The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation‐theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave–wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the perturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave–wave resonance condition which, in turn, causes the wave amplitude to cease its growth.
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July 1989
Research Article|
July 01 1989
Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities
M. Hoshino;
M. Hoshino
Code 692, NASA‐GSFC, Greenbelt, Maryland 20771
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M. L. Goldstein
M. L. Goldstein
Code 692, NASA‐GSFC, Greenbelt, Maryland 20771
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Phys. Fluids B 1, 1405–1415 (1989)
Article history
Received:
December 20 1988
Accepted:
March 22 1989
Citation
M. Hoshino, M. L. Goldstein; Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities. Phys. Fluids B 1 July 1989; 1 (7): 1405–1415. https://doi.org/10.1063/1.858971
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