Structure and evolution of magnetohydrodynamic solitary waves with Hall and finite Larmor radius effects

TL;DR

This paper explores the structure, existence, and stability of nonlinear solitary waves in Hall-magnetohydrodynamics with finite Larmor radius effects, revealing new wave types and stability properties through numerical and linear analyses.

Contribution

It introduces a numerical method to locate solitary waves in Hall-MHD with finite Larmor effects and identifies new wave solutions not previously documented.

Findings

Existence of bright and dark solitary waves in specific parameter domains.

Some solitary waves exhibit robustness in their cores but have unstable tails.

Replacing the pressure model can suppress instabilities and enable long-term wave propagation.

Abstract

Nonlinear and low-frequency solitary waves are investigated in the framework of the one-dimensional Hall-magnetohydrodynamic model with finite Larmor effects and a double adiabatic model for plasma pressures. The organization of these localized structures in terms of the propagation angle with respect to the ambient magnetic field $\theta$ and the propagation velocity $C$ is discussed. There are three types of regions in the $\theta-C$ plane that correspond to domains where either solitary waves cannot exist, are organized in branches, or have a continuous spectrum. A numerical method valid for the two latter cases, that rigorously proves the existence of the waves, is presented and used to locate many waves, including bright and dark structures. Some of them belong to parametric domains where solitary waves were not found in previous works. The stability of the structures has been investigated by first performing a linear analysis of the background plasma state and second by means of numerical simulations. They show that the cores of some waves can be robust but, for the parameters considered in the analysis, the tails are unstable. The substitution of the double adiabatic model by evolution equations for the plasma pressures appears to suppress the instability in some cases and to allow the propagation of the solitary waves during long times.