Resonant Absorption as Mode Conversion?

TL;DR

This paper demonstrates that resonant absorption and mode conversion in solar MHD are fundamentally the same process, distinguished mainly by whether energy escapes or is confined, with implications for understanding wave energy transfer.

Contribution

The study shows that resonant absorption and mode conversion are equivalent phenomena in a simple MHD model, clarifying their relationship and physical interpretation.

Findings

Resonant absorption and mode conversion are fundamentally the same.

The distinction depends on whether the wave energy escapes or remains confined.

Singularities are avoided when the converted wave can carry energy away.

Abstract

Resonant absorption and mode conversion are both extensively studied mechanisms for wave "absorption" in solar magnetohydrodynamics (MHD). But are they really distinct? We re-examine a well-known simple resonant absorption model in a cold MHD plasma that places the resonance inside an evanescent region. The normal mode solutions display the standard singular resonant features. However, these same normal modes may be used to construct a ray bundle which very clearly undergoes mode conversion to an Alfv\'en wave with no singularities. We therefore conclude that resonant absorption and mode conversion are in fact the same thing, at least for this model problem. The prime distinguishing characteristic that determines which of the two descriptions is most natural in a given circumstance is whether the converted wave can provide a net escape of energy from the conversion/absorption region of physical space. If it cannot, it is forced to run away in wavenumber space instead, thereby generating the arbitrarily small scales in situ that we recognize as fundamental to resonant absorption and phase mixing. On the other hand, if the converted wave takes net energy way, singularities do not develop, though phase mixing may still develop with distance as the wave recedes.