Guiding Center Equations for Ideal Magnetohydrodynamic Modes
Authors: Roscoe B. White
Abstract:
Guiding center simulations are routinely used for the discovery of mode-particle resonances in
tokamaks, for both resistive and ideal instabilities and to find modifications of particle distributions
caused by a given spectrum of modes, including large scale avalanches during events with a
number of large amplitude modes. 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~B = ∇ X (ξ X B) however perturbs the magnetic topology, introducing extraneous magnetic
islands in the field. A proper treatment of an ideal perturbation involves a full Lagrangian
displacement of the field due to the perturbation and conserves magnetic topology as it should.
In order to examine the effect of ideal magnetohydrodynamic modes on particle trajectories the
guiding center equations should include a correct Lagrangian treatment. Guiding center equations
for an ideal displacement ξ are derived which perserve the magnetic topology and are used to examine
mode particle resonances in toroidal confinement devices. These simulations are compared
to others which are identical in all respects except that they use the linear representation for the
field. Unlike the case for the magnetic field, the use of the linear field perturbation in the guiding
center equations does not result in extraneous mode particle resonances.
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Submitted to: Physics of Plasmas (February 2013)
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Download PPPL-4853 (pdf 1.18 MB 11 pp)
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