Nonlinear mirror instability

TL;DR

This paper develops a new asymptotic theory for the early nonlinear evolution of the mirror instability in weakly collisional plasmas, revealing secular growth of magnetic perturbations due to particle trapping, which advances understanding of plasma stability.

Contribution

It introduces a novel asymptotic framework for the nonlinear phase of the mirror instability, showing that magnetic perturbations grow secularly rather than saturate quasilinearly, and connects theory with recent simulation results.

Findings

Magnetic perturbations grow as δB/B ∝ t^{2/3} due to particle trapping.

The theory explains recent collisionless simulation behaviors.

Provides a foundation for nonlinear mirror dynamics up to δB/B = O(1).

Abstract

Slow dynamical changes in magnetic-field strength and invariance of the particles' magnetic moments generate ubiquitous pressure anisotropies in weakly collisional, magnetized astrophysical plasmas. This renders them unstable to fast, small-scale mirror and firehose instabilities, which are capable of exerting feedback on the macroscale dynamics of the system. By way of a new asymptotic theory of the early nonlinear evolution of the mirror instability in a plasma subject to slow shearing or compression, we show that the instability does not saturate quasilinearly at a steady, low-amplitude level. Instead, the trapping of particles in small-scale mirrors leads to nonlinear secular growth of magnetic perturbations, $\delta B/B \propto t^{2/3}$. Our theory explains recent collisionless simulation results, provides a prediction of the mirror evolution in weakly collisional plasmas and establishes a foundation for a theory of nonlinear mirror dynamics with trapping, valid up to $\delta B/B =O(1)$.