First-principles simulations of electron acceleration at non-relativistic shocks

The energetic charged particles are the prime sources of nonthermal radio, X-rays, and gamma rays, which are emitted by most astrophysical objects. One of the efficient sites that can produce these nonthermal particles is the shocks. Although diffusive shock acceleration (DSA) is the promising mechanism for particle acceleration, whether the processes that promote particles to DSA act similarly for electrons and protons/ions is still not well understood. To solve this puzzle, we have performed fully kinetic non-relativistic shock simulations for an unprecedented range of parameters. In this talk, I will demonstrate the results of these simulations with the help of test-particle analysis and present a minimal model for electron DSA. Finally, I will discuss the implications of our results to different environments from the planetary bow shocks to galaxy clusters.