Large-scale Compression Acceleration during Magnetic Reconnection in a Low-$\beta$ Plasma

In solar flares and other astrophysical systems, a major challenge for solving particle acceleration problem associated with magnetic reconnection is the enormous scale separation between kinetic scales and observed reconnection scale. Because of this, it has been difficult to draw any definite conclusions by just using kinetic simulations. Particle acceleration model that solves 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 Parker (diffusion-advection) transport equation using velocity and magnetic fields from two-dimensional high-Lundquist-number magnetohydrodynamics (MHD) simulations of a low-$\beta$ 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 order and second order Fermi processes. When including a guide field, we find the spectrum becomes steeper and both the power-law cutoff energy and maximum particle energy decrease as plasma becomes less compressible. This model produces 2D particle distribution that one can use to generate 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.