Higher-Order Corrections to the Theory of the Guiding Center Plasma

Abstract

The theory of the guiding center plasma is extended to include previously neglected terms proportional to the particle mass-to-charge ratio m/e. To do this it is necessary to obtain a correspondingly accurate solution of the single charged particle equation of motion. Then, one may define a conservation equation for the time average particle motion or, equivalently, for guiding centers. This equation is combined with a macroscopic momentum equation through the use of a generalized Ohm's law. Adding Maxwell's equations, the result is a self-consistent set of higher-order equations describing the behavior of the guiding center plasma. These equations are then linearized in small perturbations about a uniform equilibrium configuration to obtain stability criteria. The results show that these criteria are the same as those of the lowest-order system.