Plasmoid statistics in relativistic magnetic reconnection

TL;DR

This paper investigates the size and momentum distributions of plasmoids in relativistic magnetic reconnection using a Monte Carlo model benchmarked against PIC simulations, revealing power-law behaviors and their dependence on plasma parameters.

Contribution

It introduces a Monte Carlo simulation approach to study plasmoid distributions, providing analytical and numerical insights into their power-law slopes and dependence on plasma magnetization.

Findings

Plasmoid size distribution follows a power law, $N(w) \\propto w^{-\\chi}$.

Power law slope $\\chi$ depends linearly on the ratio of acceleration to growth rates.

Slope $\\chi$ decreases from ~2 to ~1.3 as plasma magnetization increases from 3 to 50.

Abstract

Plasmoids, quasi-spherical regions of plasma containing magnetic fields and high-energy particles, are a self-consistent by-product of the reconnection process in the relativistic regime. Recent two-dimensional particle-in-cell (PIC) simulations have shown that plasmoids can undergo a variety of processes (e.g. mergers, bulk acceleration, growth, and advection) within the reconnection layer. We developed a Monte Carlo (MC) code, benchmarked with the recent PIC simulations, to examine the effects of these processes on the steady-state size and momentum distributions of the plasmoid chain. The differential plasmoid size distribution is shown to be a power law, $N(w)\propto w^{-\chi}$, ranging from a few plasma skin depths to $\sim 0.1$ of the reconnection layer's length. We demonstrate numerically and analytically that the power law slope $\chi$ is linearly dependent upon the ratio of the plasmoid acceleration and growth rates and that it slightly decreases (from $\sim 2$ to $\sim 1.3$) with increasing plasma magnetization (from 3 to 50). We perform a detailed comparison of our results with those of recent PIC simulations and briefly discuss the astrophysical implications of our findings through the representative case of flaring events from blazar jets.