Representation of Ideal Magnetohydrodynamic Modes
Authors: Roscoe B. White
Abstract:
One of the most fundamental properties of ideal magnetohydrodynamics is the condition that
plasma motion cannot change magnetic topology. The conventional representation of ideal magnetohydrodynamic
modes by perturbing a toroidal equilibrium field through δ Β = ∇ X (xi X B) ensures
that δ B • ∇ ψ = 0 at a resonance, with ψ labelling an equilibrium flux surface. Also useful for the
analysis of guiding center orbits in a perturbed field is the representation δ Β = ∇ X αB. These two
representations are equivalent, but the vanishing of δ B • ∇ψ at a resonance is necessary but not
sufficient for the preservation of field line topology, and a indiscriminate use of either perturbation
in fact destroys the original equilibrium flux topology. It is necessary to find the perturbed field
to all orders in xi to conserve the original topology. The effect of using linearized perturbations on
stability and growth rate calculations is discussed.
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Submitted to: Physics of Plasmas (December 20112)
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Download PPPL-4844 (pdf 274 KB 9 pp)
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