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.

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].

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.

Plasma expansion and soliton formation in laser created plasma are addressed. Nonlinear acoustic waves in plasma where the combined effect of trapped and non-thermal electrons are dealt with, in plasma expansion are studied. Using the perturbation method, a modified Korteweg–de Vries equation (mKdV) that describes how the ion acoustic waves (IAW) are derived. The plasma is modeled by a Cairns distribution function for non-thermal electrons combined with Gurevich distribution function for the trapped electrons. It is found that parameters taken into account have significant effects on the properties of nonlinear waves as well as on plasma expansion into vacuum. We point out, that this work has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, combined with trapped particles. Furthermore, this study is of interest in the context of the investigation of mono-energetic ion beams from intense laser interactions with plasmas.

Based on the Gurevich distribution function, the effect of trapped electrons by the electrostatic potential rising during plasma expansion is investigated. The self similar approach is used to find the expanding profiles of density and velocity. The present work may be used to understand the salient features of the expansion of plasma produced by laser ablation.

Abstract. The expansion of semi-infi nite laser produced plasma into vacuum is analyzed with a hydrodynamic model for cold ions assuming electrons modeled by a kappa-type distribution. Self-similar analytic expressions for the potential, velocity, and density of the plasma have been derived. It is shown that nonthermal energetic electrons have the role of accelerating the self-similar expansion.

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The dynamic evolution of ionization, three-body and radiative recombination processes in high intensity laser ion acceleration mechanisms, has been studied. For that, the expansion of a collisional thin plasma slab in vacuum is modeled using mixture hydrodynamic fluids equations for ions and neutral atoms, in the presence of fast nonthermal and slow trapped electrons, obeying a Cairns-Gurevich distribution. In addition, the characteristics of ion front acceleration and ion gained energy profiles are obtained, for three types of accelerated ions (H +, C + and Al +). It is proved that, ionization and recombination processes are responsible for the energy transfer between plasma particles. These processes are also strongly influenced by the impact of electron nonthermal phenomena, generated by the interaction of an intense laser pulse with the target. On the other hand, parametric studies have proved that ion energy profiles, maximum electric fields and ion energies at the ion front acceleration are also significantly affected by these phenomena. This study is useful in applications involving the creation of energetic ion beams, such as protontherapy.