Solution of the drift-kinetic equation for global plasma modes and finite particle orbit widths

The response of a collisionless plasma to global electromagnetic perturbations of an axisymmetric toroidal equilibrium is derived. By adopting a variational formulation for guiding center motion, the perturbed distribution function is expressed in terms of the linearized guiding center Lagrangian. Finite orbit widths are retained. In particular, the high particle energy limit where mirror-trapped banana orbits are distorted into ‘‘potato-shaped’’ orbits is considered. In this limit, the time scales associated with the drift and bounce motions of a mirror-trapped orbit become comparable, yielding important consequences on plasma stability. Quadratic forms are constructed in the context of kinetic-magnetohydrodynamic (MHD) models of plasmas composed of a thermal component obeying fluid-like equations and a high-energy component described in terms of the collisionless drift-kinetic equation. Relevant applications include improved modeling of energetic ion effects on toroidicity-induced Alfvén gap modes and internal kinks.