Nonrelativistic Collisionless Shocks in Weakly Magnetized Electron-Ion Plasmas: Two-Dimensional Particle-in-Cell Simulation of Perpendicular Shock

Abstract

A two-dimensional particle-in-cell simulation is performed to investigate weakly magnetized perpendicular shocks with a magnetization parameter of σ = 6 × 10 −5 , which is equivalent to a high Alfvén Mach number M A of ∼ 130. It is shown that current filaments form in the foot region of the shock due to the ion-beam-Weibel instability (or the ion filamentation instability) and that they generate a strong magnetic field there. In the downstream region, these current filaments also generate a tangled magnetic field that is typically 15 times stronger than the upstream magnetic field. The thermal energies of electrons and ions in the downstream region are not in equipartition and their temperature ratio is T e /T i ∼ 0.3 − 0.4. Efficient electron acceleration was not observed in our simulation, although a fraction of the ions are accelerated slightly on reflection at the shock. The simulation results agree very well with the Rankine-Hugoniot relations. It is also shown that electrons and ions are heated in the foot region by the Buneman instability (for electrons) and the ion-acoustic instability (for both electrons and ions). However, the growth rate of the Buneman instability is significantly reduced due to the relatively high temperature of the reflected ions. For the same reason, ion-ion streaming instability does not grow in the foot region.

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

“…The temporal dimensions are given in terms of the inverse of the upstream ion Larmor frequency W = ,which is longer by factors of 4 and 2, respectively, than the simulations described in Kato & Takabe (2010) and Guo et al (2014).…”

“…Shock-front ripples have not yet been reported in multidimensional studies of high-Mach-number perpendicular shocks. Two-dimensional studies in out-of-plane magnetic field geometry (Matsumoto et al 2012(Matsumoto et al , 2013 Kato & Takabe (2010) with in-plane magnetic field configuration, although a visual similarity was noted for the magnetic field and density patterns at and behind the overshoot to the structures reported in Winske & Quest (1988). The results of our simulation with a magnetic field inclined at f =  45 to the simulation plane are thus in agreement with these earlier studies, and they also suggest that rippling at the gyroscale of ions will significantly contribute to shock-front nonstationarity even in 3D simulations.…”

“…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.…”

“…Instead, appropriate instabilities, solitary structures, or similar structures are required, an example of which is the Buneman instability between reflected ions and incoming electrons. The result would be strong electron heating and acceleration in the foot region (Shimada & Hoshino 2000), possibly followed by secondary accelerations through adiabatic processes or ionacoustic instability (Kato & Takabe 2010;Matsumoto et al 2012Matsumoto et al , 2013.…”

The Acceleration of Electrons at Collisionless Shocks Moving Through a Turbulent Magnetic Field

“…This mechanism requires a high Mach number in order for the efficient generation of whistler waves (Levinson 1992;Amano & Hoshino 2010). Significant electron acceleration has not been found in recent PIC simulations for collisonless shocks with high Mach numbers (Kato & Takabe 2010;Riquelme & Spitkovsky 2011;Niemiec et al 2012). Therefore, it is not clear how electrons get efficient nonthermal acceleration at quasi-parallel shocks.…”