Structure of generalized ion Bernstein modes from the full electromagnetic dispersion relation

Abstract

The structure of modes for which k┴B₀ and ω≪Ω_ (ion waves) has been studied qualitatively in the two limits κR₊ ≪ 1 and κR₊ ≫ 1, where R₊ = (κT₊/MΩ₊)^½ is the mean thermal Larmor radius, without the usual electrostatic approximation. Asymptotic forms of the dielectric tensor elements ε_ij are developed in these two limits. The modes having appreciable k × E can be called ‘generalized’ Bernstein modes. The approximation which yields the familar electrostatic Bernstein modes is ε_xx = 0. This approximation is shown to be valid only for large κR₊ and low β. However, for small and moderate values of κR₊ the generalized Bernstein modes partake of a ‘mixed’ electromagnetic- electrostatic character. In particular, for κR₊ ≲ 0(1) (but ω/κ < c) the electrostatic Bernstein modes are incorrect approximations. The warm plasma electromagnetic theory is discussed with reference to cold plasma theory for a low β plasma, and it is shown that: (1) the lower hybrid frequency is only an approximate resonance in the warm plasma; (2) electromagnetic cut-offs occur at all harmonics of the gyrofrequency as k → 0; (3) electrostatic resonances occur at all harmonics of the gyrofrequency as k→∞; (4) propagation can occur in warm plasmas at frequencies above the lower hybrid.