Numerical investigation of kinetic turbulence in relativistic pair plasmas I: Turbulence statistics

TL;DR

This study uses large-scale particle-in-cell simulations to analyze kinetic turbulence in relativistic pair plasmas, revealing turbulence statistics consistent with MHD predictions and evidence of a kinetic cascade at small scales.

Contribution

First detailed kinetic turbulence statistics in relativistic pair plasmas from high-resolution PIC simulations, linking kinetic and MHD turbulence features.

Findings

Magnetic energy spectrum follows a -5/3 power law.

Fluctuation anisotropy aligns with critical balance theory.

Evidence of a kinetic cascade at sub-Larmor scales.

Abstract

We describe results from particle-in-cell simulations of driven turbulence in collisionless, magnetized, relativistic pair plasma. This physical regime provides a simple setting for investigating the basic properties of kinetic turbulence and is relevant for high-energy astrophysical systems such as pulsar wind nebulae and astrophysical jets. In this paper, we investigate the statistics of turbulent fluctuations in simulations on lattices of up to $1024^3$ cells and containing up to $2 \times 10^{11}$ particles. Due to the absence of a cooling mechanism in our simulations, turbulent energy dissipation reduces the magnetization parameter to order unity within a few dynamical times, causing turbulent motions to become sub-relativistic. In the developed stage, our results agree with predictions from magnetohydrodynamic turbulence phenomenology at inertial-range scales, including a power-law magnetic energy spectrum with index near $-5/3$, scale-dependent anisotropy of fluctuations described by critical balance, log-normal distributions for particle density and internal energy density (related by a $4/3$ adiabatic index, as predicted for an ultra-relativistic ideal gas), and the presence of intermittency. We also present possible signatures of a kinetic cascade by measuring power-law spectra for the magnetic, electric, and density fluctuations at sub-Larmor scales.