Time evolution of the distribution function for stochastically heated relativistic electrons in a laser field of picosecond duration

We report a numerical analysis of the stochastic acceleration of electrons, stipulated by a random change in the phase of the force acting on the electron. The main source of randomness is the random spatial distribution of electromagnetic fields in the focal region of multimode laser radiation. A typical frequency of the random phase change corresponding to the maximum impact of the effect under consideration lies in the range of (0.25–0.5)ν (ν is the radiation frequency of a neodymium laser). A wave packet model convenient for calculations taking into account the radiative transitions of the neodymium ion is proposed. The dependence of the average energy of relativistic electrons on the flux density in the range of 10¹⁵–10¹⁸ W cm^-2 is calculated. The time dependence of the average electron energy during the laser pulse in the form of approximating formulas is constructed. The typical time for the development of stochastic heating of electrons is determined. It is found that the stochastic acceleration process weakly depends on the laser pulse duration, when the latter exceeds several hundred periods of the electromagnetic wave.