Electron Acceleration at Quasi-parallel Nonrelativistic Shocks: A 1D Kinetic Survey

We present a survey of 1D kinetic particle-in-cell simulations of quasi-parallel nonrelativistic shocks to identify the environments favorable for electron acceleration. We explore an unprecedented range of shock speeds v sh approximate to 0.067-0.267c, Alfv & eacute;n Mach numbers MA=5-40 , sonic Mach numbers Ms=5-160 , as well as the proton-to-electron mass ratios m i/m e = 16-1836. We find that high Alfv & eacute;n Mach number shocks can channel a large fraction of their kinetic energy into nonthermal particles, self-sustaining magnetic turbulence and acceleration to larger and larger energies. The fraction of injected particles is less than or similar to 0.5% for electrons and approximate to 1% for protons, and the corresponding energy efficiencies are less than or similar to 2% and approximate to 10%, respectively. The extent of the nonthermal tail is sensitive to the Alfv & eacute;n Mach number; when MA less than or similar to 10 , the nonthermal electron distribution exhibits minimal growth beyond the average momentum of the downstream thermal protons, independently of the proton-to-electron mass ratio. Acceleration is slow for shocks with low sonic Mach numbers, yet nonthermal electrons still achieve momenta exceeding the downstream thermal proton momentum when the shock Alfv & eacute;n Mach number is large enough. We provide simulation-based parameterizations of the transition from thermal to nonthermal distribution in the downstream (found at a momentum around pi,e/mivsh approximate to 3mi,e/mi ), as well as the ratio of nonthermal electron to proton number density. The results are applicable to many different environments and are important for modeling shock-powered nonthermal radiation.