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→0. 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 κ=kh, the magnetic field
inclination from the stratification direction θ, and the polarization
angle Ï• 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 θ and large ϕ (80∘--90∘), though it is
absent entirely when θ is exactly zero (vertical field). For wavenumbers
of helioseismic interest, the conversion region is broad enough to encompass
the whole chromosphere.Comment: 14 pages plus supplementary tables. Astrophys J (accepted 25 May
2011). Two ancillary animations (animated gif) attache