Energy partition of fast ions and fast electrons in foil plasma expansion under continuous irradiation with kJ petawatt laser light

Kilojoule-class relativistic-intensity lasers with multi-picosecond (ps) pulse durations can efficiently produce fast ions in interactions with thin foil plasmas via target normal sheath acceleration (TNSA). We derive the energy partition between fast ions and fast electrons during the expansion of a thin foil plasma irradiated by a relativistic-intensity laser over picosecond timescales. As the expansion proceeds with continuous laser heating, both ion and electron energies increase simultaneously. In this study, we show that the energy partition between fast electrons and fast ions converges to a steady-state level on a ps timescale. This level is determined by the time dependence of the effective temperature of fast electrons and the dimensionality of momentum space. The steady-state level is verified by particle-in-cell simulations. The theory can be used to predict the energy conversion efficiency from the laser to fast ions for applications such as laser-driven proton sources.