Modulational instability of finite amplitude dispersive Alfven waves

Details Modulational instability of finite amplitude dispersive Alfven waves Modulational instability of finite amplitude dispersive Alfven waves

Nov 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983jgr....88.9069s&link_type=abstract

Journal of Geophysical Research (ISSN 0148-0227), vol. 88, Nov. 1, 1983, p. 9069-9079.

Computer Science

Sound

91

Circular Polarization, Cosmic Plasma, Magnetohydrodynamic Stability, Magnetohydrodynamic Waves, Two Fluid Models, Wave Dispersion, Monochromatic Radiation, Perturbation Theory, Plane Waves, Plasma Waves, Solar Wind, Sound Waves

Scientific paper

The stability of a finite amplitude plane monochromatic circularly polarized Alfven wave is studied by using an approximate two-fluid model obtained by performing an amplitude and dual time scale expansion in which temporal changes, observed when moving with the wave, are assumed slow. The lowest order dispersive effects and coupling terms to sound waves are of the same order. A large-amplitude Alfven wave obeying an approximate dispersion relation is an exact solution of the resulting model equations. Small perturbations of this solution consisting of two sideband Alfven waves and a sound wave are then introduced. The resulting dispersion relation, which is of fourth order, is examined analytically for small wave amplitudes of the parent wave. It reveals different regions of stability and instability in a plot of wave number K0 of the unperturbed wave versus beta-0, the ratio of sound speed to Alfven speed. For long wave lengths, the left-hand polarized mode is found to be stable for beta-0 greater than 1 and the right-hand polarized mode for beta-0 less than 1. Modulational instability of the former mode occurs for beta-0 less than 1 and of the latter for beta-0 greater than 1. Decay instability is predicted near beta-0 = 0 and beta-0 = 1. Formulas for growth rates and unstable wave number bands are given.

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