Slowdown of interpenetration of two counterpropagating plasma slab due to collective effects

TL;DR

This study uses kinetic plasma simulations to show how electromagnetic instabilities slow down colliding plasma clouds by transferring momentum from forward flow to transverse directions, with the slowdown depending on the magnetic energy saturation.

Contribution

It provides a detailed analysis of the slowdown process of plasma flows due to collective electromagnetic effects, quantifying the velocity reduction and timescales involved.

Findings

Plasma clouds slow down by approximately a factor of 1/√3 due to electromagnetic instabilities.

The slowdown timescale is about ten times the instability growth time.

Flow slowdown occurs if plasma slab length exceeds the product of initial flow speed and slowdown time.

Abstract

The nonlinear evolution of electromagnetic instabilities driven by the interpenetration of two $e^-\,e^+$ plasma clouds is explored using {\it ab initio} kinetic plasma simulations. We show that the plasma clouds slow down due to both oblique and Weibel generated electromagnetic fields, which deflect the particle trajectories, transferring bulk forward momentum into transverse momentum and thermal velocity spread. This process causes the flow velocity $v_{inst}$ to decrease approximately by a factor of $\sqrt{1/3}$ in a time interval $\Delta t_{\alpha B} \omega_p \sim c/(v_{fl}\sqrt{\alpha_B})$, where $\alpha_B$ is the magnetic equipartition parameter determined by the non-linear saturation of the instabilities, $v_{fl}$ is the initial flow speed, and $\omega_p$ is the plasma frequency. For the $\alpha_B$ measured in our simulations, $\Delta t_{\alpha B}$ is close to $10 \times$ the instability growth time. We show that as long as the plasma slab length $L > v_{fl} \Delta t_{\alpha B}$, the plasma flow is expected to slow down by a factor close to $1/\sqrt{3}$.