Magnetic Diagnostics for Equilibrium Reconstructions in the ...
Magnetic Diagnostics for Equilibrium Reconstructions in the ...
Magnetic Diagnostics for Equilibrium Reconstructions in the ...
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<strong>Magnetic</strong> <strong>Diagnostics</strong> <strong>for</strong> <strong>Equilibrium</strong> <strong>Reconstructions</strong><br />
<strong>in</strong> <strong>the</strong> Presence of Non-axisymmetric Eddy Current<br />
Distributions <strong>in</strong> Tokamaks<br />
Laura Berzak, PPPL<br />
A.D. Jones, R. Kaita, T. Kozub, N. Logan, R.<br />
Majeski, J. Menard, L. Zakharov, PPPL<br />
LTX Team, PPPL
Outl<strong>in</strong>e<br />
2<br />
• Introduction to <strong>Magnetic</strong> Fusion Energy (MFE)<br />
• Overview of <strong>the</strong> Lithium Tokamak eXperiment (LTX)<br />
• <strong>Magnetic</strong> diagnostics <strong>for</strong> LTX<br />
• LTX LRDFIT – 2-D code characterization<br />
• LTX Cbshl – 3-D code development<br />
• Summary
Fusion Energy<br />
Goal: Generate power, like stars, through fusion reactions<br />
Example Reaction: D + T n + + 17.6 MeV<br />
Benefits:<br />
* Widely available <strong>in</strong>put fuel source – sea water<br />
* No risk of runaway cha<strong>in</strong> reaction lead<strong>in</strong>g to nuclear accident<br />
* Clean energy production – no greenhouse gas emission<br />
* No high-level radioactive, nuclear waste
<strong>Magnetic</strong> Fusion Energy<br />
* Fusion requires a balance of density, temperature, and conf<strong>in</strong>ement time<br />
* Required temperature too high <strong>for</strong> physical conta<strong>in</strong>ment magnetic bottle<br />
* Form a plasma <strong>in</strong>side a physical vacuum vessel<br />
* Constra<strong>in</strong> plasma particles to closed magnetic field l<strong>in</strong>es<br />
* Supply external heat<strong>in</strong>g <strong>in</strong> <strong>the</strong> <strong>for</strong>m of neutral beam <strong>in</strong>jection or<br />
radiofrequency heat<strong>in</strong>g<br />
* Highly energetic particles collide lead<strong>in</strong>g to fusion reactions and energy<br />
production<br />
* Several potential magnetic bottle ‘shapes’:<br />
Advanced Tokamak Spherical Torus Compact Stellarator
Lithium acts as a getter → reduc<strong>in</strong>g recycl<strong>in</strong>g<br />
1<br />
• Experimental confirmation of plasma per<strong>for</strong>mance enhancement with<br />
lithium usage:<br />
• TFTR lithium wall-condition<strong>in</strong>g – solid Li<br />
• T-11M, FTU lithium rail limiter – liquid Li<br />
• CDX-U tray limiter filled with 2000 cm 2 liquid lithium – liquid Li PFC<br />
CDX-U<br />
CDX-U tray limiter<br />
Red: Li, Blue: no Li<br />
Largest improvement <strong>in</strong> energy<br />
conf<strong>in</strong>ement time <strong>for</strong> an Ohmic<br />
tokamak
Lithium Tokamak eXperiment<br />
3<br />
• Extend previous lithium experimental results to operation with 85% liquid<br />
lithium coverage of last-closed-flux-surface<br />
LTX parameters:<br />
Major radius . . . . . . . . 0.4 m<br />
M<strong>in</strong>or radius . . . . . . . . 0.26 m<br />
Toroidal field . . . . . . . 2 kG<br />
Plasma current . . . . . . 15 kA 150 kA<br />
Discharge duration . . . 5 ms 25 ms<br />
1.8 m
LTX <strong>in</strong>-vessel, heated, con<strong>for</strong>mal Cu shell<br />
4<br />
• 85% LCFS covered by liquid lithium when shell is lithium-coated<br />
• Con<strong>for</strong>mal with plasma last-closed-flux surface<br />
• Two 22.5° toroidal breaks, and <strong>in</strong>board and outboard poloidal breaks<br />
• Can be heated up to 500 °C<br />
• Mechanically and electrically isolated from <strong>the</strong> vacuum vessel<br />
1.8 m
Basic <strong>the</strong>ory of magnetic diagnostics<br />
<br />
C<br />
E<br />
dl<br />
<br />
E dl<br />
E dl<br />
0 V<br />
<br />
B<br />
coil<br />
leads<br />
S<br />
<br />
ds<br />
V<br />
B <br />
<br />
S ds<br />
V<br />
0<br />
<br />
N<br />
RC<br />
<br />
NAB<br />
RC
LTX has extensive set of magnetic diagnostics<br />
5<br />
• 11 centerstack flux loops<br />
1.8 m<br />
• 16 shell flux loops<br />
• 4 saddle loops<br />
• 30 <strong>in</strong>-shell B-dot coils<br />
• 12 ex-shell B-dot coils<br />
• 18 2-axis gap B-dot coils<br />
• 26 B-dot coils <strong>in</strong> rectangular array<br />
• 2 plasma current-measur<strong>in</strong>g coils<br />
• 1 vessel current-measur<strong>in</strong>g coil<br />
• Plasma stored energy<br />
measurement<br />
Poloidal field coils
<strong>Magnetic</strong> diagnostics design requirements<br />
6<br />
• Withstand high temperatures (500 °C)<br />
contact with lithium<br />
• Ma<strong>in</strong>ta<strong>in</strong> electrical isolation between<br />
shell quadrants and between shell<br />
and vacuum vessel<br />
• M<strong>in</strong>imize distance between diagnostic<br />
and plasma<br />
• Provide data on toroidal asymmetries<br />
and<br />
• Provide full coverage of poloidal<br />
cross-section<br />
• Yield data <strong>for</strong> highly-constra<strong>in</strong>ed<br />
equilibrium flux surface<br />
reconstructions
Shell flux loops – 8 on upper shells, 8 on lower<br />
• 2-turn, center-tap grounded with separately grounded sta<strong>in</strong>less steel hous<strong>in</strong>g<br />
<strong>for</strong> noise immunity<br />
7<br />
• SS hous<strong>in</strong>g covered with Steatite ‘fishsp<strong>in</strong>e’ and MgO to provide electrical<br />
isolation between diagnostic and shell and between shell quadrants<br />
• Mounted directly to non-plasma fac<strong>in</strong>g side<br />
of shell to m<strong>in</strong>imize distance to plasma and<br />
provide full poloidal coverage<br />
• Signals valuable <strong>for</strong> code calibration, vertical<br />
null <strong>for</strong>mation, constra<strong>in</strong>ed equilibrium<br />
reconstructions
Saddle loops – 4 total; outboard of vertical midplane<br />
• Analogous materials and fabrication technique as shell flux loops<br />
8<br />
• Span toroidal gap, measure flux through gap from circulat<strong>in</strong>g shell currents<br />
• Signals essential <strong>for</strong> determ<strong>in</strong><strong>in</strong>g magnitude and evolution of shell currents
In- and ex-shell B-dot sensors<br />
• 30 <strong>in</strong>-shell, 12 ex-shell; outboard coverage <strong>in</strong>clud<strong>in</strong>g poloidal gap at 3<br />
toroidal locations<br />
9<br />
• Sensors mounted <strong>in</strong> SS hous<strong>in</strong>g to both plasma-fac<strong>in</strong>g side of shell and nonplasma-fac<strong>in</strong>g<br />
side of shell<br />
• Signals provide measure of field extremely close to plasma; evidence of<br />
toroidal asymmetries<br />
• Comparison between <strong>in</strong> and ex-shell sensors yields<br />
direct measurement of shell eddy currents
2-axis gap Mirnov coils – 9 probes upper, 9 lower<br />
• Total of 36 probes mounted <strong>in</strong> toroidal gap; provide full poloidal coverage<br />
10<br />
• Mount<strong>in</strong>g tabs plasma-sprayed with W; sensors covered by sta<strong>in</strong>less steel<br />
protective caps, leads covered with fiberglass and sta<strong>in</strong>less steel overbraid<br />
• Signals provide dense measurement of poloidal and radial fields with<br />
m<strong>in</strong>imal shell <strong>in</strong>fluence; yield measure of vertical<br />
field component and bulge of field <strong>in</strong>to toroidal gap
LTX LR circuit model with Data FITt<strong>in</strong>g capabilities<br />
• Axisymmetric (2-D), non-filamentary code developed <strong>for</strong> NSTX (J. Menard)<br />
– now tailored <strong>for</strong> LTX<br />
• Solves circuit equations based on models of vacuum vessel, shell and<br />
plasma composed of <strong>in</strong>dividual conduct<strong>in</strong>g elements with assigned<br />
<strong>in</strong>ductance and resistance values<br />
• To reduce 3-D effects to a 2-D representation – <strong>in</strong>board versus outboard<br />
shell elements’ resistivity values adjusted to account <strong>for</strong> different current<br />
path lengths<br />
‘Full Shell’ model<br />
11<br />
Z=0<br />
Z=0<br />
Shell<br />
Vacuum vessel<br />
‘No Shell’ model<br />
R<br />
R
LTX LRDFIT<br />
12<br />
‘No Shell’ model<br />
‘Full Shell’ model<br />
‘Partial Shell’ model<br />
‘Partial Shell’ model
LTX LRDFIT validation, comparison with fast camera<br />
17<br />
Visible fast camera frame<br />
Discharge <strong>in</strong>itiation
LTX LRDFIT field comparison at peak plasma current<br />
18<br />
Visible fast camera frame<br />
345.298 ms<br />
Discharge fully developed<br />
Peak I P
LTX LRDFIT field comparison at term<strong>in</strong>ation<br />
19<br />
Visible fast camera frame<br />
347.711 ms<br />
Discharge term<strong>in</strong>ation I P<br />
→ 0
Inherently 2-D, LTX LRDFIT can simulate 3-D circulat<strong>in</strong>g shell currents<br />
13<br />
0.0 0.8<br />
60<br />
1.5E-3<br />
0.4<br />
Simulated current (kA)<br />
0<br />
0.0<br />
Saddle loop flux (Wb)<br />
-20<br />
0.05<br />
Time (s)<br />
-5E-3<br />
1.5E-3<br />
-0.4<br />
Field (T)<br />
Flux (Wb)<br />
0.00<br />
0.0<br />
-0.01<br />
0.44 0.46 0.48<br />
-3E-3
Shell currents act as additional set of PF coils<br />
• Shell currents dur<strong>in</strong>g plasma discharge ~20 kA<br />
14<br />
• Provide field <strong>in</strong> opposite direction to ma<strong>in</strong> vertical field coils, elongates<br />
plasma, drives vertically unstable<br />
• Up-down asymmetry observed on magnetic<br />
diagnostics signals<br />
• Plasma reconstructions show solution high or<br />
low <strong>in</strong> plasma volume<br />
(Wb)<br />
0.004<br />
0.002<br />
0.000<br />
-0.002<br />
-0.004 Shell flux comparison<br />
0.444 0.446 0.448<br />
Time (s)<br />
(T)<br />
0.010<br />
0.005<br />
0.000<br />
-0.005<br />
-0.010<br />
-0.015 In-shell comparison<br />
0.444<br />
0.446<br />
0.448<br />
Time (s)
Next step: 3-D simulation of LTX double-walled conduct<strong>in</strong>g structure<br />
• Response function technique (L. Zakharov) coupled with three-dimensional<br />
electromagnetic model and circuit equations<br />
• Response functions – ma<strong>the</strong>matical relationship between a f<strong>in</strong>ite-size<br />
sensor and an <strong>in</strong>dividual poloidal field coil through driv<strong>in</strong>g voltage<br />
applied to <strong>the</strong> field coil:<br />
S(<br />
t)<br />
Signals<br />
<br />
<br />
B(<br />
t)<br />
B(<br />
t)<br />
<br />
<br />
<br />
t<br />
t<br />
0<br />
R(<br />
t<br />
R(0)<br />
V ( t)<br />
Spl<strong>in</strong>e<br />
<br />
) V (<br />
) d<br />
<br />
<br />
tt<br />
0<br />
0<br />
R(<br />
) V<br />
t<br />
( t<br />
<br />
) d<br />
20<br />
Response func.
Response Function Technique<br />
• Calibrate location of field coils and magnetic diagnostics by m<strong>in</strong>imiz<strong>in</strong>g<br />
difference between <strong>the</strong>oretical saturation value and calculated asymptote<br />
from measured data response function<br />
Shell flux loop #8 Response Functions<br />
21<br />
S(<br />
t) |<br />
tt<br />
<br />
0<br />
<br />
T<br />
T<br />
0<br />
R(<br />
T)<br />
V ( t T)<br />
R(<br />
) V<br />
t<br />
( t <br />
) d<br />
Value (arbitrary unit)<br />
• Matrix of response functions allows:<br />
Time <br />
• Non-plasma contribution to sensor signals to be removed<br />
• ‘Reverse’ solv<strong>in</strong>g <strong>for</strong> discharge design
Coupled with response functions, simulate eddy currents <strong>in</strong> shell and vessel<br />
• Triangular mesh calculated <strong>for</strong> shell quadrants and vacuum vessel<br />
(>18,000 elements per shell quadrant, >8,000 elements <strong>for</strong> vacuum<br />
vessel)<br />
22<br />
• Derived (L. Zakharov): analytical representation<br />
of field due to <strong>the</strong> surface current on each triangle,<br />
no surface s<strong>in</strong>gularities AND l<strong>in</strong>ked circuit equations –<br />
<br />
iT<br />
ia<br />
<br />
<br />
0.1<br />
<br />
jN<br />
T<br />
<br />
j0<br />
<br />
Eij<br />
i<br />
<br />
ext ( I<br />
a cb<br />
I<br />
b ac<br />
I<br />
c ba)<br />
i i<br />
( I<br />
r r r<br />
n)<br />
<br />
<br />
j<br />
A<br />
rcb<br />
0<br />
i<br />
(2Sd<br />
)<br />
i
Conclusions<br />
• Extensive need to diagnose eddy currents and 3-D effects, particularly as<br />
more experiments <strong>in</strong>vestigate alternative first wall and blanket concepts<br />
23<br />
• LTX magnetic diagnostics system permits quantification of eddy currents,<br />
provides path <strong>for</strong>ward <strong>for</strong> mitigat<strong>in</strong>g operational issues <strong>in</strong>troduced<br />
• LTX LRDFIT has been tailored to <strong>in</strong>clude 3-D effects, essential <strong>for</strong> start-up<br />
design and discharge development<br />
• Fur<strong>the</strong>r work: cont<strong>in</strong>ued development of a full, 3-D electromagnetic code<br />
• Double-walled conduct<strong>in</strong>g structure (shell and vacuum vessel) of LTX<br />
provides opportunity to explore liquid lithium PFCs and to develop<br />
magnetic diagnostics, 2-D, and 3-D codes of general applicability <strong>for</strong>:<br />
quantify<strong>in</strong>g eddy currents and <strong>the</strong>ir effects on plasma behavior, and<br />
optimiz<strong>in</strong>g <strong>the</strong>se effects
Acknowledgements<br />
I would like to s<strong>in</strong>cerely thank my <strong>the</strong>sis advisors, Robert Kaita and Richard<br />
Majeski, <strong>for</strong> <strong>the</strong> opportunity to be part of <strong>the</strong> LTX team and <strong>for</strong> all of <strong>the</strong>ir<br />
patience, time, and guidance.<br />
I would like to thank <strong>the</strong> LTX team as well <strong>for</strong> <strong>the</strong>ir support and help<br />
throughout my <strong>the</strong>sis work.<br />
I would also like to thank <strong>the</strong> terrific people at Krell <strong>for</strong> all of <strong>the</strong>ir help and <strong>for</strong><br />
<strong>the</strong> opportunity to be part of <strong>the</strong> SSGF program.
<strong>Magnetic</strong> diagnostics crucial <strong>for</strong> discharge development<br />
15<br />
• Basic Ohmically-driven tokamak start-up <strong>the</strong>ory:<br />
• Provide Ohmic flux to drive plasma<br />
• Form vertical/poloidal field null near<br />
peak <strong>in</strong> Ohmic flux sw<strong>in</strong>g<br />
• Provide vertical field <strong>for</strong> conf<strong>in</strong>ement<br />
after <strong>in</strong>itial electron avalanche and<br />
breakdown<br />
• Develop vertical fields <strong>for</strong> discharge<br />
control and shap<strong>in</strong>g<br />
Shell flux loop subtraction<br />
• Challenges <strong>in</strong> double-walled tokamak:<br />
• M<strong>in</strong>imiz<strong>in</strong>g required Ohmic flux<br />
• Quantify<strong>in</strong>g eddy currents <strong>in</strong> conductive structures close to plasma
Quantify<strong>in</strong>g eddy currents <strong>in</strong> <strong>the</strong> shell<br />
• Calculation of decay times<br />
16<br />
• Collect library of calibration shots: <strong>in</strong>dividual poloidal field coil pulses<br />
and pulses with operational pairs of coils, long-pulse (>300 ms)<br />
wherever possible<br />
• Expand library with poloidal field coil-only pulses dur<strong>in</strong>g shell heat<strong>in</strong>g<br />
tests
Supplemental Slides
Supplemental Slides<br />
• Ma<strong>the</strong>matically l<strong>in</strong>early superimpose poloidal fields to m<strong>in</strong>imize vertical<br />
field near loop voltage peak<br />
<br />
i1<br />
) 0<br />
• Compare with LTX LRDFIT field contour simulations<br />
6<br />
A I(<br />
t<br />
<br />
i<br />
t i
Future Work – Interpretation of <strong>Reconstructions</strong><br />
• Use reconstructions to study energy conf<strong>in</strong>ement time<br />
• Exam<strong>in</strong>e changes <strong>in</strong> current profile with reduced recycl<strong>in</strong>g<br />
• Exam<strong>in</strong>e scal<strong>in</strong>g of conf<strong>in</strong>ement time with various plasma<br />
parameters such as current, field, density, and temperature<br />
• Compare results with ASTRA-ESC simulations<br />
• Simulations utilize <strong>the</strong> Reference Transport Model (RTM), which<br />
reflects elim<strong>in</strong>ation of anomalous electron transport <strong>in</strong> LiWall<br />
regime, and fits well with CDX-U data<br />
• RTM is sensitive to diffusion coefficients, not <strong>the</strong>rmoconduction<br />
s<strong>in</strong>ce only m<strong>in</strong>imized temperature gradient is present – electron and<br />
ion transport become l<strong>in</strong>ked: e = i = D i,e = i<br />
neoclassical<br />
• Compare simulations with LTX data and reconstructions<br />
• If similar correspondence is observed, may permit first pr<strong>in</strong>ciples<br />
transport model of LTX