Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
For near circular plasmas, we must estimate L p separately. For example, for the simple circular
low beta equilibrium of section 6, we can take a model current distribution j φ0 (r) = j 0 (1-(r/a) 2 ) α .
Then l i = L p -ln(a l /a p ), with l i given as a function of α = (q a /q 0 -1). By assuming q 0 = 1 we can
then estimate l i , and make the separation.
Comments on the definition of poloidal beta
We must be careful with the definition of "poloidal beta". So far we have used Equation 12.21,
namely
β I
= 8π
µ 0
I p
2
pS φ
S φ
∫ 13.9
We could replace β I by β p (the poloidal beta), which characterizes the ratio of plasma pressure to
the pressure of the magnetic field for an arbitrary shaped cross section. It should be introduced so
that the pressure balance, Equation 12.27, is replaced by
β p
= 1 + µ p
13.10
so that β p = 1 for µ p = 0.
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