Nonlinear dynamics of the ion Weibel-filamentation instability: an analytical model for the evolution of the plasma and spectral properties

TL;DR

This paper develops an analytical model for the nonlinear evolution of the ion Weibel-filamentation instability, combining kinetic theory and filament coalescence, validated by particle-in-cell simulations, to better understand collisionless shock formation.

Contribution

It introduces a self-consistent analytical model for the nonlinear phase of the ion Weibel instability, incorporating current filament coalescence and electron screening effects.

Findings

Model predicts ion isotropization stages.

Electron screening influences simulation outcomes.

Analytical solutions match simulation results.

Abstract

We present a predictive model of the nonlinear phase of the Weibel instability induced by two symmetric, counter-streaming ion beams in the non-relativistic regime. This self-consistent model combines the quasilinear kinetic theory of Davidson et al. [Phys. Fluids 15, 317 (1972)] with a simple description of current filament coalescence. It allows us to follow the evolution of the ion parameters up to a stage close to complete isotropization, and is thus of prime interest to understand the dynamics of collisionless shock formation. Its predictions are supported by 2-D and 3-D particle-in-cell simulations of the ion Weibel instability. The derived approximate analytical solutions reveal the various dependencies of the ion relaxation to isotropy. In particular, it is found that the influence of the electron screening can affect the results of simulations using an unphysical electron mass.