Multi-hierarchy simulation of Riemann problem for reconnection exhausts

Abstract

Magnetic reconnection drives a wide range of astrophysical plasma phenomena, including solar flares, by converting magnetic energy into plasma energy through changes in magnetic field topology. Petschek reconnection is a magnetohydrodynamic (MHD) model in which magnetic field lines reconnect within a localized diffusion region, and a pair of switch-off slow shocks forms outside this region, enabling efficient energy conversion. Whether this picture remains valid when kinetic effects are included remains an open question. In this study, we examine the formation and properties of slow shocks associated with reconnection exhausts by solving a two-dimensional Riemann problem using a multi-hierarchy framework that couples MHD and particle-in-cell (PIC) simulations. We find that a slow shock close to the switch-off limit forms in the MHD domain even when slow shock formation is suppressed in the PIC domain, and that this behavior is insensitive to the size of the PIC domain. The formation of the slow shock further promotes plasma isotropization within the PIC domain. These results suggest that Petschek-like reconnection remains viable in collisionless-collisional systems, such as solar flares, where temperature anisotropy appears to be relaxed far from the reconnection region.

Figures (9)

• Figure 1: Spatial profiles of $j_{z}$ from ideal MHD and multi-hierarchy simulations at $\Omega_{\rm ci} t = 200.0$. PIC data is used between the black lines, and MHD data is used outside. $j_{z}$ is normalized by $B_{\rm 0} / \mu_{\rm 0} \lambda_{\rm i}$. The horizontal and vertical axes are normalized by $\lambda_{\rm i}$.
• Figure 2: $y - t$ diagrams of $j_{z}$ and $\nabla \cdot \bm{v}$ averaged in the $x$ direction. The panels show the results for $N_{y, \rm PIC} = 0$ (ideal MHD), $100, 200, 400$, and $800$. $j_{z}$ is normalized by $B_{\rm 0} / \mu_{\rm 0} \lambda_{\rm i}$. $\bm{v}$ is calculated using the zeroth and first moment of ions and electrons. The horizontal and vertical axes are normalized by $\lambda_{\rm i}$ and $\Omega_{\rm ci}^{-1}$ respectively.
• Figure 3: Snapshots of magnetic energy $B^2 / 2 \mu_{\rm 0}$ from ideal MHD and multi-hierarchy simulations at $\Omega_{\rm ci} t = 100.0, 500.0, 1000.0$, and $1500.0$. The magnetic field from the MHD data is only used, and averaged in the x direction. The horizontal axis is normalized by $\lambda_{\rm i}$.
• Figure 4: Top panel: Six snapshots of the firehose stability parameter $\epsilon$ from the multi-hierarchy simulation with $N_{y, \rm PIC} = 800$. The horizontal axis is normalized by $\lambda_{\rm i}$. Middle panel: Upstream--downstream Mach number difference $M_{\rm n1}^2 - M_{\rm n2}^2$ derived from the Rankine--Hugoniot relations for anisotropic plasmas. Subscripts 1 and 2 denote the upstream and downstream states, respectively. Bottom panel: Eight snapshots of the $M_{\rm n}$ in the MHD domain for the same simulation. The horizontal axis is normalized by $\lambda_{\rm i}$.
• Figure 5: Top panel: Six snapshots of the firehose stability parameter $\epsilon$ in the multi-hierarchy simulation with $N_{y, \rm PIC} = 800$. The horizontal axis normalized by $\lambda_{\rm i}$. Bottom panel: Spatial profile of $j_z$ at $\Omega_{\rm ci} t = 1200.0$ for the same simulation. The black solid curve traces the magnetic field line, and the black arrow indicates the bulk velocity. The current density $j_z$ is normalized by $B_0 / \mu_0 \lambda_{\rm i}$. Horizontal and vertical axes are normalized by $\lambda_{\rm i}$.