Variational principle for low-frequency stability of collisionless plasmas

An analysis of the stability of an arbitrary β collisionless plasma to modes with wavelengths greater than the ion gyroradius is presented. The stability of such a plasma to perturbations that grow on the hydrodynamic time scale is determined by the Kruskal–Oberman energy principle. However, a configuration which is predicted to be stable on the basis of this kinetic energy principle may still be unstable to modes that grow with a frequency comparable to the diamagnetic or curvature drift frequency. A new variational principle that gives sufficient conditions for instability of these low- frequency modes is derived. The new principle indicates that two types of instabilities are possible; the first corresponds to the low-frequency electrostatic, trapped particles mode, and the second is the low-frequency limit of magnetohydrodynamic (interchange and ballooning) modes. The kinetic modifications to the interchange (Mercier) criterion are evaluated and the effect of the kinetic terms on ballooning modes is estimated.