Alfven reflection and reverberation in the solar atmosphere

Magneto-atmospheres with Alfven speed [a] that increases monotonically with height are often used to model the solar atmosphere, at least out to several solar radii. A common example involves a uniform vertical or inclined magnetic field in an isothermal atmosphere, for which the Alfven speed is exponential. We address the issue of internal reflection in such atmospheres, both for time-harmonic and for transient waves. It is found that a mathematical boundary condition may be devised that corresponds to perfect absorption at infinity, and, using this, that many atmospheres where a(x) is analytic and unbounded present no internal reflection of harmonic Alfven waves. However, except for certain special cases, such solutions are accompanied by a wake, which may be thought of as a kind of reflection. For the initial-value problem where a harmonic source is suddenly switched on (and optionally off), there is also an associated transient that normally decays with time as or , depending on the phase of the driver. Unlike the steady-state harmonic solutions, the transient does reflect weakly. Alfven waves in the solar corona driven by a finite-duration train of p-modes are expected to leave such transients.