Electrostatic modification of variational principles for anisotropic plasmas

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Abstract
The kinetic energy principle is modified by the presence of an equilibrium electrostatic potential and the inclusion of the quasineutrality condition. By identifying terms that are fluid-like (local) and kinetic (nonlocal), one can express the change in potential energy, ΔW, in a form which is both variational and minimizing and also displays, clearly, the electrostatic effects on the various free energy sources. The kinetic energy principle determines the stability of the plasma to perturbations that grow on the time scale associated with the streaming of particles along field lines. Recently, a new variational principle has been proposed which determines the stability of the plasma to perturbations that grow on the time scale associated with the drifting of particles across field lines. The modifications of this principle due to electrostatic effects will also be considered, and cases in which necessary and sufficient conditions for instability can be found will be discussed.

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