Nonlinear dispersive waves in a Hall plasma with a finite conductivity

Abstract

The study of nonlinear magnetosonic waves in a turbulent plasma is extended to include the effects of the Hall term. The turbulence and Hall effect are characterized by an effective electrical conductivity and an ion gyrofrequency respectively. It is shown that the magnetosonic waves are governed by a nonlinear equation which can be considered as the generalization of a Korteweg & de Vries (1895) equation with dispersion. For a stationary solution two cases are considered in detail: (a) an unperturbed magnetic field is almost parallel to a wave vector, and (b) they are almost perpendicular. In the case (a) it is shown that the presence of the Hall term can lead to an oscillatory solution which decays due to the finite conductivity. In the second case the Hall effect does not affect the monotonous character of a decaying Taylor-shock profile.