English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A theory of electron injection into diffusive shock acceleration (DSA) forthe generation of cosmic-ray electrons at collisionless shocks is presented. Weconsider a recently proposed particle acceleration mechanism called stochasticshock drift acceleration (SSDA). We find that SSDA may be understood as adiffusive particle acceleration mechanism at an oblique shock of finitethickness. More specifically, it is described by a solution to thediffusion-convection equation for particles with the characteristic diffusionlength comparable to the shock thickness. On the other hand, the same equationyields the standard DSA if the diffusion length is much longer than thethickness. Although SSDA predicts, in general, a spectral index steeper thanDSA, it is much more efficient for low-energy electron acceleration and isfavorable for injection. The injection threshold energy corresponds to thetransition energy between the two different regimes. It is of the order of$0.1\text{-}1$ MeV in typical interstellar and interplanetary conditions if thedissipation scale of turbulence around the shock is determined by the ioninertial length. The electron injection is more efficient at high $M_\textrm{A}/ \cos \theta_{Bn}$ where $M_\textrm{A}$ and $\theta_{Bn}$ are the Alfv\'enMach number and the shock obliquity. The theory suggests that efficientacceleration of electrons to ultra-relativistic energies will be more easilyrealized at high-Mach-number young supernova remnant shocks, but not at weak ormoderate shocks in the heliosphere unless the upstream magnetic field is nearlyperpendicular to the shock normal.

Theory of Electron Injection at Oblique Shock of Finite Thickness