Nonlinear effects in resonant layers in solar and space plasmas

TL;DR

This paper reviews recent theoretical advances in nonlinear magnetohydrodynamic waves in solar and space plasmas, focusing on resonant layers and their impact on wave behavior and plasma stability.

Contribution

It introduces new nonlinear effects in resonant layers, including mean flows, and derives governing equations using matched asymptotic expansions.

Findings

Nonlinear effects can cause variable amplitudes to exceed linear thresholds.

Derived jump conditions are crucial for understanding resonant absorption.

Nonlinearity can influence plasma stability and energy transfer.

Abstract

The present paper reviews recent advances in the theory of nonlinear driven magnetohydrodynamic (MHD) waves in slow and Alfven resonant layers. Simple estimations show that in the vicinity of resonant positions the amplitude of variables can grow over the threshold where linear descriptions are valid. Using the method of matched asymptotic expansions, governing equations of dynamics inside the dissipative layer and jump conditions across the dissipative layers are derived. These relations are essential when studying the efficiency of resonant absorption. Nonlinearity in dissipative layers can generate new effects, such as mean flows, which can have serious implications on the stability and efficiency of the resonance.