In this work, the effect of electron trapping on the self-similar expansion of electron-ion laser plasma into vacuum, combined with the effect of non-thermal (energetic) electrons is studied. For this, a mono-dimensional, non-relativistic model where the ions are cold and governed by fluid equations is used. In the approximation of quasi-neutrality of charge, the obtained self-similar solution shows that for ion (plasma) behavior, the presence of an important number of non-energetic trapped electrons in the plasma potential wells has the effect of slowing down the expansion, whereas the phenomenon of presence of energetic electrons makes the influence of trapping effect on the self-similar expansion very weak even in the case of a very small number of energetic electrons. This study is of interest in the context of the investigation of mono-energetic ion beams from intense laser interactions with plasmas.

The one-dimensional expansion into vacuum of ion-electron plasma produced by laser ablation is investigated. The ions considered as an ideal fluid are governed by a fluid model where charge quasineutrality is assumed to prevail, while electron density follows a non-Maxwellian distribution. Showing that the expansion can be described by a self-similar solution, the resulting nonlinear Euler equations are solved numerically. It is found that the deviation of the electrons from Maxwellian distribution gives rise to new asymptotic solutions of physical interest affecting the density and velocity of plasma expansion.Plasma expansion into vacuum is a basic physical problem with a variety of applications, ranging from space to laboratory scales. 1-4 Caused generally by electron pressure, it serves as an energy transfer mechanism from electrons to ions. The expansion process is often described under the assumption of Maxwellian electrons with velocities in local thermal equilibrium ͑LTE͒, known to be isotropically distributed around the average velocity. This assumption easily fails with a lack of collisions. Indeed, in many cases of astrophysical and laboratory plasmas expansion, the electron distribution functions ͑EDFs͒ are non-Maxwellian and exhibit more complex shapes showing high-energy tails, as in the weakly collisional corona and solar wind acceleration region. 5 The fundamental reason is that fast electrons collide much less frequently than slow ones. Indeed their free path is very large since proportional to v e 4 , where v e is the electron velocity, and cannot relax to a Maxwellian. The energetic electrons could have a significant effect on ionization and expansion of the plasma. As reported by many authors, 6-8 in an expanding plasma produced by laser ablation experiments, the high mobility light electrons escape faster into vacuum compared to heavier particles, thus generating a selfconsistent ambipolar electric field that accelerates the ions and slows electrons.Another phenomenon observed in plasma expansion is that the heat exchange between electrons and heavy particles such as ions is inefficient as only a fraction of the thermal energy of the order of m e / m i is transferred per collision, where m e and m i are the electron and ion mass, respectively. This causes the electron temperature T e to differ from the ion temperature T i . T e in non-LTE plasmas is higher than T i because of insufficient electron-electron collisions which provide the essential mechanism to reach thermal equilibrium. 9 This phenomenon is also crucial in pulsed laser deposition ͑PLD͒ experiments, where the efficiency of the deposited films depends on the parameters of the laser induced plasma that expands into vacuum or in an ambient environment. A very simple view of the PLD divides the process into two main stages: first, the incident laser rapidly heats the target, then a dense, warm plasma is created near the target surface, leading the plume to expand adiabatically. Finally, the plume deposits onto a substrate with nonequ...

The expansion of semi-infinite plasma into vacuum is analyzed with a hydrodynamic model for cold ions assuming electrons modelled by a kappa-type distribution. Similarly to Mora study of a plasma expansion into vacuum [P. Mora, Phys. Rev. Lett. 90, 185002 (2003)], we formulated empirical expressions for the electric field strength, velocity, and position of the ion front in one-dimensional nonrelativistic, collisionless isothermally expanding plasma. Analytic expressions for the maximum ion energy and the spectrum of the accelerated ions in the plasma were derived and discussed to highlight the electron nonthermal effects on enhancing the ion acceleration in plasma expansion into vacuum.

A theoretical model is developed to describe self-similar plasma expansion into vacuum with two different electron temperature distribution functions. The cold electrons are modeled with a Maxwellian distribution while the hot ones are supposed to be non-thermal obeying a kappa distribution function. It is shown that ion density and velocity profiles depend only on cold electron distribution in early stage of expansion whereas ion acceleration is mainly governed by the hot electrons at the ion front and is strongly enhanced with the proportion of kappa distributed electrons. It is also found that when the kappa index is decreasing, the critical value of temperature ratio Teh/Tec, limiting the application of quasi-neutrality, becomes larger than the $5 + \sqrt {24} \approx 9.9$ value obtained in the two-electron Maxwellian Bezzerides model [Bezzerides, B., Forslund, D. W. & Lindman, E. L. (1978). Phys. Fluids21, 2179–2185].

Based on the Passoni-Lontano model [M. Lontano and M. Passoni, Phys. Plasmas 13(4), 042102 (2006)], the expansion of an intense laser produced plasma into vacuum is analyzed, assuming that hot and energetic electrons responsible for ion acceleration, in the framework of a TNSA mechanism, are nonthermal and modelled by the Cairns distribution function. Due to the presence of energetic nonthermal electron population, the electric potential, electrical field, ion maximum energy, and ion spectrum energy are enhanced during the ion acceleration process.