Preacceleration in the Electron Foreshock. I. Electron Acoustic Waves

Abstract

To undergo diffusive shock acceleration, electrons need to be preaccelerated to increase their energies by several orders of magnitude, else their gyroradii will be smaller than the finite width of the shock. In oblique shocks, where the upstream magnetic field orientation is neither parallel nor perpendicular to the shock normal, electrons can escape to the shock upstream, modifying the shock foot to a region called the electron foreshock. To determine the preacceleration in this region, we undertake particle-in-cell simulations of oblique shocks while varying the obliquity and in-plane angles. We show that while the proportion of reflected electrons is negligible for θ Bn = 74.°3, it increases to R ∼ 5% for θ Bn = 30°, and that, via the electron acoustic instability, these electrons power electrostatic waves upstream with energy density proportional to R 0.6 and a wavelength ≈2λ se, where λ se is the electron skin length. While the initial reflection mechanism is typically a combination of shock-surfing acceleration and magnetic mirroring, we show that once the electrostatic waves have been generated upstream, they themselves can increase the momenta of upstream electrons parallel to the magnetic field. In ≲1% of cases, upstream electrons are prematurely turned away from the shock and never injected downstream. In contrast, a similar fraction is rescattered back toward the shock after reflection, reinteracts with the shock with energies much greater than thermal, and crosses into the downstream.

Kinetic Simulations of Nonrelativistic High-mach-number Perpendicular Shocks Propagating in a Turbulent Medium

“…In contrast to perpendicular shocks, from which electrons cannot escape to the upstream region, at oblique shocks the particles form extended foreshock, where they drive instabilities (Bohdan et al 2022;Morris et al 2022). This adds room for particle-turbulence interactions, and hence, changes in the reflection conditions and the electron dynamics, as well as modifications of the instabilities.…”

Pre-acceleration in the Electron Foreshock. II. Oblique Whistler Waves

“…Within the context of our analysis, from Equation (7) we would expect the trapping probability to increase up until Ω ci t ≈ 125 for all reflected electrons with gyroradii small enough to be contained by the nonlinear structures. Further upstream beyond this region, the energy density of the EAWs (which are not well captured in this out-of-plane simulation), which are the subject of Morris et al (2022), would dominate. Hence, the nonlinear structures discussed here would cease to be important beyond this limit.…”

“…The first of these are electrostatic electron acoustic waves (EAWs). In paper I of this series (Morris et al 2022), we investigated the effect of changing the orientation of the upstream magnetic field on the foreshock structure by performing a series of narrow box simulations. It was found that EAWs are quickly excited within a few ion gyroradii, and the EAWs are stronger for decreasing Bn q .…”

Electron acceleration in supernova remnants

“…At oblique shocks, only electrons escape the shock forming an extended electron foreshock filled with electrostatic and electromagnetic waves resulting in efficient electron scattering. These shocks with PIC simulations have only been studied over the last 5 years [37][38][39][40][41], and the results are discussed in section 4. At parallel shocks, the foreshock physics is dominated by ions and it was mostly studied with hybrid simulations [42][43][44] where ions are represented as particles and electrons are a massless fluid.…”

“…The shock width in this case is about d sh ≈ 12.5r i . This structure is captured both with 1D [38,39] and 2D [40,41] PIC simulations. The only 3D simulation [37] is unfortunately too short to capture the electron foreshock structure.…”