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We explore electron preacceleration at high-Mach-number nonrelativistic perpendicular shocks at, e.g., young supernova remnants, which are a prerequisite of further acceleration to very high energies via diffusive shock acceleration. Using fully kinetic particle-in-cell simulations of shocks and electron dynamics in them, we investigate the influence of shock-surfing acceleration (SSA) at the shock foot on the nonthermal population of electrons downstream of the shock. The SSA is followed by further energization at the shock ramp where the Weibel instability spawns a type of second-order Fermi acceleration. The combination of these two processes leads to the formation of a nonthermal electron population, but the importance of SSA becomes smaller for larger ion-to-electron mass ratios in the simulation. We discuss the resulting electron spectra and the relevance of our results to the physics of systems with real ion-to-electron mass ratios and fully three-dimensional behavior.
Electron injection at high Mach number nonrelativistic perpendicular shocks is studied here for parameters that are applicable to young SNR shocks. Using high-resolution large-scale two-dimensional fully kinetic particle-in-cell simulations and tracing individual particles, we in detail analyze the shock-surfing acceleration (SSA) of electrons at the leading edge of the shock foot. The central question is to what degree the process can be captured in 2D3V simulations. We find that the energy gain in SSA always arises from the electrostatic field of a Buneman wave. Electron energization is more efficient in the out-of-plane orientation of the large-scale magnetic field because both the phase speed and the amplitude of the waves are higher than for the in-plane scenario. Also, a larger number of electrons is trapped by the waves compared to the in-plane configuration. We conclude that significant modifications of the simulation parameters are needed to reach the same level of SSA efficiency as in simulations with out-of-plane magnetic field or 3D simulations.
We revisit the effect of nonlinear Landau (NL) damping on the electrostatic instability of blazar-induced pair beams, using a realistic pair-beam distribution. We employ a simplified 2D model in k-space to study the evolution of the electric-field spectrum and to calculate the relaxation time of the beam. We demonstrate that the 2D model is an adequate representation of the 3D physics. We find that nonlinear Landau damping, once it operates efficiently, transports essentially the entire wave energy to small wave numbers where wave driving is weak or absent. The relaxation time also strongly depends on the intergalactic medium temperature, T-IGM, and for T-IGM << 10 eV, and in the absence of any other damping mechanism, the relaxation time of the pair beam is longer than the inverse Compton (IC) scattering time. The weak late-time beam energy losses arise from the accumulation of wave energy at small k, that nonlinearly drains the wave energy at the resonant k of the pair-beam instability. Any other dissipation process operating at small k would reduce that wave-energy drain and hence lead to stronger pair-beam energy losses. As an example, collisions reduce the relaxation time by an order of magnitude, although their rate is very small. Other nonlinear processes, such as the modulation instability, could provide additional damping of the nonresonant waves and dramatically reduce the relaxation time of the pair beam. An accurate description of the spectral evolution of the electrostatic waves is crucial for calculating the relaxation time of the pair beam.