Mode decomposition scheme for ideal magnetohydrodynamic plane waves in space-time coordinates

Abstract

Exact nonsinusoidal plane wave solutions of the linearized equations of ideal magnetohydrodynamics are used to develop a decomposition scheme for extracting the forward and backward propagating components of the fast, slow, and Alfvén modes from measured data. The decomposition technique is formulated in the space-time domain for waves propagating in one direction. The different wave modes are extracted by means of projection operators that are expressed in matrix form. Because the elements of these matrices are constants, the same projection operators can be used to obtain the mode decomposition in the frequency (Fourier) domain. The projection operators are identical to those obtained by Glassmeier et al. (1995) although they are derived here by different means. In the case of wave propagation parallel or perpendicular to the background magnetic field the wave modes are degenerate and require separate treatment. These special cases are included in the present analysis so the resulting decomposition scheme encompasses all possible propagation directions.