Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
Figure 17.5. Data from PBX.
Another technique is to look in the frequency domain. Suppose we have coils placed both
poloidally and toroidally around the plasma.
Then the relationship between the phases of
different signals identifies m and n without the amplitudes being known. By looking in the
frequency domain we can reject noise, and other modes at frequencies other than ω mn . Taking a
rectangular vessel as an example (we measure b η ), then the fundamental component of the i th coil
signal will be of the form
S i
= A i
cos( ω mn
t − δ i
) 17.26
with ω mn identified from power spectra. The relative phase shift δ i will be, for the m,n mode,
⎡
δ i
= m θ i
− r mn ⎛
1 +β
R
I
+ l i ⎞
g
⎝ 2⎠ sin ( θ ⎤
i)
⎣
⎢
⎦
⎥ +θ i
+ nφ i
+ δ 0
+ 2πk i
17.27
where (θ i ,φ i ) locates the i th coil, δ 0 +2pk i expresses the multi-valued phase property. If we were
in a circular vessel, then the phase shift would be
126