Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
Field components on a rectangle
If we want to characterize the fields on a rectangular contour, we can make use of the fact that an
arbitrary function in a plane can be expressed as
B(η,ξ ) = ∑ c m, p
ξ m η p
3.5
m, p
with c m,p constant coefficients. Here we are working in a rectalinear coordinate system ξ,η,
centered on the contour center, at R = R l , shown in Figure 3.4.
z
η
Contour l
ξ
R
R l
Figure 3.4. The geometry used in describing fields on a rectangle or square.
On a one dimensional contour there will be degeneracy. Suppose we have a "modified
Rogowski" coil whose winding density varies as some function f p (η,ξ ), so that the time
integrated output is proportional to
s p,τ
= ∫ f p
B τ
dl
3.6
l
The subscript τ refers to the tangential (normal) field component on the contour. We could also
construct the signal s p,τ from individual measurements of B τ around the contour. Further
suppose that we express the tangential field itself in terms of our functions f as
B τ
= ∑ c m
f m
3.7
m
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