Modulation of kinetic Alfv\'en waves in an intermediate low-beta magnetoplasma

TL;DR

This paper investigates how nonlinear kinetic Alfvén waves behave in a low-beta magnetoplasma, focusing on their amplitude modulation, stability, and the formation of solitons, with implications for space plasma phenomena.

Contribution

It derives a nonlinear Schrödinger equation for KAW envelopes in low-beta plasmas and analyzes the conditions for modulational instability and soliton formation.

Findings

KAWs can form bright envelope solitons or damp depending on the ratio of Alfvén to ion-acoustic speeds.

The parameter alpha influences the stability domains and MI growth rates.

Results are relevant for understanding wave dynamics in space plasmas like solar winds.

Abstract

We study the amplitude modulation of nonlinear kinetic Alfv{\'e}n waves (KAWs) in an intermediate low-beta magnetoplasma. Starting from a set of fluid equations coupled to the Maxwell's equations, we derive a coupled set of nonlinear partial differential equations (PDEs) which govern the evolution of KAW envelopes in the plasma. The modulational instability (MI) of such KAW envelopes is then studied by a nonlinear Schr{\"o}dinger (NLS) equation derived from the coupled PDEs. It is shown that the KAWs can evolve into bright envelope solitons, or can undergo damping depending on whether the characteristic ratio $(\alpha)$ of the Alfv{\'e}n to ion-acoustic (IA) speeds remains above or below a critical value. The parameter $\alpha$ is also found to shift the MI domains around the $k_xk_z$ plane, where $k_x~(k_z)$ is the KAW number perpendicular (parallel) to the external magnetic field. The growth rate of MI, as well as the frequency shift and the energy transfer rate, are obtained and analyzed. The results can be useful for understanding the existence and formation of bright and dark envelope solitons, or damping of KAW envelopes in space plasmas, e.g., interplanetary space, solar winds etc.