Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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Magnetic fields and tokamak plasmas Alan Wootton o J. A. Wesson, in Tokamaks, Oxford Science Publications, Clarendon press, Oxford, 1987. o P. Shkarofsky, Evaluation of multipole moments over the current density in a tokamak with magnetic probes, Phys. Fluids 25 (1982) 89. 6
Magnetic fields and tokamak plasmas Alan Wootton 1. SOME CONCEPTS AND DEFINITIONS Maxwell's equations We are going to make extensive use of Maxwell’s equations. In vector form, these are ⎛ ∇ × B = µ j + ∂D ⎞ ⎝ ∂t ⎠ 1.1 ∇ ⋅ B = 0 1.2 ∇ × E = − ∂B ∂t 1.3 ∇ ⋅ D = ρ 1.4 If charge is conserved we can add to these the continuity equation. We shall ignore the displacement current ∂D/∂t, and take µ = µ o , the free space value, inside a plasma. Without the last term Equation 1.1 is Amperes law. We have effectively restricted ourselves to assuming n i = n e = n, the charge neutral assumption, and that any waves have frequencies much less than the electron plasma frequency, with characteristic lengths much greater than the Debye length . We have not said E or ∇ . E = 0. When considering plasma equilibrium we shall also assume the electron mass m e approaches 0. This allows electrons to have an infinitely fast response time. Pick-up or Induction Coils This is the heart of the matter. Magnetic fields are usually measured with pick-up or induction coil circuits. Changing the magnetic flux in a circuit generates a current; the direction of this current is in a direction such as to set up a magnetic flux opposing the change. electromotence or voltage ε (∇ ε = -E, the electric field intensity) in Volts induced in a circuit equals the rate of change of flux N = ∫ B ⋅ ndS in Webers per second, i.e. S The ε = dN dt 1.5 The flux can be changed either by changing its strength, changing the shape of the circuit, or moving the circuit. Then ∫ E ⋅ dl l = − d dt ∫ B ⋅ndS 1.6 S 7
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Magnetic Fields and Magnetic Diagnostics for Tokamak Plasmas

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