Nonlinear Alfvén waves: 1. Interactions between outgoing and ingoing waves according to an amplitude expansion
Abstract
We expand the compressible magnetohydrodynamic (MHD) equations in terms of the amplitude of first-order Alfvén waves. Incompressible MHD equations are treated as a special case. We examine the evolution of mildly oblique Alfvén waves consisting of forward and backward propagating waves so that these would correspond to the interactions of outgoing and ingoing Alfvén waves in the solar wind. We obtain the solutions of these equations through second order. We find and distinguish three types of second-order modes which have zero frequency and are generated in association with nonsecular interactions of mildly oblique first-order Alfvén waves. Two of these modes have wave vectors which are perpendicular to the background magnetic field. Both are associated with magnetic energy but they do not have kinetic energy.
- Publication:
-
Journal of Geophysical Research (Space Physics)
- Pub Date:
- May 2004
- DOI:
- 10.1029/2003JA010105
- Bibcode:
- 2004JGRA..109.5103V
- Keywords:
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- Interplanetary Physics: MHD waves and turbulence;
- Space Plasma Physics: Kinetic and MHD theory;
- Space Plasma Physics: Numerical simulation studies;
- Space Plasma Physics: Turbulence;
- Space Plasma Physics: Wave/particle interactions;
- Alfvén waves;
- zero-frequency modes