Radial acceleration of ions by a laser pulse in a plasma channel

The approximate analytic solution of the Cauchy problem is constructed for a system of kinetic equations of an electron–ion plasma that describe the acceleration of ions and the collisionless heating of electrons caused by the radial ponderomotive force of a laser beam that propagates in the transparent plasma of a gas or other low-density target. Under conditions where the Debye radius, rDe, of the electrons is considerably smaller than the characteristic localization scale, L, of the laser beam along the radius, ε = rDe/L ≪ 1, this solution is found by a group transformation that is specified by the operator of approximate renormalization-group symmetries over small parameters, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon {\kern 1pt} and{\kern 1pt} \mu {\kern 1pt} = {\kern 1pt} \sqrt {Zm/M} $$\end{document}, of the initial distribution functions of particles. For an axially symmetric geometry of the laser beam, the temporal and spatial dependences of the distribution functions of particles are obtained and their integral characteristics, such as the density, mean velocity, temperature, and energy spectrum, are found. The formation of a cylindrical density cusp and the localized heating of electrons at the laser-channel boundary are analytically described.