Ab-initio Simulations of Electron Acceleration at Non-relativistic Collisionless Shocks*

Energetic charged particles (cosmic rays) are one of the main contributors to the nonthermal (NT) emissions across the universe. Diffusive shock acceleration (DSA) is a promising mechanism for particle acceleration at shocks, though the processes that inject particles into DSA are still unclear. To solve this problem, we have performed first-principles kinetic plasma simulations of collisionless shocks for a wide range of shock speeds and magnetizations. In this contribution, I will discuss under which conditions electrons participate in the DSA at quasi-parallel shocks and present a minimal model for electron DSA. The results are key to understand NT phenomenology of a variety of heliophysical/astrophysical sources that shine in NT radio, X-rays, and gamma-rays.