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The localized deposition of the energy of a laser pulse, as it ablates asolid target, introduces high thermal pressure gradients in the plasma. Thethermal expansion of this laser-heated plasma into the ambient medium (ionizedresidual gas) triggers the formation of non-linear structures in thecollision-less plasma. Here an electron-proton plasma is modelled with aparticle-in-cell (PIC) simulation to reproduce aspects of this plasmaexpansion. A jump is introduced in the thermal pressure of the plasma, acrosswhich the otherwise spatially uniform temperature and density change by thefactor 100. The electrons from the hot plasma expand into the cool one and thecharge imbalance drags a beam of cool electrons into the hot plasma. Thisdouble layer reduces the electron temperature gradient. The presence of thelow-pressure plasma modifies the proton dynamics compared to the plasmaexpansion into a vacuum. The jump in the thermal pressure develops into aprimary shock. The fast protons, which move from the hot into the cold plasmain form of a beam, give rise to the formation of phase space holes in theelectron and proton distributions. The proton phase space holes develop into asecondary shock that thermalizes the beam.

Simulation of a collision-less planar electrostatic shock in a proton-electron plasma with a strong initial thermal pressure change