Plasma expansions with a time-dependent electron temperature

Abstract

The fundamental of ion acceleration from the laser-solid interactions is the theory for describing plasma expansions into a vacuum. In the time interval of tens of femtoseconds after the laser pulse reaches the target, the plasma reaches local-thermal equilibrium and then hydrodynamic equations are available. However, it cannot reach macro-thermal equilibrium and does not satisfy Boltzmann distribution. The plasma is non-quasi-neutral and a strong charge separation exists. In fact, the electron temperature is time-dependent and the changing law is governed by the energy transfer between electrons and ions. In this Letter, an analytical solution is obtained for plasma expansions into a vacuum to describe the ion acceleration with a time-dependent electron temperature. It is obtained that the dependence of the plasma density on the potential is different from Boltzmann distribution in the time-dependent case. The time-dependent electron temperature also induces the unsteady ablation rate of the ablation plane, which is defined as the interface between the plasma and the solid (or liquid or gas). The electric field is also obtained and discussed in detail. The particular solution is given to show the influence of the time-dependent electron temperature on the laser-ion acceleration in a particular case: the electron temperature is proportional to the square of time. From that, it is concluded that laser-ion acceleration is more efficient in the time-increasing electron-temperature case than that in the isothermal case. The time-dependence of electron temperature comes from the time-dependence of laser intensity and induces the different efficiency of the laser-ion acceleration. At the ablation plane, the electron density and velocity are also predicted and explained reasonably.