Drift Instabilities in General Magnetic Field Configurations

TLDR

An energy principle shows that the special equilibrium distribution F(ε, μ) in minimum‑B mirror configurations is absolutely stable to low‑frequency drift modes when ∂F/∂ε<0 and a second condition on ∂F/∂μ holds, and the equations also capture a recently discussed low‑frequency trapped‑particle instability. The study develops a theory of low‑frequency drift (universal) instabilities in nonuniform collisionless plasmas for general magnetic field configurations, incorporating trapped‑particle effects beyond the previously studied plane geometry. The authors analyze axisymmetric toroidal configurations with closed poloidal field lines for Maxwellian equilibria with density gradients, extending the theory beyond the special stable distribution. Three unstable drift modes—a flute‑like mode, a drift‑ballooning mode localized to regions of unfavorable curvature, and a drift‑universal mode—are identified, with stability criteria and growth rates provided.

Abstract

A theory of low-frequency drift (universal) instabilities in a nonuniform collisionless plasma is developed for general magnetic field configurations including trapped particle effects, rather than the plane geometry which has previously received most attention. A type of energy principle shows that the special equilibrium distribution F(∈, μ), of interest in minimum-B mirror configurations, is absolutely stable to these modes provided ∂F/∂∈ &amp;lt; 0 together with a second condition on ∂F/∂μ. For equilibrium distributions not of this special form, in particular for a Maxwell distribution with a density gradient, the case of axisymmetric toroidal configurations with closed poloidal field lines is considered in detail. Three unstable drift modes are found, a flute-like mode, a drift-ballooning mode local to the region of unfavorable curvature, and a drift-universal mode. Stability criteria and growth rates for the modes are given. The equations also describe a recently discussed low-frequency trapped-particle instability.