Benchmarking Fast-to-Alfven Mode Conversion in a Cold MHD Plasma

TL;DR

This paper investigates the fundamental process of fast-to-Alfvén mode conversion in a simplified cold MHD model, exploring how it depends on various parameters and its implications for solar atmospheric phenomena.

Contribution

It provides a comprehensive benchmark analysis of fast-to-Alfvén mode conversion in a cold MHD plasma, clarifying the dependence on key parameters and conditions for near-total conversion.

Findings

Near-total conversion occurs at small inclination angles and high polarization angles.

Conversion is absent in vertical magnetic fields.

The conversion region spans the entire chromosphere for helioseismic wavenumbers.

Abstract

Alfv\'en waves may be generated via mode conversion from fast magneto-acoustic waves near their reflection level in the solar atmosphere, with implications both for coronal oscillations and for active region helio-seismology. In active regions this reflection typically occurs high enough that the Alfv\'en speed $a$ greatly exceeds the sound speed $c$, well above the $a=c$ level where the fast and slow modes interact. In order to focus on the fundamental characteristics of fast/Alfv\'en conversion, stripped of unnecessary detail, it is therefore useful to freeze out the slow mode by adopting the gravitationally stratified cold MHD model $c\to0$. This provides a benchmark for fast-to-Alfv\'en mode conversion in more complex atmospheres. Assuming a uniform inclined magnetic field and an exponential Alfv\'en speed profile with density scale height $h$, the Alfv\'en conversion coefficient depends on three variables only; the dimensionless transverse-to-the-stratification wavenumber $\kappa=kh$, the magnetic field inclination from the stratification direction $\theta$, and the polarization angle $\phi$ of the wavevector relative to the plane containing the stratification and magnetic field directions. We present an extensive exploration of mode conversion in this parameter space and conclude that near-total conversion to outward-propagating Alfv\'en waves typically occurs for small $\theta$ and large $\phi$ ($80^\circ$--$90^\circ$), though it is absent entirely when $\theta$ is exactly zero (vertical field). For wavenumbers of helioseismic interest, the conversion region is broad enough to encompass the whole chromosphere.