Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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Magnetic fields and tokamak plasmas Alan Wootton Therefore the maximum displacement is ∆z max = Rb z N 1 B φ 20.13 which is typically a few mm. 148
Magnetic fields and tokamak plasmas Alan Wootton 21. TOKAMAK POSITION CONTROL The axisymmetric instability We first calculate the growth rate of an axisymmetric instability in a tokamak. We only consider vertical motion, because it is easier than the calculation for horizontal motion. The driving force is written in terms of the decay index n = -(R/B z )(dB z /dR). We consider a tokamak surrounded by a conducting vacuum vessel. There is assumed to be a transverse (poloidal) insulating gap in this vessel, so that only dipole currents can flow. The equation determining the vacuum vessel current I s is d dt ( L s I s )+ d dt ( M sp I p )+ Ω s I s= 0 21.1 Here I p is the plasma current, L s is the vessel inductance, Ω s the vessel resistance, M sp the mutual inductance between plasma and vessel. We introduce the vessel time constant τ s = L s /Ω s. We can approximate the vessel as a circular shell, so that L s = µ 0π 2 R s 4 τ s = µ 0σδ s r s 2 21.2 21.3 where R s , r s , δ s are the vessel major radius, minor radius, thickness, and σ is the conductivity. Approximating the plasma as a filament initially centered within the vessel (R = R 0 = R s , z = z s = 0), the mutual inductance and its spatial derivative are given by M sp = µ 0πR s z 2r s 21.4 ∂M sp ∂z = µ 0πR s 2r s 21.5 From equations 22.1, 22.2 and 2.5 we can derive the relationship between the dipole current in the vessel and the plasma displacement z: dI s dt + I s τ s = −2 I p πr s dz dt 21.6 149
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Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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