Ion acceleration processes at reforming collisionless shocks
  The identification of pre-acceleration mechanisms for cosmic ray ions in supernova remnant shocks is an important problem in astrophysics. Recent particle-in-cell (PIC) shock simulations have shown that inclusion of the full electron kinetics yields non-time-stationary solutions, in contrast to previous hybrid (kinetic ions, fluid electrons) simulations. Here, by running a PIC code at high phase space resolution, ion acceleration mechanisms associated with the time dependence of a supercritical collisionless perpendicular shock are examined. In particular the components of $\int \mathbf{F} \cdot \mathbf{v} dt$ are analysed along trajectories for ions that reach both high and low energies. Selection mechanisms for the ions that reach high energies are also examined. In contrast to quasi-stationary shock solutions, the suprathermal protons are selected from the background population on the basis of the time at which they arrive at the shock, and thus are generated in bursts. 
R. E. Lee, S. C. Chapman, R. O. Dendy