ARTICLES Alfvbn ‘resonance’ reconsidered: Exact equations for wave propagation across a cold inhomogeneous plasma

Previous discussions of Alfvdn wave propagation across an inhomogeneous plasma predicted that shear Alfvin waves become singular (resonant) at the w = kzuA 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 Alfvdn ‘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 Alfvdn layer so that there is no wave absorption or localized heating. These equations also show that the real ‘shear’ Alfven 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 o=kzuA layer, is actually a quasielectrostatic resonance cone mode. For 04 O,i and k,=O, the o = kzuA layer turns out to be a cutoff (reflecting) layer for both the ‘shear’ and compressional modes (and not a resonance layer). For finite OIO,i and k, = 0 this layer becomes a region of wave inaccessibility. For o~w,~ and finite k, there is strong coupling between shear and compressional modes, but still no resonance.