Simultaneous Acceleration of Protons and Electrons at Nonrelativistic Quasiparallel Collisionless Shocks

TL;DR

This study uses self-consistent particle-in-cell simulations to demonstrate that both protons and electrons can develop power-law energy distributions at nonrelativistic collisionless shocks, with implications for cosmic ray origins.

Contribution

First demonstration of simultaneous proton and electron acceleration with universal spectral index at nonrelativistic shocks using self-consistent simulations.

Findings

Both species develop power-law distributions with spectral index -4.

Electron/proton ratio in accelerated particles is less than 1%.

Acceleration mechanisms involve SDA, Fermi-like processes, and Bell waves.

Abstract

We study diffusive shock acceleration (DSA) of protons and electrons at nonrelativistic, high Mach number, quasiparallel, collisionless shocks by means of self-consistent 1D particle-in-cell simulations. For the first time, both species are found to develop power-law distributions with the universal spectral index $-4$ in momentum space, in agreement with the prediction of DSA. We find that scattering of both protons and electrons is mediated by right-handed circularly polarized waves excited by the current of energetic protons via non-resonant hybrid (Bell) instability. Protons are injected into DSA after a few gyro-cycles of shock drift acceleration (SDA), while electrons are first pre-heated via SDA, then energized via a hybrid acceleration process that involves both SDA and Fermi-like acceleration mediated by Bell waves, before eventual injection into DSA. Using the simulations we can measure the electron/proton ratio in accelerated particles, which is of paramount importance for explaining the cosmic ray fluxes measured at Earth and the multi-wavelength emission of astrophysical objects such as supernova remnants, radio supernovae, and galaxy clusters. We find the normalization of electron power-law is $\lesssim 10^{-2}$ that of the protons for strong nonrelativistic shocks.