What regulates electron injection in diffusive shock acceleration?

Using fully kinetic particle-in-cell simulations, we study electron acceleration at non-relativistic quasi-parallel shocks for a wide range of shock speeds and magnetizations. We single out the necessary steps that lead to electron injection into diffusive shock acceleration and develop a minimal model that accounts for the trends observed in simulations. These scalings are key to understand the nonthermal phenomenology of a variety of heliophysical and astrophysical collisionless shocks.