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

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.