Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
⎡
δ i
= m θ i
− r mn ⎛
1 +β
R
I
+ l i ⎞
g
⎝ 2⎠ sin ( θ ⎤
i)
⎣
⎢
⎦
⎥ + nφ i
+ δ 0
+ 2πk i
17.28
By performing a best fit of the measured phase with this expression gives m and n. For example
plotting δ i -nφ i against θ i (to remove the toroidal effects) should give a line of slope m+1. An
example is shown in Figure 17.6, data from PBX. The best fit to the data was obtained using m
= 2, n = 1.
Turbulence
Figure 17.6. The phase of the experimental data shown in
Figure 17.5, together with the phase given by equation 17.28.
with m = 2, n = 1
Magnetic coils outside the plasma measure not only the low m,n “Mirnov” oscillations (tearing
modes), but also higher frequency, higher mode number fluctuations. Many m, n modes are
possible; Figure 17.7 shows an example where 1 ≤ m ≤ 40, and 1 ≤ n ≤ 12 are considered.
Each point represents a possible mode combination, the dark area shows those possible when q a
= 3.2 , q 0 = 1, and constraints to m are applied (in this case 6 ≤ m ≤ 12).
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