Electron Accelerations at High Mach Number Shocks: Two-Dimensional Particle-in-Cell Simulations in Various Parameter Regimes

Abstract

Electron accelerations at high Mach number collision-less shocks are investigated by means of two-dimensional electromagnetic Particle-in-Cell simulations with various Alfvén Mach numbers, ion-to-electron mass ratios, and the upstream electron β e (the ratio of the thermal pressure to the magnetic pressure). We found electrons are effectively accelerated at a super-high Mach number shock (M A ∼ 30) with a mass ratio of M/m = 100 and β e = 0.5. The electron shock surfing acceleration is an effective mechanism for accelerating the particles toward the relativistic regime even in two dimensions with the large mass ratio.Buneman instability excited at the leading edge of the foot in the super-high Mach number shock results in a coherent electrostatic potential structure. While multi-dimensionality allows the electrons to escape from the trapping region, they can interact with the strong electrostatic field several times. Simulation runs in various parameter regimes indicate that the electron shock surfing acceleration is an effective mechanism for producing relativistic particles in extremely-high Mach number shocks in supernova remnants, provided that the upstream electron temperature is reasonably low.

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

“…In this section, we present the structure of the two evolving shocks after W = T 4.8 i , which is comparable to the total time covered in the simulations of Umeda et al (2008), Kato & Takabe (2010), and Matsumoto et al (2012). A global picture is offered in Figure 2 where we show profiles of the transversely averaged particle densities and field energy densities, p x versus x phase-space information, and 2D distributions of the particle density and the magnetic field component B z .…”

“…We follow Matsumoto et al (2012) in the analysis of this first stage of electron heating. The relative velocity of the incoming electrons and reflected ions must be larger than the thermal speed of the electrons, which leads to the condition…”

“…Whereas the temperature ratio can deviate from unity on account of physics, the dependence on the mass ratio is important for proper interpretation of simulations that may use a small mass ratio for computational reasons. Matsumoto et al (2012) write this condition in terms of the Alfvénic Mach number and the electron plasma beta, which we consider to not be helpful because the Alfvén speed cancels in their expression. The magnetic field may be relevant, however, for the energy Displayed are the profiles of (a) the average particle-number density normalized to the far-upstream density of the dense plasma (red lines: dense plasma, black lines: tenuous plasma; solid lines: ions, dashed lines: electrons), (b) profiles of the average magnetic (solid line) and electric (red dotted line, times factor 100) energy density in simulation units, (c) the amplitude of the magnetic field B z (in sign-preserving logarithmic scale as + -B B sgn 2 log max 10 ,…”

“…One consequence of this is that gradient drift should exist, but here it does not. Turbulence in the ramp destroys this picture, and the true electromagnetic environment likely deviates from the simple concept, as demonstrated, e.g., on page 6 of Matsumoto et al (2012) and attributed there to the time dependence arising from shock reformation. The large fluctuations in the electric and magnetic fields in the shock ramp play havoc with the gradient drift because small-and medium-scale structures provide a far more dominant contribution to B.…”

“…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.…”