Saturation of the asymmetric current filamentation instability under conditions relevant to relativistic shock precursors

TL;DR

This paper investigates the saturation mechanism of the asymmetric current filamentation instability in relativistic shock precursors, using large-scale simulations to identify the magnetic trapping criterion as key to understanding instability saturation in asymmetric plasma flows.

Contribution

It introduces a new saturation criterion based on magnetic trapping for asymmetric plasma flows, extending previous symmetric case analyses to more realistic astrophysical scenarios.

Findings

Saturation occurs when the quiver frequency of the dominant inertia component matches the instability growth rate.

Theoretical approximations for the saturation level are provided.

Results are applicable to relativistic shock physics and can be generalized to other plasma conditions.

Abstract

The current filamentation instability, which generically arises in the counterstreaming of supersonic plasma flows, is known for its ability to convert the free energy associated with anisotropic momentum distributions into kinetic-scale magnetic fields. The saturation of this instability has been extensively studied in symmetric configurations where the interpenetrating plasmas share the same properties (velocity, density, temperature). In many physical settings, however, the most common configuration is that of asymmetric plasma flows. For instance, the precursor of relativistic collisionless shock waves involves a hot, dilute beam of accelerated particles reflected at the shock front and a cold, dense inflowing background plasma. To determine the appropriate criterion for saturation in this case, we have performed large-scale 2D particle-in-cell simulations of counterstreaming electron-positron pair and electron-ion plasmas. We show that, in interpenetrating pair plasmas, the relevant criterion is that of magnetic trapping as applied to the component (beam or plasma) that carries the larger inertia of the two; namely, the instability growth suddenly slows down once the quiver frequency of those particles equals or exceeds the instability growth rate. We present theoretical approximations for the saturation level. These findings remain valid for electron-ion plasmas provided that electrons and ions are close to equipartition in the plasma flow of larger inertia. Our results can be directly applied to the physics of relativistic, weakly magnetized shock waves, but they can also be generalized to other cases of study.