Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
INTRODUCTION
This series of notes tries to lay the foundations for the interpretation of magnetic fields and
fluxes, often in terms of equilibrium plasma parameters. The title, 'magnetic diagnostics', is
taken to mean those diagnostics which are used to measure magnetic fields and fluxes using
induction, or pick-up, coils. More specifically, what is often inferred is a question: "How much
can we tell about a plasma given certain measurements of magnetic fields, and fluxes, outside
that plasma" I don’t consider here diagnostics which measure the plasma current density
distribution utilizing phenomena such as the motional Stark effect, or Faraday rotation; these are
found in a series of notes on Plasma Diagnostics..
The measurements themselves are in principle simple, although in practice they are always
complicated by unwanted field components, for example from misaligned pick-up coils. There is
also the problem of allowing for image currents flowing in nearby conductors; dealing with these
image currents becomes a large part of the problem. Including the effects of an iron core also
leads to complications.
Many people think the topic under consideration is boring, in that there is nothing new to do.
You have only to read current issues of plasma physics journals to recognize that there is still
much interest in the topic. For example, equilibrium and its determination, axisymmetric stability
and disruptions are all of current interest, and all involve ‘magnetic diagnostics’. The subject
does appear to be difficult (students starting in the topic have a hard time).
The layout of the notes is as given in the list of contents. Generally I have included topics which
I have found useful in trying to understand tokamaks. Some basic concepts (inductances, fluxes,
etc.) are included, because they are made use of throughout the notes. There is also a section on
plasma equilibrium, in which the large aspect ratio, circular tokamak is described. The fluxes
and fields from this model are used as examples for application of certain ideas in the remainder
of the text.
References I find useful include:
o B. J. Braams, The interpretation of tokamak diagnostics: status and prospects, IPP
Garching report IPP 5/2, 1985.
o L. E. Zakharov and V. D. Shafranov, Equilibrium of current carrying plasmas in toroidal
configurations, in Reviews of Plasma Physics volume 11, edited by M. A.
Leontovich, Consultants Bureau, New York (1986).
o V. S. Mukhovatov and V. D. Shafranov, Nucl. Fusion 11 (1971) 605.
o V. D. Shafranov, Plasma Physics 13 (1971) 757.
o L. E. Zakharov and V. D. Shafranov, Sov. Phys. Tech. Phys. 18 (1973) 151
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