Drift Instabilities in General Magnetic Field Configurations

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 $\mathrm{F(\in ,\; \mu )}$ , of interest in minimum‐B mirror configurations, is absolutely stable to these modes provided $\text{∂F/∂∈ < 0}$ together with a second condition on $\mathrm{\partial F/\partial \mu }$ . 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.