In very many astronomical systems, ranging in scale from planetary magnetospheres to clusters of galaxies, we see evidence of charged particles with energies very much higher than those of the bulk thermal distributions in these systems. This evidence takes the form both of direct observations (cosmic rays), observations of secondary non-thermal electromagnetic radiation (synchrotron, inverse Compton, Bremstrahlung, neutral pion decay etc) and potentially in the near future observation of high-energy secondary neutrinos produced by these particles. Understanding the mechanisms that accelerate these particles, and the processes by which they generate the observed secondary signals, is the aim of theoretical high-energy non-thermal astrophysics. A primary mechanism is though to be a variant of Fermi acceleration associated with strong collisionless shock waves and indeed at the phenomenological level there is a clear association between shock waves and non-thermal signatures in systems as diverse as the solar wind, supernova remnants, jets from active galactic nuclei and intracluster shocks in the intergalactic medium.

This work relies heavily on a combination of theoretical models and numerical simulations. It sits at the intersection of plasma physics with cosmic ray studies and high-energy astrophysics.