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

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 $\ddot{I}{}_L$, 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 ($a<\ddot{I}{}_L$), the growth rate matches the prediction for the case $a=\ddot{I}{}_L$. 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 $(\ddot{I}{}_L/a{)}^{3/2}<1$) increases faster than exponentially, reaching a maximum growth rate equivalent to the linear growth rate prediction at $\ddot{I}{}_L/a=1$, before eventually saturating.

25 pages, 11 figures