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

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 $ka\approx 1\mathrm{/}\sqrt{3}$. 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 $({\rho }_L\mathrm{/}a{)}^{3\mathrm{/}2}<1$) increases faster than exponentially, reaching a maximum growth rate equivalent to the linear growth rate prediction at ${\rho }_L\mathrm{/}a=1$, before eventually saturating.