Large-scale Compression Acceleration during Magnetic Reconnection in a Low-β Plasma

In solar flares and other astrophysical systems, a major challenge for solving the particle acceleration problem associated with magnetic reconnection is the enormous scale separation between kinetic scales and the observed reconnection scale. Because of this, it has been difficult to draw any definite conclusions by just using kinetic simulations. A particle acceleration model that solves the energetic particle transport equation can capture the main acceleration physics found in kinetic simulations and thus provide a practical way to make observable predictions and directly compare model results with observations. Here we study compression particle acceleration in magnetic reconnection by solving the Parker (diffusion-advection) transport equation using velocity and magnetic fields from two-dimensional magnetohydrodynamics (MHD) simulations of a low-beta high-Lundquist-number reconnection layer. We show that the compressible reconnection layer can give significant particle acceleration, leading to the formation of power-law particle energy distributions. We analyze the acceleration rate and find that the acceleration in the reconnection layer is a mixture of first- and second-order Fermi processes. When including a guide field, we find that the spectrum becomes steeper and both the power-law cutoff energy and maximum particle energy decrease as plasma becomes less compressible. This model produces a 2D particle distribution that one can use to generate a radiation map and directly compare with solar flare observations. This provides a framework to explain particle acceleration at large-scale astrophysical reconnection sites, such as solar flares.