Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)13391Research ArticleThe Peculiarities of Acceleration of Ultra-Relativistic Electrons by the Powerful Laser Radiation at the Regime of Cyclotron AutoresonanceAbdulovN Anizami.abdulov@gmail.comMilant’evV Pvmilantiev@sci.pfu.edu.ruPeoples’ Friendship University of Russia150320163667817092016Copyright © 2016,2016Analysis of the numerical solution of the motion equations of electrons in the field of ultrashort laser pulse, propagating along the steady magnetic field at the conditions of cyclotron autoresonance, is performed. It is shown that in the absence of the condition of cyclotron resonance during injection of electrons they momentarily escape the range of interaction. Laser radiation of the circular polarization is defined in the paraxial approximation in the form of the Gaussian beams of the basic and the first modes. Corrections of the first approximation to the components of the radiation field are taken into consideration. Calculations show that corrections of the first order to the transverse components exert no sufficient influence on the autoresonant motion of electrons whereas the longitudinal components of the first approximation play a major role. It is shown also that the specific form of the pulse is inessential. Images of the spatial distribution of the vectors of the radiation field in the transverse plane depending on the longitudinal coordinate (the direction of the radiation propagation) are obtained. It is shown that the character of changes of energy of an electron beam essentially depends on their position of injection in the focal plane. In this case acceleration as well as deceleration is possible in dependence on the position of injection of electron beam. It is shown that under the optimal conditions of injection the mechanism of the cyclotron autoresonance can provide sufficiently high efficient of acceleration of ultrarelativistic electrons in the field of powerful laser radiation with sufficiently high average rate at the distance of the order of two Rayleigh lengths. The basic mode is more preferable due to more simple description of that mode, higher acceleration rate and wider acceleration zone of injection of an electron beam.cyclotron autoresonanceultra-relativistic electronshigh-power laser radiationultra-short pulsesmodes of Gaussian beamsautoresonant accelerationциклотронный авторезонансультрарелятивистский электронмощное лазерное излучениеультракороткие импульсымоды гауссовых пучковавторезонансное ускорение