Using combined Particles-in-MHD-Cells to model particle acceleration in astrophysical shocks

Astrophysical shocks can accelerate charged particles through diffusive shock acceleration. This process involves repeated shock crossings where the particle gains energy from collisions with the electromagnetic field. Eventually, these particles will reach relativistic speeds and can be observed as cosmic rays.

In order to simulate this process, we need a method that can handle both the large-scale structure of astrophysical shocks, as well as the behaviour of individual particles. We achieve this by combining the classical magnetohydrodynamics (MHD) and particle-in-cell (PIC) methods. This allows us to describe the thermal plasma of the shock through MHD, while simultaneously using PIC to follow the movement of non-thermal particles as they are accelerated. Our results show a complicated interaction that destabilizes the shock, reducing the efficiency with which particles can be accelerated.