On the Impact of the Numerical Method on Magnetic Reconnection and Particle Acceleration -- I. The MHD case

TL;DR

This study uses 2D MHD simulations to analyze how numerical methods affect magnetic reconnection rates and particle acceleration, revealing convergence conditions and the robustness of acceleration processes across different numerical schemes.

Contribution

It provides a detailed analysis of numerical convergence in MHD simulations of tearing instability and particle acceleration, highlighting the dependence on grid resolution and Lundquist number.

Findings

Reconnection rate converges only at finite Lundquist numbers and sufficient grid resolution.

Particle acceleration is largely independent of numerical details in nonlinear stages.

Power-law index of accelerated particles converges to approximately 1.7 at high Lundquist numbers.

Abstract

We present 2D MHD numerical simulations of tearing-unstable current sheets coupled to a population of non-thermal test-particles, in order to address the problem of numerical convergence with respect to grid resolution, numerical method and physical resistivity. Numerical simulations are performed with the PLUTO code for astrophysical fluid dynamics through different combinations of Riemann solvers, reconstruction methods, grid resolutions at various Lundquist numbers. The constrained transport method is employed to control the divergence-free condition of magnetic field. Our results indicate that the reconnection rate of the background tearing-unstable plasma converges only for finite values of the Lundquist number and for sufficiently large grid resolutions. In general, it is found that (for a 2nd-order scheme) the minimum threshold for numerical convergence during the linear phases requires the number of computational zones covering the initial current sheet width to scale roughly as $\sim \sqrt{\bar{S}}$, where $\bar{S}$ is the Lundquist number defined on the current sheet width. On the other hand, the process of particle acceleration is found to be nearly independent of the underlying numerical details inasmuch as the system becomes tearing-unstable and enters in its nonlinear stages. In the limit of large $\bar{S}$, the ensuing power-law index quickly converge to $p \approx 1.7$, consistently with the fast reconnection regime.