Surfatron and stochastic acceleration of electrons in astrophysical plasmas

Electron acceleration by large amplitude electrostatic waves in astrophysical plasmas is studied using particle-in-cell (PIC) simulations. The waves are excited initially at the electron plasma frequency ω_pe by a Buneman instability driven by ion beams: the parameters of the ion beams are appropriate for high Mach number astrophysical shocks, such as those associated with supernova remnants (SNRs). If ω_pe is much higher than the electron cyclotron frequency Ω_e, the linear phase of the instability does not depend on the magnitude of the magnetic field. However, the subsequent time evolution of particles and waves depends on both ω_pe/Ω_e and the size of the simulation box L. If L is equal to one wavelength, λ₀, of the Buneman-unstable mode, electrons trapped by the waves undergo acceleration via the surfatron mechanism across the wave front. This occurs most efficiently when ω_pe/Ω_e ≃ 100: in this case electrons are accelerated to speeds of up c/2 where c is the speed of light. In a simulation with L=4λ₀ and ω_pe/Ω_e = 100, it is found that sideband instabilities give rise to a broad spectrum of wavenumbers, with a power law tail. Some stochastic electron acceleration is observed in this case, but not the surfatron process. Direct integration of the electron equations of motion, using parameters approximating to those of the wave modes observed in the simulations, suggests that the surfatron is compatible with the presence of a broad wave spectrum if ω_pe/Ω_e> 100. It is concluded that a combination of stochastic and surfatron acceleration could provide an efficient generator of mildly relativistic electrons at SNR shocks.