Electron energy distribution formation under recursive accelerations by relativistic laser light

Electron energy distribution is a key for applications of relativistic laser-plasma interaction. We study the electron acceleration in a hot thin plasma created by a relativistic picosecond laser light using a plasma particle-in-cell code, PICLS. The simulation shows that electrons become more energetic than the ponderomotive scaling due to multiple interactions with the laser light. The energy distribution becomes a power-law distribution at quasi-steady state. We model the electron energy distribution formation as diffusion in the momentum space using the Fokker-Planck equation. The properties of the distribution function such as a power exponent are also derived. The energetic electron distribution formation by a kJ-class relativistic laser light results an efficient proton acceleration recently observed in the experiment [1].