Recent progress in the theory of electron injection in collisionless shocks

Abstract

The injection problem in diffusive shock acceleration theory is discussed with particular focus on electrons. The following issues are addressed: Why it has been considered to be so difficult, what is the required condition, and how it can be resolved. It is argued that there exists a critical Mach number above which the electron injection is achieved. Above the threshold, back-streaming electrons reflected back upstream by the shock front can self-generate high-frequencywhistler waves, which can scatter themselves as required for subsequent acceleration. The theoretical estimate is found to be well consistent with in-situ measurements, indicating this could provide a possible solution to the long standing problem in the diffusive shock acceleration theory.