The impacts of downstream heating on ion reflection for collisionless electrostatic shock

Collisionless electrostatic shock (CES) can accelerate ions efficiently with a narrow energy spread, making it one of the most prominent ion acceleration mechanisms using intense lasers. In CES, ions can be reflected at the shock front due to the presence of electrostatic potential, resulting in an ion beam accelerated to velocity up to twice that of the shock velocity. While the reflection plays the main role in the ion acceleration scheme and can also impact the overall shock structure, the detailed mechanism remains unknown. For instance, it is not clear how partial reflection (0 < reflection fraction < 1) is achieved when we have cold ions upstream. Contrary to previous studies attributing ion reflection to the temperature of the upstream (pre-shock) region, we argue that the reflection can be explained by the downstream heating by evidence in particle-in-cell simulation. In our proposed model, all ions travel to the downstream region, where they gain thermal energy by various kinetic instabilities. Consequently, ions show a wide velocity dispersion, and those with velocities larger than the shock velocity are "kicked" back to the upstream, constituting the reflected fraction.