Filamentation of dispersive Alfvén waves in density channels: Hall magnetohydrodynamics description

Abstract

Filamentation of dispersive Alfvén waves initiated by low or high density channels (depending on the plasma beta) is simulated numerically in the framework of ideal Hall magnetohydrodynamics, and asymptotically modeled with a two-dimensional nonlinear Schrödinger equation including a linear attracting potential. Compared with the dynamics in a homogeneous plasma, the phenomenon is accelerated and occurs for a broader range of parameters. In the case of an isolated channel with a width comparable to the pump wavelength, the transverse wave collapse can be replaced by a moderate amplification. In many cases, a relatively complex dynamics takes place, characterized by an oscillation between magnetic filaments and magnetic ribbons, leading to the formation of small scales at which dissipative effects could become relevant. Alfvén vortices, governed by the equations of the reduced magnetohydrodynamics, are also identified in the simulations, in spite of their small amplitude relative to the wave. The formation of structures under the effect of periodic or random distributions of low and high density channels is also discussed.