On electron acceleration by mildly-relativistic shocks: PIC simulations

Abstract

Radio observations revealed a presence of relativistic supernovae - a class of objects intermediate between the regular supernovae and gamma-ray bursts. The typical Lorentz-factors of plasma flows in relativistic radio-bright supernovae were estimated to be about 1.5. Mildly relativistic shocks in electron-ion plasmas are known to efficiently accelerate radio-emitting electrons if the shock is subluminous. The inclination angle of the velocity of subluminous shock to the ambient magnetic field should be below a critical angle which depends on the Mach number and the plasma magnetization parameter. In this paper we present particle-in-cell modeling of electron acceleration by mildly-relativistic collisionless shock of different obliquity in a plasma with ratio of the magnetic energy to the bulk kinetic energy σ ≈ 0.004 which is of interest for the relativistic supernovae modeling. It was shown earlier that a development of the ion scale Bell-type instability in electron-ion relativistic shock may have a strong influence on the electron injection and acceleration. In the time period of about (ωpi is the ion plasma frequency) after the shock initialization the magnetic field fluctuations generated by Bell’s instability may significantly decreases number of accelerated electrons even in a sub-luminous shock. We study here the evolution of the electron spectra of subluminous shocks of different obliquity. This is important to for modeling of synchrothron spectra from relativistic supernovae.