Abstract
The methods of modern group analysis allow an analytic solution of the Cauchy problem to be constructed for the system of kinetic equations for a fully ionised electron – ion plasma, describing the acceleration of ions during the adiabatic expansion of a cylindrical plasma. Time and spatial dependences of the distribution functions of particles are obtained and their integral characteristics, such as density, average velocity, temperature, and energy spectrum, are found. The formation of the energy spectrum of accelerated ions, asymptotically repeating the spatial distribution of their density, and the cooling of electrons in the process of ion acceleration are analytically described. Particular attention is paid to the investigation of the influence of the heavy ionic component on the dynamics of the light component. The features of ion acceleration in the case of a two-temperature electron distribution function that describes the presence of hot and cold electron components are studied, which corresponds to the typical conditions of the experiment on plasma heating by intense laser radiation.
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