Alfv\'en Reflection and Reverberation in the Solar Atmosphere

TL;DR

This paper investigates how Alfvén waves reflect and reverberate in the solar atmosphere, revealing conditions for perfect absorption and weak reflection of transients, which impacts understanding of wave dynamics in the solar corona.

Contribution

It provides a mathematical framework for understanding Alfvén wave reflection and absorption in stratified atmospheres, highlighting conditions for minimal internal reflection and transient decay behaviors.

Findings

Analytic unbounded Alfvén speed profiles show no internal harmonic reflection.

Transient Alfvén waves decay as O(t-1) or O(t-1 ln t), with weak reflection.

Special cases exhibit perfect absorption with no reflection.

Abstract

Magneto-atmospheres with Alfv\'en 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 uniform vertical or inclined magnetic field in an isothermal atmosphere, for which the Alfv\'en 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 Alfv\'en 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 O(t-1) or O(t-1 ln t), depending on the phase of the driver. Unlike the steady-state harmonic solutions, the transient does reflect weakly. Alfv\'en waves in the solar corona driven by a finite-duration train of p-modes are expected to leave such transients.