Alfvén 'resonance' reconsidered: Exact equations for wave propagation across a cold inhomogeneous plasma

Abstract

Previous discussions of Alfvén wave propagation across an inhomogeneous plasma predicted that shear Alfvén waves become singular (resonant) at the omega = k(z)v(A) layer and that there is a strong wave absorption at this layer giving localized ion heating. In this paper the three standard derivations of the Alfvén 'resonance' (incompressible magnetohydrodynamics, compressible magnetohydrodynamics, and two-fluid) are re-examined and shown to have errors and be mutually inconsistent. Exact two-fluid differential equations for waves propagating across a cold inhomogeneous plasma are derived; these show that waves in an ideal cold plasma do not become 'resonant' at the Alfvén layer so that there is no wave absorption or localized heating. These equations also show that the real 'shear' Alfvén wave differs in substance from both the ideal MHD and earlier two-fluid predictions and, in the low density, high field region away from the omega = k(z)v(A) layer, is actually a quasielectrostatic resonance cone mode. For omega much-lesser-than omega(ci) and k(y) = 0, the omega = k(z)v(A) layer turns out to be a cutoff (reflecting) layer for both the 'shear' and compressional modes (and not a resonance layer). For finite omega/omega(ci) and k(y) = 0 this layer becomes a region of wave inaccessibility. For omega much-lesser-than omega(ci) and finite k(y) there is strong coupling between shear and compressional modes, but still no resonance.