Theory of Electron Injection at Oblique Shock of Finite Thickness (original) (raw)

Influence of Thermalisation on Electron Injection in Supernova Remnant Shocks

2006

Within a test-particle description of the acceleration process in parallel nonrelativistic shocks, we present an analytic treatment of the electron injection. We estimate the velocity distribution of the injected electrons as the product of the post-shock thermal distribution of electrons times the probability for electrons with a given velocity to be accelerated; the injection efficiency is then evaluated as the integral of this velocity distribution. We estimate the probability of a particle to be injected as that of going back to the upstream region at least once. This is the product of the probability of returning to the shock from downstream times that of recrossing the shock from downstream to upstream. The latter probability is expected to be sensitive to details of the process of electron thermalisation within the (collisionless) shock, a process that is poorly known. In order to include this effect, for our treatment we use results of a numerical, fully kinetic study, by Bykov & Uvarov (1999). According to them, the probability of recrossing depends on physics of thermalisation through a single free parameter (Gamma), which can be expressed as a function of the Mach number of the shock, of the level of electron-ion equilibration, as well as of the spectrum of turbulence. It becomes apparent, from our analysis, that the injection efficiency is related to the post-shock electron temperature, and that it results from the balance between two competing effects: the higher the electron temperature, the higher the fraction of downstream electrons with enough velocity to return to the shock and thus to be ready to cross the shock from downstream to upstream; at the same time, however, the higher the turbulence, which would hinder the crossing.

Electron Injection at Quasi-Perpendicular Supernova Remnant Shocks

Electron injection process at high Mach number collisionless quasi-perpendicular shock waves is investigated by means of one-dimensional electromagnetic particle-in-cell simulations. We find that energetic electrons are generated through the following two steps: (1) electrons are accelerated nearly perpendicular to the local magnetic field by shock surfing acceleration at the leading edge of the shock transition region. (2) the preaccelerated electrons are further accelerated by shock drift acceleration. As a result, energetic electrons are preferentially reflected back to the upstream. Shock surfing acceleration provides sufficient energy required for the reflection. Therefore, it is important not only for the ener-gization process by itself, but also for triggering the secondary acceleration process. We also present a theoretical model of the two-step acceleration mechanism based on the simulation results, which can predict the injection efficiency for subsequent diffusive shock a...