Phase slips and dissipation of Alfvenic intermediate shocks and solitons

Abstract

The time evolution of a rotational discontinuity, characterized by a change of the magnetic-field direction by an angle Δθ such that π<|Δθ|<2π and no amplitude variation, is considered in the framework of asymptotic models that, through reductive perturbative expansions, isolate the dynamics of parallel or quasi-parallel Alfvén waves. In the presence of viscous and Ohmic dissipation, and for a zero or sufficiently weak dispersion (originating from the Hall effect), an intermediate shock rapidly forms, steepens and undergoes reconnection through a quasi gradient collapse, leading to a reduction of |Δθ| by an amount of 2π, which can be viewed as the breaking of a topological constraint. Afterwards, as |Δθ|<π, the intermediate shock broadens and slowly dissipates. In the case of a phase jump |Δθ|>3π, which corresponds to a wave train limited on both sides by uniform fields, a sequence of such reconnection processes takes place. Differently, in the presence of a strong enough dispersion, the rotational discontinuity evolves, depending on the sign of Δθ, to a dark or bright soliton displaying a 2π phase variation. The latter is then eliminated, directly by reconnection in the case of a dark soliton, or through a more complex process involving a quasi amplitude collapse in that of a bright soliton. Afterwards, the resulting structure is progressively damped. For a prescribed initial rotational discontinuity, both quasi gradient and amplitude collapses lead to a sizeable energy decay that in the collisional regime is independent of the diffusion coefficient η but requires a time scaling like 1/η. In the non-collisional regime where dissipation originates from Landau resonance, the amount of dissipated energy during the event is independent of the plasma β, but the process becomes slower for smaller β.