Particle-in-cell simulations of the tearing instability for relativistic pair plasmas

TL;DR

This study uses particle-in-cell simulations to investigate the relativistic tearing instability in pair plasmas, confirming theoretical predictions and exploring nonlinear evolution and transition regimes.

Contribution

It provides the first detailed simulation-based analysis of relativistic tearing instability in pair plasmas across various parameters, including nonlinear stages.

Findings

Growth rates match theoretical predictions when current sheet thickness exceeds Larmor radius.

Thinner current sheets exhibit growth rates consistent with the case where thickness equals Larmor radius.

Nonlinear evolution shows saturation and a rapid increase in growth rate at late stages.

Abstract

Two-dimensional particle-in-cell (PIC) simulations explore the collisionless tearing instability developing in a Harris equilibrium configuration in a pair (electron-positron) plasma, with no guide field, for a range of parameters from non-relativistic to relativistic temperatures and drift velocities. Growth rates match predictions of Zelenyi & Krasnosel'skikh (1979) modified for relativistic drifts by Hoshino (2020) as long as the assumption holds that the thickness $a$ of the current sheet is larger than the Larmor radius $\rho_L$, with the fastest growing mode at $ka \approx 1/\sqrt{3}$. Aside from confirming these predictions, we explore the transitions from thick to thin current sheets and from classical to relativistic temperatures. We show that for thinner current sheets ($a< \rho_L$), the growth rate matches the prediction for the case $a=\rho_L$. We also explore the nonlinear evolution of the modes. While the wave number with the fastest growth rate initially matches the prediction of Zelenyi & Krasnosel'skikh (1979), these modes saturate moving the dominant mode to lower wave numbers (especially for thick current sheets with low growth rates). Furthermore, at a late, non-linear stage, the growth rate (initially following the growth rate prediction proportional to $(\rho_L/a)^{3/2} < 1$) increases faster than exponentially, reaching a maximum growth rate equivalent to the linear growth rate prediction at $\rho_L/a = 1$, before eventually saturating.