Beat, modulational, and decay instabilities of a circularly polarized Alfven wave

Physics – Plasma Physics

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Beat Frequencies, Circular Polarization, Decay, Electromagnetic Pumps, Magnetohydrodynamic Stability, Magnetohydrodynamic Waves, Modulation, Sidebands, Wave Dispersion, Cyclotron Frequency, Interplanetary Magnetic Fields, Interplanetary Medium, Plasma Physics, Plasma Pressure, Solar Wind, Two Fluid Models

Scientific paper

A circulary polarized low-frequency electomagnetic pump wave propagating along an ambient magnetic field is known to be unstable to the growth of several parallel-propagating parametric instabilties. If ion-cyclotron effects are retained in a two-fluid description, the dispersion relation is a sixth-order polynomial. We present a series of new analytical approximations to this dispersion relation. We emphasize new results for the beat instability that occurs as an interaction of the forward propagating upper sideband with the backward propagating lower sideband. The nature of the beat instability depends on beta = (vsound/vA2 and on the sense of polarization of the pump wave. The beat and decay instabilities can occur together if the pump is left-handed (i.e., ion resonant) and if beta is less than or approximately 1, but they cannot occur together if the pump is right-handed. For a left-handed pump the beat mode is the only instability if beta is greater than or approximately 1. If the pump is right-handed and beta is greater than or approximately 1, then the beat instability exists only when the pump amplitude exceeds a threshold value, and the beat will be the only instability if the pump amplitude is large enough to stabilize the modulational instability. If the pump is left-handed and beta is less than or approximately 1, then the beat mode is stabilized when the pump amplitude becomes sufficiently large. The beat instability primarily produces a forward propagating transverse wave in the upper sideband. Thus if beta is greater than or approximately 1, the instabilities considered here do not produce the backward propagating waves which are thought to affect turbulence and the evolution of cross helicity in the solar wind. New analytical results are presented also for the decay and modulational instabilites when beta is approximately equal to 1.

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