Isofield plasma expansion in kJ petawatt laser-driven ion acceleration with a tailored fast electron temperature

Kilojoule-class relativistic intensity lasers, having multi-picosecond (ps) pulse durations, enable efficient ion acceleration in the interaction with thin foil targets. The foil plasma expands under the laser energy input over picoseconds where fast electrons keep increasing their effective temperature, while they convert a part of the energy into fast ions through generation of a sheath electric field. The temporal evolution of the sheath electric field is the key to understanding the efficient ion acceleration seen in kJ-class laser experiments. Here, we extend the non-isothermal plasma expansion model by introducing a temporal function of the effective temperature of fast electrons to obtain the sheath electric field in the expanding plasma. We theoretically derived that when the effective temperature of fast electrons increases in proportional to the square of the time, the strength of the sheath electric field is kept constant without depletion during the expansion. This ‘isofield’ expansion is confirmed by a quasi-one-dimensional particle-in-cell simulation. The isofield expansion results in a high energy ion acceleration with a small expansion length, which is favorable for realizing an efficient ion acceleration with less lateral energy loss in multi-dimensional situations.