The electron acceleration at shock waves in the solar corona

Context: In the solar corona, shock waves are generated by flares and/or coronal mass ejections. They are able to accelerate electrons up to high energies and can thus be observed as type II bursts in the nonthermal solar radio radiation. In-situ measurements of shock waves in interplanetary space have shown that shock waves attached by whistler waves are preferably accompanied by the production of energetic electrons.
Aims: Motivated by these observations, we study the interaction of electrons with such whistlers, which are excited by the protons accelerated by the shock.
Methods: We start with a resonant whistler wave-proton interaction that accounts for the initial whistler wave generation. Then, we consider resonant whistler wave-electron interaction, treated with a relativistic approach that is responsible for the electron energization in the whistler wave field.
Results: As a result, we show that electrons can be accelerated by a resonant wave particle (i.e., whistler-electron) interaction. This mechanism acts in the case of quasi-perpendicular shock waves. After acceleration, the energetic electrons are reflected by the associated shock wave back into the upstream region. The theoretical results are compared with observations, e.g., solar type II radio bursts.