Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

Magnetic fields and tokamak plasmas
Alan Wootton
The equation determining the plasma displacement z is
m d 2 z
dt ≈ 0 = −2πR I B 2 p p[ + B + ∆B
R s ] 21.7
with B R the equilibrium major radial field, B s the major radial field from the vessel currents, and
∆B a perturbation to B R . We can take the mass m of the plasma to be zero in the presence of the
vessel; we will find the vessel slows the motion sufficiently for the m(d 2 z/dt 2 ) term to be
vanishingly small. Using
B R
= nB z z
R
21.8
B z
= Γµ 0 I p
4πR p
21.9
⎛
Γ = ln 8R ⎞
p
⎜ ⎟ + l i
⎝ ⎠ 2 + β I
− 3 2
r p
21.10
K s
= B s
I s
= −µ 0
4r s
21.11
where r p is the plasma minor radius, and we assume R s = R p = R. Taking ∆B = 0, equation 22.7
can be written
0 = − nΓµ 0I p
z
4πR 2
+ µ 0 I s
4r s
21.12
Equations 22.12 and 22.6 define the problem; they have solutions
z = z 0
e γt 21.13
I s
= I s 0
e γt 21.14
The growth rate is
γ = − 1
τ s
n
n + n s
21.15
n s
= 2R2
r s 2 Γ
21.16
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