Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
We must choose q(0). Figure 6 .9 shows the resulting α as a function of q(1) for two assumed
values of q(0): the long broken line is for q(0) = 0.8, and the short broken line is for q(0) = 1.0.
An alternate prescription is to choose α so that the position x 1 of the q = 1 surface is in
approximately the correct position. For example, suppose that x 1 = 1/q(1). Then the equation for
local safety factor
x 2
q( x) = q( 1)
( 1− ( 1 − x 2
) 1+α
)
6.40
can be solved to give
⎛ 1 − 1 ⎞
q(1)
ln⎜
1 − 1 ⎟
⎝ q(1) 2 ⎠
α =
⎛
ln 1 − 1 ⎞
⎝ q(1) 2 ⎠
6.41
Figure 6 .9 (solid line) shows the resulting α as a function of q(1).
α
q(1)
Figure 6.9. The parameter α as a function of q(1), chosen such that 1) solid line:
x 1 = 1/q(1), 2) long dashed line q(0) = 0.8, and 3) short dashed line q(0) = 1.0.
We have now uniquely determined α in terms of q(1), and as such there is a unique value of q(0)
for each q(a). This is shown in Figure 6.10
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