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In order to model the magnetic field amplification and particle acceleration that takes place in astrophysical shocks, we need a code that can efficiently model the large-scale structure of the shock, while still taking the kinetic aspect of non-thermal particles into account. Starting from the proven MPI-AMRVAC magnetohydrodynamics code we have created a code that combines the kinetic treatment of the Particle-in-Cell (PIC) method for non-thermal particles with the large-scale effects of grid-based hydrodynamics (MHD) to model the thermal plasma, including the use of adaptive mesh refinement. Using this code we simulate astrophysical shocks, varying the angle between the magnetic field and the shock to test our code against existing results and study both the evolution of the shock and the behaviour of non-thermal particles. We find that the combined PIC-MHD method can accurately recover the results that were previously obtained with pure PIC codes. Furthermore, the efficiency of the code allows us to explore the available parameter space to a larger degree than has been done in previous work. Our results suggest that efficient particle acceleration can take place in near-oblique shocks where the magnetic field makes a large angle with the direction of the flow.

Using a combined PIC-MHD code to simulate particle acceleration in astrophysical shocks