow than the density profile and the

average temperature is relatively independent of the density. For the profiles

shown in Fig. 6, the toroidal field and plasma current were the same;

the electron temperature profiles are almost identical although the

densities differed by a factor of two.



87


BOL et al.

8510 6519 SOOE*ll

T-Z8.0 MS CM-3.,

D TEMP

X DENS

70.0 88.0 RADIUS 110.0

87P2 8B10 200E+11

T-30.0 MS CM-3-,

0 TEMP

X DENS

70.0 M.5 RADIUS 110.0

FIG. 6. Radial profiles of electron density and temperature. The plasma current (60 kA), the loop voltage,

(3V), and the toroidal magnetic field (16 kG) were the same in both.

The measured resistance of the plasma column is always 2 to 5 times

larger than the value calculated from the temperature profiles assuming

a Z = 1 plasma and neglecting trapped-particle effects. Assuming that

the increased plasma resistivity is due to an enhancement of the collision

frequency which is independent of the radius and affects trapped and untrapped

particles alike, we found that trapped-particle effects are unimportant.

The poloidal beta, gp = 8ir < nkTe >/Be(a) 2 , and the safety factor,

q(r) , can be calculated from the Thomson scattering profiles. For the

computation of q , the current density is assumed proportional to T 3 ' 2 #

In Figs. 7 and 8 the results obtained in the following ranges of parameters

0.8 2.5 x 10 13 cm -3

are summarized: 12 < B < 20 kG

500 < Temax < 1500 ev ; 50 < Ip < 100 kA 7 85 < R < 90 cm; and a * 17 cm.

As shown in Fig. 7a, in which gp/< ne > is plotted against q(0) for nearly

constant values of q(a) , q(0) is seen to be a significant parameter

because for q(0) > 1 the poloidal beta seems to be proportional to the

density and for q(0) < 1 , gp/< ne > decreases almost linearly. Similar

behavior is exhibited in Fig. 7b in which data obtained with values of q(a)

between 3.5 and 7.0 are included. These data yield a value of the ratio

Bp/< ne > equal to 2.5 x 10 1Z > cm -3 for q(0) > 1 .

The electron energy confinement time, Tg , defined as the ratio of the

plasma electron energy to the Ohmic power input is proportional to the ratio

of $p to the resistance, ft , of the column. Therefore, in our case Tg is

proportional to < ne >/ft if q(0) > 1 and is also directly proportional to

q(0) if q(0) < 1 . This dependence of Tg is shown in Fig. 8.


IAEA-CN-33/A 4-2 89

FIG. 1. Dependence of the ratio of the poloidal beta to the average electron density (£D/< n >) to the safety

factor, q(0). The safety factor at the limiter was kept almost constant in (a) and varied from 3. 5 to 7 in (b).

If it is assumed that the plasma resistivity has the classical dependence

on Te , then TE in ATC has a similar dependence on Te and < ne > to

that reported in Ref. 5. However, in ATC, Tg is also inversely proportional

to the resistivity enhancement factor and also decreases with q(0) as q(0)

falls below one.

Gross properties of the energy balance in ATC have been investigated

in terms of the energy loss to the limiter and through the plasma surface.

The energy loss associated with charged particle diffusion and thermal conduction

was monitored by measuring the temperature of the limiters. The

radiation and the charge-exchange losses were detected by a bolometer

devised out of a thick film flake thermistor, which had a time resolution

of = 1 msec. Peak plasma currents ranged from 40 kA to 90 kA . Some new

findings are that (1) of the 60-80% of the total energy going to the

limiters, the greatest part arrives during the steady state phase of a

normal discharge. (2) At the termination of the discharge, the energy loss

occurs mainly through the surface via radiation and/or charge-exchange.

The amount of surface energy loss at the termination is larger than the

stored plasma kinetic energy and is shown to include a large portion of the

poloidal magnetic energy for a current larger than 50 kA . In addition to

the above findings, our measurement has confirmed the results of other

existing tokamaks.°> 7 These results are as follows: (1) The charged


90 BOLet al.

.01 .02 .03 .04 .05 .06

min{q


1. MHD Behavior

IAEA-CN-33/A 4-2 91

IV. MHD BEHAVIOR AND EXPERIMENTS WITH m = 2 MODE

Poloidal magnetic field perturbations have been observed on ATC and are

qualitatively similar to those observed on other devices. > 10 The slowly

changing, oscillating kink-like modes have structures of the form

A exp[i(m6 - nd> - to t)1

mn r L Y mn J

where 9 and are the poloidal and toroidal angles, respectively, m and n

are integers, and u^ is the angular frequency of the m , n mode. Perturbations

with m = 2, 3, 4 and n = 1 have been observed with frequencies in the

range 5-25 kHz , the m number being determined with an array of poloidal

field pickup coils spaced 30° apart in the poloidal direction on the outer

180° of the ATC, and the n number with 4 coils spaced 90° apart in the

toroidal direction.

The occurrence of the modes has been compared with tearing mode

theory, x assuming the current density to be proportional to Tg' z , and

choosing that one of the four current profiles given in Ref. 11 which best

fits the data. In general, the theoretical prediction is that as the

current is raised a mode may first appear when the rotational transform near

the magnetic axis resonates with the mode; i.e., 2TT/X = m . When the resonant

surface moves out to large enough radius, the mode becomes stable, the

precise limit depending on the current profile, although for any profile

the m = 2 is unstable out to larger radii than the m = 3 . Our findings

are that the theory accommodates the m = 2 reasonably well, but that the

m = 3 can still occur when the resonant surface is beyond the theoretical

limit. xz

2. Experiments With the m = 2 Mode

It is in general possible to pass rapidly through the current range in

which modes with m > 2 are unstable, and it is presently unclear that these

modes have much effect on plasma transport. The m = 2 mode, on the other

hand, even when it does not lead to the disruptive instability-*--^, 14 still

has a deleterious effect on plasma confinement, and its stabilization or

avoidance must be an important goal of tokamak research. Operation at

currents above the unstable range may be a possibility-'--'-'-'-^ but it has received

only brief attention on ATC. The other approach, stabilization of

the mode, has been attempted with feedback and pulsed fields. These

experiments are discussed below.

(a) Feedback experiments. Figure 9 shows one arrangement of control loops

and magnetic pickup coils. The control loops generated a poloidal magnetic

field having m = 2 , n = ±1 symmetry, and unavoidable higher harmonics.

However, the results were insensitive to the details of control loop arrangement:

essentially the same results were obtained using only the two outermost

control loops, and again with two pairs of loops outside the vacuum

vessel that subtended approximately 35° each in major azimuth. The pickup

coils were located on the midplane and oriented to minimize their mutual

inductance to the control loops; opposite coils were connected in pairs in

order to cancel the main (n = 0) poloidal fields, as well as the m = 4 ,

n = 2 harmonic that may accompany the m = 2 . The signals from two such

pairs 90° apart in major azimuth were added in suitable proportion to obtain

a signal shifted by an arbitrary amount from a reference phase tied to the

mode. After going through a series of phase and amplitude compensation

circuits, the signal was fed to a half megawatt amplifier, transformercoupled

to the control loops. The compensation was necessary because the

lowest frequency pole in the equivalent circuit of the vacuum vessel lies

at f = 10 kHz , within the range of frequencies spanned by the m = 2 mode.


BOL et al.

SECTION AA'

Bfl(ANTIN00E) « B«(b) - Bfl(d) "I

NOTE : J J J \ SENSORS

Bfi

-

. o

-

\ +

.

90*

o


j 180*

"N?

*270«

+ (0.6)

/ ^ %

\ ' '

W°'*

.90* + 180/ 270* 300* x

FIG. 10. Mode frequency and amplitude changes as function of feedback loop phase shift. Curves are least

square fit of sinusoids to data.

+

o


UJ

0

a •

o 50 _ ,+ v

N ^

N^ (b)

2

o

UJ gioo

_i

u. o •

„ '50 -

< _i

UJ •


94 BOLet al.

control field at the plasma surface of about half the mode amplitude secures

locking; however, the threshold is not sharply defined: the mode may jump

in and out of synchronism before locking to the control signal, and is

locked more easily when saturated than when still growing.

Whereas the threshold shows little frequency dependence, Fig. 11 shows

the phase between mode and control signal to vary markedly with frequency.

The phases have been corrected for the vacuum vessel, and in addition the

phase of the pickup coils located near the control field nodes has been

shifted by 90° to make it correspond to the coils near the antinodes. Thus

the divergence of the points at low frequencies implies that the locked

mode is no longer a single rotating wave; a difference in amplitudes

observed at the two locations shows that a standing wave component is

generated which becomes dominant at frequencies below ~ 0.2 fmode » tne

larger amplitude occurring at the control field antinodes. (Note that the

pickup coils should not couple to the equilibrium distortions of the

magnetic surfaces produced by the control fields.)

It is interesting that when mode-locking occurs, it apparently takes

place throughout the plasma within a fraction of a cycle, according to the

signals obtained from the pickup coils and from x-ray detectors monitoring

emission from the plasma core. " Presumably, then, the effect propagates

through the plasma on the hydromagnetic time scale; skin penetration times

would be orders of magnitude longer. The implication of this result would

seem to be that the saturated m = 2 oscillations do indeed result from a

rotating quasistable helical equilibrium, •*• and that the shear free rotation

around the minor axis is due to an appropriately varying radial electric

field which compensates for the variation of the electron diamagnetic drift

frequency with radius.

FIG. 12. Suppression of mode rotation by control pulse. 12-a: (a) Plasma voltage, -2V/cm; (b) Magnetic

pickup signal (unintegrated); (c) Plasma current, 20 kA/cm. 12-b: (e) Control loop current, 200 A/cm;

(f) and (g) integrated magnetic pickup signals from control field anti-node and node positions, respectively.


IAEA-CN-33/A 4-2 95

FIG. 13. Detail of rotation arrest and mini-disruptions. 13-a: (a), (b), and (c) Plasma voltage, pickup

signal, and plasma current respectively. 13-b: (d) Plasma voltage, 1 V/cra; (e) control loop current,

200 A/cm; (f) and (g) integrated pick-up signals from control field node and anti-node positions, respectively.

Arrows show when mode was in phase with control field. Two mini-disruptions occur in the quiescent interval.

Finally, the relative ease with which mode-locking occurs also suggests

that when two modes are present simultaneously—as an m = 1 and 2 , or an

m = 2 and 3—they might lock together as soon as one of the pair has reached

large enough amplitude. Such synchronism between the m = 2 and 3 has been

observed on the ST Tokamak, where the m = 2 was detected by means of x-ray

emission and the m = 3 by magnetic pickups.22

(c) Mode-locking and stabilization by pulsed fields. The most usual

result of passing a current pulse of sufficient strength through control

loops generating anm=2 , n = 1 magnetic field component is mode-locking

at zero frequency. This is shown by Fig. 12, where the mode amplitude is

still small when rotation is stopped, but where the mode appears fully

saturated when rotation is resumed. The phase of the stationary mode with

respect to the applied field is difficult to determine precisely, because

transient perturbations accompany and obscure the locking phenomenon. In

general, it appears that the field of the locked mode may lag the control

field by any phase angle from 180° - 360° . It is not clear how this

result should be related to the measurements shown in Fig. 11. It may be

noted that the pulsed experiments were done with the external loops because

the internal ones could not withstand the electromechanical forces.

Discharges tend to be unfavorably affected when mode rotation is

suppressed: in high current discharges which are limited by the disruptive

instability, onset of the disruption occurs earlier, on the average, when

rotation is suppressed; when the control field is raised above the level


96 BOLet al.

FIG. 14. Mode stabilization by control pulse. 14-a: Zero control field (e). 14-b: With control field,

200 A/cm.

needed to stop rotation, small-scale disruptions (Fig. 13) occur with

increasing frequency. Furthermore, plasma density, which ordinarily rises

more slowly—if at all—when an m = 2 kink is present than when it is not,

frequently dropped by - 10% during the 5-10 msec that rotation was

suppressed in typical cases.

Under certain conditions it appears that the mode can indeed be

stabilized by the control field. Thus, Fig. 14 shows a case in which the

rotation persists, but the amplitude slowly decreases to the noise level

over some tens of cycles. We believe that one of the preconditions for this

effect is that the mode is not too violently unstable, but a more precise

prescription cannot yet be given.

REFERENCES

[l] FURTH, H. P., YOSHIKAWA, S., Phys. Fluids 13_, 2593(1970).

[2] BOL, K., et al., Phys. Rev. Letters 29_, 1495(1972).

[3] BOL, K., et al., Proceedings of The Third International Symposium

on Toroidal Plasma Confinement (Garching bei MUnchen, 1973), Max

Planck Institut fur Plasma Physik, Paper B-12.

[4] ELLIS, R. A., et al., Proceedings of The Sixth European Conference on

Controlled Fusion and Plasma Physics (Moscow, Joint Institute for

Nuclear Research, 1973), Vol. 1.


IAEA-CN-33/A 4-2

[5] ARTSIMQVICH, L., et al., Plasma Physics and Controlled Nuclear Fusion

Research (International Atomic Energy Agency, Vienna 1969), Vol. I,

p. 157.

[6] GORELIK, L. L., MIRNOV, S. V., NIKOLAEVSKY, R. G. , SINITSYN, V. V.,

Nucl. Fusion 12, 185(1972).

[7] DIMOCK, D. L., EUBANK, H. P., HINNOV, E., JOHNSON, L. C, MESERVEY,

E. B., Nucl. Fusion 33, 271(1973).

[8] HINNOV, E., HOFMAN, F. W., Journal Optical Society of America 53,

1259(1963).

[9] MIRNOV, S. V., SEMENOV, I. B., At. Eherg. 30_, 14(1971) [Sov. At. Energy

30, 14(1971)].

[10] HOSEA, J. C, et al., in Plasma Physics and Controlled Nuclear Fusion

Research (IAEA, Vienna, 1971) II, p. 425.

[ll] FURTH, H. P., RUTHERFORD, P. H., SELBERG, H., Phys. Fluids lb_, 1054

(1973).

[l2] We are indebted to S. VON GOELER for alerting us to the possibility

on the basis of similar observations on the ST Tokamak.

[13] BOWERS, D. L., et al. , Plasma Physics JL3_, 849(1971).

[14] ARTSIMOVICH, L. A., Nucl. Fusion 2, 215(1972).

[15] VLASENKOV, V. S., et al., Garching, Munchen Conference (1973) paper B2.

[l6] THOMASSEN, K. I., Private communcation.

[17] JOBES, F. C, HOSEA, J. C., Garching, Munchen Conference (1973)

paper B14.

[l8] VON GOELER, S., Invited paper, APS Plasma Physics Conference,

Albuquerque (1974).

[l9] VON GOELER, S., STODIEK, W., SAUTHOFF, N., Phys. Rev. Lett, (to be

published).

[20] SMITH, R. R., APS, Physics Conference, Albuquerque (1974).

[2lJ RUTHERFORD, P. H., FURTH, H. P., ROSENBLUTH, M. N., Fourth Conference

on Plasma Physics and Controlled Thermonuclear Research, Madison,

Wisconsin, 1971, Paper CN-28/F-16.

[22] VON GOELER, S., Private communication.

97


DISCUSSION

ON PAPERS IAEA-CN-33/A 4-1, A 4-2

B.P. LEHNERT: I should like to comment on the question of disruptive

instability. There is an upper limit nc^ 10 19 /a per cubic metre on the plasma

density n of a tokamak column of minor radius a for the penetration of hot

neutral particles into the plasma. Now, there are 11 papers in the Proceedings

of this Conference on hot tokamak and tokamak-like plasmas and

none of them have shown for certain that the limit nc can be exceeded. If it

transpires that the limit is really important for tokamak stability and

equilibrium, difficulties may arise when scaling up to full reactor size,

for which n> 10 nc with the models discussed so far (see also Nucl. Fusion

_13 (1973) 781).

As this critical density is approached from below, strong changes should

take place in the spatial equilibrium pressure distribution owing to ionization.

Moreover, Professor Razumova has shown that the disruptive instability is

associated with magnetic disturbances. It may be that the critical density

is related to the instability and it would therefore be interesting to study

this problem in greater depth, trying to determine what special instability

mode is involved.

E. MAZZUCATO: It is true that up to now average plasma densities

have never been found much greater than nc in standard tokamak discharges.

This seems related to the fact that with Ohmic heating alone it is impossible

to increase the plasma density without, at the same time, producing narrow

temperature profiles and magnetic disturbances. As for the nature of the

disruptive instability, I think we must wait for further clarification of this

phenomenon.

R.J. TAYLOR: In this connection I would like to make a comment on

the disruptive instability and its relation to the "high-density limit" in

ALCATOR. If we operate with q ~ 2.5, we are close to the disruptive limit

even if the machine is clean. If we increase the density from ~ 2X 10 13 cm" 3

to ~ 2 X 10 14 cm" 3 and slightly increase q, we see no disruptions. The disruptions

are more dependent on the cleanliness of the machine and on q

than on the density.

99


IAEA-CN-33/A 5-1

PLASMA CONFINEMENT IN THE ORMAK DEVICE*

L.A. BERRY, J. D. CALLEN, J. F. CLARKE, R.J. COLCHIN,

E. C. CRUME, J. L. DUNLAP, P. H. EDMONDS, G. R. HASTE,

J. T. HOGAN, R.C. ISLER?, G. L. JAHNS, N.H. LAZAR,

J. F. LYON, M. MURAKAMI, R. V. NEIDIGH, W.R. WING

Oak Ridge National Laboratory, Oak Ridge, Tenn.,

United States of America

Abstract

PLASMA CONFINEMENT IN THE ORMAK DEVICE.

Experiments in two different operating regimes of the Oak Ridge Tokamak (ORMAK), with Ohmic heating,

are discussed. The confinement characteristics of a broad-profile discharge in a low-density regime and a

peaked-profile discharge at high density are described in detail. Through charge-exchange analysis, particle

diffusion coefficients for these discharges are evaluated, and it is shown that the particle diffusion is not a

significant energy loss for the present operating conditions. Detailed examination of the radial power flow for

the ions indicates that the dominant loss from the core is heat conduction, the form (and magnitude) of which

is consistent with the neoclassical predictions, provided local collision frequencies are enhanced by an amount

comparable to that inferred from the resistance anomaly. Examination of the electron power flow suggests

anomalous behaviour of the electrons. However, for the broad-profile discharges, average confinement parameters,

such as Bn or the energy confinement time, are reasonably consistent with pseudoclassical predictions.

With increasing electron density, overall confinement improves, in spite of profile peaking (fip ~n"e/I). The

resistance anomaly is observed to scale roughly as I a /ne, where a ~ 1. At high densities, the volume-averaged

effective ionic charge, < Z.efp res, inferred from resistance anomaly, shows a rough agreement with

< Z 'eff > meas* i n f erre d from direct measurements (vacuum-ultraviolet spectroscopy, soft-X-ray, and chargeexchange

analysis of pitch-angle-scattered fast ions in the neutral-beam injection). However, with decreasing

densities, < Z,eff>res becomes (by a factor £ 2) higher than < Zeff >meas, suggesting that the possibility of

turbulent enhancement cannot be excluded.

1. Introduction

ORMAK is a low aspect ratio tokamak at the Oak Ridge National

Laboratory. Details of operation and plasma parameters have been reported

previously.[1,2,3] In this paper we discuss characteristics of typical discharges

and their transport properties in the device since the neutral beam

injector installation. Effects directly related to the injection are described

in a companion paper.[k] Some machine parameters relevant to these

experiments are the following. The major radius, R0, is 80 cm, and the

limiter radius, a, is 23 cm (giving the aspect ratio of 3.5)- The toroidal

magnetic field, &rj, was varied from l4 kG to 18 kG. The values of the flattop

ohmic heating current, I, were varied from 60 kA to l60 kA with the

typical duration of 80 ms. The working gas was usually hydrogen. Linear

average electron density, ne, measured with a 2 mm microwave interferometer,

ranged from 0.5 to 3.5 x 10 13 cm -3 . Central electron temperatures, Te(0),

measured by ruby-laser Thomson scattering, varied from 200 eV to 1200 eV,

and central ion temperatures, Tj_(o), measured with parallel and perpendicular

charge-exchange neutral analyzers, ranged between 150 eV and 350 eV.

* Research sponsored by the US Atomic Energy Commission under contract with the Union Carbide Corp.

~ University of Florida, Gainesville, Florida.

101


102 BERRY et al.

2. Discharge Characteristics

The measured plasma profiles (especially electron temperature profiles)

exhibited considerable sensitivity to the experimental conditions chosen,

and to some extent to externally uncontrollable conditions, such as wall and

limiter conditions. For example, on several occasions we observed hollow

electron temperature profiles persisting for a long time (>50 ms), which

were apparently associated with a contaminated discharge chamber wall.

Under more normal conditions, however, plasma profiles can be represented by

two types: a peaked profile (for convenience, we call this profile type A)

in the high density regime, and a broad profile (type B) in the low density

regime. Examples of these profiles are shown in Fig. 1. The radial distributions

of electron temperature and density as measured by Thomson scattering

at four different times during the discharges are plotted. The initial conditions

for the discharges differed only in initial hydrogen gas pressure.

Both discharges were macroscopically stable and reproducible. The boundary

pressure between type A and type B shows secular changes with wall cleaning,

and depends on plasma current. The other distinguishable feature of these

discharges is poloidal magnetic field (or Mirnov) oscillations (shown in

Fig. 2), as measured by small magnetic pickup loops outside the plasma. The

•to o to 20 T

—•/•(cm) I

I'M.

FIG. 1. Comparisons of the radial distributions of electron temperature and density for a type-A and a type-B

discharge.


IAEA-CN-33/A 5-1 103

10 msec

FIG. 2. Typical MHD (poloidal-field -fluctuation) behaviour for the type-A and type-fi discharge shown in Fig. 1.

10

5

V

-ifik.

V

7"!.^

(b)_

20 40 60 80 100

/(ms)

~ 4

E

—•— TYPE A (/o=4.8x10~ 4 )

~o~ TYPE B (p= 4.4 xlO" 4 )

[

-TYPE

_ A B

A &

• O

\ 1

Vr

i

A

EQUIL.

1 \

1 1

_

LASER PROFILE!

THEORY _

*_

N —

1 1*

0 20 40 60 80 100

/ (ms)

FIG. 3. Other characteristics of the type-A and type-B discharge, (a) plasma current, I; (b) loop voltage, V;

(c) line-average electron density, n"e; (d) plasma shift, A; (e) central ion temperature, Tj(0). The magnetic

axis positions calculated from the shift measurement compare well with the axis position determined by the

laser profile measurements. The laser firing timings are shown by arrows in the current trace.

type A discharge is accompanied by large amplitude oscillations with low

poloidal mode number (usually m = 2, though sometimes 3)- The type B discharges,

on the other hand, exhibit low level, higher m-number oscillations.

In Fig. 3 other characteristics of the type A and type B discharge are

compared. After breakdown and initial current buildup (supplied by a capacitor

bank) the ohmic heating current, I, is driven to the desired level

(95 kA in this case) and held constant by a feedback system until the discharge

is clamped at 60 ms and undergoes inductive decay. In general, type

A discharges have a slower buildup with a higher loop voltage, but once they

reach the flat current stage, the voltage is lower than in type B discharges.

The electron density reached during the initial few milliseconds tends to be

proportional to the gas filling pressure. In a type B discharge the density


104 BERRY et al.

decreases monotonically with time, while a type A discharge often exhibits a

second peak at about 25 msec. The plasma position (center of the outermost

magnetic surface) as measured with a set of in-out loops is shown in Fig. 3

(d). The magnetic axis positions inferred from this measurement are in good

agreement with those from the laser profile measurement. A substantial

inward excursion during the buildup is characteristic of a type A discharge.

The ion temperature near the center (Fig. 3le)), as measured by charge

exchange analysis, is higher in a type A discharge because of the higher

density.[2] Although the mechanism that creates two different profiles

with a small variation of initial conditions is not well understood, formation

of a peaked profile appears to be related to surface cooling due to

either neutral gas or impurity influx from the wall.[5] Whatever the mechanism

is, a profile, once formed, tends to persist throughout the flat-top

portion of the current pulse. Our main interest is centered on the plasma

characteristics in this quasi-steady state.

10

~ 6

<

f 4

20 40 60 80

x o~.

^

^/ 8

A

(AR)A

(C)

2h

J L

0

0

20 40 60

-*-t(m»)

80

?n

15

10

b

Ip»95kA, BT-18kG

TYPE A

TYPE B

Z.ff


IAEA-CN-33/A 5-1 105

In Fig. 4(a) and (b ) we show the time dependent 8p (plasma kinetic

pressure/poloidal magnetic field pressure) and gross energy confinement time,

Tg (plasma kinetic energy/ohmic power input), calculated from the laser profile

measurements and charge-exchange analysis (assuming the T^ profile is

of the same form as the ne profile). Since Tg is proportional to gp/Rexp

(where Rexp is the experimental plasma resistance) in the steady state, the

combination of high fL, and low Rexp makes the values of Tg higher for the

type A discharge. Fig. 4(c) shows the resistance enhancement factor, or

resistivity anomaly, A^, defined by the ratio of the experimental resistance

to pure hydrogenic Spitzer resistance, as a function of time. Effective

ionic charge, Zeff, defined by

Z _„ = S n.Z 2 /n

eff ^ i r e

is calculated from the uniform concentration of a high-Z impurity (arbitrarily

called gold — the material coating the discharge chamber) required

to make the computed resistance (including neoclassical corrections)[6]

agree with the measured value, with the given Te at each radius determining

a single ionization state. (More involved computations allowing multiple

ionization states with additional carbon and oxygen impurities have been

made. The latter results were not much different from the former, except

for changes in the proton deficiency.)[7] Such a Zeff as a function of

radius at t = 48 ms is plotted in Fig. 4(d); the volume-averaged values of


106 BERRY et al.

X 2

o

f,

0.6

-t

IP=95kA, BT=18kG

3 4 5

ne(0) (t0 13 cm" 3 }

FIG. 5. Central neutral density as a function of central electron density (upper figure). Neutral density

profiles for the type-A and type-B discharges (lower figure).

electrons is probably close to the gross energy confinement time. However,

more importantly, from the energy loss point of view, the particle confinement

times at the center are an order of magnitude higher than TE. Therefore,

in this region the energy loss due to particle diffusion is expected to be

small.

k. Ion Confinement

Next we consider the ion power balance. To be specific, we discuss it

in terms of integrated radial power flow, which is the power density integrated

over the volume of the torus of minor radius r. The power input into

ions is the electron-ion heat transfer, and the main loss channels are charge

exchange, convection due to particle diffusion, and heat conduction. (At

t = ij-8 msec there is no change in ion energy content with time.) The power


~E 0.2

5-

1:_[TP(0>]

— L [rp(0)l

L J

0.5

0.1

0.05

0.02

IAEA-CN-33/A 5-1 107

UNCERTAINTY OF

PROTON DEFICIENCY-*]" 1

TYPE B ^

r TYPE A

/p=94kA,£T=t8kG, f=48msec

TYPE A; rte=(.9X10 ,3 cm" 3

TYPEB; /5e = 1.25X10 13 cm -3

1 I I I

8 12

/•(cm)

16 20 24

FIG. 6. Particle diffusion coefficients, Dp, as a function of radius; central particle confinement time,

T (0); average particle confinement time, Tp(a), for the type-A and type-B discharges.

Qt"

I»95kA, 8T-l8kG

ff.-t.ZSxlo' 3 cm -3

TYPE B

t-48m»

(NEOCLASSICAL THEORY)

(INPUT POWER INTO IONS)

FIG. 7. Radial ion power flow for the type-B discharge. The experimental heat conduction power flow is

compared with that predicted by neoclassical theory.

200

100

50

204

10


108 BERRY et al.

flow due to the first two loss mechanisms can be determined from the neutral

density profiles, and are shown by the hatched area in Fig. 7. The unhatched

area, then, is attributed to heat conduction, which is the dominant loss

mechanism. This also can be demonstrated by the fact that the measured central

ion temperatures are relatively independent of the plasma quality

parameter (ratio of central electron density to central neutral density).[2]

Using the ion temperature profile, Tj_(r) ~[l-(r/a) 3 ], based on experiments

conducted some time later with similar type B discharges, we can calculate

the heat conduction loss predicted by the neoclassical theory.[6] This is

shown by the area between the dashed line and the hatched area in Fig. 7.

The agreement is reasonably good over most of the plasma volume, except near

the very edge where the neutral density profile has a considerable uncertainty.

With Zg-f-p derived from the high-Z impurity model, ions are predominantly

in the Pfirsch-Schluter regime. However, it is also possible to invoke an

ion heat transfer anomaly factor which has a radial dependence similar to

that shown in Fig. U(d). A similar analysis was performed for the type A

discharges with T^(r) ~[l-(r/a) 1 * e ]. The agreement between experimental heat

conduction and neoclassical prediction was not as good as that for the type

B case.

5. Electron Confinement

A power balance accounting similar to that just described for ions can

be made for electrons. Here the power input is the ohmic heating, and the

main power loss channels are convection due to particle diffusion, electronion

heat transport, radiation (including the potential energy of ionization),

and heat conduction. The difference between the input and total loss

reflects the rate of change in electron kinetic energy. Let us take the

type B discharge at ^8 msec as an example. The ohmic power input inside a

radius r = a/2 is 150 kW ,+ 10 kW (due to the uncertainty of the current

distribution, but with the assumption of a fully penetrated electric field).

The convection loss and electron-ion heat transfer loss are 10 kW and 20 kW,

respectively. We do not have a good estimate of radiation and heat conduction

losses, but for the moment let us assume that there is no radiation

loss within this radius; then, we may attribute the remaining 120 kW to the

pseudoclassical heat conduction loss[9,10] with the coefficient

V = 5 v Pp

where v is the electron-ion collision frequency with Zeff from the high-Z

impurity model, and pp is the poloidal gyroradius. Such a form of the heat

conduction coefficient gives a reasonable fit to the experimentally inferred

power input for r/a ij. The amount of power

loss appears to be too large to be attributed totally to radiation loss. In

the type A discharge the experimentally inferred heat conduction loss is even

more inconsistent with the pseudoclassical prediction than in the type B.

As is obvious in the above discussion, the pseudoclassical heat conduction

(which is already one order of magnitude above the neoclassical heat

conduction)[6] does not adequately describe the radial heat conduction in

the experiment. In addition, we do not have adequate information to untangle

the anomalous electron power transport. Therefore we turn our attention to

overall confinement parameters.

Although the classical tokamak results[11] indicated that Bp is constant

(Hg-) and Artsimovich's derivation of pseudoclassical scaling was based on

this,[9] systematic variations (Bp ~ne/l) have been observed in recent tokamak

experiments.[3,12,13] Figure 8 shows the values of Bp calculated from


1.0

0.8

0.6 -

0.4 -

0.2


-

-

1 1

TYPE A TYPE B I

A A 60 kA

o • 95kA

0 • 120 kA

IAEA-CN-33/A 5-1 109

£p~/>«

• . .V'^

.. if V •>

I


i

I !

1.0 1.5 2.0 2.5 3.0

nt/l (10 8 A"'cm -3 3.5 4.0

)

A

(BT2i18kG)

A

° 4-^^^"^

^ ^ ^ ^ A

•"•""^ O o

o


110 BERRY et al.

l4

^

4 \*

\ •


0.5 1.0


1 1

TYPE

A B / (kA)

o • (89-96)

A A (57-59)

• o

, o -V

(l0 13 en

0 j = 18 kG,H2

.5

-3)

o —

2.0 2.5

FIG. 10. Resistance anomaly, R exr/ R sp' as a f unction of volume-averaged density, , for two different

ranges of currents. Type-A discharges are indicated by open circles (I_j = 95 kA) and open triangles

(I ^ 58 kA). The fitted curves are < n > -1 .

The observed T^ for type B discharges appears to be roughly proportional to

TpC, but for the type A discharges fE is generally higher than ?pc. It is

noted also that type A discharges in general have longer gross energy confinement

times than type B discharges, mainly because of their higher electron

densities (TJ; ~Hg for constant current). The better confinement in

type A discharges may be due to lower impurity influx, as observed by spectroscopic

measurements of carbon, oxygen, and gold line radiation. On the

other hand, it was attributed by Vershkov and Mirnov to internal MHD oscillations

that prevent impurity peaking at the plasma center.[5] A third

alternative explanation is that higher shear, as expected from peaked temperature

profiles, stabilizes instabilities that may have been causing the

anomalous transport in the type B discharges.

6. Resistivity Anomaly

Figure 10 shows the resistivity anomaly calculated from the profile

measurements as a function of the volume-averaged electron density for two

different current ranges. We observe a scaling of

R

exp I"

(or-l)

"SO

sp e' e

The resistance anomaly ranges from 2 to 6.5 in the normal range of operation

(ne >0.5 x 10 13 cm" 3 ), and the (Zg^) from the high-Z impurity model ranges

from 2.5 to 12. After having considered various possible explanations[15]

(such as the current-driven ion acoustic instabilities, neoclassical effects

or incomplete electric field penetration, none of which are large enough or

operative in the parametric ranges of interest), only two explanations remain

as reasonable possibilities: impurities and a true anomaly. With respect to

impurities, vacuum ultraviolet spectroscopic measurements have identified

carbon and oxygen as the predominant impurities with concentrations estimated

to be typically 1-2$ of the central electron density for each species. Such

concentrations of these low-Z impurities can raise (Zeff> only about one unit

which is far less than required. Soft x-ray spectrum measurements also provide

an estimate of impurity densities through the absolute intensities of

both continuum and line radiations. However, with decreasing density, the

continuum spectra tend to exhibit an enhanced tail[l6] which makes the measurement

difficult to interpret. A more reliable estimate for Zeff can be


IAEA-CN-33/A 5-1 111

TABLE I. THE VALUES OF < Zeff > INFERRED FROM THE

RESISTANCE ANOMALY, AR, COMPARED WITH THOSE

INFERRED FROM THE SOFT-X-RAY MEASUREMENTS AND THE

CHARGE-EXCHANGE MEASUREMENTS OF FAST ION SPECTRA

I

(kA)

100

95

102

_

e

(x 10 13 can" -3)

2.07

2.08

1.72

Type

A

A

B

A

r,

R

2. • 9

2. 7

k. • 5

< Z eff>

from

resistivity

2.6

2.6

6.9

< Z eff>

from

x-ray

2.6

3.0

3.1

< Z eff>

from

ex

inferred from the perpendicular energy distribution of fast ions in the

injection experiments (Fig. 6 of Ref. [k"]). Some of the results of these

measurements are compared in Table I. Since the fast ion profile[17] is

peaked near the center, the average of the effective-Z from the chargeexchange

measurement is heavily weighted near the center, while Zg^ from

resistivity in the same region is higher by a factor of 1.5 than the entire

volume-averaged effective-Z. In the high density, type A regime, the Zef,„

agrees reasonably well with that determined from the resistivity. In the

low density, type B regime, however, Zeff from the more direct measurements

are significantly lower (by factor 2-3, typically) than that inferred from

resistivity. Therefore in the low density regime, impurites alone apparently

cannot explain the resistivity anomaly. The other possible contribution is

turbulent processes. Although we do not have any way to identify the instabilities,

there is a possibility that dissipative trapped electron modes[18]

might be responsible. In fact, the resistance anomaly factor apparently

increases with decreasing collisionality (AR ~(V|)^^, where (v|)min is the

minimum value of v|, the ratio of collision frequency to electron bounce

frequency in the poloidal field).[15] Such instabilities may increase the

effective electron collision frequency, leading to an increase in resistivity.

At a minimum, we cannot exclude the possibility of turbulent effects in the

low density regime.

7. Conclusion

We observe significant differences in discharge characteristics

(especially profiles) in the high and low density regimes. Using two

typical (by no means best) discharges from the two regimes, we have evaluated

their transport properties. Features of the ion energy transport can

be described within a classical framework. Electrons, however, continue to

be anomalous, although their average confinement characteristics are reasonably

consistent with pseudoclassical predictions for the low density regime.

One aspect of their anomalous properties is the resistance anomaly: Zeff

inferred from the resistivity in the low density regime appears to be higher

(by a factor 2-3) than Zeff derived from more direct measurements.

ACKNOWLEDGMENTS

We wish to acknowledge the many interesting and thought-provoking

discussions with the members of the 0RMAK Section. We are particularly

indebted to C. E. Bush and H. E. Ketterer, Jr., for operation of the charge

exchange and laser diagnostics, respectively; and to R. V. Miskell and

D. L. Shaeffer for the plasma position and electron transport calculations,

respectively. Much of the success of the experiment has resulted from the

excellent design, construction, and calibration of the diagnostics. We are

k


112 BERRY et al.

particularly indebted to: C. F. Barnett and J. A. Ray for the chargeexchange

analyzers, J. S. Culver and G. R. Dyer for the laser system, and

J. E. Franics and 0. C. Yonts for the data acquisition system. We wish to

thank V. J. Meece, T. F. Rayburn, and W. J. Redmond for the many long hours

they devoted to machine operation. Finally, the continued support, inspiration,

and encouragement of G. G. Kelley, the 0RMA.K Section Leader, is

gratefully acknowledged.

REFERENCES

[l] KELLEY, G.G., et al., 3rd Int. Symp. Toroidal Plasma Confinement,

Garching, Germany (1973) Paper B3-I.

[2] BERRY, L.A., et al., Phys. Rev. Letter 32 (197^) 362.

[3] MURAKAMI, M., et al., to be published in Nuclear Fusion.

[k] BERRY, L.A., et al., present conf., Paper IAEA-CN-33/ A 5-2.

[5] VERSHKOV, V.A., and MIRNOV, S.V., Kurchatov Preprint IAE-2298 (1973).

[6] HINTON, F.L., and ROSENBLUTH, M.N., Phys. Fluids 16 (1973) 836;

HAZELTINE, R.D., and HINTON, F.L., Phys. Fluids lF"(l973) 1883.

[7] CRUME, E.C., to be published.

[8] HOGAN, J.T., and CLARKE, J.F., 0RNL-TM-¥^ (197*0.

[9] ARTSB40VICH, L.A., JETP Letter 13 (1971) 70.

[10] YOSHIKAWA, S., and CHRISTROPHILOS, N.C., IAEA Madison (1971) Paper

IAEA-CN-28/ F-l.

[11] ANASHIN, A.M., et al., JETP 60 (1970) 2095.

[12] DIMOCK, D.L., et al., IAEA Madison (1971) Paper IAEA-CN-28/ C-9.

[13] VERSHKOV, V.A., et al., Kurchatov Preprint IAE-2291 (1973).

[lU] DEAN, S.O., et al., WASH-1295 (197*0.

[15] CA1LEN, J.D., Sherwood Meeting, Berkeley; ORMAK-TM-162 (197*0.

[16] VON GOELER, S., et al., Bull. Am. Phys. Soc. 16 (1971) 1231.

[17] CALLEN, J.D., et al., present conf., Paper IAEA-CN-33/ A l6-3.

[18] See, for example, KADOMTSEV, B.B., and POGUTSE, O.P., Nuclear Fusion 11

(1971) 67.


IAEA-CN-33/A 5-2

NEUTRAL BEAM INJECTION EXPERIMENTS

IN ORMAK*

L.A. BERRY, C.E. BUSH, J.L. DUNLAP, P.H. EDMONDS,

T.C. JERNIGAN, J.F. LYON, M. MURAKAMI, W.R. WING

Oak Ridge National Laboratory, Oak Ridge, Tenn.,

United States of America

Abstract

NEUTRAL BEAM INJECTION EXPERIMENTS IN ORMAK.

Two energetic (each ~26 kV, 100 kW) neutral beams were used to supplement the larger Ohmic heating

of the Oak Ridge Tokamak (ORMAK) plasma. Long, constant discharge-current times and beam pulse lengths

permitted an essentially equilibrium study of both plasma heating and other effects due to neutral beam

injection. Both coinjection (beam parallel to the discharge current) and counterinjection (anti-parallel to

the discharge current) were studied. Injection perturbs the plasma density and hence the electron-ion heat

transfer, an effect which must be taken into account in evaluating the ion heating due to beam power input.

The observed ion temperature increases with coinjection are in agreement with theoretical predictions both

in magnitude (ATj/Tj ranging from 40°/o to 10%) and in scaling with plasma density. Measurements of parallel

and perpendicular beam ion energy distributions are in agreement with theory, indicating little chargeexchange

beam power loss, an effective ionic charge ~ 4, and significant beam energy transfer to the

plasma. While net electron heating is sometimes observed with coinjection, the main effect of injection on

electrons is to alter the radial distributions of electron temperature and density. Counterinjection was found

to be much less effective than coinjection in plasma heating and to have a generally deleterious effect on

the discharge parameters, stability, and confinement.

1. Introduction

At the very least it is desirable, and most likely necessary, to

supplement ohmic heating in tokamaks in order to achieve the high plasma

temperature and gpoloidal of reactor regimes. Energetic neutral beam injection

is both a promising means of supplementary heating,[l], as well as a

possible probe with which to investigate the confinement and stability of

tokamak plasmas. The ORMAK experiments investigated the following points

relevant to the understanding of injection heating: (l) demonstration of

significant ion heating; (2) scaling of heating with plasma parameters;

(3) comparison with theoretical predictions; (k) effect of injection direction

on heating; and (5) beam perturbations of plasma behavior that might

eventually limit the extent of the heating [2],

2. The Experiment

Two energetic (each ~26 kV,


114 BERRY et al.

FIG.l. Schematic view of the ORMAK device showing the major elements of the experiment. The numbered

items indicate (1) a beam ion source, (2) beam neutralizing cell (conceptual), (3) 26 keV H° beam, (4) plasma,

(5) inner vacuum chamber, (6) vertical field coil, (7) conducting shell, (8) plasma current primary coil,

(9) a toroidal field coil, (10) laser diagnostic, (11) iron core and limiter azimuth, (12) perpendicular chargeexchange

analyser, and (13) parallel charge-exchange analyser.

about 6 cm. The injectors are aimed approximately tangential to (8 cm

inside) the magnetic axis and are oppositely arranged, providing beam injection

both in the same direction (coinjection) and in the opposite direction

(counterinjection) to the discharge current. Any of these injectors (all of

the "duoPIGatron" type developed by 0. B. Morgan and co-workers at Oak

Ridge)[5] can serve as a coinjector or a counteringector by reversing the

discharge current direction and the externally applied vertical field.

The time relationship and typical magnitude of some of the discharge

parameters are shown in Fig. 2. A large loop voltage (~^5 V) ionizes the

fill gas (Hg or D3) and drives the rapid initial current rise. The desired


300

250

200

150

100

50

0

IAEA-CN-33/A 5-2 115

/?e (10 11 cm" 3 )

0 20 40 60 80 100 120

TIME (ms)

FIG. 2. The chord-average electron density (Tig), the beam current pulse (Ibeam). tne ion temperature (Tj),

and the discharge current (I) for a typical discharge.

toroidal current is usually reached in 10-20 ms, and then is held nearlyconstant

by a feedback system until the experiment is terminated after ~70

ms, usually because the iron core has begun to saturate. The discharge is

clamped at this time and undergoes inductive decay. The start of the beam

pulse is delayed after the initiation of the discharge, usually by more than

5-10 ms, and the beam pulse could be as long as 0.2 s, if that were useful.

Both the constant current time of the discharge and the beam pulse length

are long (^50 ms) compared to typical plasma heating and confinement times

(~5-10 ms), permitting an essentially equilibrium study of both plasma

heating as well as other effects of neutral beam injection.

For these experiments, the plasma current was varied from 60 kA to 120

kA, the central chord-average electron density was varied from < 10 13 cm -3

to ~3 x 10 13 cm" 3 , the toroidal magnetic field was varied from Ik kG to 18

kG, and both hydrogen and deuterium plasmas and beams were studied. These

variations gave average central ion temperatures from 150 eV to 350 eV,

central electron temperatures from ^00 eV to > 1000 eV, and central neutral

densities ^1 to 2 x 10 s cm -3 [3].

3. Evaluation of Ion Heating (with Coinjection)

An example of the response of the ion temperature and the average

electron density due to beam injection starting at ~10 ms is shown in Fig. 3.

The electron density increase following injection is typically ~15$, but has

varied from < % to nearly 50$, depending upon the initial electron density.

This density increase with coinjection is not due to the captured beam ion

density nor to the neutral gas streaming from the source neutralizing cell


116 BERRY et al.

280

240

200

160

120

80

40

/

*=~=^ Cr—|^

S A-

7\

O N 0 INJEC TION

A If MJECTIOr

"~"*^

\ \ \ \ \ s

"**"-J. N

X \

\

> \

\

0 10 20 30 40 50 60 70 80 90 100

/ (ms)

FIG.3. The effect of coinjection on the average ion temperature and electron density.

s

s

(X10 13 )

as this gas is efficiently pumped and no density increase is observed when

the source is operated without an extracted beam. This density increase is

seen in other experiments[6,73 and may indicate a beam-produced influx of

neutrals, although there is some spectroscopic evidence to the contrary

in OKMAK.

Whatever its origin, the beam-produced density increase complicates the

evaluation of that part of the ion temperature increase due solely to the

power input from beam ions slowing down, since the still dominant electronion

heat transfer Pe^ varies[8] as ne s /*/£±. Experimentally, we try to

remove this complication by plotting T^ vs ne at constant discharge current,

with and without injection, as in Fig. k. The results shown are for hydrogen

discharges and ~100 kW H° beams for a discharge current of 95 kA. The

measured values of Tj_ and ne are averages over the time interval t = kO ms

to 50 ms after the start of the discharge. This plot shows ~ho4> AT^/T^ at

low density and ~10$ ATj/T^ at high density when comparing coinjection (•)

vs no injection (o) at the same density. D + plasma and ~70 kW D° injection

give similar values for ATj.

A perturbation calculation by Callen, et al.,[9] (valid for Pj_n-j -j

« P, ei where Pinj.i ^ s ^ e injected beam power transferred to the plasma

ions) predicts an ion temperature rise AT^ given by

AT.

~T7

l

rP. . An 9071 T.

1 + n

Ei

L P n \ S n„

An 'bSn T.

^)1

3.0

- 2.5

2.0

1.5

1.0

0.5

hlh T-

Ei\

a ?•

where T^^ is the ion energy lifetime and nQ the neutral density. Using this

equation and the (*) points of Fig. k as "no injection" starting points, the

ATj_'s expected from the beam power input alone have been calculated, using

the experimentally relevant equilibrium density and temperature profiles to

evaluate the volume-averaged quantities ~P±nj ± and Pe^ [93. The ATn-


280

260

240

220

2 200

180

160

8



X


IAEA-CN-33/A 5-2 117

• • •

o

o


118 BERRY et al.

•o I 73

10 5

10 3

10 2

10<

10°

10 H

NO-INJECTION

^=260 eV

(Tn=317eV)

H + PLASMA 96 kA

BT=17.5 kG ne=1.3x10 1

T=30-50 ms

-CO-INJECTION

T,.= 300 eV

(T,,= 390eV)

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

E(keV)

FIG. 5. The perpendicular ion energy distribution for coinjection versus no injection showing ion heating and

the .presence of a high-energy "tail" of beam ions. The parallel ion "temperatures" are also indicated.

Figure 6 shows the energy distributions (l/v^)dN/dE obtained with coinjection

along with theoretical Fokker-Planck calculations of the fast (beam)

ion distribution [9], Both f|( (on the left) and fx (on the right) show the

steep thermal Maxwellian falloff at lower energies. The indicated T|| is

higher than Tj_ and probably reflects a toroidal drift distortion of the

thermal plasma distribution since T|| changes with the direction of the discharge

current, whereas T_,_ does not. A similar difference between Ty and

Tx is indicated in Fig. 5.

Consider first the parallel fast-ion energy distribution on the left of

Fig. 6. The three energy components of the H° beam are evident (at E0, E0/2

and E0/3 where E0 ~26 keV), corresponding to the extraction of three ion

species from the source (IT, Hg + , and H3 + ). The energy distribution is

fairly constant below each of the injection energies, indicating fast ion

slowing down (and resulting heating of the plasma) and a relatively small

amount of beam power lost by charge exchange (with high neutral density the

fast ion energy distribution would fall sharply for energies below the injection

values). The theoretical curves shown, each labelled by a different

"effective" ionic charge , are for the plasma center and the injection

angle (9j_n-j ~26°) with the exception of the dotted curve (here = k,

9 = 0°, i.e., along BT). Comparison of the experimental points with the

theoretical curves below 8 keV indicate that the


10 5

10 f

10 3 -

102

10'

I0 C

1


120 BERRY et al.

Consider next the perpendicular fast-ion energy distribution on the

right of Fig. 6. Here the falloff for energies above the main thermal distribution

is steeper and is also more sensitive to the (Z) of the plasma

(since this parameter determines the rate at which the perpendicular distribution

is populated by pitch-angle scattering.[6,9] T he best agreement

with the theoretical curves for r = 0 and 9 = 90° is for (Z) ~k. This value

for (Z>, as well as those inferred from soft x-ray measurements and vacuum

ultraviolet spectroscopic measurements, is significantly lower than that

inferred from the resistance anomaly ( ~ll).[3] The data and calculations

shown in Pig. 6 are for a coinjected beam. Similar measurements with counterinjection

show similar energy distributions, although considerably fewer (by

up to a factor of 5) counterinjected beam ions scatter through 90° a ^d slow

down to thermal energies. Nevertheless, this indicates that some counterinjection

beam heating is present.

5. Coinjection Heating vs Counterinjection Heating

By contrast with coinjection (•), the counterinjection points (A) in

Fig. k fall within the spread of the no-injection points (o), indicating

little net ion heating. Also, both injectors together give about the same

ion heating as coinjection alone. The reduced counterinjection ion heating

seems to be due primarily to the fact that for counterinjection, fast ions

can pitch-angle scatter into the "loss region" produced by the large radial

excursions (to the limiter or the wall) of the unconfined fast-ion "banana"

drift orbits (for particular pitch angles) before losing a significant part

of their energy to plasma ions, as calculated by Callen, et al., (see

Figs. k-G of Ref. [9]).

In addition, counterinjection is accompanied by deleterious effects on

the discharge: increased plasma instability, poor discharge reproducibility,

and a tendency toward a decrease in density (see Section 7). It appears

that these deleterious effects offset the small counter-beam heating effect,

whereas the beneficial effects of coinjection (increased plasma density and

tendency toward stability) supplement the larger co-beam heating.

By contrast, the ATC results indicate a significant amount of counterinjection

heating (~75$ of that produced by coinjection) [5]. This difference,

as compared with OEMAK, may be a combination of two factors in ATC.

First, charge-exchange loss of beam ions is unimportant in ORMAK, while in

ATC charge-exchange loss should be the dominant beam power loss mechanism at

ATC's higher neutral densities (~10 9 cm" 3 ). Thus beam ions can be lost by

charge exchange before scattering into the loss region. Second, in ATC much

of the beam power is below the energy threshold of the loss region, whereas

this is not true in ORMAK, and these lower-energy beam components also heat

ions more efficiently in ATC. For larger machine sizes and higher poloidal

fields, differences between coinjection and counterinjection due to loss

region effects should become unimportant, even at low neutral densities,

since the effect of the loss region scales as Pp/a, P_ being the ion gyroradius

in the poloidal field and a the plasma radius.

6. Effect of Injection on the Electron Distribution

Calculations (see Fig. 2 of Ref. [9]) show that beam components with

injection energies above ~35 Te, ~lU-35 keV in ORMAK, should give up most of

their initial energy to electrons in the course of slowing down, whereas

beam components below these energies should predominantly heat ions. Since

the highest injection energy component in these studies was, ~26 keV, ion

heating (as observed with coinjection) should be accompanied by electron

heating. The main effect of injection on electrons, however, is to alter

the radial electron distributions. Usually coinjection tends to peak the

electron density and temperature profiles near the axis, sometimes with net


600 -

400 -

200

o

5

2 3

l«= 2

1

-

-

"3

0 10

RADIUS (cm)

)~

IAEA-CN-33/A 5-2 121

LIM.

i I i i i ^H*

-10 0 10

20 f

RADIUS (cm)

LIM.

IP=94kA, BT = 18k6

t = 40ms

ne= 1.8x10 13 cm" 3

V~ 2.3v (NO INJECTION)

o NO INJECTION

x CO-INJECTION

• CTR-INJECTION

FIG.7. The effect of coinjection and counterinjection on the radial profiles of electron temperature and

density for a medium density discharge.

electron heating but often with the volume-average Te not changed appreciably.

As with ion temperature increases, the changes in ne(r) and Te(r)

are largest at low density where the injected power per plasma particle is

highest. Since the central electron temperature increases accompany changes

in the radial temperature profiles, it is difficult to separate the beamproduced

heating from that which may be due to a redistribution of the ohmic

heating current.

Figure 7 shows a specific example from a set of radial profiles of

electron temperature and electron density measured with laser Thomson scattering

at a time kO ms into the discharge, indicating effects of coinjection

and counterinjection on the electron distribution. Coinjection (solid

curves) in this example increases both the average electron density and net

(volume-average) electron temperature and shifts the plasma center outwards

by ~4-5 cm (more commonly ~2-3 cm). On the other hand, counterinjection

here leads to an overall decrease in electron density and temperature and a

large decrease in central electron temperature (in fact creating a hollow

temperature profile), with little or no shift of the plasma center.

7. Other Injection Effects

There are other examples of deleterious perturbations of the plasma

behavior by counterinjection and more benign perturbations due to coinjection.

Measures of plasma stability (MHD oscillation amplitude and fre-


122 BERRY et al.

0 20 40 60 80 100 120

TIME (MS)

FIG. 8. The effect of delayed counterinjection (dashed lines) versus coinjection (solid lines) on plasma

stability (MHD)and wall/limiter interactions (light intensity).

4.00 -p

3.50 —I

3.00 —l

0 20 40 60 80 100 1

TIME (MS)

FIG.9. The effect of delayed counterinjection (dashed lines) versus coinjection (solid lines) on gross plasma

behavior.


IAEA-CN-33/A 5-2 123

quency), plasma shift, and wall/limiter plasma interactions (CIII and Hg

light, hard x-rays) indicate that coinjection tends to stabilize the plasma

behavior while counterinjection tends to make the plasma more unstable,

especially if the discharge parameters happen to fall near the boundary separating

stable and unstable discharges. Figure 8 shows the effect of delayed

injection (beam on at kO ms and off at 80 ms) on Hg and CIII light intensity

and MHD amplitude (^poloidal)' These plasma parameters are increased with

counterinjection (dashed curves) over the eoinjection values (solid curves),

but the casual relationships are not yet clear.

Similarly, Fig. 9 shows the effect of delayed injection on the discharge

current, loop voltage, plasma line density and Hg light. Counterinjection

(the dashed curves) leads to shorter plasma current decays, higher loop

voltages, reduced plasma density, and increased Hg light, as compared with

coinjection. Since the discharge current is regulated by a feedback system,

the changes in loop voltage indicate changes in plasma resistance (also

reflected in the changes in the L/R current decay times), with the higher

resistance values obtained for counterinjection. Part of this voltage change

may also be due to a current perturbation induced by injection [9]. The time

for the outside voltage to respond to changes in the internal current or

temperature distribution indicates that the magnetic diffusion (skin) time

is no longer than ~15-20 ms.

In addition, most of the time coinjection improves general confinement

characteristics (such as particle lifetime and Bpoioidai) WQ il e counterinjection

decreases them. This can be inferred from Fig. 9 where the no-injection

curve (not shown, however, for clarity) for 5e would be slightly above the

counterinjection ne curve and the no-injection Hg curve would be slightly

above the corresponding coinjection curve. Thus for coinjection the plasma

density increases while the neutral feed rate (indicated by Hg) decreases

slightly, indicating an increase in particle confinement time over the noinjection

value. Conversely, for counterinjection the opposite behavior

occurs, indicating a decrease in confinement time. The changes in $p0i0icial

follow the same pattern and reflect mainly the changes in plasma density.

There are also indications of increased toroidal flow (Av ~2 x 10 s cm/sec),

as would be expected from a beam momentum input, in the parallel chargeexchange

energy spectrum for coinjection (see Fig. 5), but not for counterinjection.

The deleterious effects of counterinjection on different aspects of the

plasma behavior may be due either to current redistribution in the plasma

influencing the plasma stability, or to the presence of the large loss region

for counterinjected ions. Once scattered into this region, these energetic

ions rapidly hit the wall, perhaps releasing gas and sputtered particles,

effects which could drastically alter the discharge behavior. Unfortunately,

the time relationship between the signals in Fig. 8 does not permit elimination

of either possibility.

8. Conclusions

Our investigation of injection heating shows significant ion heating

for coinjection that is in good agreement with theoretical predictions, both

in magnitude and in scaling with density. The lack of appreciable net

heating with counterinjection can be explained by the loss region for

counterinjected fast ions and the deleterious effects of counterinjection on

the plasma. These plasma perturbations underline the fact that neutral beam

injection can have other effects on the plasma besides the desired heating.

Even at present beam power levels, these effects are significant and must be

taken into account in evaluating the extent of the plasma heating, although

no limitation, as yet, has been found to this heating.


124 BERRY et ai.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the important contributions and

theoretical calculations of J. D. Callen, R. J. Colchin, R. H. Fowler, and

J. A. Rome, whose work is described in a separate paper [9]. None of the ion

or beam energy distribution measurements could have been made without the

seven-channel charge-exchange analyzers designed, constructed, and calibrated

by C. F. Barnett and J. A. Ray. Other valuable contributions to this

study were ORMAK injector development by L. D. Stewart, spectroscopic

measurements by R. V. Neidigh, Thomson scattering measurements by H. E.

Ketterer, Jr., computer data acquisition and analysis by J. E. Francis and

0. C. Yonts, and machine operation by R. R. Hall, L. A. Massengill, V. J.

Meece, T. F. Rayburn, and W. J. Redmond. Finally, the initial ideas and

continuing motivation and direction of this effort are due to G. G. Kelley

and 0. B. Morgan, with the encouragement of J. F. Clarke and H. Postma.

REFERENCES

[1] KELLEY, G.G., et al., Nuclear Fusion 12 (1972) 169.

[2] CALLEN, J.D., CLARKE, J.F., and ROME, J.A., Proc. 3rd Int. Symp.

Toroidal Plasma Confinement, Garching, Germany (1973).

[3] BERRY, L.A., et al., present conf., Paper IAEA-CN-33/ A 5-1.

[k] BARNETT, C.F., et al., 6th European Conf. on Controlled Fusion and

Plasma Physics, Moscow, USSR (1973).

[5] STEWART, L.D., et al., Proc. 3rd Int. Symp. Toroidal Plasma Confinement,

Garching, Germany (1973)•

[6] CORDEY, J.G., et al., Nuclear Fusion ik (197*0 k6l.

[7] BOL, K., et al., present conf., Paper IAEA-CN-33/ A J+-1; also BOL, K.,

et al., Phys. Rev. Letters 32 (197*0 66l.

[8] ARTSIMOVICH, L.A., Nuclear Fusion 12 (1972) 215.

[9] CALLEN, J.D., et al., present conf., Paper IAEA-CN-33/ A l6-3, and

refs. cited therein.

[10] CORDEY, J.G., and STOTT, P.E., Bull, Amer. Phys. Soc. 19 (197*0 898;

also CORDEY, J.G., present conf., Paper IAEA-CN-33/ A lo"-l.


DISCUSSION

ON PAPERS IAEA-CN-33/A 5-1, A 5-2

B. COPPI: What is your present interpretation of the effects of counterinjection?

M. MURAKAMI: The reduced counter-injection ion heating is primarilydue

to the "loss region" produced by bad fast-ion orbits. The perturbation

theory of Callen et al. (paper A 16-3) predicts an increase in ion temperature

of about 10 eV, which is marginally outside the spread of the ion temperature

measurement. That an increase is not seen in the experiments is probably

due to its deleterious effects on the plasma, as exemplified by electron

temperature profiles (Fig. 7 in paper A 5-2).

T. KAWABE: What is the difference between the fluctuations in ORMAK

for high-and low-density discharge— in bothMHD mode and microscopic mode?

M. MURAKAMI: In type-A discharges, we observe typical poloidal

magnetic field oscillations Be/Be =1- 2%. The oscillation of the average

density An^ng is also of the order of 1 - 2%. In type-B discharges these

amplitudes are lower by an order of magnitude. MHD-wise quieter discharges

therefore have resistance anomalies.

125


NEUTRES ATOMIQUES ET

IMPURETES DANS TFR

EQUIPE TFR

Association EURATOM-CEA sur la fusion,

Departement de physique du plasma et de la fusion contr61ee,

Centre d'etudes nucleaires de Fontenay-aux-Roses,

Fontenay-aux-Roses, France

Abstract-Rdsumf

IAEA-CN-33/A 6-1

ATOMIC NEUTRALS AND IMPURITIES IN THE TFR DEVICE.

The results given in this report are concerned in particular with a discharge at Ip = 200 kA, B^- = 40 kG

in hydrogen (diaphragm 0O = 400 mm). The radial profile of the neutral density nHo(r) at 180° of the diaphragm

gives a central density of 10 8 cm" 3 and a peripheral density (r = 17 cm) of 7 x 10 cm" 3 . In the case of the

impurities, a series of measurements was made for three values of the plasma current Ip (100, 200, 300 kA).

The main impurity is oxygen. The surface density of the ion O s+ is from 1 to 2 x 10 12 cm" 2 for the three

currents. The surface densities of the ions Mo 12+ and Fe 14+ are lower by a factor of 10 to 100. The carbon

content varies greatly, depending on the series of experiments. Zeff as determined from the conductivity is

close to 6 for discharges in hydrogen, regardless of the value of Ip on the plateau. For deuterium, Zeff is of

the order of 4 for 200 kA, and increases to 5.5 for 315 kA. If one considers only the ion 0 8+ , a Zeff of

6 corresponds to an 0 8+ ion content of 2°]o in relation to the electron density. The results lead to a model in

which the ions from 0 + to O 6 * are localized in a peripheral layer in which the confinement time is short (~ 1 ms).

The flux of O 6 ions towards the centre, which indicates, after ionization to the state O + , the proportion of

this ion present at the end of the discharge, is a small part of the peripheral flux deduced from line radiance

measurements.

NEUTRES ATOMIQUES ET IMPURETES DANS TFR.

Les resultats donnes dans ce rapport concernent plus specialement une decharge a Ip = 200 kA, Bj = 40 kG

dans l'hydrogene (diaphragme 0O = 400 mm). Le profil radial de la densite des neutres nuo(r) a 180° du

diaphragme donne une densite centrale de 10 8 cm" 3 et peripherique (r = 17 cm) de 7 • 10 cm" 3 . Pour les

impuretes, une serie de mesures a ete faite pour trois valeurs du courant plasma Ip (100, 200, 300 kA).

L' impurete dominante est l'oxygene. La densite superficielle de l'ion 0 5+ est de 1 a 2 • 10 12 cm -2 pour les

trois courants. Les densites superficielles des ions Mo 12+ , Fe 14+ sont d'un facteur 10 a 100 plus petites. Le

carbone est en proportion tres variable selon les series d'experiences. Le Zeff determine a partir de la conductivity

est voisin de 6 pour des decharges dans l'hydrogene, quel que soit Ip sur le plateau. Pour le deuterium

Zeff est de l'ordre de 4 pour 200 kA et augmente a 5,5 pour 315 kA. Si on considere uniquement l'ion 0 8+ ,

un Zeff de 6 correspond a" une proportion de 9°/o d'ions 0 8+ par rapport a la densite electronique. Les resultats

conduisent a un modele ou les ions de 0 + a O s+ sont localises dans une couche peripherique ou le temps de

confinement est faible (~ 1 ms). Le flux vers le centre des ions 0 s * rendant compte, apres ionisation a l'etat

O + , de la proportion de cet ion, en fin de decharge, est une faible part du flux peripherique deduit des mesures

de radiance des raies.

1. DISPOSITIF DE MESURES.

L'implantation des differents diagnostics utilises dans

la derniere campagne de mesure est indiquee sur la figure 1.

En partant du diaphragme dans le sens du courant plasma on

trouve : a cp = 0 , un detecteur multicanal a fibres de verre

pour la determination de la densit§ n„o (r, t) des neutres a

partir de l 1 emission Hg , un interferometre hyperfrequence I

9 canaux (A = 2 mm) ; a q> = 45° un monochromateur donne la

radiance des raies de l'hydrogene et du carbone (CIV 5801,

127


128 EQUIPE TFR

FIG. 1. Disposition des diagnostics sur la machine.

CIII 4647), un duochromateur pour 1'ultraviolet lointain pour

les raies des ions de l'oxygene, du molybdene et du fer

(O V 930, 0 VI 1032, Mo XIII 341, Fe XV 284). L'etalonnage_

energStique a ete fait par la methode des raies couplees £ 1_//

un spectrometre pour 1'analyse du rayonnement cyclotronique ;

a tp = 90° un interf§rometre a A = 337 nm utilisant un laser

HCN, la detection de neutres rapides pour la determination de

la temperature ionique ; a cp = 135° un spectrometre a semiconducteur

Si(Li) pour la bande de 2 a 30 keV (resolution 3%

a 6 keV), un systeme de detection dans la bande 1 a 10 keV

comprenant des absorbants, un scintillateur (Nal) et un photomultiplicateur

; a 9 = 180° la diffusion Thomson et une mesure

du profil radial Hg similaire a celle faite a cp = 0 ; a

q> = 225° et


200 kA

U0 kG

IAEA-CN-33/A 6-1 129

t = 100 ms I

v r n

De v A

— ^ /i\

BH (h) V \

•^ V \

^ / \\

, i • y ' 1

X

\ '

hfcm) 10 r(cm) 20

•I 31 1

FIG.2. Repartition radiale des neutres H . Bpjft(r) radiance de la raie symetrisee. ne(r), Te(r) densite

et temperature electroniques utilisees pour le calcul de n^o(r). lp = 200 kA, Bf = 40 kG, $£, = 400 mm,

gaz: hydrogene.

et de temperature electroniques utilisees lors du calcul de

nHo(r) a partir de la population mesurSe n^(r) du niveau

superieur de la raie Hg ._On_utilise dans ce calcul les tables

de Johnson et Hinnov / 2_/. Le profil mesure a


130 EQUIPE TFR

Tt (r=0)

200 t (ms) 250 0

FIG. 3. Evolution des densites superficielles des ions C 3 * O s+ , Mo 12+ , Fe 14 * de la densite moyenne rle et de la

temperature centrale Te(r = 0). Ip (plateau) = 200 kA, BT = 40 kG, *D = 400 mm, gaz: hydrogene.

IU

10I 2

7

k


in

Ol

>o> -jj


Q a.

3

in

.J1

1U

10

-

I



I


k

?

H2'


k

I

I

100 200 Ip(kA) 300


,

o-' i

c 3 *

_ 14+

Fe

Mo 12+

FIG.4. Densites superficielles des ions C 3+ , O s+ , Mo 12+ et Fe 14 en fonction du courant plasma au plateau

(100 kA, 30 kG; 200 kA, 40 kG; 300 kA, 50 kG). *£, = 400 mm, gaz: hydrogene.

%

T


-

,


IAEA-CN-33/A 6-1 131

tire la densite superficielle de l'ion considere en supposant

qu 1 excitation et ionisation se font dans une couche assez fine

pour que densite et temperature §lectroniques ne(r) et Te(r)

puissent etre consid§rees comme constantes.

La figure 3 dqnne l 1 evolution de ces densites pour une

d§charge a 200 kA. La figure 4 montre qu'elles sont pratiquement

constantes lorsque le courant varie de 100 a 300 kA.

Notons que le carbone est sensiblement plus abondant dans cette

serie de mesures que dans la decharge particuliere representee

sur la figure 3. En fait la quantite de carbone est tres variable

d'une serie d'experiences a une autre. Pour l'oxygene, le

niveau donne fig.3 est sensiblement plus ilev§ que le

niveau moyen des decharges de la figure 4. La pression de

remplissage etait, dans ce cas particulier plus elevee et les

conditions de l'equilibre du plasma etaient modifiees.

(Constante de temps de la coque 30 ms au lieu de 80 ms).

B.~ Interpretations.

Considerons d'abord l'oxygene comme l'impurete dominante.

On suppose que cette impuret§, emise a 1'etat neutre par le

diaphragme et la paroi, franchit tres rapidement ses premiers

degres d'ionisation et se r§partit autour de 1'ensemble du

plasma en une couche dont l'epaisseur est de l'ordre de la

profondeur de penetration des neutres d'oxygene (quelques

centimetres). Dans cette couche, les temps caracteristiques

(en particulier pour 1'ionisation) sont plus petits que le

temps de confinement des particules T jusqu'a un degre

d'ionisation limite pour lequel 1'inverse se produit : l'oxygene

passe rapidement a l'ion 0 6+ (0 5+ -»• 0 6+ , xi = 138 eV ,

t^^O/l ms) . Par contre, cet ion a un temps d'ionisation tres

long (06+ -* o 7 + , xi = 74 ° eV , t js 1 s) et l'oxygene restera

a l'etat d'ion 0 6 + , sa quantite etant limitee par les pertes

vers la paroi et une migration vers le centre oH temperature

et densite permettent le passage aux ions 0 7+ et 0 8+ . La

radiance B (ph s -1 cm -2 sr -1 ) de la raie observee de_l'ion_

0 5+ (0 VI 1032) est directement liee au terme source Q*ne/dt]Q0

du au flux d'oxygene venant de l'exterieur

Idt Jo° ^ ^ Q^

ou Ar est l'gpaisseur de la couche, Z la charge de l'ion

limite (Z = 6 pour l'oxygene). S5 et Qi-n sont respectivement

le coefficient d'ionisation et d'excitation de l'ion 0 5+ .

Le calcul de ce terme source n§cessite la connaissance de Ar.

Si on l'estime cependant a quelques centimetres, il vaut

3.1016 cm -3 s~l. Ces memes electrons, supposes uniformement

repartis dans le volume du plasma, correspondraient a un gain

approximatif de 10 16 cm -3 s -1 , valeur tres superieure S celle

deduite des mesures en hyperfrequence. A cette source d'electrons

correspond un temps de confinement petit tel que, si ces

electrons Staient reellement perdus § partir de la zone centrale

chaude, la puissance correspondante serait sensiblement

superieure a la puissance injectee. Les phenomenes observes

sont done limit*§s a la couche peripherique o\X le temps de

confinement d§duit du terme source est voisin de la milliseconde.

La puissance perdue correspondante se partage entre la

puissance de chauffage des electrons et la puissance dans les


132 EQUIPE TFR

raies, (la seule raie 0 VI 1032, rayonne 0,15 MW en supposant

l 1 emission uniforme sur toute la surface du plasma). La puissance

totale ainsi perdue correspond a une fraction importante

de la puissance inject§e (0,6 MW).

Dans ce modele, la densite totale d'oxygene dans la

couche est pratiquement egale a la densite d'oxygene 0 6+

2_, n. w n6 ; ce qui conduit a une densite superf icielle

O 1 6

2 Ar£ n. « 3.10 13 cm" 2

o

Pour le molybdene, le modele utilise pour l'oxygene est

encore valable pour evaluer l'ordre de grandeur du flux (temps

d'ionisation dans la couche ~ 1 ms). II vaut approximativement

lO^ 2 cm -2 s -1 et est environ 5.10 3 fois plus petit que

le flux d'oxygene. Pour le fer, le temps d'ionisation de 1'ion

Fe 11++ est beaucoup plus long que le temps de confinement dans

la couche et la raie observee ne-peut pas s'interpreter en

terme de flux.

C- %eff st impuretes au centre.

Ce calcul a et§ fait en supposant le champ electrique E

et Z5ff independants de r suivant la formule

>ff = rL

lM[^(w^^^rdr

LogA(r)

ou YT est la correction de Lorentz, la quantite entre cro-_

chets gtant due aux electrons pieges ponderee par v* / 3_7

qui tient compte de la transition entre les regimes plateau et

banane. Les barres representent les cas extremes ou v* est

N 9

8

7

6

5

A

3

2

1

I

Hydrogene

-

-

T

|

i

•0-


IAEA-CN-33/A 6-1 133

soit nul,soit tres grand. Les triangles representent les valeurs

obtenues en calculant v* a partir des profils experimental^

de temperature et de densite. (figure 5).

Dans l'hypothese du paragraphe precedent, a un Zeff de

6 correspond une proportion d'oxygene 0 8+ de 9% par rapport

a la density electronique. La densite correspondante en fin de

dScharge est par consequent de 4,1012 cm~3. si cette densite

finale resulte d'un flux d'oxygene 0 5+ venant de la couche

peripherique et ionis§ jusqu'a 0 , le flux calcule en

prenant un temps de confinement central de 300 ms est de

2 10 13 cm -3 s~l . Le flux entrant d'oxygene, a la pgripherie

est de 5 10 15 cm -3 s -1 . Une petite fraction migre done vers

le centre, la majorite retournant a la paroi.

REFERENCES

Z~l_7 HINNOV, E. et HOFMANN, F.W. - Journal Optical Society

of America 5_3 (1963) 1259.


IAEA-CN-33/A 6-2

DECHARGES A FORT COURANT DANS TFR

EQUIPE TFR

Association EURATOM-CEA sur la fusion,

Departement de physique du plasma et de la fusion contrdlee,

Centre d'etudes nucleaires de Fontenay-aux-Roses,

Fontenay-aux-Roses, France

Abstract-R£sumd

HIGH-CURRENT DISCHARGES IN THE TFR DEVICE.

Macroscopically stable discharges have been obtained in D2 and H2 up to currents of 300 kA and durations

of 0.5 s, with a toroidal field of 50 kG. A servo control device ensures satisfactory plasma equilibrium.

For Ip = 300 kA, the safety coefficient at the edge is q = 2. 8; the average electron temperature Te = 1 keV;

the central ion temperature Tj = 850 eV (D2) and 1 keV (H2); the average electron density fig = 4 x 10 13 cm" 3 ;

the liner density of kinetic energy W = 22 J/cm (D2) and 18 J/cm (H2); the energy confinement time

Tp = 16 ms (D2) and 11 ms (H2). During the discharge W increases with the current. The numerical simulation

of the discharges follows the experimental results, retaining classical behaviour for the ions, but keeping the

transport coefficient abnormal for the electrons. When %


136 EQUIPE TFR


1-1- Caracteres g£n6raux d'une decharge .

IAEA-CN-33/A 6-2 137

La figure 1 montre, pour lp= 300 kA, BT = 50 kG, Involution temporelle

des principaux parametres d'une decharge dans H2 .

L'equilibre radial et vertical du plasma est assure par la coque en cuivre

et par une boucle de contre reaction . A la fin du plateau de courant,d t=370ms,

la tension aux bornes du circuit d'induction est invers^e pour require rapidement

le courant, jusqu'au temps t=430ms. II decroft ensuite avec sa constante de

temps propre jusqu'a 60 kA, puis tombe a z£ro en 4ms. Dans les premieres dechafges

de TFR / l / , cette rupture brutale se produisait spontanement a partir

du plateau de courant; les experiences ricentes ont montre que cette rupture

etait associee a un mauvais centrage du plasma.

La croissance de la density electronique moyenne (TTe) est Vindication

du recyclage 6 la paroi. Pour toutes les decharges effectu6es avec a=20cm on

trouve : 7Te = (1,3 * 0,2) 1 0l 1 lp ( cm-3) o0 lp est en kA . ( Pour des decharges

de faible in tensite, lp = 100 a 150kA, realis^es avec a=17cm, Involution de

7Te pendant le plateau de courant varie suivant I'etat de proprete de la chambre:

apres une remise a l'air"neCiC te / apres un etuvage prolonge~rTe decroft d'un

facteur 2 en 100ms).

Des mesures thermomgtriques montrent que la majeure partie de I'energie

dissipee pendant le plateau de courant tombe sur la paroi; le diaphragme

n'en recevant qu'une faible part.

La temperature electronique centrale atteint tres t6t son maximum

(t=40ms) puis decroPt Ugerement malgre I'augmentation du courant, alors que

la temperature ionique centrale, ainsi que l'6nergie contenue dans le plasma

croissent en meme temps que le courant .

I -2- Profils de Te et ne .

Les resultats des mesures de la density et de la temperature electroniques

par diffusion Thomson sont portes sur les figures 2a et 2b pour I =300kA dans H2 .

(L 1 interpretation des spectres diffuses tient compte de I'effet relativiste).

•f*

8

*U


8

6

U

2

-

l

I "

D

T—

a

A

1 1 1 1

-20 -15 -10 -5 0

r (cm)

0

A

r


D

A


1

a

A

1

a

A


....,

a

A


-r — r

erreur typique

1

D

A

1 1 1 1

+5 +10 +*> +20

FIG. 2a. Profil de densite electronique (H2 - 50 kG - 300 kA).

• 40 ms; A 100 ms; D 300 ms.

-


138 EQUIPE TFR

2 -

1

1

D

I

A

0


A

a


1

A


D

1

-20

i

-15

i

-10

i

-5 0

r (cm)

i

+5

i

+10

i

+15

i

+20

A

Q

1


1 1 !

I erreur typique

FIG.2b. Profil de temperature electronique (H2 - 50 kC - 300 kA).

• 40 ms; A 100 ms; D 300 ms.

FIG.3. Temperature electronique centrale Te(o) et moyenne Te pour differentes valeurs du plateau de courant.

C Te (O) - H2; A Te(o) - D2; • T^ - % • T2 - D2.

Au cours de la croissance du courant, le profil de temperature s'elargit

comme indique' dans le tableau ( r0 est le rayon a mi-hauteur ). Cet effet se

t

r o

40 - 50 ms

0,3 a

100 - 150 ms

0,4 a

D

A

300 ms

0,5 a

retrouve dans I'ensemble des decharges etudi6es. Par contre, la largeur du

profil s'est av&r6e stationnaire sur le plateau de courant.

Sur la figure 3 , les valeurs des temperatures 6lectroniques,centrale

Te(o) et moyenne Te,sont port6es en fonction de lp; notons que ne croPt

avec lp comme indiqu6 plus haut (S 1-1).


IAEA-CN-33/A 6-2 139

Les valeurs obtenues pour la density integree sur un diametre par diffusion

Thomson, par interferom§trie microondes (A= 2mm) et par interferometrie

infrarouge (* = 0,337 mm ) sont en accordJusqu'a lp= 200 kA;les profils obtenus

par diffusion Thomson et microondes s'accordent; au-dela,le profil mesure par

microondes est beaucoup plus large et de forme differente. Notons que ce dernier

est obtenu d 10cm du diaphragme (mesures le longdu tore), alors que la mesure

par diffusion Thomson en est a 300cm.

1-3- Temperature ionique .

La temperature ionique centrale a ete deduite du spectre des neutres

rapides, et, pour les decharges intenses dans le deuterium, du flux de neutrons

d'origine thermonucleaire. Pour les plus faibles courants ( lp


140 EQUIPE TFR

tXM-

1 ,15 2

Xr?(IpBTReR 2 HA^

FIG.5. Loi d'echelle pour la temperature ionique. O D2; •Hj. (Ip: kA, BT : kG, rig: cm" , R: cm).

) __ -r, . 77efoJ

experimentaux de ne et Te ( § 1-2 ) et en admettant que Ii.v'-i ~~ '< '' >'/n.{. (o)

Pour ^valuer la partie resistive VR de la tension par tour mesur6e Vm, on a utilise

le fait que , sur le plateau de courant, le profil de Te etait stationnaire,

done VR (plateau) = Vm (plateau) . Pour d'autres instants de la decharge, la

partie selfique de Vm a ete deduite des mesures magnetiques.

L'evolution de


IAEA-CN-33/A 6-2 141

FIG. 6. Temps de confinement de l'energie. BT = 50 kG; O H2; A D2 - BT = 40 kG; V D2; D H2; O H2

conditions differentes - BT = 20 kG; + H2; x D2; en noir: etat stationnaire.

tout effet de peau soit supprime au d£but de la decharge et que le coefficient

de sScurite sur 1'axe reste ^ 1 . Cet accroissement de Ke peut s'interprSter

comme un effet d'instabilit^s dues a dJ / dr \ 0 au d6but de la d^charge et

a qaxe^ 1 ensuite.

4- La quantite de neutres entrant dans la d^charge reste constante apres

les premieres dizaines de ms.

II- Interaction plasma-parois;

La premiere campagne de mesures sur TFR (avril a juin 1973 ) fut interrompue

par le percement de I'enceinte a vide au cours d'une dgcharge alors que

les parametres gtaient : lp ss. 150kA; By = 35 kG; ~iTe = 6.10l2Cm-3. Ce percement

, d'abord attribug a la fusion d'un 6l6ment en molybdene du canon a

electrons utilise 1 pour initier la d6charge /!/, r^sultait en fait d'une forte

interaction du plasma avec la paroi /2/ .

Des dgcharges analogues ont pu etre reproduites et l'4chauffement d/'un

plan d'6preuve ( portion de paroi d'environ 40 cm2 de surface, mobile suivant

un rayon vertical ) a 6t6 mesur6 par television, en observant Involution de son

image infrarouge. Le d6p6t d'Snergie-est tres localise ( ^ lcm2), commence

tSt ( C —50 ms ) et se poursyit jusqu'a Pextinction du courant. Pour

"n"e cs 1013 cm-3 , I = 150 kA, une dur6e de 0,4 s, l'6nergie recue a 22 cm

de I'axe peut atteindre 200 J. Cette €nergie est suffisante pour expliquer les

impacts observes sur la chambre en inconel de 0,5 mm d'6paisseur /2/. L'6nergie

d6pos6e d^croft quand la density 6lectronique croft, les Energies mesur6es

varient de quelques joulesa 200 joules.


142 EQUIPE TFR

FIG.7. Deplacement de l'impact sur le plan d'epreuve en fonction de sa position radiale (35 kG - 130 kA).

Cette interaction est due a des electrons £nergiques pieg£s dans les miroirs

locaux et d£rivant verticalement dans le champ toroidal . L'energie transversale

de ces electrons r£sulterait d'une instability prenant sa source dans le

faisceau d'electrons decouples. Les observations suivantes supportent cette

interpretation :

- L'interaction n'apparaft que dans les decharges a faible density, et

ne commence que lorsque la densite d£crort au-dessous d'une densite critique

^e ^ 1 • 10'^ cm"*3. Ce type de decharge est favorable a la creation d'electrons

decouples. Leur energie, deduite de leur spectre de freinage sur les ions du

plasma mesure perpendiculairement a leur vecteur vitesse/est de I'ordre de

6 MeV.

- La position de la zone d'impact varie avec le deplacement radial

du plan d'epreuve en restant sur une surface isobare magn6tique (fig .7).

- Les impacts correspondent au sens de derive des electrons. L'inversion

du sens du champ toroidal transfere les impacts du bas, vers le haut de la

configuration .


Frequence [GHz]

150 300

1/X [cm- 1 ]

FIG. 8a. Spectre d'emission du plasma entre

50 et 400 GHz - decharge avec interaction:

n^ = 8 • 10 12 cm" 3 ; BT = 40 kG.

IAEA-CN-33/A 6-2 143

Frequence [GHz]

150 300

1/X [cm" 1 ]

FIG. 8b. Spectre d'emission du plasma entre

50 et 400 GHz - decharge normale: n^ = 3,5 • 10 13 cm"

B'p 40 kG.

- L'analyse des rayons X emis par le plan d'6preuve permet d'evaluer

l'6nergie des electrons qui s'y d£posent a 50 keV.

- Les electrons sont expuls6s du plasma par bouff6es pe>iodiques toutes

les 200 a 300 fjs. Cette modulation s'observe a la fois sur le courant collects

par le plan d'6preuve, sur le rayonnement X et sur le rayonnement HF 6mis

entre 50 et 400 GHz.

2)

- L'analyse du rayonnement HF montre que la puissance €mise dans

les d^charges avec interaction est maximale pour des frequences d£cal


144 EQUIPE TFR

des ions s'explique par la conductivity thermique neoclassique et I'echange de

charge. La faible croissance de Te et £?£ pour L >• 200 kA pourrait etre en relation

avec des coefficients de transport anormaux associes a des instabilit^s

ou (et) 6 la contamination du plasma par les impuret6s.

Une forte interaction plasma-paroi existe pour des densites

~ne -^ 10^3 cm" . El I e est le fait d'electrons energiques pi£ges dans les miroirs

locaux qui seraient chauffes transversalement par une instability faisceau d'£lectrons

decouples - plasma.

REFERENCES

/!/ Premiers resultats TFR- Equipe TFR, Vlth European Conference

on controlled Fusion and Plasma Physics - Moscou (URSS)

30-7 au 3-8 1973.

/2/ Plasma wall interactions in the TFR machine- Equipe TFR,

Conference on Surface Effects in controlled Thermonuclear Fusion

Devices and Reactors.- Argonne (USA), 10-12 January 1974.

/3/ Neutres atomiques et impuretes dans TFR - Equipe TFR, 5eme

Conference sur la Physique des Plasmas et la Recherche concernant

la Fusion NucUaire ContrSlge - Tokyo, 11-15 Novembre 1974,

ces comptes rendus, IAEA-CN-33/A6-1 .


DISCUSSION

ON PAPERS IAEA-CN-33/A 6-1, A 6-2

A. Y. WONG: The observed lack of increase of Te and 7"confin t with

increasing tokamak current is probably at variance with your original

design goals. Could you comment on the causes of such discrepancies

and their impact on future machines?

J. TACHON: Two interpretations are possible to explain our results

f° r T confinement an< * Te:

1) The high-Z content in the plasma core could dissipate the energy

by line radiation, free-free and free-bound bremsstrahlung;

2) The energy losses by impurity radiation would be mainly concentrated

at the plasma edge. Turbulence would increase the heat

transport from the centre to the edge.

As regards future machines, I should point out that we cannot extrapolate

our results for currents higher than 3 00 kA. However, we think that an

increase in the size will bring great advantages as far as the impurity and

heat-conduction problems are concerned.

145


IAEA-CN-33/A7-2

OPMA nOIIEPEHHOrO CEHEHH5I nJIA3MEHHOrO

UIHYPA B nEPCTEHbKOBOM TOKAMAKE

A.B.BOPTHHKOB, H.H.EPEBHOB,

C.H.rEPACHMOB, B .T . XYKOBCKHH,

I0.C.MAKCHMOB, B.H.nEPrAMEHT,

M .K .POMAHOBCKHH

HHCTHTYT axoMHOfi 3HeprHH HM . H .B .KypMaTOBa,

MocKBa,

C0103 CoBeTCKHX CoLiHanHCTHiecKHX Pecny6;iHK

Abstract-AHHoramw

THE SHAPE OF THE TRANSVERSE CROSS-SECTION OF A PLASMA COLUMN IN THE FINGER-RING TOKAMAK.

It follows from theoretical calculations that, all other conditions being equal, the gain in discharge

current density in the finger-ring tokamak, as compared to the tokamak with a circular section, is determined

by the degree of elongation of the plasma column. The authors report experimental results relating to the shape

of the plasma cross-section in the T-9 device (finger-ring tokamak), in which the plasma column was

shaped solely by a copper casing. The size and shape of the cross-section were evaluated by measuring the

spatial distribution of electron density and of the luminous intensity of certain spectral lines (Hg, C III, C V),

and also from the distribution of the poloidal field near the casing. The experimental results show that during

the shaping process the plgsma column is elongated in a vertical direction, the semi-axis ratio being b/a ^ 2.

At certain values of the discharge current and initial pressure of the neutral gas, there may also be two plasma

columns, above and below the plane of symmetry. When the shaping process is complete, the elongation of

the plasma section diminishes and there is a sharpening of the electron density distribution and discharge current

density distribution profiles — in other words, there is a contraction of the plasma column as a function of

discharge current, plasma density, and toroidal magnetic field. In the experiments described, the discharge

current ranged up to 20 kA, toroidal magnetic field intensity up to 10 kG, and mean plasma density up to

3 x 10 3 cm -3 .

*OPMA nOIIEPEHHOrO CEHEHHfl nJIA3MEHHOrO HIHYPA B nEPCTEHbKOBOM

TOKAMAKE.

H3 TeopeTHHecKHX pacieTOB cneayeT, «JTO Bbinrpbim B njioTHOCTH pa3p»flHoro TOKa

B IlepcTeHbKOBOM TOKaMaKe no cpaBHemuo c TOKaMaKOM Kpyr/ioro ceieHHH onpcue/iaeTcfl npH

npoMHx paBHbix ycnoBwix cTenem>io BMTHHVTOCTH njia3MeHHoro mHypa. B .gaHHofi pa6oTe H3-

.naraioTCH SKcnepHMeHTanbHMe pe3yjibTaTH no onpeaejieHwo $OPMM ce^eHHH njiaaMeHHoro mHypa

B yciaHOBKe T-9 (IlepcTeHbKOBbiH TOKaMaK), Koraa


148 EOPTHHKOB H ap.

BBE^EHHE

npeae/ibHoe 3HaneHHe Be/iHHHHbi TOKa B TOKaMaKe MOXHO noBHcmb

nyxeM H3iieHeHH3 (£opMbi nonepe^Horo ceneHHH n;ia3MeHHoro uiHypa, a

HMeHHo: nyTeM BbiTflrHBaHHfl ero B,no/ib OCH CMMMeTpHH npw HeH3MeHHOM

paana/ibHOM pa3Mepe [1 ] . B STOM c/iynae win nra3MeHHoro uiHypa snnvm-

THMecKoro ceneHHH c no/iyocflMH "a" H "b" Bbipa^ceHHe RJIH q HMeer BHA:

cBT a2 + b2

^ l'27rR0 2ab (1)

A cBT

AHa^orHMHoe Bbipa>KeHHe M,JIH uiHypa Kpyr;ioro ceHeHMJj q = . „ ,

TO-ecTb, npH oflHHaKOBbix BT , R0 H q no/iynaeTCfl Bbinrpbiui B nnoTHOcTH

a 2 +b2

TOKa B ———— oe3 yueHbmtHHH Benvmmibi KOsqExfjHnneHTa 3anaca ycTOH-

MHBOCTH.

B aaHHOH pa6oTe npuBe^eHM 3KcnepHM6HTa;ibHiie pe3y;ibTaTbi no onpeaenemvo

opMbi nonepe^Horo ce^eHHH nra3MeHHoro uiHypa B ycTaHOBKe

T-9 ("IlepcTeHbKOBbiH ToKaMaK 1 ').

OnHCAHHE YCTAHOBKH H .HHArHOCTHHECKOH AnnAPATYPBI

CxeMa ycTaHOBKH T-9, reoMeTpHMecKne pa3Mepbi H 3/ieKTpOTexHHMec-

Kwe napaMeTpbi onHcaHbi B pa6oTax [2,3] . 06mHH BHA KOHCTpyKTHBHbix

3/ieMeHTOB js.au ua pnc . 1 . BHeiiiHHfl BaKyyMHaa KaMepa cae^aHa H3 Hep-

»aBeiomeH cTa/in B Bune flByx nonyTopoB npaMoyro/ibHoro nonepe^Horo ce-

MeHHa . 06e no/iOBHHbi coeanHeHbi c noMOinbio BaKyyMHOro yn;ioTHHTe;ifl

H 3;ieKTpMMecKH H30/iHpoBaHbi flpyr OT apyra.

BHyTpn KaMepbi ycTaHOB/ieH MeflHbiH KO>Kyx, nonepeHHoe ceneHHe KO-

Toporo HMeeT cpopMy cerMeHTa. To^mHHa cTeHKH Koxyxa - 6 MM. KOacyx

HMeeT flBa nonepenHbix pa3pwBa IIIHPHHOH 15 MM. B O^HOM H3 nonepeMHbix

pa3pbiB0B 3aKpen/ieHa Bo;ib


norm

IAEA-CN-33/A7-2 1

PHC.I. CxeMa ycTaHOBKH T-9. BT = 10 Krc ; J = 20 KA ; ncp = 3 • 10 13 CM" 3 ; R0= 36 CM ; 2a0

2b =56 CM; K = ^-= 4

o a0

noc^eaoBaTejibHO c B03jtyuiHbiM HH^yKTopoM. Be^HMHHa KOMneHcnpyromero

noiiH perynHpoBanacb KOjiHHecTBOM noflK^iOHaeMbix BHTKOB. KpoMe TOTO,

3TH BHTKH co3flaioT nonepeHHoe MaramHoe none &nn. y#ep>KaHHH n;ia3MeH-

HOTO uiHypa B paBHOBecHH. Co3aaHHeH noflflepxaHHe BbiTHHyTOH $opMbi

nonepe^Horo ce^eHHH n/ia3MeHHoro umypa o6ecneMHBaeTCfl Me^HbiM Koxy-

XOM H CHCTeMOH H3 IIieCTH TOKOBblX KaTyUieK. O^HaKO, B OnHCaHHblX HHJKe

SKcnepHMeHTax STH KaTyiiiKH He Hcno/ib30Ba;iHCb. CeMeHHe nna3MeHHoro

niHypa (JopMHpoBa^ocb TO/ibKO MeflHbiM KOxyxoM. Be/iHMHHa TopoH^a^b-

HOTO MarHHTHoro nona B^ Bapbupc-Ba/iacb B npeae^ax OT 3 Krc RO 10 Krc.

MaKCHMa/ibHasi Be/iHHHHa ycTO&HHBoro TOKa pa3pfl#a — 20 KA . JlaBneHHe

BOflopoaa B KaMepe H3MeH5i;iocb B npe^e/iax 6 • 10 Topp


150 BOPTHHKOB H ap.

pacnpeae^eHHH cflBuroB (|)a3 B nonepeHHOM ceneHHH n;ia3MeHHoro uiHypa.

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3/ieKTpoHOB; 3) c^enaTt KaMecTBeHHbie 3aK;noHeHHH o pacnpeae/ie-

HHH n^oTHOCTH 3/ieKTpoHOB B ceMeHHH njia3MeHHoro umypa.

Pacnpeae/ieHHe sjieKTpoHHOH TeMnepaTypbi, flHHaMHKa pa3orpeBa,

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npOCTpaHCTBeHHOH H BpeMeHHOH 3aBHCHM0CTH HHTeHCHBHOCTH CneKTpaflb-

HHX /IHHHH: H6(X = 4861A); CIIKX = 4647A) ; CV(X=2271A); OV(A = 2781A)

B ropH30HTajIbHOM H BepTHKajIbHOM HanpaBJieHHHX.

YCTOHHHBOCTB nJIA3MEHHOrO IIIHYPA

06^acTb ycTOHMHBoro npoieKaHHH KBa3HCTau.HOHapHoro pa3pH^a Sbi/ia

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MarHHTHOro nojia H HanaxibHbix flaBJieHHHx BOflopofla. TaKaH 3aBH-

CHMOCTb j\m P„ = 2-10" 4 Topp npHBe^eHa Ha pHc.2.

IlpH $HKcnpoBaHHOM 3HaneHHH BT BejiHHHHa MaKCHMajibHoro TOKa BHana/ie

xiHHefiHO B03pacTaeT c POCTOM HanpH^ceHHH Ha o6xofle. OflHaKO np« onpe-

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25-

20-

15 -

10-

-

/

/ -

/

/BT=iOKrc

9 / x

c/ y&^itSurc

df °BT=5Krc

y

/*BT-3,8Krc

1 1 1

i i i i

12 16 20

(B)

24 28

PHC.2. 3aBHCHMOCTb Be^HHHHM MaKCHMa^bHoro TOKa OT Haia;ibHoro HanpaaceHHH Ha o6xoae.


IAEA-CN-33/A7-2 151

flaioTca pe3KHM HapacTaHHeM aMn^HTy^bi BbicoKonacTOTHbix Ko;ie6aHHH Ha

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B npOTHBO$a3e C KO«e6aHHHMH TOKa, CUTHajlbl C 30HflOB B BepXHeH H HHX"

Hefl o6«aCTH Ca3Hp0BaHbI C H3MeHeHH3MH TOKa.

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TO-ecTb, npoHcxo^HT cKpyrvieHne ceneHHH nra3MeHHoro umypa.

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B pexHMax c J> J'Kp Ha6juoaaioTCH Hepery/istpHbie Ko;ie6aHHJj $opMbi nonepeMHoro

ceneHHa n;ia3MeHHoro uiHypa. Be^HMHHa KpHTHnecKoro TOKa cyiyecTB€HHO

33BHCHT OT BaKyyMHOH noaroTOBKH pa3paiflHOH KaMepw . IloBe-

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J< JKp , 2a= 14 CM,P = 2-10" 4 Topp.

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Haeicfl pa3orpeB n;ia3Mbi (noHBJiaeTCH H3/iyHeHHe AHHHH CV), yBe/iHHHBa-

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O pa3Mepax H $opMe nonepenHoro ceqeHHH n^a3MeHHoro niHypa MOX-

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(Br) nojionn.anbuoro nonn, H3MepaeMoro B6^H3H BHyTpeHHefi no-

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152 EOPTHHKOB H Ap.

< 20

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yKa3biBaex Ha cTaSH^BHOcib opMbi nonepeHHoro ceieHHfl n;ia3MeHHoro uiHypa

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npHBO^HTb SKcnepHMeHTa/ibHbie aaHHbie ann TpeTbeft MH^^wceKyHflbi.


IAEA-CN-33/A7-2 153

-16 -8 0 8 16 bz(cM)

BT=10Krb;t = 2MC

PHC.4. 4>a3QBbie KpHBbie B MOMem BpeMeHH t=2 MC nocne HaHa/ia pa3p«4a.

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A 6 i ^

a (CM)

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t=3MC

t a 3MC

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b,(cM>

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s^eKTpoHOB B ceHeHHH naa3MeHHoro iiiHypa pacTeT c yBe/iHieHHeM TOKa.

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BepTHKa/iH npaKTHMecKH He 3aBHCHT OT Be^tHMHHbi TOKa pa3pH^a.

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cTeneHb HarpeBa no ceneHHio n;ia3MeHHoro niHypa, 4aHW

Ha pHc.7. EC^H outeHHBaTb BMTiiHyTOCTb nna3MeHHoro niHypa ("K") no


154

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-16 -12 -8 -h 0 A 8 12 b2(cM)

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a„ (CM)

x/l^ |\\ N *

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1 i%

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Ka^H (bz) ann pa3nHMHj>ix TOKOB pa3paaa.

OTHOiueHHio xapaKTepHbix pa3MepoB pacnpeae/ieHHH H3 pnc.7, TO JUJIH

2a = 12 CM "K" c/ia6o 3aBncHT OT BejiHHHHbi TOKa H paBeH 1,4 nnx /IHHHH

CV H 1,6 RJIH nHHHVi CIII . Jinn 2a = 14 CM pacnpeae^eHHH HHT6HCHBHOCTH

IIHHHH CV no BepTHKajiH He 6M;IH H3MeHeHbi, o^HaKO B paAHa;ibHOM HanpaB-

/ieHHH oHa Ha6/no,aaeTC5i B 6ojibweii o6.aacTH. BoAee cvuibnoe ynjiomenvie

B LteHTpe yKa3HBaeT Ha nporapaHHe ;IHHHH CV Ha OCH njia3MeHHoro uiHypa.

PacnpefleneHHH TaHreHU.a/ibHoro KOMnoHeHTa noTOHfla^bHoro now BT

npHBeaeHbi Ha pnc.8 JUIH flByx pa^HanfaHbix pa3MepoB n/ia3MeHHoro iimypa.

Pacnpefle/ieHHe BT npw cyHKCHpOBaHHOH BejiHMHHe 2a He 3aBHCHT OT BenH-

MHHbi TOKa pa3pfl.ua . OflHaKO, npH 2a = 12 CM pacnpeae/ieHHe 6o;iee O6OCT-


IAEA-CN-33/A7-2 155

tf>—xy^lf

o 20 KA

x 17 KA

A 9 KA

0 1 2 3 4 5 6 7 8 9 10

MAI"HHTHblE 30Hqbl

BT = 10Hrc PH =2-10" 4 TOPP t=3Mc

2a

14

12

CM

CM

12 CM

PHC.8. Pacnpeae^eHHe TaHretiqHanbHoro KOMnoHeHTa no;iOH,aa.ni>Horo no;ra BT .

16 12 8

nl-10 U cM 2

BT = 10Kfc P=2-10Topp t = 3MC

H2

PHC.9. PacnpeacneHHe $a30Bbix cuBHroB npH KpHTtraecKHX 3HaMemwx TOKa pa3p»aa ana pa3-

^HHHoro no^oxeHHfl noABHXHOH 4Ha$parMbi.


156

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/

If /£Ss

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\V\

V -*-x-x-x-x-,,..:

- 2Q4

2 Q

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QR(CM)

BOPTHHKOB H ap.

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A-J = 8 KA

X-J = 12KA

-6 -A -2 0 2 4 6 8 10 bz(cM)

BT=10Krc ^ =2-10"'TOPP t = 3MC

PHC.10. PacnpeaeneHHe HHTeHCHBHOCTH CBeneHHH /IHHHH CHI H CV npn KpwTiroecKHX sHaneHHHx

roxa pa3pfl.ga una pa3;iHHHMX no/io*eHHH noaBHKHOH ^Ha$parMi.i.

peHHoe, neM npw 2a = 14 CM. H3 cpaBHeHHH 3KcnepHMeHTa;ibHbix pacnpefle^eHHH

C TeOpeTHMeCKHMH MO>KHO CKa3aTb, 1TO n^a3MeHHbIH IUHyp B 3TOM

cjiynae HMeex pacnpe^e^eHHe II;IOTHOCTH TOKa, cooTBeTCTByiomee 6onee

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BbiT^HyTyjo $opMy. Ilpw qpHKCHpoBaHHOH BenHMHHe 2a cpopMa n/ia3MeHHoro

iiiHypa He 3aBHCHT OT Benvmnuu xoKa pa3pflfla. H3 cpaBHeHHH $opMbi nonepeMHoro

ceMeHHH una. pa3^HMHbix pa3MepoB 2a crce^yeT, HTO donbmeMy

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ceneHHH.

B CBH3H c TaKOH Ha6jiio,zieHHOH 3aBHCHMOCTbro npe,acTaB/iJi;io HHTepec

npoBecTH SKcnepHMeHTbi no n3MepeHHio


IAEA-CN-33/A7-2 157

Be/iHMHHbi KpHTHnecKoro TOKS, TaK H K CKpyrneHHio nxia3MeHHoro uiHypa.

JXanhHeiimee yMeHbmeHHe pa^Ha/ibHoro pa3Mepa Mexay a«a$parMaMH ny-

TeM nepeMemeHHH noflBH^KHOH aHacjjparMbi npHBOflHT jiHiiib K yMeHbiueHHio

BejIHHHHbl KpHTH^eCKOrO TOKa 6e3 H3MeHeHHH K03(|) 6bi, flo;i>KHa yMeHbiuaTbCH KaK a 2 . OflHaKO oqeHKH

(no paccTOHHHio Me»ay flHaparMaMH H/IH no pacnpe^e/ieHHio CHI H3 pHC.10)

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0,5.

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0 5 10 15 20 bz(cM)

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BpeMeHH.


158 BOPTHHKOB H np.

HEKOTOPblE OUEHKH

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3 0,5

200 300 400

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500


IAEA-CN-33/A7-2 159

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KOHxypa MamnTHOH noBepxHOCTH Sj (pHc.ll). BHAHO, MTO oqeHOMHaa


RELAXATION OF TOROIDAL DISCHARGES

TO STABLE STATES AND GENERATION

OF REVERSE MAGNETIC FIELDS

J.B. TAYLOR

Eur atom-UKAEA Association for Fusion Research,

Culham Laboratory, Abingdon, Oxon,

United Kingdom

Abstract

IAEA-CN-33/PD-1

RELAXATION OF TOROIDAL DISCHARGES TO STABLE STATES AND GENERATION OF REVERSE MAGNETIC

FIELDS.

A striking feature of toroidal discharges is the appearance of a quiescent state in which, if the pinch

ratio 6 is large, there is a reversed toroidal magnetic field. It is shown that this remarkable behaviour is

the result of plasma relaxation under topological constraints. For a perfectly conducting plasma there is an

infinity of such constraints, essentially one for each field line. When all these are taken into account the

final state may be any equilibrium. However, in the presence of small departures from perfect conductivity,

lines of force may break and only one constraint remains. The final state is then a unique, stable configuration

depending only on the pinch ratio 0. The critical value of 0 for the onset of reversed field in this

unique state agrees well with measurements on Z.ETA. When 0 exceeds a second critical value, the final

state becomes helically deformed and the onset and amplitude of this deformation are calculated. When

the TOKAMAK regime is examined it is found that the relaxed state exhibits a marked qualitative difference

in field structure according as q is greater or less than unity.

1. Introduction

A well-known method for magnetic confinement of plasma is the toroidalfl

21

pinch as used in ZETA. ' In such experiments a toroidal field B0 is created

by external coils and a toroidal current I is then induced in the plasma. The

pinch-effect associated with this current produces the plasma compression and

confinement and the degree of compression depends on the ratio 2l/a B0 = 6,

where a is the minor radius of the torus.

A remarkable feature of these experiments is that after an initial,

violently unstable, phase the plasma frequently relaxes into a "quiescent"

state in which it appears to be grossly stable. Furthermore when the pinch

ratio 0 exceeds some critical value this relaxation is accompanied by the

generation of a reversed toroidal field in the outer regions of the plasma. A

similar quiescent behaviour is seen in TOKAMAK experiments but in these there

is no tendency to produce a reverse field - as one would expect since the G

values are always very small (« 1).

In this paper we describe a theory of the relaxation of toroidal plasma

which accounts for this remarkable behaviour and predicts the critical value

of 9 for the generation of reversed field. It also describes other phenomena

observed in toroidal discharges.

161


162 TAYLOR

In this theory the plasma is regarded as a conducting but viscous fluid

enclosed in a rigid, perfectly conducting, toroidal vessel. The initial state

is arbitrary except that both the magnetic field and current are tangential to

the conducting wall. The system is not in equilibrium and when released will

therefore move (usually violently) and dissipate energy before coming to rest.

Only when its energy is a minimum is it incapable of further rapid movement.

Hence the final state must be one which makes the energy a minimum subject to

[3]

any constraints which are imposed on the allowed motion. The major problem,

of course, lies in determining and applying the proper constraints.

2. Perfectly Conducting Plasma

For simplicity it is first assumed, as is indeed the case in most experi­

ments, that the plasma internal energy is negligible compared to the magnetic

energy Wm = /(B 2 /2)dT. Then we wish to minimise Wm subject to any con­

straints on the variations in B (without which the minimum would be B = 0).

These constraints arise from the fact that in a perfectly conducting fluid the

magnetic field must satisfy

where v is the fluid velocity.

|| - VX (v X B) = 0 (1)

As is well known, Eq»(l) implies that lines of force may be labelled by

the fluid elements on them and so be regarded as moving with the fluid velo­

city. Since this velocity is continuous, field lines cannot break or coalesce

(except where B = 0 which we exclude) and all topological properties of the

field lines are therefore invariant. Closed lines remain closed and if two

closed field lines are initially linked n-times then they must remain so

linked at all times.

These topological constraints can be expressed through the vector

potential, B = V X A. From Eq (1) this must satisfy

BA -> -»

|E = VXB + ^ (2)

where x is an arbitrary gauge. Since the energy is to be minimised over all

fluid motion there is no restriction on the component of (BA/9t) perpendicular

to B. It might appear that because of the arbitrary gauge the parallel com­

ponent is also unrestricted. Locally this is true, but since

3A*-«.if.

and x must be single-valued, (9A/9t) must be constrained so that

/ di ^ 8A . / dS =• 9A

.pB-s-aT and ) , |w| B -8F

vanish on any closed field line and on any magnetic surface respectively.


IAEA-CN-33/PD-1 163

These constraints on A can be expressed more conveniently as follows:-

for every volume V bounded by field lines the quantity

K = / A.B dT (3)

•'V

is an invariant of the motion. When the field lines are closed there is one

invariant for each line (the volume V then being an infinitesimal flux tube);

when the field generates magnetic surfaces there is one' invariant for each

surface.

The invariants K determine the number of field lines which link a given

line. That every K is indeed constant can be shown by calculating dK/dt

directly from Eqs (1) and (2). Furthermore one can show that if dK/dt = 0

for every flux tube then 3A/3t can be expressed in the form (u X B + \#). (The

velocity u need not be the fluid velocity v because the velocity of lines of

force is not unique. However^this difference leads to no observable

effects. ) Consequently, all the restrictions on 3A/9t, and therefore on

variations 6A, which arise from Eq.(1) are embodied in the invariants K.

The state in which the magnetic energy %/(V x A) 2 is stationary for all

variations 6A which leave the invariants unchanged and satisfy the boundary

condition that the electric field vanish, is given by

Vx B = X(a,b) B (4)

where X(a,b) is any function which is constant along field lines (B.^\. = 0).

This may be shown by introducing the constraints directly, with Lagrange

multipliers, or more simply by exploiting the equivalence of the constraints

and Eq (1) which implies that small variations 6A must be of the form

(ftf X B).

We see from Eq (4) that when all the constraints appropriate to a

perfectly conducting fluid are observed the state of minimum magnetic energy

is a force-free configuration. Exactly which force-free configuration can

only be found by determining X(a,b) from the values of the invariants K.

3. Imperfectly conducting plasma

In section 2 it was shown that the relaxation of an ideal plasma can be

described in terms of an infinity of invariants K. This description was

introduced so that we may now discuss the changes produced by small departures

from the perfect conductivity approximation of Eq.(l).

It is well known that the main consequence of any small departure from

perfect conductivity is that topological properties of the magnetic field are

no longer preserved and lines of force may break and coalesce. This can occur

even though departures' from perfect conductivity are too small to give rise to

significant overall dissipation. It seems inevitable therefore that during

the violent phase of the diffuse pinch such topological changes will occur.


164 TAYLOR

Once lines of force may break and coalesce the constraint that /A.B be an

invariant for each line of force must clearly be relaxed. However changes in

field topology are brought about by very small changes in the field itself.

Consequently the sum of JA.B over all field lines will remain invariant if de­

partures from perfect conductivity are small and the main effect of the topo­

logical changes will be merely to re-distribute the integrand among the field

lines involved. Hence we may expect the integral /A.B over the total volume

of the system to be a good invariant even though /A.B over each flux tube

certainly is not.

In an imperfectly conducting plasma, therefore, the final state of relax­

ation will be the state of minimum energy subject only to the single invariant

f

K0 = / A.B dT (5)

•Vo

where V0 is the total volume of the system. This minimum state is easily

found, using a Lagrange multiplier, and is given by

V X B = uB (6)

where u is now a constant and has the same value on all field lines. Thus, as

a result of the relaxation of topological constraints, the final state is no

longer any force-free configuration but must be a specific one, completely

specified once the value of [i and the appropriate solution of Eq.(6) are known.

4. Determination of \i

The determination of u and of the appropriate solution of Eq.(6) can be

carried out when the invariant K0 and the toroidal flux ^ are given. One pro­

cedure is illustrated in this section and another in section 6.

A torus of large aspect ratio may be represented by a cylinder of radius

a and length 27rR provided the ends of the cylinder are identified with each

other to simulate the topology of the torus. Then a solution of Eq*. (6) is

Bz = B0 Jo(^r) Be = B0 J^ur) (7)

where r,9,z are cylinder coordinates and Br = 0. The corresponding vector

potential is

Az = —(J0(ur) - J0(ua)) A9 = -^ Jx(ur)

where the arbitrary constants have been chosen so that

!*

r

6 Ae r de = v!' 0 Az dz = 0

The invariant K0 and the flux t can now be evaluated and the scale factor B0

eliminated to give

^o R j" ua(Jo 2 (ua) + Ji 2 (|aa)) - 2 Jp(ua) Ji(ua)

* 2 ~ a L Ji 2 (ua) j (8)

which defines u in terms of the ratio K0/ty 2 .


IAEA-CN-33/PD-1 165

It may be shown that KQ/H' represents the "Volt-Seconds" stored in the

plasma so that u is determined by the ratio (Stored Volt-Seconds/Toroidal

Flux). It is also related to the pinch parameter 6 by 9 = ua/2 as shown by

integrating Eq.(6) over the cross-section.

5. Appearance of Reverse Field

At this point it is convenient to discuss the appearance of reverse mag­

netic field. It is now clear that this will occur whenever the ratio K0/*!' 2 is

such that the appropriate solution of Eq,(6) possesses such a reverse field.

For the large aspect ratio torus this obviously occurs when J0(ua) changes

sign, i.e. when ua > 2.4 or when 9 > 1.2. This is in good agreement with the

experimental value of 9 ~ 1.4 observed for the onset of field reversal in

ZETA. [6 ''

6. General Solution

The situation is really more complicated than indicated in section 4, for

Eq.(6) may possess several solutions with the same value of K0 from which we

must select that of lowest energy. This is made easier by observing that the

energy difference between two solutions corresponding to the same KQ can be

expressed as

WA - WB = %(UA - ^B) KO (9)

so that selecting the lowest energy solution is equivalent to selecting that

with smallest u.

The general solution of Eq. (6), in a cylindrical system, can be

written: [7 ' 8]

B = L amk B mk (r)

where the individual modes are given by

with y = (u 2 - k 2 ) 2 r.

Br = (u 2 '-\*)h { k J ' m(y) + "^ Jm(y) j Sin (me + kz)

(u 2 - k 2 )^ i ^ J ' m(y) + j~ 3 * (y) }

Bz = Jm(y) Cos (m9 + kz)

Cos (me + kz)

The m = 0, k = 0 mode, which is identical with the solution discussed in

section 4, differs from all other modes. It satisfies the boundary condition

for any value of u and provides the toroidal flux ^. All other modes satisfy

the boundary condition only for certain discrete (eigen) values of u and do

not contribute to the toroidal flux *. These m £ 0 modes can therefore occur

only in conjunction with the m = 0, k = 0 mode.


166 TAYLOR

In seeking the lowest energy solution we need consider only the smallest

of the discrete uj.. A detailed investigation shows that this occurs when

ra = 1, ka = 1.25 and has the value ua = 3.11.

There are, therefore, two possibilities for the state of lowest energy.

Either (A), the lowest energy state is the symmetric configuration,

B = a0 B°(ur), in which a0 and u are determined by KQ and ^ as in section 4.

Or (3), the lowest state is a mixed m = 0, m = 1 configuration,

B = a0 B (ur) + a1 B lk (ur), with ua = 3.11 and ka = 1.25. In this case a0 is

determined by the toroidal flux ^ and a1 may then be found from KQ. (In fact

KQ/V|/ 2 now determines the ratio aj/a0.) No other states need be considered

as they must correspond to ua > 3.11 and so have higher energy.

We have shown, therefore, that the symmetric state described in section 4

is the state of lowest energy when its value of ua is < 3.11; that is when

K0A!' 2 < 8.21 'a. When this limit is exceeded the symmetric state will

have higher energy than the mixed m = 0, m = 1 configuration and the system

will relax to this helical state.

In the helical configuration ua and 9 do not increase with Ko/^ 2 ; any

increase in the VoSlt-Seconds applied to the plasma leaves 9 unchanged at 1.56

but increases the amplitude of the helical distortion.

7. Toroidal Effects - TOKAMAK

Toroidal solutions of Eq.(6) have been computed numerically. These show

that in the diffuse pinch regime (9 ~ 1) toroidal effects are negligible.

Field reversal still occurs at 9 - 1.2 even in a torus of aspect ratio 2:1.

a/

However in the TOKAMAK regime (e ~ R) there are marked toroidal effects.

One specifically toroidal feature is that whereas in all cylindrical

solutions the pitch of the lines of force decreases with radius, in toroidal

solutions the pitch may increase with radius. This occurs when ua < 2.7 a/R.

At this point the parameter q is ~ 0.8.

8. Conclusions

The behaviour of toroidal discharges is well described as relaxation to

the state of minimum energy subject to relevant constraints. If the plasma is

perfectly conducting there is a topological constraint associated with every

field line and the final state may be any equilibrium. However, in the

presence of small departures from perfect conductivity, topological con­

straints on lines of force are relaxed; they no longer retain their identity

and consequently only one constraint remains. The final state is then a

unique configuration depending only on the ratio'Stored Volt Seconds/Toroidal

Flux', or equivalently on the pinch ratio 9.


IAEA-CN-33/PD-1

By the manner of its derivation this unique state must be hydro-

magnetically stable (as may be shown directly from the Energy Principle). The

present argument therefore establishes the existence of stable discharges, in

both the TOKAMAK and pinch regimes, to which unstable discharges may relax.

In the diffuse pinch regime we deduce that when 0 exceeds ~ 1.2 the

relaxed state will be one with a reversed toroidal magnetic field, in agreerfi

i

ment with observations on ZETA. We also deduce that when 6 exceeds ~ 1.6 the

relaxed state will be helically deformed, a result for which there is also

T91

experimental evidence from ZETA and HBTX. The changeover from the

symmetric to the helical relaxed state is in accord with the boundary of

resistive instability in the symmetric state. However, unlike linear in­

stability theory, the present theory determines the amplitude of the helical

deformation.

In the TOKAMAK regime we find an important difference in the field

structure of the relaxed state according as q is greater or less than a

critical value qQ ~ 1. For q < q0 the pitch of the field lines decreases with

radius whereas for q > q0 the pitch increases with radius. This is a speci­

fically toroidal effect and in view of the sensitivity of stability to pitch

variation may be experimentally significant.

Acknowledgments

It is a pleasure to acknowledge the help and encouragement of

Dr R. S. Pease. I am also grateful to C. L. Thomas for the computations

referred to in section 7.

References

[1] ROBINSON, D.C., KING, R.E., Proc. 3rd Int. Conf. Plasma Physics and

Controlled Nuclear Fusion Research, Novosibirsk, USSR 1968, IAEA, Vienna,

Austria 1969.

[2] BUTT, E.P., et al., 2nd UN Conf. Peaceful Uses At. Energy (Proc. Conf.

Geneva, 1958) UN, Geneva, Switzerland, 1958.

[3] KRUSKAL, M., KULSRUD, Phys. Fluids 1, (1958) 265.

[4] NEWCOMB, W.A., Annals of Physics 3 (1958) 347.

[5] WOLTJER, L., Proc. Natl. Acad. Sci. US 44 (1958) 489.

[6] ROBINSON, D.C., Plasma Phys. 11^ (1969) 893.

[7] CHANDRASEKHAR, S., KENDALL, P.C., A. Phys. J. 126 (1957) 457.

[8] BARBERIO-CORSETTI, P., Plasma Phys. 15_ (1973) 1131.

[9] BODIN, H.A., et al., This Conf. proceedings.

[10] GIBSON, R.D., WHITEMAN, K., Plasma Phys. 10 (1968) 1101.

167


Session II

TOKAMAK EXPERIMENT II


Chairman: M. B.GOTTLIEB (USA)

Papers A 8-1 to A 8-4 (Alcator, Pulsator, Cleo, LT-3) were presented

by A. GIBSON as Rapporteur

Papers A 9-1 to C 5 (TM-1, TM-3, TO-1, FT-1) were presented

by V.V. ALIKAEV as Rapporteur

Papers A 10-1 and A 10-2 (Doublet) were presented

by T. OHKAWA as Rapporteur


ELECTRON RUNAWAY IN LT-3

J.D. STRACHAN

Department of Engineering Physics,

R.L. DEWAR

Department of Theoretical Physics,

Australian National University,

Canberra,

Australia

Abstract

IAEA-CN-33/A 8-1

ELECTRON RUNAWAY IN LT-3.

The occurrence of electron runaway before the onset of the disruptive instability has been examined

experimentally for different machine parameters by inserting a tungsten wire into the plasma. The duration

of electron runaway was found to be the duration of the collapse phase prior to the disruptive instability as

predicted by the trapped-particle pinch effect. The runaway rate varied as expected with toroidal magnetic

field and filling pressure. The runaway signals in the stable discharges are of the same order of magnitude

as expected theoretically. The data can be interpreted as diffusion due to imperfections of the drift surfaces

with an RMS radial step length of about 1 mm per transit of the torus.

It is the aim of this paper to describe the influence of the discharge

parameters on the runaway process in LT-3. LT-3 operates as a tokamakW

(B


172 STRACHAN and DEWAR

down and when the magnetic surfaces become reformed as the turbulence decays,

the runaways can be contained in the plasma. We found experimentally that the

recovery time was independent of BA and p at about 200 jus.

v o

As the surfaces become formed, both electron runaway and particle

trapping effects can become important and the plasma column enters the collapse

phase. Magnetic probe measurements^ indicated that the plasma boundary moves

inward with a velocity a = - E^/Bg which has been interpreted as due to the trapped

particle pinch effect^ 3 '. The plasma column collapses from the magnetic aperture

(a ^ 0.08 m) until the safety factor reaches a value (q ) below which the plasma

becomes unstable^ 4 '. Neglecting the change in R and raking a flat current profile,

the duration of the collapse phase is

2TTEA

In

* 2TTB,

It can be seen (fig. 1) that the duration of the X-ray signals T is equal

to this collapse duration if the delay time T for the runaways to reach a measurable

energy (30 keV) is taken into account and if inductive corrections to E^ are

ignored. We have taken q = 1 (N. B. q(a ) « 1.5) so that we presume that the disruptive

instability is due to the onset of the unstable m = 1 kink mode as suggested

by magnetic probe results( >.

The data in figure 1 supports the idea that the plasma boundary collapses

at the velocity - E^/Bo and not necessarily the trapped particle explanation of this

collapse. The inward diffusion due to the trapped particle pinch effect for LT-3

conditions should be smaller than effects due to spatial and thermal diffusion^ 5 ). The

dominant scaling confirmed by fig. 1 is T a E. -1 with the E^ changes occurring as

B$ was varied. The correspondence of the collapse phase with the runaway duration

300

200'

100

100

Collapse Duration

FIG. 1. The duration of the X-ray signals, rxr (points with error bars), the duration of electron runaway,

T xr + T A (single points), and the duration of the collapse phase prior to the disruptive instability (solid line)

as described by the trapped-particle pinch effect (equation (1)).

200

R

(1)


IAEA-CN-33/A 8-1 173

holds for variations in the filling pressure, p (between . 7 and 1.2 mtorr H , below

which the plasma entered the stable regime and above which the plasma entered the

dissipative regime) and for variations in the toroidal magnetic field, B^ (between . 4

and.7T).

When the filling pressure was lowered to 0.5 mtorr H9, LT-3 happened to

go into the stable regime and we were able to obtain a radial scan of the runaways

with our wire target. The stable discharges in LT-3 so far always feature a delay to

breakdown of about 800 ^s which might be associated with improved vacuum condition

in a manner observed with other devices^). The delay to breakdown has also caused

partial core saturation and the reduced coupling has decreased the plasma current so

that q(a ) has increased from ~1.5 to ~ 2.5. The delay to breakdown and reduced

coupling are necessary but not sufficient conditions for stable discharges in LT-3.

LT-3 apparently operated very close to the boundary between stable and

unstable since subsequent discharges (fig. 2) under identical machine settings could

be either stable or unstable. The stable discharges feature runaways in a burst near

peak current and sporadically thereafter.

stable

:==saSilMBl;

•MMMltlllMMMi

B&llliSMBBiHlM,

500 ^sec/div.

unstable

FIG. 2. Stable and unstable discharges in LT-3 with identical machine parameters (p0 s 0. 5 mTorr H2,

Bp ~ 0.5 T). Late breakdown has induced considerable core saturation in the stable discharges and accounts

for the different current profile.

3. RUNAWAY TRANSPORT

In order to relate the flux of runaways onto the wire to the plasma behaviour,

we consider the runaways to be described by a distribution function f (r, p, t) obeying

the equation

If + V i + eE *| = ifr !;> -H(r-y)vf + 6(P)n (2)

where H is the Heaviside step function and the usual collision operator can be neglected

due to the high parallel momentum, p, of the runaways. Neglecting toroidal corrections,

the runaway population changes in time due to the radial velocity, V(r,t), of the

drift surfaces; the acceleration by the electric field, E^ ; radial diffusion described


174 STRACHAN and DEWAR

by the coefficient, D(r, p, t); destruction of the runaways which strike the wire probe

with its tip at r = y at an effective collision frequency v = vd/4n^ rR (v is the electron

velocity, and d is the wire diameter); and creation of the runaways at essentially zero

momentum at the rate T](r, t), respectively.

In the absence of accurate knowledge of the motion of the drift surfaces with

respect to the probe we take V = 0. Although the current channel is moving away from

the probe due to variations in both the plasma major and minor radii, the runaways

need not follow such motion, particularly if the inward motion is caused by drifts of

trapped particles across magnetic surfaces. It might turn out that the magnetic

surfaces are expanding; however we note the convective term in equation (2) cannot be

the dominant transport mechanism since V would be an order of magnitude too high to

explain the observed results^).

In order to treat the radial diffusion coefficient D, we must consider a

diffusion mechanism that is consistent with the concept of runaway electrons.

Radial diffusion mechanisms which depend upon diffusion in momentum space

(either through turbulent or Coulomb scattering) are inconsistent with the observed

existence of runaway electrons since the condition that the runaways leave the

thermal region of velocity space leads unavoidably to extremely small diffusion coefficients.

One attractive mechanism is stochastic wandering of the electron lines

of flow as, for example, due to wandering of the lines of force. In this case D is

proportional to velocity: D(p) = v(p)G. This diffusion mechanism implies that the

bulk plasma can have a reasonable containment time while the high energy electrons

are poorly confined.

The boundary condition on f at r=y is provided by solving equation (2) in

the region r > y and matching logarithmic derivatives at r=y. f is approximately

proportional to exp [-(d/4TT* R y G)2 r] for r >y. From the reduced flux of runaways

incident upon the wire as another probe was inserted into the plasmaC 7 ), a

value for G can be estimated at about G~ 3 x 10"^ cm, which is an order of magnitude

estimate only. The rms radial step length per transit of the torus is (2TTRG)2 =*l mm.

which places an upper bound on the size of possible magnetic islands that is much

smaller than ones suggested to exist in ORMAFO 8 '.

Since the boundary condition is independent of v, equation (2) can be solved

by Dini series expansion, in which the expansion functions are J (X r/y)> and X

obeys the condition

ki/la] J o


IAEA-CN-33/A 8-1 175

If T > eEA y / A, G, then the behaviour of F is dominated by the m=l term,

exp (- X^GT/eE^y 2 ),where X.,-2.6 for y=2 cm and G = 3 x 10

diffusion fusion dominated limit, even electrons born near the center of

time to diffuse out across y.

-5 cm. Li this

of the discharge have

If T«eE30 keV) is in the strong diffusion limit and

F ot T](t) exp (-T/5 keV) (5)

Such a rapid fall-off seems inconsistent with the experimental time - integrated

spectrum ( 2 ) and an overestimate of G by a factor of five could explain the results.

In the present experiment, we have measured the integrated X-ray signal

over the duration of the collapse phase of the instability cycle which is

r max 2 r

I dTT

F dt (6)

Equation (6) was obtained using the appropriate relations for thick target bremsstrahlung

of electrons incident upon a high Z material, with little or no absorber,

and with a linear detector response^ 9 '. Previous results on LT-1 indicated consistency

with a theoretical runaway rate by Lebedev* 10 )

n * exp [-1.13 (10 8 ) - ^

n

1

jr-S-l (7)

volt °K


176 STRACHAN and DEWAR

FIG. 4. The integrated X-ray signals, S, prior to a disruptive instability, as a function of the toroidal magnetic

field. The solid line is given by Eq.(9).

FIG.5. The integrated X-ray signals, S, prior to a disruptive instability as a function of the torus filling

pressure. The solid line is given by Eq.(9).


IAEA-CN-33/A 8-1 177

If we suppose that Y = n /E T varies slowly during the collapse phase,

according to Y(t) = (1 - t/ T ) and can estimate T from the time variation' 1 ^

of E^ and T (we do not have n (t) so we presume n (t) = constant), and find that

TY c*250 us. Carrying out the integrations in equation (7), we find that the time

dependence of the runaway rate is the dominant effect so that

S a exp ( TXI/25MS) (8)

where is the average value of the runaway rate given by equation (7).

Experimentally, we find that this dependence is approximately followed.

In figure 3, the dependence of the runaway signal on the runaway duration is taken

from data obtained using identical machine settings (IJ, , BA , p ) but spanning various

degrees of vacuum condition. No strong correlation was found between the integrated

X-ray signal and the other parameters (e. g. Ei, T ). We expect that the disagreement

between the theoretically expected time dependence in equation (8) and the

experimental dependence may be due to a time varying electron density. The experimental

points more accurately fit an exp ( T /31 MS) dependence. When the machine

parameters were varied (figs. 4 and 5), the runaway signal obeyed the empirical law

S a exp( Txr/31Ms) (9)

The discrepancy with variations in the filling pressure could be explained if n was

not directly proportional to the filling pressure but instead, that a constant portion

of n came from, for example, wall materials (i. e. up to 40% of n at the lower

filling pressures).

The stable discharges in LT-3 yield runaway signals which are in agreement

with the empirical formula (equation (9)). This dependence on the theoretical

runaway rate is in contradiction to the results obtained on the similar dimensioned

machine* 1 ', TM-3, where an anomalous braking mechanism was observed which

was apparently due to the interaction of the accelerated electrons with plasma

oscillations and which accounted for some plasma heating at the expense of electron

runaway* ). The LT-3 conductivity temperature rise can be accounted for by

purely ohmic heating without appreciable losses and the maximum temperatures

«200 eV) are lower than those for TM-3.

The integrated X-ray signals were hollow radially about the minor axis

and this distribution was essentially the same for stable and unstable discharges

and for all variations in p and B^ . The observed hollow profile of S is expected

from equation (4) for any localized profile of T](r). However, until more is known

about the diffusion process, one cannot conclude any contradiction between these

results and those of larger tokamaks( 13 H14) wnere runaway distributions were found

which peaked on the minor axis.

4. CONCLUSIONS

The runaway electron durations before the onset of the disruptive

instability correlate with the time expected for the plasma column to collapse from

the magnetic aperture to a q value of unity under the influence of the trapped particle

pinch effect. The relation between the integrated X-ray signal and the runaway


178 STRACHAN and DEWAR

duration indicates that the measured X-rays arise from runaways which are accelerated

on magnetic surfaces inside the radius of the probe. The motion of the runaways onto

the probe is probably determined by stochastic wandering of the magnetic field lines.

This mechanism implies that electrons with energies greater than 30 keV are poorly

confined while the bulk plasma remains well contained. The number of runaways

striking the probe seems to varydue to the time varying runaway rate. The runaway

signals are consistent with theoretical runaway rates both for stable discharges and

for machine variations in unstable discharges.

ACKNOWLEDGEMENTS

The authors are indebted to J. A. Barber, R. Goldberg and R. McLeod

for help in performing the experiments and H. Hawes for preparation of the manuscript.

Helpful discussions with I. H. Hutchinson, B. S. Liley and A. H. Morton, as well as

the support and encouragement of Professor S. Kaneff are gratefully acknowledged.

REFERENCES

(1) BOWERS, D. L., LILEY, B.S., MORTON, A.H. and VANCE, C. F.,

Plasma Physics 1.3, 849(1971).

(2) MORTON, A.H. and SRINTVASACHARYA, K.G., Plasma Physics 14,

687 (1972).

(3) WARE, A. A., Phys. Rev. Lett. J5, 15 (1970).

(4) ARTSIMOVICH, L.A., Nuclear Fusion 12, 215 (1972).

(5) HINTON, F.L. and ROSENBLUTH, M. N., Phys. Fluids JJ, 836 (1973).

(6) GORBUNOV, E. P., DOLGOV-SAVE LEV, G.G., MUKHOVATOV, V. S.,

STRELKOV, V.S., and YAVLINSKII, N.A., Sov. Phys. Tech. Phys. 5,

1089 (1960). Zh. Tekh. Fiz. 30, 1152 (1960). See fig. 2.

(7) MORTON, A.H., STRACHAN, J.D. and VANCE, C.F., Nuclear Fusion,

JL3, 631 (1973).

(8) CHRISMAN, P. , CLARKE, J. and ROME, J., ORNL-TM-4501 (1974).

(9) EVANS, R.D., "The Atomic Nucleus", McGraw-Hill (New York, 1955),

pp. 615, 713.

(10) LEBEDEV, A. N., Sov. Phys. JETP21, 931 (1965).

(11) ARTSIMOVICH, L.A., BOBROVSKY, G.A., GORBUNOV, E.P., IVANOV, D.P.

KIRILLOV, V.D., KUZNETSOV, E.I., MIRNOV, S.V., PETROV, M. P.,

RAZUMOVA, K.A., STRELKOV, V.S. and SHCHEGLOV, D.A. ,

Nuclear Fusion Special Suppl., 17, (1969).

(12) KADOMTSEV, B. B., Zh. Eksp. teor. Fiz. _53, 2025 (1967).

(13) VERSHKOV, V.A. and MIRNOV, S.V., Fifth European Conf. on Contr.

Fusion and Plasma Phys. _1, 1 (1972) (Grenoble).

(14) von GOELER, S. and STODIEK, W., Fifth European Conf. on Contr. Fusion

and Plasma Phys. 1, 2 (1972) (Grenoble).


WELL-CENTRED DISCHARGES

IN THE PULSATOR-I TOKAMAK

O. KLUBER, S. CORTI, J. GERNHARDT, F. KARGER,

G. LISITANO, D. MEISEL, S. SESNIC

Max-Planck-Institut fur Plasmaphysik, Garching,

Euratom-Association,

Federal Republic of Germany

Abstract

IAEA-CN-33/A 8-2

WELL-CENTRED DISCHARGES IN THE PULSATOR-I TOKAMAK.

The use of programmed vertical magnetic fields in the Pulsator-I facility allows good long-term centring

of the plasma column and, therewith, stable, reproducible discharges with q-values down to 2. 3. In the

case where the vertical-fie Id program is not optimized, the discharge at low q-values is very susceptible to

the disruptive instability. The experiments show two different forms of this instability, a "hard" and a "soft"

type one; these are clearly governed by the position of the plasma column before the onset of the instability,

i.e. whether it is displaced inwards or outwards, respectively. The difference is explained in semiphenomenological

terms by using the equilibrium diagram. Both types can be selectively triggered in an

arbitrary way by displacing an otherwise well-centred plasma column.

Pulsator-I is a tokamak with an iron-core transformer and a copper

shell. The main parameters are: R = 70 cm, limiter radius aL = 12 cm

and a toroidal magnetic field of B^, =30 kG maximum, giving q = 3 for

I = 100 kA. The equilibrium position of the plasma column can be adjusted

by two sets of vertical field windings. One of them is located outside the

main field coils and is used for d.c. operation. The second set is mounted

within the copper shell on a stainless-steel torus surrounding the liner and

is fed with programmed currents, which allow good long-term centring of

the plasma column. The presence of a secondary vacuum chamber plus

the inner vertical field windings leads to the unusually large ratio of

b/a g b/aL = 1.63 where b = 19.5 cm is the inner radius of the copper shell.

As a consequence, the plasma would undergo a very strong outward

displacement if there were no applied vertical fields. This is shown in the

equilibrium diagram, Fig. 1 [ 1] . Here it is assumed that the plasma

radius is a = a, - |A|, where the displacement A is given by the Shafranov

equation.

From the experimental data the following features can be emphasized:

The temporal evolution of the discharge current can be influenced

appreciably by varying the vertical-field program.

The plasmas produced in the Pulsator-I device are especially susceptible

to the disruptive instability if the plasma column is not centred carefully.

Certainly, one of the reasons for this is the large ratio b/a. The

instability itself is manifested in the familiar manner: negative voltage

spike, sudden inward displacement of the plasma column and decrease

of the plasma current, electron density and electron temperature.

179


180 KLUBER et al.

The onset of the disruptive instability always occurs for nearly integral q

but not necessarily for the smallest integral q which is reached. Rather,

the deciding factor for occurrence of the instability appears to be how

well the plasma is centred at the time when q attains an integral value.

There are two types of the disruptive instability, a "hard" and a "soft"

one. The "hard" type is characterized by the total decay of the plasma

current within a few microseconds. In the case of the "soft" instability,

the current decrease is much slower, and usually the current increases

again. The occurrence of the two types is clearly governed by the

horizontal position of the plasma column before the onset of the instability.

That is to say, the disruption always is "hard" if the plasma is displaced

inwards and it is "soft" if the plasma is displaced outwards.

The features listed above are illustrated by Figs 2 and 3 which show

the temporal evolution of the plasma current, the loop voltage and the

horizontal displacement A for two subsequent shots differing only in the

programmed vertical magnetic field Bz. The result is a "soft" disruption

in the case shown in Fig. 2 and a "hard" disruption in the case of Fig. 3.

(It should be added that the above statements also apply to the discharges

produced in the presence of steady-state vertical fields.)

The onset of disruptions at nearly integral q-values is probably

related to the fact that the MHD-mode with mode number m = q has its

maximum amplitude when q is integral. However, this condition alone

is not sufficient for the production of a disruptive instability. Experiments

have shown that crossing of integral values of q § 3 with increasing current

is possible if the plasma column is centred sufficiently well; the maximum

permissible value of |A| tends to decrease with decreasing q. From this

one may infer — at least for the q-regime covered by the experiments —

that enhanced interaction of the plasma with the limiter plays an important

role in the onset of the disruptive instability. The mechanism of that interaction

is unknown as yet. A possible explanation is the formation of

I [ a [cm]

- s / N. ?A = 1 - 25

1 1 1 , r-i »-

-5 0 5 10 15 20 AC cm]

FIG. 1. Equilibrium diagram of Pulsator-I. The plasma radius is given by a = aL-| A|, where a, is the

limiter radius and A is the displacement of the plasma column. Ag = 2-nb B^/f^I is the contribution to A

that is due to the vertical magnetic field B^.


100

80

60-

40-

20

200-•

100 T

i? M

it

if'

—i—i—i— -.—.-a -t

20 40 60

1 1

80

1

100

'["»]

IAEA-CN-33/A 8-2 181

U loop M

\

k^ .

/[ms]

•10

•1

-1

10-

A [cm]

lyx

— i — i — i — i — i — i i—i t —

0 20 40 60 80 100

f [ms]

20 40 60 80 100

l[ms]

FIG. 2. Typical example of a shot where a "soft" disruption occurs because of outward displacement of the

plasma column. B = 22 kG.

magnetic islands due to the MHD-modes [ 2] . For integral q-values, such

islands are created close to the edge of the limiter. One would expect that

in this case even a small displacement of the plasma column should have

a strong influence on the island structure. This explanation is supported

by the results of the experiments with superimposed helical fields in

Pulsator-I [3], where islands are also created by the stellarator windings.

On the premises that an enhanced interaction of the plasma column with

the limiter is essential for the onset of the disruptive instability, the

existence of the two types of the disruption can be explained, in connection

with Fig. 1, by taking into account the fact that the disruption itself leads to

an inward displacement of the plasma column and to a slight decrease of

the current. In the presence of a vertical magnetic field, this leads to an

increase of the force directed inward, proportional to Bz/I. If the plasma

is displaced outward before the onset of the instability, both effects improve

the centring of the plasma column and reduce the interaction with the

limiter; thus, the current is able to recover. If the plasma is initially

displaced inward, instead, these effects drive the plasma still further inward.

It is easily possible to test the validity of the explanations given above

since a stable, well-centred plasma column can be displaced arbitrarily

by use of the programmed vertical field. Inward or outward displacement


182 KLUBER et al.

20 40 60 80 100 0 20 40 60 80 100

t [rns] t [msj

/[ms]

FIG. 3. Typical example of a shot where a "hard" disruption occurs owing to inward displacement of the

plasma column. All discharge conditions are the same as in the shot in Fig. 2, with the exception of the

vertical-field program.

must then lead to a "soft" or "hard" disruption, respectively. This has

actually been found as is clearly demonstrated by the sequence of shots

shown in Fig.4. Shot No. 1884 is a well-centred, stable discharge. The

decrease of Bz in shot No. 1886 causes only a small decrease of the current,

but no instability, whereas in shot No. 1888 it leads to a "soft" disruption

followed by a current increase. On the other hand, the small increase

of Bz in shot No. 1891 is sufficient to produce a "hard" disruption. These

experiments may be regarded as a convincing confirmation of the validity

of the model developed above. In addition, it should be pointed out that

at the time when the Bz-curves begin to deviate from each other, the

q-value is 2.7, which is much further from an integral value than in the

case of "spontaneous" disruption. Apparently, by displacing a stable plasma

column, the disruptive instability can be triggered at an arbitrary q-value

with predictable results, i.e. whether it is "hard" or "soft". This

reinforces the view that an enhanced interaction of the plasma with the

limiter plays a dominant role in the onset of the disruptive instability.

It is seen in Fig.4 that, owing to careful programming of the vertical

field, it is possible to produce stable discharges with q < 3. For this shot,

Qmin =2.5. The minimum q-value attained to date has been 2.3. This


I3U

100-

50-

j[kA]

I-

•-I

i

0 50 100 150 200

( [ms]

IAEA-CN-33/A 8-2 183

150 200

I [ms]

150 200

t[ms]

FIG. 4. Influence of a fast perturbation of the vertical field on the discharge. The shots No. 1884 —

1886 , 1888 and 1891 -. -. - differ only in the programmed vertical field Bz. B„ = 29 kG.

value has been reached under very different discharge conditions, i.e. for

different toroidal magnetic fields, electron densities, etc. Figure 5

illustrates such a case where the toroidal field is 2 9 kG (almost the

maximum value); the plasma current corresponding to q = 2.3 is 125 kA.

The maximum electron temperature is 1.5 keV and the electron densityaveraged

over the plasma radius is 3.5 X 10 13 cm" 3 .

The consequences of good plasma centring are also clearly demonstrated

by the results of other diagnostic methods. It has been found that the


184 KLUBER et al.

200

100 ••

150 200 50 100 150 200

tints'}

150 200

t [ms] ' C ms J

FIG. 5. Example for a discharge with optimized vertical-field program leading to qmin = 2. 3,

displacement A of the current centre measured by the magnetic probes is

always accompanied by corresponding displacements of the electron density

and electron temperature maxima. In general, the displacement of the

maxima of Te and ne is larger than A.

In conclusion, the experiments have shown that the plasmas produced

in Pulsator-I are much more sensitive to external magnetic fields than

what is known from other tokamak devices. Nevertheless, stable discharges

for q-values lower than 3 can be sustained with the aid of programmable

vertical fields. Furthermore, such fields provide additional possibilities

to investigate the stability behaviour of tokamak plasmas.

The authors wish to thank Dr. K. McCormick for many helpful

discussions.

REFERENCES

[1] MUKHOVATOV, V.S. , SHAFRANOV, V. D. , Nucl. Fusion JU (1971) 605.

[2] CHRISMAN, P. , CLARKE, D. , ROME, J. , ORNL-TM-4501.

[3] KARGER, F. , et al. , these Proceedings.


ELECTRON CYCLOTRON EMISSION

FROM A TOKAMAK PLASMA

Experiment and theory

A.E. COSTLEY*. R.J. HASTIE, J.W.M. PAUL,

J. CHAMBERLAIN*

Euratom-UKAEA Association for Fusion Research,

Culham Laboratory, Abingdon, Oxon,

United Kingdom

Abstract

IAEA-CN-33/A 8-3

ELECTRON CYCLOTRON EMISSION FROM A TOKAMAK PLASMA : EXPERIMENT AND THEORY.

The first measurements of the power, polarization and frequency spectrum of the electron cyclotron

emission from a tokamak plasma are presented. The radiation is not polarized, does not have the

previously predicted spectrum, and under certain circumstances is an order of magnitude above the predicted

power level. The results are interpreted in terms of a scrambling of polarization on reflection within the

torus and in terms of the emission from supra-thermal electrons.

We present measurements of the power, polarization and frequency

spectrum of the millimetre-wave electron cyclotron emission from the hot

plasma of a tokamak device. The plasma investigated is produced by the

C LEO -TOKAMAK [ 1 ] . It has a toroidal magnetic flux density B^2.0T,

a mean electron density rig ~ 2 X 10 19 m~ 3 , a central electron temperature

Teo ~300 eV, a central ion temperature Ti0 ~200 eV, a major radius

R0 =0.9 m, a minor radius a0 = 0.18 m and a duration up to 180 ms.

The emission measurements were made by observing the plasma along

a major radius through a wedge-shaped window of z-cut crystalline quartz.

A Fourier transform technique employing a two-beam interferometer was

used. The path-difference (x) within the interferometer was scanned in

1 0 ms over the range - 1 mm < x < 9 mm by oscillation of one of the mirrors

and the resulting sequence of interference patterns (Fig. 1) produced during

the 180 ms or so of emission was detected with a liquid-helium-cooled

Putley InSb detector. The spectrally integrated emission was also detected

for monitor purposes. Calibration of the apparatus and Fourier transformation

of suitable interference patterns yielded the emission spectra. In the

calibration, the time-dependence of the path-difference was measured using

an HCN laser (X = 337 /um) and the absolute power response of the interferometer-detector

arrangement was determined with a dc mercury arc lamp.

The emission spectrum from a typical tokamak shot about 50 ms after

triggering is shown in Fig. 2 (curve a). The resolution R in the spectrum

(determined by the total scan D used in the Fourier transform according to

R = c/D) is 3 7.5 GHz. As expected, emission peaks occur at the cyclotron

harmonics (nuce, n = 2, 3 and 4) for the magnetic flux density B0 at the

centre of the plasma. "We have measured the frequency of the second

* Division of Electrical Science, National Physical Laboratory, Teddington, Middlesex, United Kingdom.

185


186 COSTLEY et al.

33

Time (ms

9 8 6 4 2 0 - 1 0 2 * 6 8 9

Path-difference (mm)

FIG. 1. Signal from the interferometer showing two scans of the interference pattern, traversed in opposite

directions. (Time is from initiation of discharge).

40

30

20

10

L L T>

n

-

. Experiment

c 1

J

,.M

A a,c —t K •—

b— —.

» ih \ 2 IB for

\ /A T=300eV

% \l \

W\ x

/ \\ A

i \J V.^

H \

m y^T7 jheor . y

100 200

Frequency (GHz )

300

0 1 2 3 4 5 6

t SL

U)pe Wee

FIG. 2. Emission spectra. Experiment: (a) from single scan (R = 37. 5 GHz); (b) from composite scan

(R = 25 GHz); (c) single scan but with appreciable runaway. L = limit of detectability. Theoretical:

prediction with polarization scrambling (ordinary mode: horizontal hatching; unpolarized: cross hatching,

o>pe is plasma frequency).

53


IAEA-CN-33/A 8-3 187

harmonic at two values of BQ giving a ratio 1. 33 and found the corresponding

ratio of frequencies 1.29, in good agreement. By combining data recorded

on two identical tokamak shots at equivalent times but over different ranges

of x, spectra with an improved resolution of 25 GHz were obtained (Fig. 2b).

Any emission at n = 1 could not be deduced by the normal procedure since

the calibration system was insensitive in this region; however ^is believed

to lie below the limit L shown (Fig. 2).

Change of the tokamak conditions revealed a clear correlation between

the level and spectrum of the emission (e.g. Fig. 2c) and the level of hard

X-ray emission; a correlation also found for variations during a given shot.

Some discharges showed a progressive change from form (c) to form (a)

of Fig. 2. For relatively intense X-ray emission, the spectrally unresolved

monitor signals showed an increase of up to tenfold. (Note that copious

hard X-ray emission is an indication of the presence of high-energy runaway

electrons).

The uncertainties in the spectroradiometric method are such that the

relative shapes and frequency positions of the spectral features are reliable

to about ± 10%, and that the absolute level of the spectra is reliable to about

an order of magnitude (i.e. a factor of 3 either way).

Experiments with wire grid polarizers showed that the recorded emission

spectra were the same to within the discharge reproducibility limits (± 10%)

for all polarizer orientations selected between shots and indicated that the

detected radiation was unpolarized (to within this uncertainty) at all times

and frequencies examined. To understand this lack of polarization we

examined the depolarizing effect of multiple reflections within the stainless

steel torus by irradiating the system (with no plasma present) with a

linearly polarized beam of 2 mm wavelength radiation and measuring the

polarization state of the radiation emanating from several radial ports.

Radiation from all ports with


188 COST LEY et al.

TABLE I. RESULTS FOR n = 2, 3, 4

/ aeds

1 - r(w)

[l-(r-f)]

n = 2

1.00

5.46 X lO" 3

18.6 x 10- 3

n = 3

2.96 x 10" 3

6.69 x 10" 3

19.8 x lO -3

n =4

1.46 x 10" 5

7.72 X 10" 3

20. 9 X 10" 3

arbitrary n^s), Te(s), and defined B(s) = B0(l -s/R0), |sjsa0. For each u

and harmonic n, the resonance u = nwce(Sj.) defines the position sr, so that

n-l

The results are listed in Table I together with 1 -r(w) for stainless steel

and corrected for f. We note that harmonics n < 3 are optically thick

(/ffeds » 1 -r), n > 3 are optically thin (J aeds « 1 -r), while n = 3 is intermediate.

Using equation (4), Te can be determined from the ratio of any

two harmonics provided they are not both optically thick.

On comparing the predictions of this theory with the emission measurements

obtained under low runaway conditions, we find three major

discrepancies: (i) the measured absolute magnitudes exceed the predictions

by more than the estimated factor of three uncertainty; (ii) the measured

ratios of the intensities of the harmonics yield inconsistent values for the

electron temperature and (iii) the measured radiation is unpolarized. We

consider the third and most important discrepancy first.

If, on the basis of the subsidiary experiment mentioned above, we

assume that each reflection produces some scrambling of the polarizations

and define a transfer fraction p between the two polarizations, the boundary

condition for the reflected intensity, I', becomes

^O.e) = r{I (0>e) + P [l (e,0) " W > (5)

and the transport equation with aQ - 0 yields a solution

Ie = IB [1 -exp(- /aeds)J/[l -rexp(- /


IAEA-CN-33/A 8-3 189

estimated uncertainty. The observed ratios of the peaks yield predicted

electron temperatures I3/l2~* 720 eV, I4/l2^ 1-9 keV. 1 Even allowing for

the calibration uncertainty, the discrepancy in I4 is large and we must look

for an alternative explanation for this emission, in particular in terms of

runaway phenomena.

For simplicity we simulate runaways by a second Maxwellian distribution

of perpendicular velocity with temperature Tr » Te and density nr


HIGH- AND LOW-CURRENT-DENSITY

PLASMA EXPERIMENTS WITHIN

THE M.I.T. ALCATOR PROGRAMME

IAEA-CN-33/A 8-4

U. ASCOU-BARTOLI 1 ", G. BOSIA+, G. BOXMAN 0 ,

P. BROSSIER*, B. COPPI'-; L. DE KOCK 0 , B. MEDDENS 0 ,

B. MONTGOMERY' 1 ; A. OOMENS 0 , L. ORNSTEIN 0 ,

R. PARKER* L. PIERONI 1 ", S. SEGRE 1 ", R. TAYLOR' 1 ;

P. VANDERLAAN 0 , R. VAN HEYNINGEN 0

>;< Massachusetts Institute of Technology, Cambridge, Mass., USA

Association Euratom-FOM, Jutphaas, the Netherlands

' Association Euratom-CNEN, Frascati, Italy

* Association Euratom-CEA, Fontenay-aux-Roses, France

+ University of Turin, Italy

Abstract

HIGH- AND LOW-CURRENT-DENSITY PLASMA EXPERIMENTS WITHIN THE M.I.T. ALCATOR PROGRAMME.

The operation of Alcator at relatively high magnetic fields (up to 60 kG) and with a plasma radius of

about 9 cm has led to plasma currents up to 200 kA corresponding to poloidal fields up to 4.4 kG and

average current densities near 750 A/cm . Pulses up to 300 ms have been obtained without a feedback

system to maintain plasma equilibrium. Neutron production of 10 count/ms has been detected from

deuterium plasmas for the entire duration of the best discharges, A relatively large range of plasma

densities from 5 x 10 /cm upward has been reached. Peak electron temperatures up to 1. 8 keV have

been measured by laser scattering. The constancy of the average density, as of the soft X-ray emission,

and the features of neutron emission during long discharges and when switching from deuterium plasmas to

hydrogen and vice versa, are indications of a relatively low influx of high-Z impurities. Poloidal field

fluctuations with m = 4, 3, 2 are detected when q-values lower than 3 are obtained. - The initial operation

of the Rector device for the investigation of MHD-equilibrium and stability of plasmas with comparable

dimension as Alcator but non-circular cross-section has indicated that vertical elongation can be achieved

while maintaining the plasma column position by a feedback system.

1. PHILOSOPHY OF ALCATOR EXPERIMENT

The purpose of the Alcator experiment is to produce toroidal plasmas

carrying relatively high currents (a fraction of a megaampere) and current

densities [1] (of the order of 1 kA/cm 2 ). The argument for this is that

high values of the former parameter make it possible to confine plasmas

with thermal-energy densities of thermonuclear interest while high current

densities can produce efficient Ohmic heating even for electron temperatures

in the multiple keV-range. With the ability to combine these values

of electron temperatures with plasma densities as high as 10 14 /cm 3 , the

possibility exists to obtain also relatively high ion temperature and

investigate plasmas for which both the electron and the ion populations

are in the trapped particle regimes (see footnote section 3.4.).

191


192 ASCOU-BARTOLI et al.

2. ALCATOR COMPONENTS

To achieve the high-current-density goal, the development of suitable

high magnetic-field technology has been necessary. This has involved in

particular the construction and operation of a cryogenic toroidal Bitter

coil which has been tested up to values of 100 kG magnetic field on the

axis, and of a magnetic storage and air core transformer system whose

central element has been tested up to magnetic fields of the order of

100 kG corresponding to a variation of magnetic flux of about 0.9 Vs.

The principal magnetic systems, the vacuum system and diagnostics

(refer to Fig.l) are briefly summarized in the remainder of this section.

2.1. Magnetic systems

The toroidal Bitter magnet is made of 250 pie-shaped, square plates

of copper which are interleaved with insulating sheets and reinforcing sheets

made of stainless steel. The latter are required to support the magnetic

stresses which occur at the 120 kG design field. The entire assembly is

prestressed by means of two fibreglass hoops which encircle the magnet,

resulting in a monolithic structure.

The central element of the Ohmic heating (OH) system is an air core

solenoid. In series with it are three pairs of coils, the function of which

are to minimize the stray transverse magnetic field in the plasma volume.

In operation, the OH system is charged to a maximum value of 1.2 Vs by

means of a 6-MW power supply. The current is then switched to zero

through a programmable sequence of resistors by means of a 40 kA, 30 kV

vacuum breaker switch assembly. By variation of resistance values and

timing, it is a relatively simple matter to vary the time profile of the

release of flux, and hence the time profiles of loop voltage and plasma

current.

Three additional pairs of coils are used for static horizontal and

dynamic vertical field control. The latter coils are energized by switching

into the ohmic-heating circuit; hence, a fraction of the OH energy is

recovered for use in applying the dynamic vertical field. In this way fields

up to 3 kG can be applied with essentially constant value during the

discharge duration.

The entire magnetic system is cooled to 77°K by circulating LN2. This

allows operation of the Bitter magnet to fields of 100 kG with 30 MW of

generator power. An ancillary benefit is the relatively long L,/R times of

the vertical field (1 s) and copper shell (0.5 s) systems. Pulsing the magnet

at 60 kG every 4 minutes consumes 250 gallons/h, while heat losses

(primarily because of keeping the temperature of the vacuum system near

room temperature) consumes 200 gallons/h.

2.2. Vacuum system

The vacuum system is constructed by connecting four large flanges

which are an integral part of the Bitter magnet by steel bellows quadrants.

Each bellows is formed from 0.5-mm-thick 304L stainless steel and is

nested in a copper shell of thickness 1.25 cm. The shell quadrants are

electrically isolated and rigidly supported by the flanges in order to withstand

the large forces caused by interaction of equilibrium currents and


IAEA-CN-33/A 8-4 193

FIG. 1. Layout of Alcator Experiment: 1. soft X-ray window; 2. pumping station; 3. liquid nitrogen

manifold; 4. HCN interferometer port; 5. liquid nitrogen cryostat; 6. limiter port; 7. pumping station;

8. Thomson scattering port; 9. vertical field coils; 10. transformer assembly; 11. Bitter magnet;

12. RF heating port; 13. microwave interferometer; 14. Bellows vacuum chamber; 15. Magnetic diagnostics.

the toroidal field. The system is pumped by two 500 litre/s turbomolecular

pumps and has a base pressure of 5X 10 -9 Torr following 300°C bakeout.

All components of the vacuum system were electropolished and vapoured

and ultrasonically degreased immediately before assembly. Conditioning

of the chamber is done by a combination of baking and discharge cleaning,

which is performed by applying 200 kW, 2.5 kHz pulses (duty factor ~ 5%)

to the Ohmic system.

The limiter is constructed of two crescents of molybdenum, forming

the top, bottom and inside surfaces, and a straight bar of tungsten-rhenium

alloy forming the outer surface. Only relatively minor surface melting

of the outer portion was found after the first 6 months of plasma operation.


194 ASCOI2-BARTOLI et al.

The major radius of the device is 54 cm, the inside bore of the vacuum

chamber is 25 cm. The straight segment of the limiter is movable, and

for the experiments described below, the maximum circular bore was

chosen to be 19 cm.

2.3. RF-heating configuration

Auxiliary heating by injection of RF-power is being investigated as part

of the Alcator program. The RF-source is an 80 kW CW tube operated at

2.54 GHz. The power is coupled to the plasma by means of a waveguide

which is flush-mounted in the wall of the vacuum chamber. The radiation

is expected to couple to lower-hybrid waves [2] which are strongly absorbed

by ions near the lower hybrid frequency (~wpi). For this to occur, the

plasma density must exceed 5 X 10 13 cm" 3 . An additional possibility for

heating results from the enhancement of plasma resistivity by the RF [3],

2.4. Diagnostic systems

To present the experimental data obtained from the operation of Alcator

at high current densities, a description of the diagnostic systems that have

been prepared is given. We refer to Fig.l for a view of the distribution of

these systems around the machine. In the following sections, we indicate

the poloidal angle by 9 and the toroidal angle by cp.

2.4.1. Magnetic probes

A number of Be pick-up coils are mounted around the minor circumference,

all located in depressed grooves in the middle of the four bellows

sections (Fig.l). Two types of coils exist: belts with 8 or 12 discrete

identical coils evenly distributed along the minor circumference and

additional pick-up belts of which the azimuthal winding density varies to

a high approximation as cos mfi or sin m0 (where m = 0, 1, ... 6). With

these coils instantaneous Fourier analysis of poloidal magnetic field variations

is possible. The simultaneous occurrence of signals of the same

frequency at other m-coils with other m numbers than the exciting mode

can be explained in terms of the eccentricity and toroidicity [4] of the plasma

column.

2.4.2. Interferometers

To measure the electron density integrated along the optical path through

the plasma a 4-mm microwave interferometer is used. It employs a simple

and reliable system for the direct read-out of the phase shift due to the

presence of the plasma, i.e. a not necessarily integer number of fringes [5].

An HCN-interferometer working in the Mach-Zehnder configuration

has been developed and has verified so far the data of the 4-mm interferometer;

eventually it will be used to measure electron densities above the

4-mm cutoff [6],

2.4.3. Diamagnetic probes

The diamagnetism of the plasma is measured by single loops at the

same locations as the magnetic probes. Changes in the main toroidal


IAEA-CN-33/A 8-4 195

magnetic field, deficiencies in the enclosure of the magnetic flux within the

magnet, as well as variations of the magnet current due to coupling with

the plasma current are all compensated by subtracting a complex (but mainly

real) fraction a of the magnet current, as measured by a Rogowski coil in

the bus bar system. Errors due to poloidal misalignment, i.e. pick-up of

horizontal and vertical fields, have still to be compensated.

2.4.4. X-ray measurements

The soft-X-ray measurement is based on a foil-absorption technique

using a krypton-filled proportional counter as a detector. The detector

views the plasma through a 2-mil Be-window in the horizontal midplane,

and mainly responds to the hottest region of the discharge. Two identical

systems of Al- and Be-foils are made to rotate in front of the detector at

60 Hz, thus yielding signals which, in principle, give a temperature

measurement every 8.3 ms. In initial experiments, the films were 0, 80,

225 and 500 /Jim of Be, and 37.5 and 425 fim in Al. In view of the high

temperatures observed, the Be-films gave poor discrimination and a

simpler system consisting of no film, and 37.5 and 42.5 jum Al was adopted.

The electron temperature was computed by assuming that the emitted

intensity is proportional to exp (-E/Te) and computing the effects of film

and detector absorption. The ratio between transmission through no film

(taking into account window air and detector losses) and 37.5 jum Al film

was found to be most effective for determining Te .

Hard X-rays were monitored by means of an Nal scintillator and a

photomultiplier located on the vertical axis of the machine approximately

2 m from the horizontal midplane. The total hard X-ray flux energy was

also monitored by dosimeters placed in the vicinity of the limiter.

2.4.5. Thomson scattering measurement

A 90° Thomson scattering system, for the measurement of electron

temperature, employs a pulsed (20 ns) high energy (10 J) ruby laser fired

vertically through the plasma and focused on the median plane. Scattered

radiation is collected radially with an aperture of 2 X 10~ 2 sterad and is

analysed by a grating spectrograph providing a contrast above 5 X 10 3 .

A further contrast factor of 10 2 is provided by a two-stage interference

filter rejector (which can be inserted if necessary). The radiation is

detected by an array of 10 photomultipliers which are gated on for ~ 10 /us;

the outputs are fed to a set of fast gated integrators. The vertical laser

beam can be scanned radially and hence temperature profiles obtained.

The measured stray light signal is equal to the Rayleigh scattering signal

from N2 at 5 m Torr.

2.4.6. Neutron detector

Neutrons are detected by a BF3 counter surrounded by 10 cm paraffin

and 1 cm lead. The counter is 30 cm long and 2.5 cm in diameter and has

been calibrated by a 1-Ci neutron source (Pu-Be).


196 ASCOU-BARTOLI et al.

3. EXPERIMENTAL RESULTS FROM ALCATOR

3.1. Range of operating conditions

Following a period of operation with the magnet system at room

temperature (R^ S 20 kG), the machine was cooled to cryogenic temperatures

and operation in the range of toroidal fields between 35 kG and 55 kG

was explored. Plasma currents of up to 200 kA have been achieved.

The value of q at the limiter was generally between 2.5 and 4.0, with

the most stable and longest discharges of duration up to 300 ms occurring

for q - 4. Fill pressures of 2-5 X 10" 4 Torr (a) H2 or D2 were used.

3.2. Equilibrium and stability

The plasma equilibrium is obtained by the combination of externally

applied transverse field (1 kG at 200 kA plasma current) and the action

of the copper shell. In the absence of the external field the outward shift

in plasma position {> 2 cm) and the corresponding loss of current results

in operation with q > 6. Normally, the external field is applied on the time

scale of the plasma current rise. A fraction of the field acts on the plasma

at the time it is applied (through gaps in the copper shell), the rest of the

field diffuses through the shell as the image currents dissipate. In this

combination, the copper shell can be considered as a high-frequency feedback

system with a low-frequency component of the field programmed

externally. The diffusion of the applied vertical field through the copper

shell in the region away from the gaps is shown in Fig.2c.

Dramatic improvements in position and in the current - for increasing

values of the transverse field Bv — can be seen from Figs 2a and 2b. In

the case of insufficient Bv during the late phase of a given discharge, the

current disruption is often preceded by a violent m = 2 oscillation in the

poloidal magnetic field. The frequency of this oscillation exhibits large

changes in the sense that it slowly decreases, or fluctuates and decreases,

as the time of disruption is approached. In all the cases where a well

centered discharge is produced and relatively high current levels are produced,

corresponding to q* 2.5, poloidal field oscillations with m = 4, 3

are observed during the current rise and a steady m = 2 oscillation during

the plateau of the current pulse (see Figs 2d and 2e). The onset of m = 4

and m = 3 oscillations occurs at the moment when q at the limiter reaches

values of 4 and 3. The occurrence of m = 2 oscillations during the plateau

may be associated with a constriction of the column 17],

3.3. Electron temperature and bremsstrahlung radiation

Results of peak electron temperature measurements in deuterium over

the range of currents from 50-120 kA are shown in Fig.3a. With density

and (peak) electron temperature increasing approximately linearly with

current, this implies j3poi % constant as shown in Fig.3b. In hydrogen

discharges investigated thus far, peak electron temperatures are lower

(


0

T)

i

B,

(arb) •^

0.15

0

0 40 80 120 160

time (ms) *•

(c) 072274

vertical field outside shell

vertical field under shell

i . i . i . i

0 40 80 120 160

time (ms) —•

X-roy

IAEA-CN-33/A 8-4 197

(e) Instabilities near current disruption

**vw*v*


198 ASCOLI-BARTOU et al.

1.5

1 -

0.5

(a) (b

• O 00

+

0 O O

50 100

ID(kA)

0 20 40 60 80100 120 U0 160

tlms)

2

* 1.5

5

K

* 1

I-*

0.5

50 60 70 «0 90 100 110 120 130

x IpJkA)

50 60 70 80 90 100 110 120 130

UkA)

l (d> A-«L

v. /

/ / Tx»\

*/. * /

/ /

- / v

f / A 30ms

/ / • 15 ms

" / /

/

0.5 1 1.5

Tt(LASER)(keV)

FIG. 3. a) Electron temperature versus current in deuterium discharges; b) Density and Spoi versus current;

c) Oscilloscope traces showing voltage, current and output of soft X-ray detector; d) Comparison of soft

X-ray temperatures and laser temperatures.

density, as measured both by the interferometer and the Thomson scattering

experiment, and the decrease of total bremsstrahlung emission (proportional

to rjg) suggest the absence of strong interaction with the vacuum chamber

in this mode of operation.

The hard X-ray flux is relatively weak for these discharges, amounting

to ~ 10 mR/pulse near the limiter. This emission occurs primarily in two

bursts, one about 25 ms after the initiation of the discharge (the effect can

be seen in the soft-X-ray detector) and the other during the termination

stage. The effect of hard X-rays on the soft-X-ray system is negligible

except during the aforementioned bursts, as the detector output is reduced

to zero by 0.5 cm of Al at all other times.


IAEA-CN-33/A 8-4

FIG. 4. a) Neutron emission signal (N) showing no correlation to the hard X-ray signal (X). The two other

traces are loop voltage (V, 5 V/div) and plasma current (I, 150 kA/div). B^, = 55 kG, ne = 1. 5 x 10 13 /cm 3 ,

filling pressure 1.7 x 10 -4 Torr (g) D2. The neutron signal is not influenced by the presence of MHD disturbances

seen on the voltage traces; b) Same conditions as a) but the filling gas is H2; c) Some X-ray activity

is seen in the neutron detector signal in addition to the neutron flux (D2 gas); d) X-ray activity dominates

the neutron detector signal (H2-gas). Note the increase of the electric field (V trace) in c) and d).

3.4. Neutron measurements

The neutron emission from Alcator can be detected for Ip l 80 kA and

Bq, 1 27 kG. The flux varies from 100 neutrons/s at the low end up to

10 000 neutrons/s at Ip .= 140 kA, B^ = 55 kG. The emission usually

appears between 30 and 40 ms after the initiation of the discharge and

reaches its "steady state" value in 10 ~ 20 ms. Once a fixed rate is

established, the emission is likely to continue at that rate for more than

100 ms, even in the presence of mild MHD disturbances. This is shown in

Fig.4a. The ion temperature 1 derived from neutron data varies from 400 eV

to 800 eV. 'Figure 5 shows the variation of the neutron flux with plasma

current and toroidal field.

As it is characteristic of tokamaks, the neutron detector may be influenced

by hard X-ray emission. The following three regimes of operation

are seen in Alcator when the activity of the hard X-ray detector is compared

with that of the neutron detector:

1. No correlation (low recycling level, ne ^1X 10 13 /cm 3 ,

En < 0.003 V/cm, Fig.4a - D2 gas fill, Fig.4b - H2 gas fill).

2. Limited X-ray activity present in the neutron signal. (Recycling

level is not stable, EH «s 0.005 V/cm, Fig.4c).

3. X-ray activity dominates the neutron detector signal. (The machine

is not clean, recycling level is high, EN > 0.01 V/cm, Fig.4a).

1 In this connection we notice that the ratio y" 1 = tfjj(Ro/r)/wbi can be considered as an index of

penetration into the trapped ion regime. Here v^ is the deuterium impurity collision frequency, r is the

minor radial variable, and o^j = [vthiAqRo)] (r/Ro) ' s is the average bounce frequency of trapped deuterons.

Then, for the case of Alcator (R = 54 cm) we obtain

~{r}* n(r)q^Zeff(r) X2 - 5Xl ° 3

where TTj(r) indicates the ion temperature in keV, n(r) the electron density in 10 13 /cm 3 , Zeff is the

effective charge number and X = In A/(15), In A being the well known Coulomb logarithm. Thus, if we

assume that for r = 7 cm, Tj = 1, fi = 2, q = 2. 5, Zeff = 2, we have y K 10.

199


200 ASCOLI-BARTOLI et al.

IU

lO 3

lO 2

in i i i —

|

3

in

80

Toroidal

Field

o

i

D


O


0

D

27 kG

36 kG

45 kG

55 kG

O

O



• OO

1 i 1

100 120

ID(kA)


o

1



1

140

-

-

800

700

600

-

-500

--400

FIG. 5. Neutron counting rates and derived ion temperatures for various operating conditions. Filling

pressure = 2 x 10" 4 Torr (g) D2, rig = 2 x 10 l3 /cm 3 .

Iiooms}

time -+•

FIG. 6, a) Neutron emission in D2-gas; b) Neutron emission in the first discharge in H2 gas after

prolonged operation in D2-gas; c) Second discharge in H2-gas after prolonged operation in D2-gas.

Ip = 120 kA, B(f = 45 kG.


0 TOROIDAL WINDING

0 OH,Bv,BR WINDING

I

ELONGATION FIELD

WINDING

IAEA-CN-33/A 8-4 201

GftIN-1

- ^ - I

CURRENT

N/-OUT

- -„- UP'OOUN

(d)

^V IN^OUT

-^AAA/W— UP ' 00UN _V^'VVW

FIG. 7. a) and b) Arrangement of the field windings on Versator and Rector devices; major radii 54 and

56 cm, respectively; c) Sensitivity of the plasma equilibrium position to external variations in the radial

field (± 2 G and ± 1 G) with field curvature n = - 1 (unfavourable curvature). In/out refers to radial position;

up/down refers to axial position. Ip = 20 kA, B-„ = 4 kG, Te - 250 eV (laser), ne « 10 13 /cm 3 (u-waves);

d) Plasma equilibrium with feedback. The four different traces illustrate the effect of the loop gain.


202 ASCOII-BARTOLI et al.

After subjecting the plasma chamber to discharge cleaning and producing

a considerable number (250) of discharges in D2, and changing the gas

fill from D2 to H2, the neutron emission vanishes in 1 or 2 discharges

as shown in Fig.6. This apparent lack of gas reflux from the vacuum wall

is also indicated by optical measurement of Ha and Da, in experiments

where D2(H2) is used after prolonged operation with H2(D2).

4. VERSATOR AND RECTOR EXPERIMENTS

Our experimental programme has been broadened to investigate some

aspects (MHD stability and equilibrium, ionization phenomena and wall

interactions) of tokamak behaviour on easily assembled toroidal devices.

Two machines, Versator with circular cross-section and Rector with

rectangular cross-section of the vacuum chamber have been realized. Both

devices have the magnetic field coils wound on the vacuum chamber. No

copper shell or limiter has been employed in either device. (See Fig.7a

and 7b for dimensions and coil placement). Versator has been designed

to investigate the MHD-equilibrium properties of a configuration of the

same size as Alcator but without a copper shell. The results proved

encouraging and an extension of the same equilibrium study is now being

made to a non-circular-cross-section device (Rector), for which we may

envision the possibility to achieve ellipticity factors up to 2 : 1.

The Versator experiments (Ip = 20 kA, B^, = 4 kG), showed that good

equilibrium is possible at q «« 2.5, just as the case in Alcator, but without

a copper shell. In particular, these experiments were concerned with the

effect of the transverse equilibrium field curvature on positioning of the

plasma column. It is known that in order to keep the plasma in the midplane

of the torus, the transverse field must have an index of curvature, n, between

0 and 1.5 (practically n^0.75). Experiments were conducted with n = -1,

n = 0, and n = 1. In all cases it was found that the current channel did not

stay in the midplane of the torus for longer than 2 ms due to stray radial

fields. The sensitivity of the plasma position to slight radial fields is shown

in Fig.7c for n = -1 (unfavourable curvature). The combination of favourable

curvature field and a small radial field, however, tend to stabilize the

plasma position but with significant displacement out of the midplane. In

turn, this produces a reduction of the plasma size which then results in

perturbation of the radial equilibrium position. This interaction between

the two orthogonal displacements makes the plasma operation difficult.

We found that the plasma can be kept in the midplane through the application

of a small radial field (few Gauss) by a feedback system. The resulting

up-down stability is shown in Fig.7d as a function of the loop gain of the

feedback system. The stabilization of the plasma position with favourable

and unfavourable field curvature make it possible to plan an elongatedcross-section

experiment.

Experiments on plasma elongation in Rector are carried out by increasing

the curvature (in the unfavourable direction) of transverse field. At

the same time, midplane stability is maintained by a feedback system. The

results obtained show an increase of the current up to 80% over the value

obtained for a circular cross-section for fixed values of the magnetic field.

The elongation is monitored by the modification of the plasma light distribution

along the vertical dimension (Fig.8). Radiation measurements in the


| is .

c.

o 1.0

%


DISCUSSION

ON PAPERS IAEA-CN-33/A 8-1, A 8-2, A 8-3, A 8-4

R.S. PEASE: I should like to ask one of the authors of paper A 8-4 what

the Z-effective is in Alcator.

B. COPPI: The observed Z-effective in deuterium — without corrections

for temperature, density and current-density profiles — is a function of the

ratio of the electron flow velocity to the electron thermal velocity. The

maximum observed value is about 15 and a reduction factor should be considered

to allow for these profiles.

205


IAEA-CN-33/PD-2

INFLUENCE OF RESONANT HELICAL FIELDS

ON TOKAMAK DISCHARGES

F. KARGER, H..WOBIG, S. CORTI, J. GERNHARDT,

O. KLUBER, G. LISITANO, K. McCORMICK,

D. MEISEL, S. SESNIC

Max-Planck-Institut fur Plasmaphysik, Garching,

Euratom-Association,

Federal Republic of Germany

Abstract

INFLUENCE OF RESONANT HELICAL FIELDS ON TOKAMAK DISCHARGES.

The resonant interaction of external helical £ = 2 fields with the q = 2 surface and the m = 2 modes of a

tokamak discharge is studied, information on the disruptive instability and its stabilization is gained, and

possible applications of this new resonant-helical-field (RHD) method are mentioned.

With external helical S. - 2 fields a resonant interaction with the q = 2

surface and the m = 2 MHD-modes in a tokamak discharge can be achieved

which leads to new information about the nature of the disruptive instability

and its stabilization.

This resonant-helical-field (RHF) method was employed, for the first

time in a tokamak, in Pulsator-I [ 1 ]. Helical H - 2, n = 1 windings, placed

within the copper shell of Pulsator-I, can be fed by either a transistor -

controlled capacitor bank capable of arbitrary current programming or by a

50-kW audiofrequency generator.

For given plasma paremters, if the helicities of the tokamak magnetic

field and the superimposed helical field are in the same sense, a certain

well reproducible level (Jtfel) °f "the current in the helical windings leads to

a current disruption (Fig. 1). With the help of a 16-channel transient

recorder this disruption was compared with the spontaneous disruptive

instability. No characteristic differences in the phenomena accompanying

the instability (m = 2 modes, negative voltage spike, change in plasma

position and radius, current disruption) have been observed to date. For

helicities of opposite sense no destabilizing effect occurs even when

Jhel > 30 J hel •

The critical current J^ decreases with decreasing safety factor

q (Fig. 2). For example, at a limiter q-value of 3. 5, a helical current of

250 A (corresponding to a vacuum rotational transform L/2TT < 10" 5 for

Bo = 3 T) is sufficient to produce a disruption. In this case the magnetic

fields within the plasma generated by the helical windings are of the same

order of magnitude as the helical fields produced by the spontaneous MHDmodes.

The destabilizing effect of the RHF is not due to a direct lowering of

the q-value (the variation of q in most cases is less than 0. 01%); rather, it

is a resonance phenomenon. It can be explained by island formation based

upon geometrical resonance of the unperturbed tokamak field with the

superimposed helical 4 = 2 field (RHF). To study this effect numerically,

207


208 KARGER

0M[A)

20 40 60 80 100

i [ms]

FIG. 1. Plasma behaviour for a helical current exceeding the stability limit Jfjer

2.0

•1.5

1.0

0.5

p£L [arb. units]

"x


IAEA-CN-33/PD-2 209

J plasma = WOk A

Jhel=500A

Li miter

FIG.3. Island structure at the q = 2 surface produced by £ = 2 helical windings for Pulsator-I parameters.

the magnetic surfaces have been calculated for the case of a linear superposition

of an external helical field on the unperturbed tokamak field. These

calculations show that on the q = 2 surface two islands originate (Fig. 3)

whose width increases approximately as vJhei . This linear superposition

does not predict how the plasma currents are changed by the helical islands,

but it is very likely that a helical current structure within the plasma will

result. A break-up of the island structure by unstable helical currents in the

plasma itself or by a contact between the islands and the limiter are possible

explanations for the subsequent current disruption. It is also conceivable

that the island configuration can lead to a peaking of the current profile,

thereby reaching a critical q-value. However, to date it has not been possible

to ascertain any change in the temperature profile through activation of the

helical windings. These possible explanations are also applicable in the case

of the spontaneous disruptive instability and partially applicable in the case

of the instability produced by decentring the plasma [ 1 ].

To obtain some more information about the conditions for the disruption,

the quantity «V J hel/£*


210 KARGER

BQ = 3T

-'plasma = 40 kA

= 12kA

FIG.4. Higher-mode island structure produced by St = 2 helical windings for Pulsator-I parameters.

by adjusting the solid curve to the experimental points. The agreement

supports the hypothesis that island-limiter contact plays an important

role in the onset of the disruption. But more experimental data and better

non-linear theories are necessary in order to reach a definite decision

among these explanations.

The calculations indicate that, owing to the non-linear influence of

the torus curvature, lower amplitude resonances for q >2 also appear,

the corresponding number of islands on the q = 3, 4 .. and rational surfaces

occurring at higher helical currents (Fig. 4). Experimentally, in agreement

with these predictions, one can produce breaks in the current for discharges

where q = 2 is no longer present, the breaks becoming less abrupt for higher

q-values.

When the helicities of the tokamak magnetic field and the helical windings

are in the opposite sense, the resonance condition is not fulfilled. In this

case, the calculations show no islands.

The current disruption produced by the RHF occurs for constant q with

increasing helical field as well as for constant helical field with decreasing q.

Hence, the disruption is not due to electrical fields or currents induced

within the plasma. A change of the direction of the current in the helical

windings, which leads to a rotation of the island position by 90°, does not

change Jh*j.

The disruptive instability can be triggered with the help of the RHFmethod.

For example, pulsing the helical magnetic field above B^ for ~ 1 ms

leads to a negative voltage spike ~1. 5 ms after the peak of the pulse, thereby


B hel

arbitrary

units * ..

5 +

B * —

J hel

4 ••

3-

2-

1 ••

IAEA-CN-33/PD-2 211

loop voltage

negative voltage spike-

1ms

H h


loop

voltage

M

'•-100

-•-200

FIG.5. Relaxation time for instability occurrence. Helical current pulses of different lengths followed by

a disruptive instability ® or without effect on the plasma stability ®.

MHD mode amplitude

FIG.6. Mode damping by RHF.

disruption

resulting in a current disruption (Fig. 5@). The relaxation time for the

occurrence of the instability is of the order of 1 ms (such island production

is a resistive process). A pulse less than ~1 ms in length does not produce

a disruptive instability even when the helical field is 20% greater than the

instability level (Fig. 5@). This "penetration" effect was also measured

by means of the audiofrequency generator. Helical fields from 2-6 kHz

with an amplitude Bhel ~ Bh 5 el have no effect on the stability of the plasma.

When one applies a RHF whose value lies between 60% - 95% of the

critical RHF, a stabilizing effect is observed:


212 KARGER

1) The amplitudes of the lower MHD-modes (especially m = 2) are strongly

reduced (Fig. 6) with irregular, higher-frequency, lower-amplitude

oscillations remaining.

2) For a constant plasma current, the spontaneous disruptive instability

can be avoided, resulting in a reproducible extension of the plasma

current duration up to a factor of three (Fig. 7).

The stabilizing effect becomes the greater, the closer the RHF approaches

the instability level. The exact nature of this stabilization is not yet clear.

Probably, the RHF produces a fixed helical structure within the plasma which

hinders a rotation of the MHD-modes and also therewith a convective growth

of the perturbation. Damping of MHD-modes is also observed for the case

when the helicities have the opposite sense, but only at about ten times higher

helical fields.

'plasma

M 75--

50--

25- -

•without RHF

. with RHF stabilization

20 40 60 80 100

t \ms\ -

FIG.7. Plasma stabilization by RHF.

Possible applications of the RHF-method are:

1) The helical fields which can measurably influence the plasma are very

small. Thus thin helical conductors are sufficient. With a system of

i = 1, 2, 3 . .. helical windings, it is possible to produce, with definite

frequency, islands on the corresponding q = 1, 2, 3 ... and rational

surfaces. These can be localized by means of X-ray diagnostics [2],

thereby allowing a rough determination of the current profile.

2) By triggering the disruptive instability through the RHF-method we

can investigate the instability in more detail than was possible up to

now (X-ray, laser), especially its dependence on the plasma temperature,

the toroidal magnetic field, the neutral-gas pressure and

impurities. In addition, one can, by feedback interaction of the RHF

with the spontaneous MHD-modes, expect to obtain a stabilization which

is still better than the stabilization achieved through constant RHF.

120


IAEA-CN-33/PD-2 213

We gratefully acknowledge the suggestion of Dr. von Gierke td instal

helical windings in Pulsator-I. Furthermore, we are indebted to Drs Pfirsch

and Tasso for helpful discussions.

[1] KLUBER, 0.,etal., these Proceedings.

[2] BRETZ, N., et al., these Proceedings.

REFERENCES


DISCUSSION

ON PAPER IAEA-CN-33/PD-2

J. TACHON: Is a sudden disruption of the current always accompanied

by magnetic oscillations of mode m = 2? In the TFR-experiment some of the

sudden current disruptions are associated with growing oscillations of mode

m = 2, but some disruptions also exist without any displacement and without

detectable oscillations. This second case could correspond to the expulsion

of a filament of uncoupled electrons against the diaphragm, causing an influx

of impurities, cooling the periphery of the plasma and reducing the radius of

the current channel. The result would be an abrupt current decay since q,< 1.

F. KARGER: The current disruption in Pulsator-I is not always

introduced by a chain of growing m =2 oscillations. In a few cases we

observed only a quarter- or half-turn of a fast-growing m = 2 perturbation

before the negative voltage spike, which always precedes the disruption.

215


IAEA-CN-33/A9-1

HATPEB nJIA3MbI A3HMyTAJIbHO

HECHMMETPHHHOH HOHHO-1JHKJIOTPOHHOH

BOJIHOH B yCTAHOBKE TOKAMAK TM-l-BM

B.JI.BflOBHH, B.JI.PyCAHOB,

H.B.niAnOTKOBCKHH

HHCTHTyT aTOMHOH SHepTHH HM . H .B .KypMaTOBa ,

MocKBa,

C0103 CoBeTCKHX CouHa^HCTHMecKHx Pecny6;iHK

Abstraa- AHHoramm

PLASMA HEATING WITH AN AZIMUTHALLY NON-SYMMETRICAL ION CYCLOTRON WAVE IN

TOKAMAK TM-l-HF.

With the aid of a non-symmetrical system, an ion-cyclotron wave with m = 1 and X = 30 cm was

excited and identified in hydrogen, deuterium and helium in Tokamak TM-l-HF. The optimum

absorption areas with respect to concentration and magnetic field were determined. In the absence of a

magnetic beach, up to 200 kW HF power was introduced into the plasma. The maximum increase in nT

according to the diamagnetic signal in the deuterium was 2 x 10 15 eV/cm 3 with a concentration of

n « 10 13 cm -3 and initial pressure 10 15 eV/cm 3 . Evaluation of the rise in ion temperature from the carbon

impurity line yielded approximately 80-90 eV.

HArPEB IIJIA3MM A3HMYTAJIBHO HECHMMETPHHHOH HOHHO-LJHKJIOTPOHHOH BOJI­

HOH B YCTAHOBKE TOKAMAK TM-l-BH.

B ycTaHOBKe ToKaMax TM-l-BH B Boaopofle, flefiTepHH H re;iHH c nOMombw HecHMMeTpHM-

HOH CHCTeMM B036yxaeHa H HaeHTH$HUHpoBaHa HOHHO-MHK/ioTpoHHafl Bo/ina cm= 1 H \z= 30 CM.

HafiaeHbi onTHMa/ibHbie o6;iacTH norviorneHHH no KomieHTpaiiHH H MarHHTHOMy no;no. IlpH OTcyT-

CTBHH MarHHTHoro 6epera B nna3My BBoavinocb ao 200 KBT BM-MOIIIHOCTH. MaKcmna;ibHi>ift

npHpocTnT no flHaMarHHTHOMy CHrHa^y B aeftTepHH cocTaBHn 2-10 15 3B/CM 3 npH KOHueHTpaqHH

n* 10 13 CM" 3 H Hana/ibHOM flaBneHHH 10 15 3B/CM 3 . Ouemca npHpocTa HOHHOS TeMnepaTypM no

npHMecHOii HHHHH yrviepo,n.a aaei npHMepHO 80 -f 90 aB .

BBEflEHHE

B ycTaHOBKe ToxaMaK TM-l-BH (6o;ibiiioH paflHyc R = 40 CM, paflHyc

aHa$parMBi 7-8 CM, Hmax = 14 K3, Jmax = 30 KA, TJ = 6 MC) HccneflyeTCH

Aono^HHTe^bHBiH HarpeB BomaMH B6;IH3H HOHHO-IJHKJIOTPOHHOH lacTOTH

H ee rapMOHHK. B HaiHHX npeflBiayniHx Hcc^eflOBaHHHx [1] H3yna^Hcb ycnoBux

pacnpocTpaHeHHS H HarpeB ropHMefi TopoHfla/ibHOH ruia3Mbi 6bicTpbi-

MH MarHHTH03ByKOBbIMH BOJIHaMH . RjlSi B03 6y?K,TJ,eHHH BOJIH HCriO;ib30Ba ~

/iacb o^Ha cHMMeTpniHaa neTna KaK B H30^HI4HH, TaK H 6e3 H30;IHIJ,HH.

C nOMOUlbK) CHrHajIOB MaTHHTHBIX 30HflOB H BHOCHMOrO COnpOTHB^eHHH B

BHTOK CBH3H 6bI/IO nOKa3aHO B036y>K,KeHHe MarHHTH03ByKOBMX BOJIH HaMH-

Haa c yc^OBHH OTnHpaHHfl n.ria3MeHHoro BOJiHOBOfla 12].

B 3THX pa6oTax, npoBO^HMbix npH cpe^HHX MOUIHOCIHX (Si 50 KBT),

MM HaS^Bfla^H TaKxe H HarpeB HOHOB . H3MepeHHH aonn^epoBCKHx IHHPHH

JIHHHH CIII H Hell o6Hapy>KH/iH HarpeB OCHOBHOH Maccbi HOHOB B HecKO/ib-

KO fleCHTKOB 3^eKTpOH-BO/[bT.

B HacTOHiuefi pa6oTe Hcc/ie,zj,yioTCfl HOHHO-i*HK.rioTpoHHbie BO^HH B BO-

^opofle, flefiTepHH H re/iHH. OcHOBHwe Hcc/ieflOBaHHJi npoBOAH/iHCb Ha nac-

TOTe 6,95 Mrq, cxoflHbie pe3y/ibTaTW no-rcyneHbi Ha MacTorax 12 H 14,8 Mrq.

IlapaMeTpbi n/ia3Mbi H cHCTeMbi B036yx^eHHH Bbi6Hpa/iHCb H3 yc/iOBHH 06-

217


218 BflOBHH H .up.

pameHHH BHyTpH n/ia3MH B 6ecKOHeHHOCTb nepneHaHKy^apHoro BO/IHOBOTO

BeKTopa K (6/iaro.aapjJ TopoHflanbHOMy MarHHTHOMy nomo), MTO npHBOflHT

K yciOBHK) Kz =

HBie [2] .

CHCTEMA CB533H

, ,2 2

i-n

w- (3fleCb fi = , OCTa/IbHbie C>6o3HaHeHHH o6bIH~

^ tot

Rim B036y«fleHHH HOHHO-L[HK./IOTpOHHbIX BO^H MM HCnO;ib30Ba;iH 3a~

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IAEA-CN-33/A9-1 219

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IAEA-CN-33/A9-1 221

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IAEA-CN-33/A9-1 223

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curtiajia *, CHrHa^ 30H.ua, H3MepHwmero MarHHTHoe no;ie pa3p«4Horo TOKa, n^oTHocTb ajieKTpo-

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IAEA-CN-33/A9-1 225

(-rp-< 0). B HacTOHmee BpeMS MBI He MOXSM cae;iaTb cooTBeTCTByiomero

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B TeneHHe pacna.ua nT n;iOTHOCTb n/ia3Mbi npaKTHHecKH HeH3MeHHa, T.e.

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noKa3ajiH, MTO BK/iafl pe30HaHCH0H nepe3ap«aKH B ox/ia?K,r[eHHe HOHOB npe-

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3aBHCHMOCTb H3MepeHHbix 3HaMeHHH Tj OT HOHHOH TeMnepaTypw (H = 12 K3,

J= 10 KA).

BHAHO flOBO/ibHO xopomee cor^acwe c "HeoK/iaccHHecKOH" Teopneft

HOHHOH TennonpOBOflHOCTH B 06/iacTH "njiaTo" [4] .

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HHK), HeOflHOpOflHOCTHMH KOHUeHTpai|HH H MaTHHTHOTO nOJW TOKaMaKa .

3TOT MeT04 no3BO/iH/i noMTH B Tpn pa3a yBe^HMHTb TenjioByio SHeprnio TO-

KOBOTO uiHypa.

SHepreTHMecKoe BpeMH >KH3HH pacna^aiomeHCfl n;ia3Mbi c ropflMHMH

HOHaMH B TOKaMaKe onpeflejiaeTCfl HOHHOH Ten/ionpoBoaHOCTbio, 6;iH3KOH

K HeoK/iaccH^ecKOMy 3HaHeHHK>.

JIHTEPATYPA

[1] BflOBHH, B.JI. H AP-, nwcbMa )K3T* 1£ (1971)228; J_7(1973)4.

B/(OBHH,,B . JI. H ap •, IHeciaa EBponeiicKaH KOH$epeHUH$i no ynpaB^HeMOMy TepMO-

H^epHOMy cHHTe3y H $H3HKe nna3Mbi, MocKBa, 1_(1973)553.

[2] CTHKC, T., TeopHS II;ia3MeHHMX BOJIH, M., ATOMH3flaT, 1965.

[3] OBMHHHHKOB, C.C., IHBEU,, O. H ap., IlHCbMa 5K3T* 1^(1970)277.

[4] rAJIEEB, A.A., CArflEEB, P.3., Bonpocbi TeopHH njia3Mii, T.7. M., ATOMH3aaT,

1973.


THE FRASCATI TURBULENT TOKAMAK

EXPERIMENT (T.T.F.)

R. LUPPI, M. MARTONE

Laboratori Gas Ionizzati,

Associazione CNEN-EURATOM,

Frascati, Italy

Abstraa

IAEA-CN-33/A 9-2

THE FRASCATI TURBULENT TOKAMAK EXPERIMENT (T.T.F.).

Reducing the H2 filling pressure to 4 x ltr 4 Torr, and improving the magnetic-field configuration,

current pulses with a duration up to 0.4 ms have been obtained. The time behaviour of the density measured

with a 2-mm microwave interferometer shows that the maximum value for the density during the confinement

phase is 3. 6 x 10 +13 cm -3 . Using ruby-laser Thomson scattering, an electron temperature of less than 5 eV

has been measured on the axis during the confinement phase. For the same discharge, the existence of an

electron population having a temperature varying in time from 2. 5 keV up to 4 keV has been inferred from

soft X ray measurements using the absorber technique. Increasing the plasma current rise time, the electron

temperature measured by laser scattering increases to more than 20 eV.

INTRODUCTION

The T.T.F. experiment [1,2] has been designed to study the confinement

of a turbulently heated plasma in a tokamak-like configuration. The main

characteristics of this experiment are the following: the toroidal magnetic

field (BT) coils (24 coils, 3 turns each, RT= 32 cm, rT = 12 cm) are driven

by a capacitor bank, the maximum BT value is 10 kG with a flat top time

(-5% of the maximum value) of 0.2 ms. A stainless-steel toroidal vacuum

chamber (R = 30 cm, a = 5 cm) with a circular niobium limiter (4 cm inner

radius) has been used, a glass break (5 cm wide) allows the longitudinal

electric field directly applied at the break to penetrate across the liner.

A vertical magnetic field up to 100 G d.c. with a curvature ensuring stability

has been provided.

The results reported at the Moscow Conference [2] had shown that the

discharge at a filling pressure of about 1 mTorr had the tendency of shrink

and after 50 /LIS a more rapid decrease in the plasma current, a fast increase

in the loop voltage, and an increase in the plasma luminosity in the visible

region indicated the end of the confinement phase. Moreover, the presence

of a stray field from the toroidal coils had been established. Consequently,

modifications have been introduced to improve the ionization of the H2 gas

(by means of an appropriate timing of the electric-field pulse, creating

the pre-ionizing current, with respect to the high-voltage spark producing

the primary electrons), as well as the magnetic-field configuration (by a

more accurate positioning of the toroidal coils and feeding cables).

EXPERIMENTAL RESULTS

Typical results obtained with the improved device are shown in Fig. 1

where the time derivative Ip of the plasma current, the plasma current I

227


228 LUPPI and MARTONE

—.

u

5 '

X

—^

| [ i —

\/-~—^ —^ JVA/ 1

v - i

— I 1 — 1 1 1 , 1 , 1

0.1 0.2 0.3

1 (ms)

0.4 0.5

FIG. 1. Time behaviour of a discharge in hydrogen with a filling pressure of 4 x lCT 4 Torr. (n0 = density,

I = plasma current, I = plasma-current time derivative.)

P v P v

15r 30 -

-10-

L 0

FIG. 2. Time behaviour of electron temperature (Te) and density (ne) on the axis, measured by laser

scattering (I = plasma current).


IAEA-CN-33/A 9-2 229

and the peak density n0 are plotted versus time (n0 represents the maximum

value for a parabolic density.distribution with a radius equal to the limiter

radius). The density measurements have been obtained with a 2-mm microwave

interferometer in radial direction in the equatorial plane.

An HCN c.w. laser interferometer [3] has also been used, giving results

in agreement with those from the microwave interferometer. The H2 filling

pressure is 4 X 10" Torr, the toroidal magnetic field BT = 6.8 kG and the

vertical field Bv = 54 G.

The electron temperature on the axis has been measured by using

ruby-laser Thomson scattering. A rejection system [4] has been used to

eliminate the stray light. This system has a contrast of about 10 4 at

100 A from the 6943 A laser line and a transparency of 0.25. The total

contrast including the monochromator was 10 , sufficient to eliminate the

stray light completely. As a result, an electron temperature of less than

5 eV is obtained during the confinement phase. For the same discharge

soft-X-ray measurements using the absorber technique show the presence

of an electron population having a temperature that varies from 2.5 keV

at t = 55 jus to 4 keV at t = 200 /us. This behaviour may be caused by the

fact that during the build-up phase of the discharge the current, in this case,

rises much faster than the plasma density. In fact, it was possible to show

that, if current and density are made to rise on the same time scale, the

electron temperature obtained from laser scattering increases, reaching

more than 20 eV (Fig.2); in this kind of discharge, however, the vertical

field was insufficient to ensure long-time confinement.

From streak photography, it is seen that the discharge starts displaced

towards the inner side of the vacuum chamber. This fact is consistent

with the presence, at the beginning of the discharge, of the imposed d.c.

field for the equilibrium, together with the vertical field from the image

currents in the metallic walls. Successively, the discharges are subject

to an outward drift lasting for a time longer than the current diffusion

time in the walls (40 /JS). Reducing the value of the d.c. vertical field the

discharge is more centred at the beginning, but the current pulse lasts for

a shorter time as the discharge touches the outer wall earlier.

CONCLUSIONS

Improving the magnetic configuration and reducing the working H2

pressure to 4 X 10" 4 Torr, longer current pulses (0.4 ms) have been obtained.

The low electron temperature (Te < 5 eV) found by Thomson scattering and

the presence of a high-temperature population as seen from X-rays

(Te = 2.5- 4 keV) might be due to the plasma current rising much faster

than the density in these discharges. The electron temperature from

Thomson scattering, in fact, reaches more than 20 eV when the current

is built up on the same scale as density, byt in these cases the vertical

field was insufficient for long-time confinement.

ACKNOWLEDGEMENTS

The authors wish to thank F. Engelmann for useful discussions and

R. Verbeek for density measurements with the 2-mm microwave

interferometer.


230 LUPPI and MARTONE

REFERENCES

[1] MARTONE, M., in Toroidal Plasma Confinement (Proc. 3rd Int. Symp. Garching, 1973) B. 7.

[2] MARTONE, M., in Controlled Fusion and Plasma Physics (Proc. 6th Europ. Conf. Moscow, 1973) 2.

[3] GIANNELLA, R., GROLLI, M., et al., Report LGI. R/PLAD/74/9 Laboratori Gas Ionizzati, Frascati,

Rome, Italy.

[4] BARONE, I., DEANGELIS, A., GAROSI, F., to be published.


IAEA-CN-33/A9-3

3KCIIEPHMEHTLI IIO BLICOKOHACTOTHOMY

HArPEBY IIJIA3MLI HA TOKAMAKE $T-1

B.E.rOJIAHT, H.n.rHA£KOBCKHH,

B.B.flB34EHKO, M.M.JIAPHOHOB, JI.C.JIEBHH,

E.A.MHXAHJIOB, B .B .POJKflECTBEHCKHH,

r.A.CEPEBPEH'BIH, O.H .II(EPEHHHH

H3HK0-TeXHHUeCKHH HHCTHTyT HM . A . $ . Ho$(|)e

AKaaeMHH HayK CCCP,

JleHHHrpaa,

C0103 COBeTCKHX Coijua/iHCTPmecKHX Pecny6;iHK

Abstract-AHHOTaiyffl

HIGH-FREQUENCY PLASMA HEATING EXPERIMENTS IN THE TOKAMAK FT-1.

The absorption of electromagnetic wave energy at the lower hybrid resonance frequency can be used for

heating plasma in toroidal traps. Transformation of the electromagnetic wave into plasma oscillations at the

lower hybrid resonance frequency provides an absorption mechanism which remains highly efficient even at high

plasma temperatures. In the vicinity of the lower hybrid resonance there is also strong collisional absorption.

The authors describe experiments carried out in the Tokamak FT-1. Power of up to 40 kW was .applied to the

plasma at a frequency of 280 MHz and satisfactorily absorbed over a broad range of plasma densities. The

heating effect, however, as determined from the diamagnetism, was small. The life-time of the energy applied

during high-frequency heating was not greater than 100 us, whereas for ohmic heating it can attain values of

450-750 lis. High-frequency oscillations in the plasma produce fast ions with energies of up to 3 keV, but their

lifetime is short — 40-50 us. The authors suggest that the high-frequency oscillation energy is absorbed by

the cold plasma close to the antenna without reaching the lower hybrid resonance region. This may be due

to collisional absorption in the external plasma layers. The generation of fast ions, however, indicates a

considerable effect of non-linear processes in the high-frequency wave field that may be due to parametric

instability. .The short life-time of the fast ions can be explained in these conditions by the fact that they are

formed in the external layers of the plasma. Parametric instability and collisional absorption resulting in

dissipation of the high-frequency energy in the external plasma layers may accordingly be an obstacle to the

use of the lower hybrid resonance for plasma heating.

SKCTIEPHMEHTM nO BBICOKOMACTOTHOMy HArPEBY nJIA3MH HA TOKAMAKE *T-1.

rioiviomeHHe 3HeprHH s^eKTpoMarHHTHWx BO/IH ripn nacTOTe HHacHero rH6pn,n.Horo pe30HaHca

(HTP) MoaceT 6MTB Hcno/ib30BaHO ana HarpeBa n/ia3Mbi B TopoHaa^bHwx /lOByuiKax. TpaHC-

(JiopMauHSJ aneKTpoMarHHTHOH BO/IHbi Bn/ia3MeHHyio npw HTP o6ecneHHBaeT MexaHH3M nornomemis,

3eKTHBHOCT& KOToporo ocTaeTCH 6O;II>IIIOH H npH BBICOKOH TeMnepaType nna3MM.

B6AH3H HTP BejiHKO Taicace crojiKHOBHTe;ibHoe norjiomemie. OnHcaHbi sxcnepHMeHTbi, Bbino/i-

HeHHbie Ha ToxaMaKe 4>T-1. B n/ia3My BBO.ZI.HTCH ao 40 KBT Ha nacTOTe 280 Mru. BBoaHMaa

MomHOCTb xopomo nor^omaeTcn B IHHPOKOM flHana30He n^oTHOCTeft nnasMu. O/tHaxo 3$$eKT

HarpeBa, onpeae/ifleMbiH no flHaMarHeTH3My, Man. BpeMH JKH3HH SHeprHH, BBOAHMOH npwBH-

HarpeBe, He npeBbimaex 100 MKC, Toraa KaK npH OMHnecKOM HarpeBe OHO cocTaBnneT 450-750MKC

Iloa fleficTBHeM BH-KO^e6aHHH Bn^aaMe no«B;iHioTCH 6wcxpwe HOHW C SHeprHefl ao 3 KSB .

OaHaico HX BpeMH XH3HH Mano H cocTaB;weT 40-50 MKC. BbiflBHHyTO npeano^o»eHHe,


232 ronAHT H ap.

Ha ToKaMaKe $>T-1 B $H3HKo-rexHHiecKOM HHCTHTyTe HM. A .


a?

10 2

10

10" 1

1

IAEA-CN-33/A9-3 233

1 10 10 2 10 3 10 4

V

PHC.1 . 3aBHCHMOcrn noKa3aTejiefi npe/iOMJieHiui H 3aTyxaHH» OT ruioTHOcTH nra3Mii B o6nacTH HTP.

y»e npH flOCTaTOMHO HH3KOH n/IOTHOCTH njia3MBI, V = 50, He3aBHCHM0

OT Be/IHHHHM MarHHTHOrO TIOJIX, K03


234 TOJIAHT H flp.

Pnc.2. CxeMa BBoaa BH-MOIUHOCTH B KaMepy ycTaHOBKH 4>T-1 .

no aaHHbiM flHaMarHHTHbix H3MepeHHH aaeKTpoHHasi TeMnepaTypa

aocTHraaa 100 aB npH TOKe pa3pn,zia 22 KA . H3MepeHHfl no npoBOflHMOCTH

aaiOT HHJKHIOIO oqeHKy a^eKTpoHHOH TeMnepaTypw 30 aB . 3HepreTnnecKoe

BpeMH KH3HH cocTaBJiaeT 0,45 MC ripn TOKe pa3pH#a 10 KA H 0,75 MC npH

TOKe 22 KA .

HCTOMHHKOM BbicoKOMacTOTHOH MOII(HOCTH cnyyavin JiaMnoBbifi reHepa-

Top. ^acTOTa ero cocTaB/iHua 280 MTIJ, MTO cooTBeTCTByeT nacTOTe HTP

npH H = 5 K3, n = 7«10 12 CM" 3 . MomHOCTb, nopoaHMaa K aHTeHHOMy ycipoftcTBy,

cocTaB/iH/ia 40 KBT B HMnyjibce zi^HTe/ibHOCTbio 1 MC . BBO,H BBIcoKOHacTOTHOH

MOIUHOCTH B n^3My cxeMaTHMecKH H3o6paxeH Ha pHc.2.

OH COCTOHT H3 flByx BHTKOB, oxBaTMBaiomHX pa3pa/i Ha paccroHHHH 15 CM

oflHH OT apyroro (1). BHTKH HaxoaflTCH B TeHH aHa$parMbi H 3aK7iK)MeHbi

B KBapqeBbie rpy6KH. KoaKCHa/ibHbie H,ziepbi pa3HOH fl;iHHbi o6ecneHHBaioT

nHTaHHe BHTKOB OT reHepaTopa B npoTHBO$a3e. 3a cieT npoTHBO


IAEA-CN-33/A9-3

H3MepeHna noKa3ajiH, MTO BM-KO/ie6aHHH xopomo norjiomaiOTCH B

n/ia3Me. ITorjiomeHHe Ha6/iioflaeTCH BO BpeMH pa3pH#a H B noc^ecBeMeHHH,

npH CpeflHHX n/IOTHOCTHX OT 5 • 10 11 £0 2 • 10 13 CM -3 . BHyTpH pa3pHflHOH

KaMepbi nor/iomaeTCH OT 75 #0 90% noflBOflHMOH MOIIIHOCTH.

3(|)HCHHTb noBbimeHHeM TeMnepa­

Typbi. CKopee OHM yKa3biBaioT Ha HHaceKijHio n;ia3Mbi, co^epacameft npHMe-

CH, H3 06/iacTH BH-BBoaa B pa3paa. YBe^HMeHHe ^HaMarHeTH3Ma O6T>HC-

1 -

a {10 efl. CGSE)

l{OTH.efl.)

40 80

P(KBT)

a

° Ta=303B

PHC.3. 3aBHCHMOCTH npoBoaHMOcTH nnasMU H HHTerpa^bHoro cBeneHHH OT MOIUHOCTH OMHiecKoro

HarpeBa.

120

235


236 TOJIAHT H 4p.

2

o

CO

"o

t 1

o TE=0,A5MC

T =0,63MC

J L J L

40 80

120

P(RBT)

TC = 0,75MC

PHC.4. 3aBHCHMOCTb 4HaMarHeTH3Ma nna3tAhi OT MOIUHOCTH OMHMecKoro HarpeBa.

PHC.5. OcuHnnorpaMMM (cBepxy BHH3>: HMnynbca BbicoKOiacTOTHoft MOIUHOCTH, TOKa pa3pH.ua,

Hanp»*eHHH Ha o6xo4e, HHTerpa/ibHoro CBeieHHa H ruioTHOCTH nna3MM.


IAEA-CN-33/A9-3 237

E(K3B)

PHC.6. 3HepreTHMecKne cneKTpw aTOMOB nepe3apaaKH: 1-npH owmecKOM HarpeBe; 2- npw oaHO-

BpeMeHHOM OMHiecKOM H BM-HarpeBe ; 3- npH BM-HarpeBe pacnaaaiomeftcH n;ia3Mi>i.

HaeTca yBe;iHHeHHeM naoTHOCTH, a He TeMnepaTypbi. H3MeHeHHH B cBene-

HHH cneKTpajibHbix JIHHHH TaK*e He yKa3BiBaioT Ha noBbinieHHe TeMnepaTypbi.

Bo BpeMH BH-HMny;n>ca yBe;iHHHBaeTCfl CBeieHHe ;IHHHH C HH3KHMH noTeH-

L(Ha^aMH B036yXJ5eHH3 (Oil, CII1), HO He B03paCTaeT HHTeHCHBHOCTb .TCHHHH

OV, HMeiomeH 6onee BMCOKHH noTeHqwa/i B03 6yacjneHHH.

H3yHanocb TaK*e B/iHHHHe BH-HarpeBa Ha 3HepreTHmHxcH nyTeM nepesapH^KH HOHOB. Pacno^o^ceHHe aHa;iH3aTopa noica-

3aHO Ha PHC.2. AnnapaTypa perwcTpHpoBajia aTOMbi, BbijieTaiomHe nepneH-

^HKy/iapHO OCH pa3pH.ua B ceieHHH, oTCToameM Ha 1 M OT B^I-BBoaa. Ebi-

JIO o6Hapy)KeHo pe3Koe yBe;iHHeHHe noTOKa aTOMOB c BHCOKHMH 3HeprnaMH

BO BpeMH BH-HMny^bca. 3TO yKa3HBaeT Ha noflB/ieHHe B pa3pfl#e ycKO-

peHHHX HOHOB. SHepreTHMeCKHH CneKTp CHflbHO OTKAOHfleTCfl OT MaKC-

Be^noBCKoro pacnpe^e^eHHH 3a cneT o6orameHHH ycKopeHHHMH MacTHua-

MH. noHB^tHioTCH MacTHqbi c 3HeprHflMH OT 1 tfo 3 IOB, Boo6me He Ha6;iK>aaBiUHeca

npH OMHMecKOM HarpeBe. Ha pHc.6 npHBe^eHbi cneKTpbi, cHHTbie

npH OMHMecKOM HarpeBe (1), npH OMHHecKOM HBH-HarpeBe (2), H npnBH-HarpeBe

B pacnaaaiomeHCH njiasMe npw njiOTHOCTH MeHee 5*10 CM" . B noc-

/te^HeM caynae noTOK 6bicTpwx nacTHU. caMbifi HHTeHCHBHbifl.

BH^O onpeae/ieHO BpeMfl 5KH3HH ycKopeHHbix HOHOB B njia3Me. OHO

onpefle^a/iocb no oc;ia6;ieHHio noTOKa 6bicTpbix aTOMOB nocrce OKOHHaHHH

BH-HMny^tca. Ha pwc.7 npHBe^eHbi BpeMeHHbie 3aBHCHMOcTH noTOKa nac-

THU. c SHeprHeH 500 aB (1) H 1000 aB (2). MoMeHT oKOHiaHra Bl-Harpe-

Ba OTMeieH CTpejiKOH. BpeMeHa >KH3HH M,JI%. 3THX SHeprwH cocTaBjunoT

50 H 40 MKC . 3TH BpeMeHa 3HaMHTe;ibHO MeHbiue, neu BpeMH 3aMefljieHHH

TaKHX HOHOB B n;ia3Me, cociaB/ifliomee 350 MKC . OHH npH6;iH3HTe;ibHO paB-

Hbi BpeMeHH Apeiifya B HHCTO TOpOH^a^bHOM MarHHTHOM nojie 6e3 BpamaTe/ib-


238 TOJIAHT H ap.

-ff (oraefl.)

PHC.7. BpeMeHHwe 3aBncnMocTH noxoxa aioMOB nepesapHflKH nocne OKOHiaHHH BM-HMny/ibca:

1- c 3HeprHefi 500 aB ; 2- c SHeprHeft 1000 aB.

Horo npeo6pa30BaHHH, Heo6xoaHMOMy A/IH Biixofla HOHa 3a npene/ibi flHa-

^parMBi. JlerKO BH^eTb, MTO THKOBO .ROJITKHO 6bixh BpeMH *H3HH HOHa,

ycKopeHHoro BO BHeuiHefl o6;iacTH paspnfla. TaKOH HOH npH pH«eHHH no

apeH(|)OBOH xpaeKTopHH nori)KeH nepecenb paspnflHyjo KaMepy H BHHTH 3a

npeaejibi ,a;HaT Ha TO, MTO BH-

MomHOCTb nor^omaerca BO BHem.HHX C/IOHX n;ia3Mbi. B pe3y;ibTaTe 3neK-

TpoMarHHTHafl Bo/iHa He aocTHraeT o6jiacTH HTP, pacnojio^eHHOH B qeHT-

pe pa3pH^a. HaCTHMHO 9TO MO*eT 6bITb oStflCHeHO CTOTIKHOBHTe;ibHbIM

nor/iomeHHeM B XO/IOAHOH npncTeHOMHOH n/ia3Me. KaK 6M;IO noica3aHO, Ta-

Koe norviomeHHe BO3MOXHO, ecjiH nnoTHocTb XO/IOAHOH nna3Mbi He C/IHHIKOM

MaJia. npflMWX H3MepeHHH nJIOTHOCTH B TeHH flHaiJparMbl He npOBOflH^OCb.

Ho npH yMepeHHOM pa3pHflHOM TOKe H MajiOH £/iHTe/ibHOCTH pa3p«aa Ha HameH

ycTaHOBKe MOMO npeano^araib, MTO n.na3MeHHbiH umyp He HMeeT

pe3KOH rpaHHUbi.

OflHaKO He BCe Ha6;iK>,ZiaeMbie JIB;ieHHH o6'BHCHflK)TCfl CTO/IKHOBHTe;ibHbIM

noMomeHHeM. EtoHB^eHHe 6biCTpbix HOHOB B njia3Me CBHneTe/ibCTByeT o

TOM, MTO nor^omeHHe MOIUHOCTH MO»eT 6biTb CBS3aHO c He;iHHeHHbiMH npoueccaMH

B none sneKTpoMarHHTHOH BO^HH . PaccMOTpHM B03M0Mbie MexaHH3Mbi

ycKopeHHH HOHOB no.a aeficTBHeM BH-Ko^e6aHHH. IlpHMoe ycKOpeHHe

B a^eTpHMecKOM none BO^HBI, BH4HMO, HeB03M0JKH0, nocKonbKy tL>>wCi.

Ilpn BH-Hanpa*eHHHHaaHTeHHe nopfl^Ka 1000 B OKpy^caiomeH n^33Me MoryT

6biTb aneKTpHMecKHe nona nopflflKa 100B/CM. Ocu.H/i.njiTopHafl 3HeprHH HOHa B

TaKHx noflflx He npeBbimaeT 10" sB. O^HaKO ocn.H;i;i5iTOpHas[ SHeprHH

37ieKTpOHOB npH flBHJKeHHH UROJlb MarHHTHOTO YIOJIH COCTaB/ISeT y>Ke 20 3B,

TO ecTb 6;iH3Ka K HX xennoBOH SHeprHH. Ilo cymecTByiomHM TeopeTHMecKHM

npeacTaB/ieHHHM [4] STO 3HaMHTe;ibHO npeBocxoaHT nopor A/IH pa3BHTHH

napaMeTpHMecKOH HeycTOHMHBOcTH B BbicoKOMacTOTHOM none. B MacTHOc-


IAEA-CN-33/A9-3 239

TH, ciaHOBHTCH BO3MO»HI>IMH pacnaflHbie npoqeccbi, npHBo^amHe K o6pa30-

BaHHK) HOHHO-3ByKOBBIX KO/ie6aHHH H yCKOpeHHK) HOHOB B nO/IHX 3THX KO^e~

6aHHH. TaKHM o6pa30M, nojx aeficTBHeM BBicoKOMacroTHbix nonen B6/IH3H

aHTeHHoro ycTpOHCTBa MoaceT pa3BHBaTbCH o6;iacTb Typ6yjieHTHOCTH, B

KOTOPOH nor^omaeTCH SHeprnfl s^eKTpoMarHHTHOH BO/IHH H ycKopfliarcfl HOHBI .

TaKHM o6pa30M, napaMeTpH^ecKafl HeycroHHHBocTb H cTO/iKHOBHTe;ib-

HaH jJHCCHnaUHH MOryT 6bITb npHMHHOH nOr^OIUeHHa BblCOKOMaCTOTHOH

MOIIIHOCTH BO BHeuiHHX C/IOJIX n^a3Mbi H Ma/iOH 3KT* 43 (1973) 1632.

[2] rAJIAKT HOHOB,. B.B., flbflHEHKO, B.B., JIAPHOHOB, M.M., mEPBHHHH, O.H.,

)KT4>44_(1974)729.

13] TOJIAHT, B.E., nHJIHfl, A.fl., y$H 104(1971)413.

[4] CHJIHH, B.n., riapaMeTpH^ecKoe Bo3aeftcTBHe W3ny*ieHux Eo/ibiuoH MomHOCTH Ha

Il;ia3My, M., "HayKa", 1973 r.


IAEA-CN-33/A9-4

HCCJIE^OBAHHE $YHK1JHH PACnPEflEJIEHHfl

3JIEKTPOHOB no SHEPrHHM H EE H3MEHEHHH

B nPOlJECCE HArPEBA HA 3JIEKTPOHHO

UiHKJIOTPOHHOM PE30HAHCE

B.B.AJIHKAEB, T . A.EOEPOBCKHK , B.H.n03H5IK,

K.A.PA3yMOBA,K).A.COKOJ[OB

HHCTHTyT aTOMHofi sHeprHH HM . H. B. KypnaTOBa,

MocKBa,

C0103 CoBeTCKHX CouHa/tHCTHMecKHX Pecny6;iHK

Abstraa- AHHorauHH

INVESTIGATION OF THE ELECTRON ENERGY DISTRIBUTION FUNCTION AND ITS VARIATION DURING

ELECTRON CYCLOTRON RESONANCE HEATING.

Microwave heating on Tokamak TM-3 continues to be studied. The electron energy distribution

function has been examined by means of X-ray and microwave plasma diagnostics. Variations in the

spectral radiation pattern during auxiliary heating show a region of the distribution function where interaction

with electromagnetic waves takes place, giving rise to diamagnetic effects observed previously.

HCCJIEflOBAHHE *yHKU,HH PACnPEflEJIEHHfl 3JIEKTPOHOB IIO SHEPrHHM H EE H3-

MEHEHHfl B nPOIJECCE HArPEBA HA 3JIEKTPOHHOUHKJIOTPOHHOM PE30HAHCE.

Ha ToKaMaKe TM-3 npoflon*eHO HccjieflOBaHHe CBH-HarpeBa. Jinn AHarHOCTHpoBaHHH

dpyHKqHH pacnpeaeneHHH a^eKTpOHOB no 3HeprHHM perHCTpnpoBa;iocb peHTreHOBCKoe H CBM-

H3^yMeHHe nna3MH. H3MeHeHHe cneKTpoB H3/iyHeHHa npu AononnHTeJibHOM HarpeBe aaeT BO3-

MOJKHOCTb yxa3aTb Ty o6;iacTb $yHKi]HM pacnpeaeneHHfl, c KOTopofi B3aHMOfleflcTByioT aneKTpo-

MarHHTHbie BOAHBI, o6ycnoB/iHBaa ha6/iKweHHi>iH panee AHauarHHTHiiH s$$eKT,

I . BBE£EHHE

IlepBbie 3KcnepHMeHTbi no flono/tHHTeflbHOMy HarpeBy n;ia3Mbi TOKaMaKa

Ha 3JieKTpOHHO-IJ[HK.riOTpOHHOM pe30HaHCe (3U.P) nOKaaa^H 3


242 AJIHKAEB nap.

JljaHHaH pa6bTa nocBHmeHa BbiacHeHHio po/iH pa3;iHMHbix MexaHH3MOB Harpe-

Ba nna3MbI H, B MaCTHOCTH, BWHCHeHHK) BOnpOCa O TOM, KaKaH MaCTb (|>yHKU.HH

pacnpe^eneHHH sneKTpoHOB onpe^e^aeT yBenHMeHHe aHaMarHeTH3Ma ruia3Mbi.

II . OCOBEHHOCTH PE)KHMOB C SJIEKTPOHHO-I^HKJIOTPOHHblM

HArPEBOM H B03MO)KHbIE MEXAHH3MH HArPEBA IIJIA3MbI

B 3KcnepHMeHTax no 3;ieKTpoHHO-u.HK/ioTpOHHOMy harpeBy(3U,--HarpeB)

Hcno/ib30Ba;icfl reHepaTop c X ~ 1 CM , ,q;iHTe./ibHocTbio HMny^bca no 2 MC H

MomHocTbio^o IOOKBT. 06;iacTb pexHMOB, B KOTopwx Ha6^icwajicH ,qono;i-

HHTe/ibHbiH HarpeB: 5 K3< H * 15 K3, 10 KA S J < 20 KA, ne


IAEA-CN-33/A9-4 243

2. MarHHTHHMH 30H^aMM H3Mepfl/iocb CMemeHHe nna3MeHHoro umypa A

B^o^b 6o/ibiuoro pa^Hyca Topa, KOTopoe nponopqHOha^bHO cyMMapHOMy

(npoflcribHoe + nonepe^Hoe) flaBJieHHio n/ia3Mbi.

3. HanoxeHHe #onojiHHTe;ibHoro nepeMeHHoro HanpH^ceHHH HH3KOH

HacTOTbi Ha o6xoae KaMepbi no3Bo;uuio onpe#e;iHTb MMeHeHHe HH^yKTHBHO-

CTH nna3MeHHoro uiHypa[3l .

4. HoHHan TewtnepaTypa H3MepHJiacb nyTeM aHa/iH3a cnexTpa HeHTpa^b-

HBIX aTOMOB nepe3apH^KH.

5. Jinn H3yMeHHH pacnpe^enenHH 3/ieKTpoHOB no SHeprHHM Hcno/ib3o-

Ba^HCb cneKTpbi peHTreHOBCKoro H3/iyHeHHH B £Hana30He 2,5-50K3B. B 06nacTH

7-50 KSB fleTeKTopOM c/iyxH/i TOHKHH KpHCTann NaJ(Tl) c OKHOM H3

SepujuiuH. RJIH nojiyneHHH jiymnero pa3peuieHHH npH perHCTpaijHH ;IHHHH

xapaKTepHCTHqecKoro cneKTpa npHMeceft B flHana30He 7-50 KSB Hcno;ib30-

Baaca no^ynpOBOflHHKOBHH aeTeKTop Si (Li). Pa3peuieHHe fleTeKTopa -

1,2 KSB. B flHana30He 2,5-10 KSB MM Hcno;ib30Ba;iH nponopu.HOHa;ibHbiH Kce-

HOHOBHH cMeTMHK. Ero pa3pemeHHe — 13% Ha TIHHHH FeK . Bo Bcex c/iy-

Maax cHCTeMa KOMHMauHH rapaHTHpOBa;ia oxcyTCTBue KBaHTOB, nona^aroinHx

B CMeTMHK c noBepxHOCTH jrafiHepa.

6. PerHCTpHpoBaxiocb CBH-H3JiyMeHHe H3 n/ia3Mbi Ha fl/iHHax BOJIH

0,8; 1,3; 2 CM. B STOM ,HHana30He H3/iyHeHHe nna3Mbi onpeflejuieTCH

T0pM03HbIM H UHKHOTpOHHblM H37tyHeHHeM SJieKTpOHOB. OflHaKO HyBCTBH"

TenfaHOCTb cynepreTepo^HHHbix npneMHHKOB (10 -11 — 10" 12 BT) flaBana BO3-

MOXHOCTb HaZie^HO peTHCTpHpOBaTb qHKJIOTpOHHOe H3HyMeHHe H He n03B0~

nsuia perHCTpHpoBaTb TopM03Hoe H3^yMeHHe, win KOToporo n;ia3Ma npo3paMHa.

MHTepnpeTaqHH H3MepeHHH u.HK.noTpoHHoro H3JiyqeHHH ocrcoacHHeTcn

r , ^

HeoflHopoflHocTbio MarHHTHoro nojiH B pa3pH^HOH KaMepe Hz(r) = ,— H ,

r,qe R = 40 CM , r ^ 8 CM H cymecTBOBaHHeM o6nacTn c n , 6o;ibiiieH KPHTH-

MecKOH , fljia H3^yMeHHH c X ~ 2 CM . B cnynae , Korfla no^e Ha OCH KaMepbi

TOMHO cooTBeTCTByeT 311P, H3nyMeBHe B flnana30He AHHH BO;IH 1,3 H2 CM

HcnycKaeTca ycKopeHHWMH sneKTpoHaMH, npoflOHbHaa sHeprHH KOTopbix

E„ * 6 KSB SJIH \ = 1,3 CM H E(| ^ 70 KSB AHH \ = 2 CM . HMKHHH nopor AJIH

X = 2 CM MO*eT yMeHbinaTbCH npH Ha^HMHH B KaMepe o6;iacTH c ne , Bbime

KpHTHMeCKOH.

HeKorepeHTHoe H3/tyMehHe c A ~ 0,8 CM Toace MO«eT onpe#e;iHTbCH

yCKOpeHHblMH 3-HeKTpOHaMH, OflhaKO B 3TOM C^yMae paCMeT HHTeHCHBHOCTH H3"

^yMehHH ocaoxHHeTca nornoineHHeM STOTO H3/iyHeHHH B paHOHe BepXHerH6pHUhoro

pe30HaHca. BpeMeHHOH xofl H3^ynehHH c A~ 0,8 CM MoaceT cooTBeT-

CTBOBaTb H3^yMeHHK) yCKOpeHHHX SJieKTpOHOB.

IV. SKCnEPHMEHTAJIBHME PE3yJIbTATbI

Rjia BblHCHeHHH OTHOCHTe^bHOH pOJIH OCHOBHOH KOMnOHeHTbl H yCKOpeHHblX

S^eKTpOHOB B norVIOmeHHH CBH'MOIIIHOCTH SKCnepHMeHTbl npOBO#H/IHCb B

flByx pe*HMax. B nepBOM pexHMe npo^OTibHoe MarHMTHoe nojie cooTBeTCTBO-

Bano 3IJP Ha OCH KaMepbi ( w He/ w r~ D> BO BTOPOM — wHe/wr Ha OCH cocTaB-HH-

TIO 1,3. KoHueHTpaLjHa H TOK pa3pH^a 6binH o^HHaKOBbi: T>e~3 * 10 CM" 3 ,

J = 13KA. IlepBbiH pexHM 6bin Bbi6paH ana oSecneneHHH HaH6o^ee 6jiaronpHHTHbix

ycnoBMH 311-harpeBa OCHOBHOH Maccbi 3/ieKTpoHOB. BpeMH

cnafla flHaMarHHTHoro curuana H AononmnenhHoro CMemeHHH nocrce BbiK^io-


244 AJIHKAEB nap.

^'* Ma *V«NS^*«^J.

p»i


IAEA-CN-33/A9-4 245

PHC.2. OcuHnnorpaMMM CBH-H3.nyHeHHH n^a3MU Ha animax BOJIH 8, 20 H 13MM, CMemeHHH

n;ia3MeHHoro uiHypa H npoH3B04Hofi MarHHTHoro noTOKa B pexukie OL /W =1,3.

qeHHfl reHepaTopa 6;IH3KO K BpeMeHH acH3hn sHeprnH AO CBH-HMny;ibca (pwc . 1).

Bo BTOPOM pe«HMe uHKJioTpoHHoenorjiomeHHe CBH-MomHOCTti OCHOBHOH KOMnoHeHTOH

ManoBepoaTHO. 3Ty MOUIHOCTB flojiachbi norviomaxb a^eKTpOHM c

npo^o^bHbiMH 3HeprHHMHE|, >. 10 K3B. BpeMH cna^a ^HaMarHHTHoro cwrHana

B 3TOM pe«HMe cymecTBeHHO npeBbiiuano sHepreTtmecKoe (pHc.2).

TaKoe pa3,aejieHHe pe>KHMOB aoBO/ibHO ycjioBHO. HHor^a B nepBOM

pe>KHMe H3MeHehhe HaMa/ibHbix yc/iOBHH npHBO^HT K BpeMeHHOMy xoay

$ H J A , TaKOMy xe KaK H npn wHe/ur = 1 ,3. Jinn Taxoro pexHMa Ha

pHc.3 noKa3aHbi odjhJuiorpaMMbi CBH-H3nyueHna (X = 0,8CM), $ H JA

npH BKTiKHeHHH reHepaTopa B pa3^HHHbie MOMeHTbi pa3pafla. 3aperHCTpHpoBaHHoe

CBM-H3/iyMeHHe HcnycKa^ocb KaK ochOBHOH MaccoH, TaK H ycKO-

1MC


246 AJIHKAEB H Ap.

1 MC

1MC

PHC.3. OcuMflJiorpaMMU CBM-n3/iyHeHHa Ha AJIMHC BO/WM 8MM, cMe«eHHH naasMeHHoro owypa

H npoH3BoflHOH npcwoabHoro MarHHTHoro noroKa am AByx MOMCHTOB BK/IKHCHHH HMny^bca CBH-

Harpesa B pe*HMe wHe /«or = 1. HaianbHoe A&Bnenne PQ =2,3 • 10" 4 Topp.


IAEA-CN-33/A9-4 247

Pnc.4. OcmuiJiorpaMMbi HHTCHCHBHOCTH \i3nyveHnn Ha Anane BO/IHM 8MM, CMemeHHH njia3MeH-

Horo uiHypa H npoH3BOflHOH MarHHTHoro noToka B pe*HMe "He/wr = 1: P = 5 • lO^TOpp.

peHHblMH S^eKTpOHaMH. H3^yMeHHe yCKOpeHHblX 3/ieKTpOHOB 6y^eT BhOCHTb

6onee cymecTBeHHMH BK^a^, weM H3jiynehae sneKTpohOB c TennoBoii sHeprHefl,

TSK KaK pe30HahCHoe MarHHTHoe no;ie Ann \ = 0,8 CM pacnoTioaceHO Ha nepH-

$epHH nna3MeHHoro mHypa, rae Ma;ia KOHueHTpauHH ajieKTpoHOB H HX nonepeqHaa

3HeprHH . CjieaoBaTe;ifeho, yBe/iimeHHe CBH-H3^yMeHHH B TeMe-

HHe pa3pn^a iioxeT CBHaeTe/ibCTBOBaTb 06 yBe^HMeHHH HHcna 6bicTpbix

saeKTpoHOB H/HJIH HxnonepeMHOH 3HeprHH. npH BKjiwieHHH reHepaTopa

BHanane pa3pn^a, Koaa CBH-H3/tyHeHHe MHHHMajibHo (pnc .3a), MM He

BHflHM H3MeneHHH STOI-O H3nyqeHHH, a BpeMeHHOH XOR $ H JA He yKa3bi-

BaeT Ha cymecTBeHHbifi HarpeB 3/ieKTpOHOB c 6ojibiiiKM BpeMeHeM *H3HH.

no Mepe nepeMemeHHH MOMeHTa BKnianeuaH reHepaTopa K KOHuy pa3pa^a

noHB^neTCH flono;iHHTe;ibHoe CBH-H3;iyMeHHe KaK B TeneHHe HMny^bca

HarpeBa, iaK H nocjie Hero (pHC.36). XapaKTep ocqwirtorpaMM $ H JA

yKa3MBaeT Ha HarpeB 6bicTptix a^eKTpoHOB. BpeMeHHofi XOA H3JiyHeHnn

nocjie HarpeBa xopouio KoppejiHpyeT c XOAOM CMenjeHM.

Bo3pacTaHHe H3nyneHHH n;ia3Mbi B TeieHHe pa3pnflHoro HMnyjibca H H3-

MeHeHHe xapaKTepa CBH-HarpeBa roBopHT o BO3MO>KHOM yBejiHneHHH

HVicna ycKopeHHbix 3/ieKTpoHOB H cooTBeTCTByiomeM B03pacTaHHH nor^omeH-

HOH HMH SHeprHH. TaKHM o6pa30M, MM BHUHM , 1TO npH 0JHe /(Jr = 1 KOHKypH"

pyioT AB3. npoqecca norviomeHHH CBH-MOIIJHOCTH: OCHOBHOS Maccofi nJia3MW

H yCKOpeHHblMH 3/ieKTpOHaMH.

IIpH yBenimeHHH KOHU.eHTpau.HH n;ia3Mbi HCMe3aeT CBH-H3.ayHeHHe

(X = 0,8CM) H OTcyTcTByeT HarpeB MacTHU, c 6o/ibiiiHM BpeMeHeM «H3HH

(CM. ocqH/morpaMMbi 4 H JA Ha pHc.4).

1 . PeHTreHOBCKHe H3MepeHHH

IIocTaHOBKa peHTreHOBCKHX H3MepeHHH npec;ie,aoBa;ia flBe qe;iH: oqe-

HHTb KOJIHMeCTBO yCKOpeHHMX SneKTpOHOB B nJia3Me H yCTaHOBHTb 06^aCTb


248 AJIHKAEB HAp.

1000

9

8

7

6

5

4

3

100

9

8

7

6

10

KJKr)

KJKr)

20 30 40

EUaB)

PHC.5. CneKTp peHTreHOBCKoro H3nyneHHH, 3aperncTpHpoBaHHMfi aeTeKTopoM Si (Li) B peatH-

Me Wjjg /wr = 1. HanantHoe naBneHHe Bcujopana PQ = 2 ,5 • 10" 4 Topp, HaianbHoe 4aBfleHne KpnnTo-

Ha P, =2 • 10" 7 Topp,

$yHKL(HH pacnpe^e^eHHH a^eKTpoHOB, c KOTopoft B3aHMO,neHCTByioT sneKTpo-

MarHHTHbie BOJiHbi npH 3U,-HarpeBe B O6OHX yKa3aHHbix peatHMax.

J3,JIH peiueHHH nepBoii 3aflaMH B ruia3My aoGaB^Hnocb Majioe #o3HpoBaH-

Hoe KonmecTBO KpunTOHa. Ha pHc.5 npe^cTaBneH cneKTp X-H3/iyMeHHH,

CHHTMH Si(Li)-fleTeKTopoM B pa3pH#e c npoflcmbHbiM MarHHTHbiM noneM,

cooTBeTCTByiomHM '•JHe/wr = 1 > B OTcyTCTBHe 3U.~HarpeBa. Ha cneKTpe

BH^Hbi K-;IHHHH Kr H Mo. Mo/iH6#eH XEJixeTcn MaTepnajiOM AHa


500

400 I

300 •

A

200

100 - v

7

m

0 V . c

5fS

5

3

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7

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-

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o\

o

IAEA-CN-33/A9-4 249

1 I I I

l 1 ! 1

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(T)

z 5

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V

0 o

0 \ 0 O • •

v

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20 30 40


I 1 ! 1

E(ioB)

EOoB)

10 12

50 60 70

PHC.6. CneKTpM peHTreHOBCKoro n3nyHeHnn B peatHMe wHe/wr = 1, 3aperHCTpHpoBaHHbie:

a - nponopiiHOHa/ibHMM CHCTHHKOM C KCCHOHOBMM Hano^HeHHeM. KpHBan 1 — c 3IJ-HarpeB0M;

KpHBaa 2 -6e3 flonojiHHTejibHoro HarpeBa; KpHBaa 3- pa3HOCTb Meatfly nepBMMH AByMH KPMBW-

MH; 6 - CUHHTWUIHTOpOM Naj(Tl) TOflmHHOfl lMM.


250 AJIHKAEB a flp.

BepoHTHOCTb /iyopecueHUHn JUIH K-O6O;IOMKH, cr —ceneHHe HOHH3au.HH,

f (E) — yHKUHH pacnpe#e;ieHHH 3/ieKxpoHOB no sHeprHHM , Ej — nopor HOHH-

3auHH,nKr — KOHueHTpaqHH HOHOB KpHnTOHa. nojib3yncb TeM,MTO ce^eHHe

HOHH3aUHH flJIfl K-060/IOHKH KpHnTOHa CJ1SL6O H3MeHHeTCH B flHana30He 3Hep~

THH OT 1 ,5 Ea RO 30 Ej , MOMO BbmecTH a. H3-nofl 3HaKa HHTerpana. Tor^a

B npeflnojio»eHHH,MTo MM HMeeM ^e^o B OCHOBHOM C MacTHqaMH, ycKopeH-

HBIMH BRonb MamHTHoro no;i5i, HHTerpa/i #aeT HaM Be./iHMHHy, nponopuHO-

Ha^ibHyio TOKy B nJia3Me. 3TOX TOK 0Ka3biBaexcn ~1 KA. PacneTbi Bbino;i~

HeHbi B npeflno^oxeHHH, HTO KpHnTOH He TepneTca Ha CTeHKax pa3pfl#BOH Ka-

Mepw, a, Hao6opoT, oxKaiHBaeTCH BHyTpb n;ia3Mbi H3 o6jiacTH TeHH flna$parMbi

B pe3y/ibTaTe "HOHHOH oTKaviKH" . KonmecTBO 3/ieKTpoHOB c 3HeprHefl

6o;iee 15 KOB OKa3biBaeTcn ~ 1 • 10 1 qacTHu. Ha 1 CM Rjivmbi njia3MeHHoro

uiHypa.

JS,na peiueHHH BTopoii H3 nepeMHcneHHbix Bbiuie 3a#aM cpaBHHBanHCb

cneKTpw , CHHTbie B To«flecTBeHHbix ycnoBHHx c 3I}-HarpeBOM w 6e3 Hero.

TaKoe cpaBheHHe 6bino npOBeaeHo B ^Hana30He 2,5-IOKSB C noMombio

nponopqHOHanbHoro CMeTHHKa H B ^Hana30He 7-50 IOB c noMombio CU.HHTH;I-

H3iiHOHHoro cieTMHKa B pe*HMax wHe /wr = 1 HwHe/wr=l,3. X-H3^yMeHHe

perHCTpHpoBa/iocb B xeneHHe 2 MC B cepe^Hne HMny^bca pa3pHfla. #JIH-

Te/ibHOCTb CB^-HMny^bca 6bi/ia 1 MC . TeHepaTop BK;iKMa/icfl oflaoBpeMeH-

HO c HaMajioM perHCTpauHH X-H3nyMeHHH.

PHC.6 HTiJiiocxpHpyeT nepBbiii H3 yKa3aHHbix pexHMOB. CneKTpbi c 3U,-

HarpeBOM H 6e3 Hero coBnaflaior RJIH xecTKoii o6.rcacTH (pnc.66) H pacxoaaT-

CH B o6;iacTH Ma/ibix aHeprHH (pHc.6a). Ha pHC.6a MOKHO Ha6^icwaTb

Hepa3peuieHHbie K-^HHHH sjieMeHTOB, BXOAHIUHX B cocTaB HepacaBeiomeH

cTa^H.KpHBaH 3 pnc.6a npe,qcTaBJifleT pa3HOCTb HHTeHCHBHOCTeS flByx cneKTpoB.

HaK/ioH ee cooTBexcxByex MaKCBe/i^oBCKOMy pacnpe/te^eHHio c xeMnepaTypoH

2-2,5 K3B.

CpaBHHBaJi 3Ty TeMnepaTypy c 3HeprneH, 3anaceHHOH B nonepeMHofi

KOMnoHeHTe B pe3yjibTaxe 3U,-HarpeBa (~ 1,5 • 10 ' sB Ha CM flnHHbi uiHypa),

MOMO 3aKJiKHHTb, MTO RO cTo/ib 6o^biuoH TeMnepaTypbi He MoryT HarperbCH

Bee 37ieKTpoHbi njia3MH, a xcflbKO 1/4 Macxb noJiHoro HXHHCM.

PHC . 7 wi;nocTpHpyeT peacHM wHe/ur = 1,3. BH£HO coBnafleHHe O6OHX

cneKxpoB B o6;iacxH Ma/ibix sHeprHH H HeKOTopoe npeBbimeHHe B HHxeHCHB-

HOCTH, Ha6/ncwaeMoe c 3U,-HarpeBOM, npH SHeprHflx, 6o;ibiiinx 40 KSB.

2. Pe3y/ibxaxbi H3MepeHHa CBH-H3^yMeHHH n-rta3Mbi

B pe>KHMax c WHe/ w r ~ 1 H w He/ w r ~ 1>3 6MJIH nojiyneHbi a6co;iiOTHbie 3Ha-

MeHHH HHTeHCHBHOCTH H3^yMeHH3 n/ia3MbI B flHana30HaX RJ1HH BOJIH 0,8, 1,3 H

2 CM.

Ha pHc.2 npeflCTaB^eHbi $ , JA H M3;ryHeHHe Rnn ^\iel^>T = 1,3. B xeMe-

HHe CBM-HMny^bca flexexxopbi npHeMHHKOB c X - 1,3 H 2 CM neperpyxa^HCb.

MH BHflHM,iTo noc/ie 3U,-HarpeBa B03pacxaex H3^yMeHHe Ha Bcex pemcxpnpyeMbix

fl^HHax BO^H. 3XO roBopHx o TOM,MTO 6bicxpbie s^eKxpoHbi

B iunpoKOM flHana30He 3HeprHH nor^oiyaioT CBH-MomHocxb. MOJKHO oue-

HHXb Be^H^HHy 3HeprHH, norviomeHHOH 6bicxpbiMH MacxHqaMH.

Bbi^o noKa3aHO, MTO B pexHMax c wHe/ur = 1 H i^e /wp = 1,3 njia3Ma 6bma

a6co^K)THo MepHOH MiH A = 1,3 CM. (KaK H3BecTHO, n^a3Ma B TOKaMaKe HaxoflHTCH

B MeTaji/iKHecKOH KaMepe, KOTopyro MOXHO paccMaTpHsaTb KaK

pe30HaTop c BaKyyMHOH #o6poTHOCTbK> ~ 10 .) EtocKOJibKy nor/iomeHHan

CBH-SHeprHH npH u /w =1,3 a^HTe^bHoe BpeMH coxpaHneTca B n^a3Me,


*

1000

7

5

100

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5

3-

10

W^SAs

IAEA-CN-33/A9-4 251

12

E(KSB)

PHC.7. CneKTp peHTreHOBCKoro H3^yMeHHH B peacHMe UHe/ u r = *>3> saperHCTpHpoBaHHbift:

a - nponopiiHOHa/ibHMM CWCTHHKOM; 6 - KpHCTanaoM NaJ(Tl). TOHKH cooTBeTCTByioT pexHMy

c 31J-HarpeBOM, xpyatKH — peacHMy 6e3 flono^HHTe^bhoro HarpeBa.

U


252 AJIHKAEB H Ap.

MOXHO npe,qno;io>KHTb, MTO sHeprHH norviomaeTCfl MacTHtjaMH c 6ojibiiioH

npoflojibHofi cKopocTbio, KOTopbie H onpeflejinior "MepHOTy" n;ia3Mbi B Ka-

Mepe. npe^noJiaraH TaKJKe,MTo STH sjieKTpoHbi HMeiar MaKCBeMOBCKoe

pacnpe^ejieHMe no CKOPOCTHM, MOXHO onpe^e^HTt HX nonepeMHyio TeMnepa-

Typy. OHa cociaBJiaeT 10-15K3B.

H3 HHTeHCHBHOCTH K-JIHHHH KpHnTOHa Mbl 3HaeM MHC.7IO 3/ieKTpOHOB

B ceneHKH nna3MeHHoro uiHypa c SHeprHeii, 6onbuieii 15K3B: ~ 10 CM" .

OTcro^a MO^CHO noxiy^HTb oueHKy AO/IH flono^HKTenBHOH 3HeprHH, 3anaceH-

HOH B 3neKTpouax c EB S15K3B. OueHKa noKa3HBaeT, ITO 3Ta Be;iMMMHa

cocTaB^aeT 20-30% OT sHeprHH, H3MepeHH0H no ^HaMarHeTH3My njia3MM.

Ha pHc. 1 - f , JA H H3^yMeHHe npH u /u = 1. B STOM c/iyMae npHeM-

HHK c X = 1 ,3 CM npHHHMaeT H3^yMeHne sjieKTpoHOB c BHeprHHMH EM s 6KSB.

E;iaro,ziapH HM n^a3Ma no-npeKHeMy flo/iacHa H3JiyMaTb KaK qepHoe Te/io Ha

3TOH A/WHe BOJIHbl . OflHaKO Mbl BH£MM,MTO B 3TOM CJiyMae ^OnO/IHHTe^bHblH

HarpeB n;ia3Mbi He conpoBOXflaeTcn K3MeHeHMeM H3/iyMeHHH n;ia3Mbi. Cneno-

Baxe/ibHO, ponb 6bicTpbix MacTHU B noraomeHHH CBM-MomHOCTH npH

^He / u r " * M e H t u i e > M e M n P H u He/ u r = 1 >3 •

C^eflyex noMHHTb,MTO npoBefleHHan oqeHKa CBH-SHeprnn, noraomeH-

HOH 6HCTPHMM MacTHuaMH, HBMeicfl £OBO/ibHo rpy6on.

3. 06 H3MeHeHHH HHflyKTHBHOCTH n7ia3MeHHoro uiHypa npH 3D|-HarpeBe

B pa6oTe [2j yKa3biBa;iocb Ha coBnafleHHe Be^rnHH 6/3]_ H 5j3 B npouecce

3U,-HarpeBa. EtepBan onpefle/ineTca H3 flHaMarHHTHbix H3MepeHHH,

nT • 8?r \

8fi± = 5 ( ~2 ) , r^e H. -nojie TOKa; BTopan Be/iHMHHa- H3 flono^HH-

Te/ibHoro cMemeHHH B npeflno^oaceHHH, MTO HH^yKTHBHOCTb iuHypa He H3-

MeHHeTca npH HarpeBe , S|3 = — (6/3X + 5j3(|). CoBna^eHHe /(Byx BenmHH Mor-

/io 6biTb c/ie^CTBHeM 6bicTpoH, nopHflKa 100 MKC, H30TponH3aqHH nor/iomeH-

HOH CBH-3HeprHH, MTO HMeeT MecTO RJIH cpaBHHTejibHO xonoflHbix sneKTpo-

HOB .

YBenHMeHHe CMemeHHH npH 3IJ-HarpeBe MOJKCT 6biTb CBfl3aHO H C

yBejiHMeHHeM Hh^yKTHBHOCTH L, n/ia3MeHHoro iimypa. HJIH H3MepeHHa 5L

npHu) /u =1,3 (CM. ocuh/inorpaMMy JA Ha pHC.2) Ha o6xoAe xaMepbi

npHK^aflbiBa^ocb Aono/iHUTe/ibHoe nepeMeHHoe HanpnaceHHe c MacTOTofl

f ^SKTU. Ko^e6aHM5i c Tanon nacTOTon cKHHhpyioTCH Ha pa^Hyce uiHypa c

aneKTponpoBO/tHocTbio a K 2-10 efl . CGSE . npHMeHeHHbin ueroA no3BO-

/ineT H3MepHTb H3MeHeHne HH^yKTHBHOcTH n/ia3MeHHoro mnypa npH 3IJ-HarpeBe.

IlocKo^bKy H3MepeHHaH cpe^HHH no ceMeHHio mHypa 3/ieKTponpoBO#HOCTb

oKa3a^acb a-(1-2) • 10 en. CGSE, 30HflHpyeMaH 06/iacTb pacncrcaraeTCJi

Ha nepHcpepHH nna3MeHHoro uiHypa. riosTOMy MO«HO 3aK/ircMHTb, MTO H3Me-

HeHHe HH^yKTHBHOCTH Bcero uiHypa npH HarpeBe He MeHbiue 6"L = 10% L,

H3MepeHHoro Ha qacTOTe f.

TaKoe H3MeHeHHe HHAYKTHBHOCTH npH yMeTe 5jSx , no/iyMeHHoro M3

AHaMarHHTHbix H3MepeHHH, MoaceT o6xacHHTb yBe^HMeHHe CMemeHHH, 3aperncTpHpoBaHHoe

npH 3L[-HarpeBe. B STOM c^yMae AOJiymna OTcyTCTBOBaTb

H30TponH3aqHH flono/iHHTe^bHOH 3HeprHH, T.e. AOJix.eH npoHcxo^HTb HarpeB

S^eKTpOHOB AO 6o/IbIIIHX SHeprHH .


IAEA-CN-33/A9-4 253

ToMHOCTb H3MepeHHH 5L He no3BonaeT, o#HaKO, no;iHocTbio HCK/HCHHTB

B03M0>KH0CTb H30TponH3aU.HH SHeprHH.

H3MeHeHHe HH^YKTHBHOCTH n/ia3MeHHoro uiHypa MOxeT 6biTb Bbi3BaHo

Typ6y;iH3auHeH ero nepHepHH [4] . QHHH H3 BepoflTHbix MexaHH3MOB Typ-

6y/iH3aqHH — HOHHO-3ByKOBbie KO/ie6aHHfl, B03HHKaiomHe npn pacna^ax 3,/ieK-

TpoMarHHTHofi BO/IHW . OflHaKo oTcyTCTBHe H3MeHeHHH B cneKTpe HeflTpa/ib-

HMX aiOMOB nepe3apH^KH npH Ha^oaceHHH CBH-HMny^bca (npH u^ /w = 1 H

1,3) fle/iaeT Ma;iOBepoflTHbiM npeflno^oxeHHe 06 onpe^enHiomeH po;iH pacna^Hbix

MexaHH3MOB c B036y>K,aeHHeM HOHHOTO 3ByKa npn 3U,-HarpeBe B

HamHX yc/iOBHflx.

V. 3AKJIKHEHHE

EtpoBefleHhbie SKcnepHMeHTbi noKa3anH, MTO cymecTByeT HecKonbKO

KOHKypHpyiOmHX MexaHH3MOB nOr/IOmeHHJI CBH-MOmHOCTM . OTHOCHTe^b-

Has po;ib Kaxfloro H3 STHX MexaHH3MOB noiviomeHHfl MeHaeTca npH H3Me~

HeHHH ycnoBHii pa3pH^a B TOKaMaKe.

B pe)KHMe c yH /u>r =1 H3 cooTHomeHHH iiexfly flononHHTenbHofi 3HeprHefl

, H3MepeHHOH no flHaMarHeTH3My, H BenwmHoii TeMnepaTypbi, oueHeH-

HOH no peHTTeHOBCKHM H3MepeHHHM, MOXHO 3aK^KH HTb , M TO yBejIHH HTb

TeMnepaTypy Ha 2-3 KSB MOXCT He 6onee 1/4 9/ieKTpoHOB n.rca3Mbi. 3TOT

(|>aKT ztonycKaeT Asa pa3^H^Hbix o6i>flCHeHMH:

1. HarpeB H/ieT B OCHOBHOM Ha SLIP. Tor^a 3KHTb , MTO B

STOM cnynae SHeprHfl nornomaeTca B OCHOBHOM ycKopeHHbiMH sjieKTpoHaMH,

BpeMH XH3HH KOTOpblX 6oilhWe , M eM BpeMfl JKH3HH OCHOBHOH n/ia3MiI . Ka~

MecTBeHHO B nojib3y TaKoro npeflnojioxeHHH roBopHT yBejuweHVie H3/iyMeHHH

Ha A. =1,3 H 2 CM , a TaKace yBenHMeHHe HHT6HCHBHOCTH acecTKoro peHTreHOB-

CKOrO H3/[yMeHHfl .

OqeHKH, c^ejiaHHbie H3 a6cojiK>THbix H3MepeHHH CBH-H3/iyHeHHfl njia3MH,

noKa3biBaioT, ITO 3HaHHTe;ibHafl flo/iH SHeprHH, 3anaceHHofi B npouecce 3Ll-HarpeBa,

^eficTBHTenbHO norjiomaeTcn 3JieKTpoHaMH c npoaojibHOH SHeprHeii

S20K3B.

Tax KaK MM He Ha6;no.naeM CKonbKO-HH6y^b 3awieTHoro 3


254 AJIHKAEB nap.

JIHTEPATYPA

11] AJIHKAEB, B.B. M ap. , riwcbMa *3T* J_5 (1972) 41 .

(2j ALIKAEV, V.V. etal., 5th European Conf. Controlled Fusion and Plasma Phys.,

Grenoble 1 (1972) 108.

[3] HBAHOB, M-Il. u ap. , B c6. RnarHOCTHKa Una3MM, ATOMnanaT, M . , 1963, CTp.292.

14] ALIKAEV, V.V. etal., 6th European Conf. Controlled Fusion and Plasma Phys.,

Moscow 1 (1973) 63.


MArHHT03ByK0B0H HATPEB IIJIA3MBI

B TOKAMAKE TO-1

H.B.HBAHOB, H.A.KOBAH

HHCTHTyT aTdMHOH 3HeprHH HM. H .B .KypnaTOBa,

MocKBa,

C0103 CoBercKHX Cot?Ha^HCTHMecKHX Pecny6/iHK

Abstraa-AHHOTaijMH

IAEA-CN-33/A9-5

MAGN'ETOACOUSTIC HEATING OF PLASMA IN TOKAMAK TO-I.

The results of experiments on the excitation and absorption of inherent magneto-acoustic oscillations

of the plasma column in Tokamak TO-1 as well as the influence of these oscillations on the plasma state

are presented. A loop exciter connected to a fixed frequency generator was used to achieve a HF-power

input to the plasma. The plasma oscillations were recorded by a magnetic probe and the Q-factor of the

plasma resonator was determined from the probe signal. The resonator is a measure of the dissipative

capacity of the plasma. The low level of absorption measured (Q-factor = 5000) is associated with the ion

viscosity mechanism. Excitation of magneto-acoustic oscillations in Tokamak TO-1 is accompanied by

doubling of the plasma diamagnetism, outward shift of the plasma column, and increase in the current of

the equilibrium regulators. In addition, the temperature of the plasma ion component was observed to

increase from 100 to 170 eV. This was recorded from the Doppler broadening of the carbon impurity line

C V and by measuring the energy distribution of the charge exchange atoms. Observation of particle and

energy balance showed that magneto-acoustic oscillations exert a twofold influence on the plasma state.

Firstly, all the dissipated energy is expended on heating the plasma ions. Secondly, the presence of

oscillations results in an additional increase in the plasma energy content due to increase in the energy

lifetime of the electrons as well as increase in the diffusion life-time of the plasma. The latter is attributable

to the stabilizing effect of magneto-acoustic waves on the instability responsible for anomalous electron

thermal conductivity and plasma diffusion in the tokamak.

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IAEA-CN-33/A9-5 257

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258

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IAEA-CN-33/A9-5 259

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IAEA-CN-33/A9-5 261

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IAEA-CN-33/A9-5 263

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DISCUSSION

ON PAPERS IAEA-CN-33/A 9-1, A 9-2, A 9-3, A 9-4, A 9-5

J.D. CALLEN: Can you conclude from these experiments what maximum

poloidal /3 can be achieved in tokamaks?

V. V. ALIKAEV: The results obtained in experiments on tokamaks with

supplementary heating show that the maximum value of poloidal 0 is at least

half the theoretically possible value.

265


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Abstract- AHHorauMfl

IAEA-CN-33/C-5

PRODUCTION OF A HOT ION PLASMA AT THE LOWER HYBRID RESONANCE AND MEASUREMENT OF ITS

PARAMETERS.

Electromagnetic fields delayed along a magnetic field have been created within a plasma with the

aid of a loop encircling the plasma column. When these waves propagated transversely in relation to the

magnetic field within a plasma with density rising along its radius they were delayed in the direction of

propagation. The amplitude and phase distribution of the electromagnetic fields along the radius of the

plasma column was measured at different instants of time. The existence of an absorption band of these

waves within the plasma was detected. The absorption band was shifted toward the outer boundary from

the plasma when plasma density was increased. By four independent methods it was established that the

gas-kinetic pressure of the plasma, measured on the basis of its diamagnetism, is determined by the ion

component. It was found that the energy of ions at right angles to the magnetic field is considerably less

than the ion energy. The cause of limited heating was an increase in density and energy losses in the

charge-exchange process. To improve vacuum conditions, the loop encircling the plasma was placed in

a metallic chamber, and the ultrahigh-frequency plasma source used in the original experiments was replaced

by a film-hydride source. This made it possible to increase the internal energy of the plasma to

3 x 10 15 eV- cm -3 at a density of (1-3) x 10 lz cm -3 . The mean energy of atoms leaving the plasma at right

angles to the magnetic field as a result of charge exchange reached 1 keV. The region of change in plasma

parameters (density and magnetic field) for which heating was observed corresponded to the linear transformation

theory. Non-linear effects could occur only in the first stage of heating, when the electric

fields were strong, but plasma temperature was low. Heating efficiency was measured by a reflectometer

installed in the co-axial line connecting the generator and HF input coil to the plasma. The measurements

showed that =*2Cflo of the power generated is consumed in heating the plasma.

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MarHHTHwe nona, 3aMea/ieHHbie Bflo/ib MarHHTHoro no^a. IlpH pacnpocTpaHeHHH STHX BO/IH

nonepeK MarHHTHoro nona B nna3Me c B03pacTaiomeH no paanycy nnoTHOCTbio nponcxo,zi,H;io HX

3aMeflneHHe Bflo/ib HanpaB/ieHHH pacnpocTpaHeHHa. H3MepeHO pacnpcaeneHHe no paanycy

n/ia3MeHHoro cro;i6a aMn/iHTyaw H $a3bi aneKTpoMarHHTHwx nojiefl B pa3ntwHMe MOMeHTbi

BpeMeHH. 06HapyjiceH0 cymecTBOBaHHe B n/ia3Me c/ioa norviomeHHH STHXBO/IH. IIpH yBCiH-

MeHHH nnoTHOCTH njia3Mbi 06/iacTb nornomeHan CMemanacb K BHeuiHefi rpaHWje c n/iasMbi.

HeTbipbMfl HeaaBHCHMbiMH MeToflaMH ycTaHOBneHo, mo ra30KHHeTn»iecKoe flaB^HHe nJia3Mbi,

H3MepeHHoe no ee flHaMaraeTHSMy, o6yc;iOB;ieHO HOHHMM KOMnoHeHTOM. HaflaeHO, MTO SHeprna

HOHOB nonepeK MarHHTHoro no;iH 3HaHHTenbH0 MeHbiue HOHHOH. IIPHHHHOH, orpaHHMHBaioaieH

HarpeB, RBnajiocb yBejinqeHHe JIJIOTHOCTH H noTepb 3HeprHH B npouecce nepe3apa.21.KH. Rna

ynymiieHHH BaKyyMHwx ycnoBHH BHTOK , oxsaTbiBaBiiiHH nM3My, noMema^ca B MeTannnnecKyio

KaMepy, a CBM HCTOHHHK n/ia3Mbi, Hcno^b30BaBmHfica B nepBOHana/ibUbix onbiTax, 3aMeHen

nneH0MH0-rnapK«HbiM HCTOIHHKOM. 3TO no3Bo;iHJio yBe;iHMHTb BHyTpeHHioio 3HeprHio njia3Mii

flo 3 • 10 15 aB - CM" npH nflOTHOCTH (1 - 3) • 10 CM" . CpeflHHa SHeprna aTOMOB, noKHflaioiiinx

nna3My nonepeK MarHHTHoro noJia B pe3y;ibTaTe nepe3apaflKH, aocTHrana 1 KSB. 06;iacTb

267


268 TJIArOJIEB H ap.

H3MeHeHHH napaMeTpoB nnasMH (nnoTHOCTH H MarHHTHoro nonn), npH KOTopoft Ha6nKwa;icH

HarpeB, cooTBeTCTBOBajia TeopHH /IHHCHHOH TpancifiopMauHH. He/iHHeflHbie 3$$eKTbi MOT/IH

HMeTb MecTo nwah Ha nepBofi cTajtjmi HarpeBa, Kor\aa a^eKTpimecKHe no^a 6MJIH BCAHKH, a

TeMnepaTypa njia3MH HH3Ka. 3$eKTHBHocTb HarpeBa H3MepeHa c noMomtio pe$neKTOMeTpa,

ycTaHOBneHHoro B KoaKCHanbHOH ;IHHHH, CBH3MBaiomeH reHepaTop H BHTOK BBoaa BM-MOIUHOCTH

B n/ia3My. H3MepeHHH noKa3a/iH,Mio Ha HarpeB n/ia3Mbi pacxoflyeTCH -20% MOUIHOCTM, CO3-

AaBaeMOH reHepaTopoM.

Ha MeTBepTOH KOH


IAEA-CN-33/C-5 269

KTEHEPATOPy

5 6

0-900

\

K ocumm

PHC.I. CxeMa aiccnepHMeHTajibHOH ycTaHOBKH: 1—nneHOMHO-rngpHaHbift HCTOMHHK n«a3Mbi;

2 - cHnoBbie JIKHHH wtarHHTHoro nana; 3 — 30Ha HarpeBa B6JIH3H BHTKa CBH3H; 4 — .ziByxnpoBO.zi-

HaH /IHHHH, cBH3aHHaH c reHepaTopoM Ka6e;ieM, OKaHMHBaiomHMCH netneii; 5 —npo6cmm>ie Ka-

TyniKHJ 6 - MHOrOCeTOMHMH 30H4.

1 2 3 0

PAflMyC(cM)

PHC.2. AMn^HTyaa H $a3a a^eKTpOMarHHTHwx

nojieft B nna3Me.


270 TJIArOJIEB H ap.

B TeieHHe nepBbix 40 MKC , Korvja #HaMarHHXHbiH cnraa/i 6bin nesenHK,

Ha6/ncwanocb yBe;iHHeHHe pa#Ha.ribHoro s/ieKxpMMecKoro no/in no cpaBHeHHio

c BaKyyMHBiM B 7-10 pa3. ripo,no/ibHoe MarHHTHoe BbicoKonacxoTHoe none

Hz B n;ia3Me cymecxBeHHO He H3MeH5Jjiocb. 3xo yKa3biBa;io Ha oTcyxcTBHe

MarHHT03ByKOBoro pe30HaHca. Ilo Mepe B03pacxaHHH nnoTHOCTH pa#Ma/ibHoe

aneKTpHMecKoe none BO^HBI Er yMeHbiua;iocb a B03pacTa/io BHOBB xo;ibKO B

MOMeHT , Koryia flHaMarHHXHHH CHrHaji flocxHra/i MaKCHMyMa. Taxoe noBefle-

HHe SneKTpOMarHHTHblX nOJieH MOXHO o6T>HCHHXb Ha OCHOBe AHCnepCHOHHblX

KpHBbix pacnpocTpaHeHHH BO/IH B n;ia3Me c HapacxaiomeH n/ioxHOcxbio. Ilpn

3TOM c/ie#yex 3aMexHXb,HXo AJiHHa BO/IHBI HarpeBHoro reHepaTopa B CBO-

6O#HOM npocTpaHCTBe 60/ibuie pa3MepoB nna3Mti. OflHaKo B njia3Me npo-

Hcxoflnno 3aMeweHne BO/IH Bflojib HanpaB^eHna pacnpocxpaHeHHH B 100 pa3.

Cor/iacHO xeophM, npw Ha/iHMHH 3aMe.il/1eHHfl BO/IHM Bflonb MarHHraoro nojia

(nepneHflHKy/inpHo HanpaBTieHHio pacnpocxpaHeHHn) Me*ay rpaHHuefi n/ia3Mbi

H njioTHocTtio, npM Koxopofi BO3MOKHO pacnpocTpaheHHe, MMeeTCH 30Ha Henpo3paHHOCTH.

ToHKe Havana pacnpocxpaHeHHfl E-BOJIHBI cooTBeTCTByeT

nfloraocTb, onpefleJiaeMa^ paBeHcxBOM w = wQe (npHw = 10 pa#/c ,n = 10 8 CM" 3 )

(uoe—sneKxpOHHan neHTMiopoBCKaH Macxoxa). CBH~HH«eKXop co3^aBa/i

nna3Mti c n/ioxHOcxbio n > 10 8 CM" 3 . IlosxoMy E-BOjiHa pacnpocxpaHH/iacb

B nna3Me c MOMeHxa BKnKHeHM BH-reHepaxopa. npH flajibHefiuieM B03pacxaHhH

n/ioxHocxH MO BenwiHHbi n = 10 CM , onpe^e^fleMOH paBeHCXBOM

, ,2

'J '

oe

W He ' T,n,e W H _ 3/ieKXpOHHaH UHK/IOXpOHHaH MaCXOXa, CXaHOBhJIOCb

BO3MOKHHM pacnpocxpaHeHHe H-BO/iHbt. npH 9TOM kr = 0. M3 ypaBHeHMH

/ 1 3H\ E


IAEA-CN-33/C-5 271

/IHJIO ~100. a3a BOJIHH B ToiKe SKCTpeMyMa npeBOCxo^Hjia a3y Ha rpa-

HhU.e fflHypa,MTO COOTBeTCTBOBaflO HanpaBJieHHK) (|)a30BOH CKOpOCTH OT TOMKH

3KCTpeMyMa.

B CBH3H c TeM,MTo sjieKTpoMarHHTHafl BO^Ha B njia3Me HMe^a aHOMajib-

Hyio flHcnepcHio npH npoaojibHOM 3aMe^eHHH Ha noBepXHOCTH, rpynnoBan

CKopocTb 6bina HanpaB/ieHa npoTMono^oxHO a30B0H, T.e. K TOMKC SKCTpe-

MyMa. TaKHM o6pa30M , MaKCHMyM KPHBOH pacnpefle/ieHHH


272 rJiArojiEB H ap.

no3BOTinjio yBenvsHHTb TeMnepaTypy HOHOB AO T. = 300 aB H flHaMarHeTH3M

njia3Mbi Ao 5 • 10 sB • CM . BMecTe c TeM ocTaBa/iocb HencHbiM, KaKOBa

ROJIH HarpeTwx HOHOB no OTHOUICHHIO K o6meMy KcnnqecTBy HOHOB B n;ia3Me

H KaKOBO cooTHomeHHe Mexfly nonepenHOH H npo^o^bHOH 3HeprHHMH HOHOB.

2. H3MEPEHHE COOTHOIIIEHHfl ME)Kfly HArPETbIM H XOJIO^HblM

KOMnOHEHTOM riJIA3MbI

J\nn H3MepeHMH sHeprHH njia3MH 6M;IH HcnoJib30BaHbi c^ieflyiomHe

MeTOflHKH:

1) onpe#ejieHHe cpeflHefi 3HeprHH no AHaMaraeTH3My H njioTHOCTH

njia3Mbi;

2) H3MepeHHe sjieKTpOHHOH TeMnepaTypbi MHoroceTOMHbiM 30HAOM;

3) H3MepeHHe HOHHOH npoac/ibHOH H nonepeHHOH sHeprnH MHoroceTOM-

HblM 30H40MJ

4) onpe^te^eHHe nonepeHHofi sHeprnn HOHOB 30HAOM, H3MepHiomHM

HOHHbiH TOK nonepeK MarHHTHoro nora;

5) H3MepeHHe cneKTpa aHeprHH aioMOB nepe3apH#KH no Mero^HKe,

aHa/torn^HOH [6] .

ITpHMeHeHHe pa3^HMHbix ueTOROB uccnenoBamm 6w^o HeoSxo^HMO B

CBH3H C TeM,MTO KajKflblH H3 HHX B OTfleJIbHOCTH He n03BO/IH.7I 04H03HaMHO

cy^HTb o deneHH HarpeBa HOHOB. TaK, KOHcxpyKqHH 30Hfla, H3MepHBiuero

nonepeMHyRD SHeprnio HOHOB, He no3Bo;i5ijia perHCTpnpoBaTb MacTHUbi c Ma-

^HMH ^apMopoBCKHMH paiiHycaMH. H3MepeHHe cneKTpa aioMOB nepe3apHfl-

KH 6bIJIO B03MOXHO, HaMHHafl C SHeprHH 100 SB, B CBH3H C HH3KOH 3$eKTHB-

HOCTbio perncTpauHH Majibix 3HeprnH. ,I[HaMarHHTHbiH CHraan perncTpHpoBaji

jiHiiib cyMMapHoe ra30KHHeTHHecKoe aaBJieHHe HOHOB H sjieKTpoHOB.

B CBH3H C 3THM nOTpe6oBaJ!OCb npOH3BeCTH flOnO^HHTe/IbHbie H3Mepe~

HH3 C nOMOUlbK) MHOTOCeTOMHOrO 30H^a, HaXO^HBIIierOCH B H3MeHHeMOM

BHeuiHeM MarHHTHOM no;ie. H3MeHeHHe BHeuiHero no/ia BJIWUIO Ha cooTHome-

HHe Mexfly npcziojibHOH H nonepeMHOH sHeprneH nacTHu. H BojibTaMnepHbie

XapaKTepHCTHKH 30Hfla.

no^o6HbiH cnoco6 H3MepeHHfl nonepeMHOH SHeprHH HOHOB H3noxeH B

pa6oTe [7] , sneKTpoHOB —B pa6oTe [8] .

Pacnpeac/ieHHe HOHOB B 30He HarpeBa, r^e HanpnaceHHocTb MarHHTHoro

nojia HQ , MOMO anpoKCHMHpoBaTb MaKCBeMOBCKHM pacnpe/iejieHHeM,

npeflcTaBHB ero B BH,ne npoH3BefleHH5i pacnpe^eneHHH no nonepe^HbiM H

npoflo^bHbiM SHeprnHM:

-WJ./TL

F=FJ_(WX) • I?,^,), rne Fx(Wx)=Ae

-W /T

E. = Be " " , A,B = const.

MOXHO noKa3axb, MTO n;ioTHocTb xoKa Ha KonneKTop 30H.ua, Haxo^Hiuerocn

B oc7ia6/teHHOM no^e (H -AH), BbipaxaeTCH $opMyjioH

j = 27rABT„ Tj.ll-f(x)J


3aecb

IAEA-CN-33/C-5 273

C noMombio HHcneHHoro cneTa 6binn nonyqeHbi rpaqpHKH f(x) npH pa3Hbix x.

9TH rpa^HKH Hcnonb30BajiHCb n.nn cpaBHeHHH c SKcnepHMeHTa^bHO nony-

MeHHBIMH BOTIbTaMnepHblMH XapaKTepHCTHKaMH . OnHCaHHBIH MeTOfl MOXeT

6bITb MOflH(|)HUHpOBaH TaK,MTO B o6naCTH 30Hfla C03^aeTCH yCH^eHHOe

MarHHTHoe none. OflHaxo B STOM cnynae ycnoBHH npoxoacneHHH ceTOK

MHoroceTOMHoro 30H^a yxyn.maiOTCfl , T.K. yBennnHBaeTCH oTHOiueHHe

nonepeHHOH CKOPOCTH K npon.onbHOH. CxeMa H3MepeHHH no onpefle/ieHHio

nonepeMHOH SHeprnn nna3Mbi c noMombio BonbTaMnepHbix xapaKTepHCTHK

3 0Hfla , H3MepflK>mero npoflonbHyio SHeprnio, npHBen.eHa Ha pHC . 1 . 3TH

H3MepeHHH 6binH BbinO^lHeHbl B HeflOCTaTOHHO MHCTblX BaKyyMHblX yCnOBHHX,

Korfla BaKyyMHOH KaMepoH HBranacb KBapueBaa Tpy6a AnaMeTpoM 100 MM.

nna3Ma, o6pa30BaHHaH pa3pnn.0M Ha noBepxHOCTH THTaHOBOH maH6bi, HacbimeHHOH

BOAopoflOM (l), pacnpocTpaHJinacb B^ojib cnnoBbix JIHHHH OAHOpoaHoro

MarHHTHoro nonn (-2) H nonaflana B 30Hy HarpeBa (3). Ha pnc. 1

(4) — AByxnpoBOflHaH /IHHHH , CBH3aHHan c reHepaTopoM. ripn BKHKHCHMH

KaTyiueK (5) B 30He HarpeBa co3flaBanocb MarHHTHoe none THna an.na6aTHqecKOH

noByuiKH. MHoroceTOMHbiH 30HZ( noMemancn 3a npo6oHHOH KaTym-

KOH Ha paccTOHHHH ~1,5M OT MecTa HarpeBa. MaKCHManbHan BennqHHa

MarHHTHoro no/ia B 30He HarpeBa cocTaBnana 3K3, npmeM MarHHTHoe

none 2,2 K3 cooTBeTCTBOBano HHXHeMy rn6pHnHOMy pe30HaHcy nnoTHOH

nna3Mbi,T.e. paBeHCTBy u 2 = w • w , ryie u = 2 rf (f — pa6oMaa nacTOTa

. He Hi

reHepaTopa). TexHiraecKHe npuwHHbi He no3Bonflnii nonymiTb B MecTe

pacnono)KeHH5i 30H#a MarHHTHoe none CBbime 1,8K3. IlonepeMHan sHeprna

MacTHu onpeaerajiacb nyieM cpaBHeHHH xapaKTepHCTHK 30Hna B MarHHTHOM

none 1,7K3 H 40 3. TOK Ha 30Hfl yMeHbirtancn o6paTHO nponopuHOHanbHO

MarHHTHOMy nonio H B none 40 3 6bin MeHbine TOKa B none 1,7K3~B 40 pa3.

3TO cooTBeTCTBOBano pacTexaHHio nna3Mbi Bnonb MarHHTHbix cnnoBbix AHHHH

ocna6neHHoro nona. IIocKonbKy pac^eTHbie KpHBbie He yqHTbiBann H3MeHe-

HHH nnoTHOcTH TOKa B pacceHHHOM none, xapaKTepHCTHKH 30Hfla B none

40 3 nepecMHTbiBanncb TaK,MTo6bi HOHHbie TOKH npn 3an.ep2CHBaiomeM no-

TeHUHane 100 B, a aneKTpoHHbie TOKH npn noTeHunane 0, coBna^ann. Ilo-

TeHunan 100 B Bbi6paH B CBH3H C TeM,HTo B6nH3H Hero npoHcxo^Hn H3noM

BonbTaMnepHoii xapaKTepHCTHKH 3a cieT noTeHunana cnon , ycKopnio-

IUerO HOHH B6nH3H BXOflHOH CeTKH 30Hfla.

OcHOBHbie SKcnepHMehTanbHbie pe3ynbTaTbi H3MepeHHH aHH36TponHH

HarpeBa nna3Mbi naHbi Ha pnc.3. B npoH3BonbHbix enHHHuax 3£ecb npencTaBneHbi

flBa ceMeftcTBa 3aBHCHMOCTeH HOHHBIX I. H aneKTpoHHbix I TO-

KOB Ha KonneKTop MHoroceTOMHoro 30Hn.a OT noieHunana Ha 3an.ep;KHBaiomeH

cTeHKe 30H^a. CnnomHbie AHHHH cooTBeTCTByiOT 3KcnepHMeHTanbHbiM 3a-

BHCHMOCTHM. KpHBbie 1 H 3 nonyqeHbi, Kor#a 30H£ Haxoflnncn B none

1,7 K3, KpHBbie 2 H 4 — B none 403. IlyHKTHpHbie HHHHH- pacweTHbie KpH­

Bbie . PacqeTHan KpHBan "a" noKa3biBaeT 3aBHCHMOCTb OT 3aflepxHBaiomero

noTeHunana TOKa Ha 30H# HOHOB, HMeiomnx MaKCBennoBCKoe pacnpe^ene-

HHe no npo^onbHHM CKOPOCTHM npH T(| =330 3B H se = 0. PacqeTHaa KpHBan

11 b" xapaKTepH3yeT 3aBHCHM0CTb TOKa HOHOB C TOH xe TeMnepaTypofi T||

npn ae = 0,5. Hcnonb30BaHHe cnnBHo H3MeHHK>merocH MarHHTHoro nonn

yBennMHBano TOMHOCTB H3MepeHHH, T.K. B STOM cnyqae pa3nHMHe sKcnepn-


274 TJiAroJiEB » ap.

I.

j

1

0,5

0 100 200 300 400 500 600 700

U(B)

PHC.3. BonbTaMnepHbie xapaKTepHCTmcH 30H.na, noMeiqeHHoro B H3MeHaeMoe MaraHTHoe none.

1,3-H = 1,7K3 a-AH=0 T„ = 330 aB

2,4-H=403 b-AH=H T^T,, = 0,5

MeHTa^bHbix KpHBbix 6HJIO 6ojiee pe3KHM. ripH 9TOM 36 - T /T|| . IlonepeMHasr

TeMnepaTypa HOHOB T^ B 30He HarpeBa B MarHHTHOM none 3K3,

BbiMHcneHHaH B npeflno/ioaceHHH coxpaHeHHH aanaSaTimecKoro HHBapHaHTa,

paBHHTiacb 280 sB npH T^ = 210 3B. AHajiorHMHbie H3MepeHH«, npoBe^eHHbie

npH HarpeBe njia3MBi B o^Hopo^HOM MarHHTHOM none, noKa3a/iH, MTO

T. = 150 sB npn T|°j=250 sB, T.e. TL/T||=0,6. 3TH H3MepeHHH noKa3biBa~

K>T,MTO HOHM npn HarpeBe npno6peTa;iH He TOJibKo nonepe^Hyio, HO H npo-

AonbHyio SHeprHio.

CraeflyeT oTMeTHTb,HTo B oSnacTH SonbuiHx SHeprHH HaSnicaanocb

oTCTynneHHe OT MaKCBejuioBCKoro xapaKTepa pacnpefleneHHH HOHOB no

SHeprHHM. O^HaKO B 06/iacTH sHeprnii, cooTBeTCTByiomHX HanSo/iee

pe3K0My H3MeHeHHK) HOHHOrO TOKa Ha MHOrOCeTOMHblH 30Hfl npH H3MeHeHHH

3a^epxHBaiomero noTeHana/ia, pacnpe,ge/ieHHe MaKCBe^a «B/ifl/iocb yflOBneTBOpHTenbHOH

anpoKCHMaqneH pacnpeae/ieHHH, HanaeHHoro 3KcnepnMeH-

TaflbHO.

Uoa TeMnepaTypoH HOHOB H sneKTpoHOB B STHX SKcnepHMeHTax noflpa3yMeBanacb

nonepeMHaH H nponojibHasi sHeprnn »iacTHU., BHOcaqHx HaH-

6onbuiHH BKJia,a. B o6myio SHeprHio flaHHoro KOMnoHeHTa.

IlpH H3MepeHHHx TeMnepaTypw HOHOB, HarpeBaeMbix B npo6oMHOM

MarHHTHOM none, HCTOHHHKOM cHCTeMaTiwecKHx OIUHSOK HBJixnocb Hajimne

o6nacTH ycnneHHoro nojiH Mexfly o6nacTbio HarpeBa H MHoroceTOMHbiM

30HflOM. B 3TOM CJiyMae MaCTHUbl C 6onbUIHMH nonepeMHblMH CKOpOCTHMH

y^ep^HBa/iHCb B MarHHTHOM none aanaSaTHMecKOH noByuiKH H He nona#a;iH

Ha 30Hfl . IlpH npo6oMHOM OTHOUieHHH 1,5 3TO OTHOCHTCH K MaCTHU.aM,,y

KOTopwx T . > 2 T|(- - 400 sB. B TO ace BpeMH , H3MepeHHH cneKTpa aTOMOB


10'

10'

10*

10 1

IAEA-CN-33/C-5 275

W,=1,3K3BJ W2=1,3K3B H = 3K3

-o*b^6— L

0,5 1 1,5 2 2,5

W^UaB)

p = 6-10 Topp

PHC.4. CneKTp 3Heprnfi aTOMOB nepe3apanKH.

nepe3apH£KH H anaMarHeTH3Ma noKa3a;iH, MTO nonepe^Han sHeprHH HOHOB

He Morjia npeBbimaTb 300 sB. 3TO yKa3biBa;io Ha oTcyTCTBHe B OTHX

SKcnepHMeHTax B pacnpe,ae;ieHHH no sHeprHHM Sojibiuoro MHCJia HOHOB C

SHeprvieH Bfaiine 300 sB.

Ha pHC. 3 noMHMO xapaKTepHCTHK HOHHoro TOKa npHBeneHbi BO^bTaMnepHbie

KpHBbie 3aBHCHMOCTH TOKa aneKTpoHOB (B npoH3Bo/fbHbix eaHHHuax)

OT noTeHqHa/ia 3a^epxKH. Cpe^HHH SHeprHH 3,/ieKTpoHOB, BbiMHcueHHan no

KpHBofi 3, CHHTOH B MarHHTHOM none 1,7 K3, paBHa 120 aB. KpHBan 4 no;iy-

MeHa, Korfla MarHHTHoe none B MecTe pacno^o*eHHH 30H^a cocTaBnano

40 3. Cpe^HHH aHeprHH o^eKTpoHOB, paccHHTaHHaa no OTOH KPHBOH, paB-

HH/iacb 40 aB. YMeHbineHHe cpe^Heii sHepr-HH aneKTpoHOB B pacceHHHOM

none, no-BHflHMOMy, CB33aHO c TeM,MTo HarpeB 3/ieKTpoHOB nponcxo^Hn

B noBepxHocTHOM cnoe naa3MeHHoro iimypa [1J. TeMnepaTypa aneKTpoHOB

B ueHTpe umypa MHHHMaJiBHa. B pacce^HHOM none Ha 30H£ nonaaa/iH sjieKTpoHbi

H3 6o.rcee xono^HOH ijeHTpajibHOH MacTH nna3MeHHoro uiHypa H cpe^HHH

SHeprHH aneKTpOHOB CHHymanacb.

TaK KaK cyMMapHaa SHeprHH nna3Mbi, H3MepeHHaa no ee AHaMarHeTH3-

My, paBHa nonepeMHofi 3HeprHH HOHOB, TO nonepeHHaa oHeprnn sjieKTpoHOB

B nOBepXHOCTHOM C/IOe 3HaiHTe/IbHO MeHbUie HOHHOH.

OnpeneneHHe nonepeHHoii sHeprHH HOHOB nyTeM yqeTa B^HHHHH H3MeHe-

HHH MarHHTHoro nojiH Ha xapaKTepHCTHKH 30H^a , H3Mep3Bmero npo#o;ibHbie

sHeprHH HOHOB, npoH3B04nnocb c KBapueBOH BaKyyMHOH KaMepoH. C nenbK)

fla/ibHeftiiiero yjiymneHHH BaKyyMHbix ycjioBHH 6bina H3roTOB;ieHa MeTa^HuecKafl

BaKyyMHaa KaMepa, B KOTopyio noMemancfl BHTOK CBH3H.

B STHx ycnoBHHx 6MJI nonyMeH cneKip aHeprHH aTOMOB nepe3ap?inKH,

H3o6paaceHHMH Ha pHC.4. OMUHHTentHofi oco6eHHocTbK» sioro cneKTpa

HBJineTcn OTcyTCTBHe aTOMOB c aHeprHeH, MeHbineS 380 3B. JXn.n Toro,

MTo6bI y6eflHTbCH , MTO 3TO HB-rteHHe He CBH3aHO C yMeHbffleHHeM MyBCTBH-

3,5


276 rjiArojiEB H ap.

Te^BHOcTH MeTo^HKH B flHana30He Manbix SHeprHH HOHOB , B KaMepy Hanyc-

Ka^ca HeHTpa/ibHhiH Bo^opofl. Ilpn yBejiH^eHHH £aBJieHHH HeHTpa;ibHoro

ra3a AO 5 • 10" Topp B cneKTpe aHeprHH aTOMOB nepe3apHflKH noHB/iH/incb

HOhbi Ma/ibix 3HeprnH. ,D;ono;iHHTe/ibHbiM cnoco6oM npoBepKH HBJIH^OCB

H3MeHeHHe KOHHrypau,HH MaraHTHoro TIOJIH C npoGoHHOH Ha oflHopoflHoe.

RaBJieHne HeHTpa;ibHoro ra3a MOJKHO 6bi/io no,go6paTb TaK,MTo B no/re

a4Ha6axi«ecKOH /ioByuiKH HOHH Ma/iofi SHeprHH OTcyxcTBOBa/in, a B OAHOpo^HOM

perHCTpnpoBa/iHCb. 9TO o6ocHOBMBa^o pacMeT cpe#HeH SHeprnn

HOHOB c noMombio rpaHCH5ieTCfl TeM, MTO HacTHUbi c Ma/ibiMH nonepen-

HHMH 3HeprHHMH He yflepacHBaiorcfl B no^e a^Ha6aTHqecKOH jioByuiKH B

yc/iOBHHx, Kor/ja 3,/ieKTpoHbi HarpeTM BflOJib MarHHTHoro nora. Hon #eH-

CTBHeM oneKTpocTaTHMecKoro 3apH^a, o6pa3yeMoro 3/ieKTpoHaMH c 3Heprnen

~ 100 sB, STH HOHM noKnata/in jioByuiKy. ^ononHHTe/ibHbiM $aKTopoM,

O6T>HCHHK>W,HM OTcyTCTBHe HOHOB Majibix 3HeprHH nhjinncH o6HapyxeHHbiH

SKcnepHMeHTanbHO npo^onbHbiH HarpeB HOHOB. Be;iHqHHa corviacyeTCJi

c flaHHWMH, nonyMeHHbiMH H3 H3MepeHHH ^HaMarHeTH3Ma n.rca3Mbi H

nepe3apH^KH. B STHX sKcnepMMeHTax 6bina nonyneua n;ia3Ma c Be.rtHMHHOH

nT -3 • lG^sB ' CM' 3 .

Ha pHC. 5 ^aHbi 3aBHCHM0CTH OT MarHHTHoro no/in nonepe^HOH sHeprnn

HOHOB, H3MepeHHofi no cneKTpa/iH sHeprnfi aTOMOB nepe3apH^KH H nnoTHo-

CTH nonepeMHOH sHeprHH HOHOB nT , HafweHHOH H3 anaMarHHTHbix H3MepeHHH,

2

H(K3)

0,75

CO

0,5 «

PHC.5. IlonepeHHaH 3HeprHH HOHOB H ra30KHHeTHHecKoe aasnenne KaK $YHKUHH MarHHTHoro

nonn B noByuiKe.

0,25


IAEA-CN-33/C-5 277

E=1,5ioB 0 20 40 60 80 100 120 MKC

H=3,3K3

PHC.6. OcuwinorpaMMbi H3MeHeHHH BO BpeMeHH flnaMarHHTHoro cnrHa^a H noToxe nepe3apa-

AOHHOU HeiiTpanH.

06e 3aBHCHMocTH HMeiar CXOAHMH xapaKTep,HTo CBH^exe/ibCTByeT o TOM,

MTO nonepe^HaH SHeprnn onpenejiHeTca. HOHHMM KOMnoHeHTOM njia3MM.

BKpaTqe pe3y;ibTaTbi H3MepeHHH STHMH iieTo^aMH MOXHO copMy;iHpOBaTb

c/ieflyiomHM o6pa30M.

1) "IIonepeHHaH" TeMnepaTypa HOHOB, H3MepeHHaa no cneKTpy aTo-

MOB nepe3apH/(KH B 4Hana30He sHeprufi 0,3-3 IOB, xopomo corviacyeTCH

C H3MepeHHHMH no pa37IHMHK) xapaKTepHCTHK 30H£8 npH H3MeHeHHH MarHHT"

HOTO nojiH;

2) npH HarpeBe npoHcxo^HT Henocpe^cTBeHHoe B03pacTaHHe 3HeprnH

HOHOB nia3Mii;

3) cneKTp aHeprHM HOHOB o6orameH SOXEBIUHMH aHeprHstMH no cpaBHe-

HHK) C MaKCBCnJIOBCKHMJ

4) nonepewHan sHeprmi n;ia3Mbi cocpeflOToweHa B HOHHOM KOMnoHeHTe;

5) npH HarpeBe B npo6oMHOM none T.±- 1 , 5T. : npH HarpeBe B oflHOpofl-

HOM none Tu - 0 ,6 T - 150 aB.

Han6onee BepoHTHofi npHMHHOH, orpaHHMHBaiomeH RanbHeiimee yBenuneHHe

TeMnepaTypbi nna3MBi, HB/IHIOTCH noTepH 3HeprHH npH nepe3apHj5Ke.

Ha pHc.6 naHbi xapaKiepHbie 3aBHCHM0CTH H3iieHeHHa BO BpeMeHH

AHaMarHHTHoro CHraana H noTOKa nepe3apH^oHHOH HefiTpanH. H3 STOH

ocuHnnorpaMMbi cae#yeT,HTO noTOK nepe3apH£OHHOH HeHTpa;iH HaMHHaeT

B03pacTaTb HecKO/ibKO no3xe Hanajia pocTa ^HaMarHHTHoro CHraana. IIocne

BbiKJiKneHHH HarpeBaiomero BH-reHepaTopa flHaMarHHTHbifi CHTHSLJI cna-