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

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.

14 pages, 11 figures

References in corpus (15)

• PLUTO: a Numerical Code for Computational Astrophysics
• Formation of Hard Power-laws in the Energetic Particle Spectra Resulting from Relativistic Magnetic Reconnection
• Numerical Tests of Fast Reconnection in Weakly Stochastic Magnetic Fields
• Modeling the Emission Processes in Blazars
• ECHO: an Eulerian Conservative High Order scheme for general relativistic magnetohydrodynamics and magnetodynamics
• Prompt GRB emission from gradual energy dissipation
• A kinetic approach to cosmic ray induced streaming instability at supernova shocks
• Multi-dimensional Numerical Scheme for Resistive Relativistic MHD
• Simulations of Ion Acceleration at Non-relativistic Shocks. III. Particle Diffusion
• Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions
• Particle acceleration by relativistic magnetic reconnection driven by kink instability turbulence in Poynting flux dominated jets
• Properties of the First-order Fermi acceleration in fast magnetic reconnection driven by turbulence in collisional MHD flows
• A Constrained Transport Method for the Solution of the Resistive Relativistic MHD Equations
• MHD simulations of three-dimensional Resistive Reconnection in a cylindrical plasma column
• Fast magnetic reconnection structures in Poynting-flux dominated jets

Cited by in corpus (1)

• Search for magnetic accretion in SW Sextantis systems