Articles | Volume 32, issue 12
Regular paper
09 Dec 2014
Regular paper |  | 09 Dec 2014

Energy exchange and wave action conservation for magnetohydrodynamic (MHD) waves in a general, slowly varying medium

A. D. M. Walker

Abstract. Magnetohydrodynamic (MHD) waves in the solar wind and magnetosphere are propagated in a medium whose velocity is comparable to or greater than the wave velocity and which varies in both space and time. In the approximation where the scales of the time and space variation are long compared with the period and wavelength, the ray-tracing equations can be generalized and then include an additional first-order differential equation that determines the variation of frequency. In such circumstances the wave can exchange energy with the background: wave energy is not conserved. In such processes the wave action theorem shows that the wave action, defined as the ratio of the wave energy to the frequency in the local rest frame, is conserved. In this paper we discuss ray-tracing techniques and the energy exchange relation for MHD waves. We then provide a unified account of how to deal with energy transport by MHD waves in non-uniform media. The wave action theorem is derived directly from the basic MHD equations for sound waves, transverse Alfvén waves, and the fast and slow magnetosonic waves. The techniques described are applied to a number of illustrative cases. These include a sound wave in a medium undergoing a uniform compression, an isotropic Alfvén wave in a steady-state shear layer, and a transverse Alfvén wave in a simple model of the magnetotail undergoing compression. In each case the nature and magnitude of the energy exchange between wave and background is found.

Short summary
The equation for conservation of wave action is explicitly derived for magnetohydrodynamic waves in a plasma that varies slowly in space and time. Together with generalized ray-tracing equations, it is equivalent to a WKBJ solution of the problem and allows the computation of energy exchange between wave and background plasma as well as the variation of the amplitudes of the field components along the ray. The method is illustrated by application to simple examples.