Three criteria for particle acceleration in collisionless shocks

Collisionless shocks have been the subject on many studies in recent years, due to their ability to accelerate particles. In order to do so, a shock must fulfill three criteria. First, it must be strong enough to accelerate particles efficiently. Second, both the upstream and the downstream must be collisionless. Third, the shock front must be surrounded by electromagnetic turbulence capable of scattering particles back and forth. We here consider the encounter of two identical plasma shells with initial density, temperature, and velocity n ₀ , T ₀ , v ₀ , respectively. We translate the three criteria to the corresponding requirements on these parameters. A non-trivial map of the allowed region for particle acceleration emerges in the (n ₀ , T ₀ , v ₀ ) phase space, especially at low velocities or high densities. We first assess the case of pair plasma shells, before we turn to electrons/protons.