Parametric instabilities of parallel-propagating Alfven waves: Some analytical results

Journal Article · Mon Nov 01 04:00:00 EST 1993 · Journal of Geophysical Research

DOI:https://doi.org/10.1029/93JA02208· OSTI ID:146548

Jayanti, V; Hollweg, J V ^[1]

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1. Univ. of New Hampshire, Durham, NH (United States)

The authors consider the stability of a circularly polarized Alfven wave (the pump wave) which propagates parallel to the ambient magnetic field. Only parallel-propagating perturbations are considered, and they ignore dispersive effects due to the ion cylotron frequency. The dissipationless MHD equations are used throughout; thus possibly important effects arising from Landau and transient time damping are omitted. The authors derive a series of analytical approximations to the dispersion relation using A=({Delta}B/B{sub 0}){sup 2} as a small expansion parameter; {Delta}B is the pump amplitude, and B{sub 0} is the ambient magnetic field strength. They find that the plasma {beta}(the square of the ratio of the sound speed of the Alfven speed) plays a crucial role in determining the behavior of the parametric instabilities of the pump. If 0<{beta}<1 they find the familiar result that the pump decays into a forward propagating sound wave and a backward propagating Alfven wave with maximum growth rate {gamma}{sub max}{proportional_to} A{sup 1/2}, but {beta} cannot be too close to 0 or to 1. If {beta} {approx} 1, they find {gamma}{sub max}, {proportional_to}A{sup 3/4}; if {beta}>1, they find {gamma}{sub max} {proportional_to}A{sup 3/2}, while if {beta}{approx}0, they obtain {gamma}{sup max} {proportional_to}A{sup 1/3}; moreover, if {beta}{approx}0 there is a nearly purely growing instability. In contrast to the familiar decay instability, for which the backward propagating Alfven wave has lower frequency and wavenumber than the pump, they find that if {beta}{approx_gt}1 the instability is really a beat instability which is dominated by a transverse wave which is forward propagating and has frequency and wavenumber which are nearly twice the pump values. Only the decay instability for 0<{beta}<1 can be regarded as producing two recognizable normal modes, namely, a sound wave and an Aflven wave. 36 refs., 19 figs.

• Sponsoring Organization: USDOE
• OSTI ID: 146548
• Journal Information: Journal of Geophysical Research, Journal Name: Journal of Geophysical Research Journal Issue: A11 Vol. 98; ISSN JGREA2; ISSN 0148-0227
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALFVEN WAVES
DISPERSION RELATIONS
MAGNETOHYDRODYNAMICS
PARAMETRIC INSTABILITIES
POLARIZATION