Electron Shock Surfing Acceleration in Multidimensions: Two-Dimensional Particle-in-Cell Simulation of Collisionless Perpendicular Shock

Abstract

Electron acceleration mechanism at high Mach number collisionless shocks propagating in a weakly magnetized medium is investigated by a self-consistent two-dimensional particle-in-cell simulation. Simulation results show that strong electrostatic waves are excited via the electron-ion electrostatic two-stream instability at the leading edge of the shock transition region as in the case of earlier one-dimensional simulations. We observe strong electron acceleration that is associated with the turbulent electrostatic waves in the shock transition region. The electron energy spectrum in the shock transition region exhibits a clear powerlaw distribution with spectral index of 2.0−2.5. By analyzing the trajectories of accelerated electrons, we find that the acceleration mechanism is very similar to shock surfing acceleration of ions. In contrast to the ion shock surfing, however, the energetic electrons are reflected by electron-scale electrostatic fluctuations in the shock transition region, but not by the ion-scale cross-shock electrostatic potential. The reflected electrons are then accelerated by the convective electric field in front of the shock. We conclude that the multidimensional effects as well as the self-consistent shock structure are essential for the strong electron acceleration at high Mach number shocks.

Nonrelativistic Perpendicular Shocks Modeling Young Supernova Remnants: Nonstationary Dynamics and Particle Acceleration at Forward and Reverse Shocks

“…They eventually escape from the potential wells and start to drift downstream. However, if a particle gains enough energy at the first encounter with the Buneman waves and its gyroradius increases, it can enter the electrostatic wave region again from the downstream side and experience another SSA cycle (see also Amano & Hoshino 2009b). As shown in Section 3.2, Buneman-type turbulence is generated in the foot in both the forward and the reverse shock, and in the former it grows to nonlinear amplitudes.…”

“…The turbulent structure of the shock transition may also play an important role in impeding a return of electrons to the foot region or suppressing the SDA of electrons in the shock ramp, which should accompany the electron SSA process (Matsumoto et al 2012). Kato & Takabe (2010) attributed the lack of efficient electron acceleration to the specific orientation of the upstream magnetic field in the plane of the simulation, which was different from the out-of-plane configuration assumed in Amano & Hoshino (2009b). The simulations by Matsumoto et al (2012) and Matsumoto et al (2013) with out-of-plane magnetic field and moderate plasma beta, b = 0.5 p , show a high efficiency of electron energization.…”

“…Our simulations thus complement the two-dimensional (2D) PIC simulations of Matsumoto et al (2013) and Matsumoto et al (2015), who have covered the parameter range b  0.5 e and both sonic and Alfvénic Mach numbers around 40. In contrast to all earlier studies of high-Mach-number perpendicular shocks using either in-plane or out-of-plane configurations of the homogeneous magnetic field, and often finding a different efficiency of, e.g., electron heating by electrostatic modes (Amano & Hoshino 2009b), we set our regular magnetic field component at an angle of  45 to the simulation plane. We expect that such a setup will better approximate the physics of fully three-dimensional (3D) systems.…”

“…The Buneman modes excited at the shock foot may give rise to SSA of electrons (Leroy et al 1981;Amano & Hoshino 2009b;Matsumoto et al 2012). Despite the electron heating in the far-upstream region, the high sonic Mach number of the shock exceeds the threshold for the growth of Buneman modes (see Equation (4)) as the first stage of electron acceleration.…”

Hadronic jet models today

“…However in order to get electrons to participate together with protons in the diffusive shock acceleration process, electrons must be first preheated up to average energy (to be strict -up to average momentum) of protons heated by randomization and compression in the shocked plasma. Several scenarios have been investigated for such electron preheating, both analytically and in PIC-simulations (Amato & Arons 2006;Amano & Hoshino 2009;Sironi & Spitkovsky 2010). Some of them indicate the formation of a power-law energy distribution with the slope 1 < q e < 2.…”