Parametric Instabilities in Shallow Water Magnetohydrodynamics Of Astrophysical Plasma in External Magnetic Field

TL;DR

This paper investigates parametric instabilities and wave interactions in shallow water magnetohydrodynamics of astrophysical plasma under an external magnetic field, revealing new decay and amplification mechanisms.

Contribution

It introduces a novel analysis of three-wave nonlinear interactions and instability mechanisms in shallow water MHD with a vertical magnetic field, using asymptotic multiscale methods.

Findings

Identified four types of decay instabilities among magneto-Poincare and magnetostrophic waves.

Derived interaction equations for multiple wave interactions in the plasma layer.

Calculated growth rates of instabilities and amplification factors for different wave processes.

Abstract

This letter discusses rotating magnetohydrodynamics (MHD) of a thin layer of astrophysical plasma. To describe a thin plasma layer with a free surface in a vertical external magnetic field we use the shallow water ap- proximation. The presence of a vertical magnetic field essentially changed the wave processes dynamics in astrophysical plasma compared to the neu- tral uid and plasma layer in a thoroidal magnetic field. In present case thre are three-waves nonlinear interactions. Using the asymptotic mul- tiscale we deduced nonlinear wave packets interaction equations: three magneto-Poincare waves interaction, three magnetostrophic waves inter- action, the interaction of two magneto-Poincare and one magnetostrophic wave and two magnetostrophic and one magneto-Poincare wave interac- tion. The existence of decay instabilities and parametric amplifications is predicted. We found following four types of decay instabilities: magneto- Poincare wave decays into two magneto-Poincare waves, magnetostrophic wave decays into two magnetostrophic waves, magneto-Poincare wave de- cays into one magneto-Poincare wave and one magnetostrophic wave, magnetostrophic wave decays into one magnetostrophic wave and one magneto-Poincare wave. Also following mechanisms of parametric amplifications were found: parametric amplification of magneto-Poincare waves, parametric amplification of magnetostrophic waves, magneto-Poincare wave amplification in magnetostrophic wave presence nd magnetostrophic wave amplification in magneto-Poincare wave presence. The instabilities growth rates and parametrical amplifications factors were found respectively.