Cosmic rays are charged particles that have been accelerated to high velocities as they cross astrophysical shocks. This acceleration process involves repeated interactions between the particles and the local magnetic field, which not only influence the velocity of the particles, but the morphology of the magnetic field, and therefore the shock structure, as well. 

In order to simulate the particle acceleration and the changes in the astrophysical shocks, we need a code that can efficiently model the large-scale structure of the shock, while still taking the small-scale  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 efficiency of grid-based hydrodynamics (MHD) to model the thermal plasma, including the use of adaptive mesh refinement for increased computational efficiency.

Using this code we simulate astrophysical shocks, varying both the Mach-number and 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  PIC-hybrid 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. Contrary to what was previously thought, 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.