Low-Frequency Stability of Nonuniform Plasmas

Abstract

A collisionless plasma in equilibrium with a slightly nonuniform magnetic field is studied to determine its stability against growing low-frequency oscillations whose propagation vector is perpendicular to the magnetic field. The method employs the collisionless Boltzmann equation and Maxwell's equations to obtain the eigenfrequencies of the oscillations. Previous work on this problem was based on a longitudinal approximation, i.e., the oscillation was assumed to have electric vector parallel to its direction of propagation. The present work does not make this approximation and finds: (i) a mode which corresponds to the mode found in longitudinal approximation, with the same eigenvalue as given by that approximation; (ii) modes with polarization similar to the ``longitudinal'' mode which are purely oscillatory; (iii) a purely transverse mode which is unstable. These results are compared with magnetohydrodynamic and other approximations.