Energy dynamics and current sheet structure in fluid and kinetic simulations of decaying magnetohydrodynamic turbulence

TL;DR

This study compares fluid and kinetic simulations of decaying MHD turbulence, showing they produce similar large-scale energy decay and current sheet structures, while capturing different small-scale dissipation mechanisms.

Contribution

It demonstrates that kinetic simulations can replicate large-scale MHD turbulence dynamics and accurately model small-scale kinetic physics simultaneously.

Findings

Energy decay rates are similar in both codes.

Current sheet dimensions agree between models.

Kinetic dissipation is consistent with collisionless damping mechanisms.

Abstract

Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfv\'{e}n waves, which interact and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of $k_{\perp}^{-1.3}$. The kinetic code shows a spectral slope of $k_{\perp}^{-1.5}$ for smaller simulation domain, and $k_{\perp}^{-1.3}$ for larger domain. We estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. The length scales linearly with the driving scale of the turbulence. In the fluid code, their thickness is determined by the grid resolution as there is no explicit diffusivity. In the kinetic code, their thickness is very close to the skin-depth, irrespective of the grid resolution. This work shows that kinetic codes can reproduce the MHD inertial range dynamics at large scales, while at the same time capturing important kinetic physics at small scales.