# Theory of Stochastic Shock Drift Acceleration for Electrons in the Shock Transition Region

## TL;DR

This paper introduces stochastic shock drift acceleration (SSDA), a new electron acceleration mechanism that extends SDA by including stochastic pitch-angle scattering, explaining in-situ observations and potentially accelerating electrons to relativistic energies.

## Contribution

The paper develops a theoretical model of SSDA, demonstrating its power-law energy spectrum and scaling laws, supported by Monte Carlo simulations and observational comparisons.

## Key findings

- Steady-state electron spectrum becomes a power-law under strong scattering
- Spectral index is independent of scattering coefficient
- Maximum energy scales linearly with pitch-angle scattering coefficient

## Abstract

We propose a novel electron acceleration mechanism, which we call stochastic shock drift acceleration (SSDA), that extends the standard shock drift acceleration (SDA) for low-energy electrons at a quasi-perpendicular shock to include the effect of stochastic pitch-angle scattering. We demonstrate that the steady-state energy spectrum of electrons accelerated within the shock transition region becomes a power-law in the limit of strong scattering. The spectral index is independent of the pitch-angle scattering coefficient. On the other hand, the maximum energy attainable through the mechanism scales linearly with the pitch-angle scattering coefficient. These results have been confirmed by Monte Carlo simulations that include finite pitch-angle anisotropy. We find that the theory can reasonably well explain in-situ observations of quasi-perpendicular Earth's bow shock. Theoretical scaling law suggests that the maximum energy increases in proportion to the square of the shock speed, indicating that the thermal electrons may be accelerated up to mildly relativistic energies by the SSDA at quasi-perpendicular supernova remnant shocks. Therefore, the mechanism provides a plausible solution to the long-standing electron injection problem.