Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
j r = πa2 j
J
= ( 1 +α) ( 1 − x 2
) α 6.34
Figure 6.6 shows j r as a function of x for α between 0 and 5; these curves represent the shape of
the current density profiles with the constraint that the total current J is constant.
j r
5
4
3
2
1
α = 0
x
Figure 6.6 The normalized current density distributions j r (x)
The poloidal field B θ is given by
( ( ) 1+α
)
B θ
= B θ 0
( 1) 1 − 1 − x 2
x
6.35
with B θ0 (1) the value at r = a, or x = 1: B θ0 (1) = µ 0 J/(2πa). The ratio B θ /B θ0 (1) is shown in
Figure 6.7 as a function of x for α between 0 and 5.
B θ ____
Β θ1
5
4
3
2
1
α = 0
Figure 6.7. The normalized poloidal field distributions B θ /B θ0 (1)
x
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