  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.
