Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
Then we would have the output from the 'modified Rogowski' coil
∑
s p,τ
= c m
f m
f p
dl
∑
m
∫
= c m
4a m + p
m
l
⎡
⎣
⎢ m + 1 +
( ) a
a ⎤
p +1⎦
⎥
for m, p even 3.16
= 0 otherwise 3.17
Equations 3.16 and 3.17 show specifically how, by including a finite number of terms (say p max
= m max = 5) we will end up with a set of linear equations relating the measured signals to the
required constants c m . We must now solve them to obtain the coefficients c m as functions of the
measured s p,τ ; a similar procedure provides the d m as functions of the signals s p,n . The result is
not as elegant as the Fourier analysis applicable on a circular contour, where a single coil can be
wound to measure each individual Fourier coefficient, but I don’t know another way to represent
the fields on a square contour. Of course, instead of using these specially wound coils to
measure s p,τ and s p,n directly, the required integrals can always be constructed from individual
coil signals of B τ and B n around the contour l.
An example of a saddle coil for a particular f = η(1+ξ/R l ) is shown in Figure 3.5. Here R l is the
major radius of the contour center. These strange looking coils are actually useful for helping
determine plasma position
Figure 3.5. A saddle coil suitable for winding on a square vessel
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