Nonlinear resonant absorption of fast magnetoacoustic waves in strongly anisotropic and dispersive plasmas

TL;DR

This paper develops a nonlinear theory for fast magnetoacoustic wave interactions in anisotropic, dispersive plasmas, revealing how dispersion reduces energy absorption and generates higher harmonics during wave resonance in a structured plasma environment.

Contribution

It extends previous nonlinear MHD wave theories to include fast wave interactions in inhomogeneous, dispersive plasmas, providing analytical solutions for energy absorption and harmonic generation.

Findings

Dispersion decreases energy absorption in the slow dissipative layer.

Higher harmonics are generated due to nonlinearity and dispersion.

Linear MHD accurately describes Alfvén resonance energy absorption.

Abstract

The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly anisotropic and dispersive plasmas, developed for slow resonance by Clack and Ballai [Phys. Plasmas, 15, 2310 (2008)] and Alfv\'en resonance by Clack \emph{et al.} [A&A,494, 317 (2009)], is used to study the weakly nonlinear interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar plasma. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localized slow or Alfv\'{e}n dissipative layer and are partly reflected, dissipated and transmitted by this region. The nonlinearity parameter defined by Clack and Ballai (2008) is assumed to be small and a regular perturbation method is used to obtain analytical solutions in the slow dissipative layer. The effect of dispersion in the slow dissipative layer is to further decrease the coefficient of energy absorption, compared to its standard weakly nonlinear counterpart, and the generation of higher harmonics in the outgoing wave in addition to the fundamental one. The absorption of external drivers at the Alfv\'{e}n resonance is described within the linear MHD with great accuracy.