Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
B R
N
( R 0
, z) = ∑a n
z n 18.3
n= 0
N
B z
( R,0) = ∑ b n
R n
18.4
n= 0
The magnetic axis is found where from the zero crossing of the resulting polynomials. The flux
function is found by integration:
( ) = −R 0
a n
z n
ψ R 0
, z
N
∫ ∑( )dz + const 18.5
n=0
N
ψ( R ,0)= ∫ ∑( b n
R n+1
)dR + const 18.6
n= 0
The current density is then obtained as
µ 0
j = ∂B R
∂z − ∂B z
∂R
18.7
The constants (giving ∂B R /∂z at z = 0 and ∂B z /∂R at R = R 0 ) must be determined by making
some assumptions concerning the plasma shape, say that it is mostly elliptic. Some examples of
the results of this analysis, where N = 5, are shown in Figure 18.4 for the fluxes and Figure 18.5
for the current density.
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