A dynamical monte carlo simulation of a collisionless shock

We report results from a new time-dependent, self-consistent simulation of a plane-parallel collisionless shock, including the acceleration of energetic particles. In this simulation we model the basic physics of scattering off magnetic irregularities with a prescribed scattering algorithm. This algorithm simply requires isotropy and conservation of energy in a particle's local flow frame during a scattering. A single constant parameter, the scattering time, characterizes the scattering. Since the scattering time is taken to be constant and the same for all particles, this implies that a particle's mean free path is proportional to its velocity. The collective behavior of a large number of such particles models a collisionless fluid with a background magnetic field parallel to the shock normal. We begin the simulation with a gas of particles having both a thermal distribution and a net motion toward a massive reflecting wall. The wall, similar to a piston moving supersonically through a stationary gas, causes a shock wave to develop. The shock evolves and propagates across the box (away from the wall) in a configuration similar to that used in hybrid simulations. A power-law tail of accelerated particles develops as the shock evolves. Furthermore, the flow pattern is modified by the energetic particles, as seen in earlier hybrid simulations. We present time-dependent shock simulation results, including density and velocity profiles, phase-space particle plots, and spectra. We also present a few tests of the validity of this new method, as well as an analysis of the time-dependent evolution of the subshock.