Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
Figure 1.10. The poloidal flux ψ in the plane z = 0 for a circular current loop,
radius 1 m, current I = 1/µ 0 . The solid line is the exact solution, the long dash line
is the far field solution, and the short dash line is the very near field solution (zero
order in ρ/R terms only).
ψ
exact
very near
zero order
first order
Radius R (m)
Figure 1.11 The poloidal flux ψ in the plane z = 0 for a circular current loop,
radius 1 m, current I = 1/µ 0 . The solid line is the exact solution, the short dash line
is the first order expansion in ρ/R 0 solution keeping terms of order ρ/R 0 , and the
long dash line is the very near field solution (zero order in ρ/R terms only).
We can also compare the zero order, first order and exact solutions by plotting contours of ψ in
(R,z) space. This is done in Figure 1.12, for the conditions described in the caption of Figure
1.11. We see that it is very important to include the first order in ρ/R 0 terms; even then the
solution contours are significantly different from the exact solution contours. This is very
different from the case of the vector potential, where the zero order solution was accurate.
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