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)2220410.22363/2658-4670-2019-27-2-133-142Research ArticleOn the radiation losses during motion of an electron in the field of intense laser radiationDobrovaEkaterina V<p>student of Institute of Physical Research and Technology</p>dobrova03@icloud.comMilantievVladimir P<p>Professor, Doctor of Physical and Mathematical Sciences, professor of Institute of Physical Research and Technology</p>vmilant@mail.ruPeoples’ Friendship University of Russia (RUDN university)1512201927213314222112019Copyright © 2019, Dobrova E.V., Milantiev V.P.2019<p>Motion of the relativistic electron in the field of intense laser pulse of the arbitrary shape is considered. The pulse dimension is supposed to be of the order of the Gaussian laser beam dimension in the focal plane. It is supposed that the pulse is propagating along the external constant magnetic field. In the paraxial approximation the corrections of the first order to the vectors of the field of radiation as well as the force of the radiation friction are taken into account. Averaged relativistic equations of motion of electron are obtained with the help of averaging over the fast oscillations of the laser radiation. It is shown that with taking into account corrections of the first order to the field vectors an averaged force arises. This force is defined by pulsed character of radiation and proportional to the intensity but not to gradient of intensity. It is shown that radiation losses are of little importance in the transverse plane but may considerably act on the longitudinal motion of electron.</p>relativistic electronintense laser pulseparaxial approximationGaussian beamradiation frictionрелятивистский электрон, интенсивный лазерный импульс, параксиальное приближение, гауссов пучок, радиационное трение[L. D. Landau, E. M. Lifshitz, Field theory [Teoriya polya], Nauka, Moscow, 1988, in Russian.][J. D. Jackson, Classical electrodynamics, J. Wiley, NY-L., 1962.][V. L. Ginzburg, Theoretical physics and astrophysics [Teoreticheskaya fizika i astrofizika], Nauka, Moscow, 1975, in Russian.][N. P. Klepikov, Radiation damping forces and radiation from charged particles, Soviet Physics Uspekhi 28 (1985) 506-520. doi:10.1070/PU1985v028n06ABEH005205.][V. S. Krivitskii, V. N. Tsytovich, Average radiation-reaction force in quantum electrodynamics, Soviet Physics Uspekhi 234 (1991) 250-258. doi:10.1070/PU1991v034n03ABEH002352.][G. F. Efremov, Radiative damping of a relativistic electron in classical electrodynamics, Journal of Experimental and Theoretical Physics 89 (1998) 899-904. doi:10.1134/1.558738.][I. V. Sokolov, Renormalization of the Lorentz-Abraham-Dirac equation for radiation reaction force in classical electrodynamics, Journal of Experimental and Theoretical Physics 109 (2009) 207-212. doi:10.1134/S1063776109080044.][A. L. Galkin, Dynamics of an electron in a relativistically intense laser field including radiation reaction, Journal of Experimental and Theoretical Physics 115 (2012) 201-207. doi:10.1134/S1063776112070072.][A. V. Bashinov, A. A. Gonoskov, A. V. Kim, M. Marklund, G. Mourou, M. Sergeev, Electron acceleration and emission in a field of a plane and converging dipole wave of relativistic amplitudes with the radiation reaction force taken into account, Quantum Electronics 43 (2013) 291-299. doi:10.1070/QE2013v043n04ABEH015101.][K. Seto, H. Nagamoto, J. Koga, K. Mima, Equations of motion with radiation reaction in ultrarelativistic laser-electron interactions, Physics of Plasmas 18 (2011) 123404. doi:10.1063/1.3663843.][L. W. Davis, Theory of electromagnetic beams, Physical Review A 19 (1979) 1177-1179. doi:10.1103/PhysRevA.19.1177.][D. Bauer, P. Mulser, W. Steeb, Relativistic ponderomotive force, uphill acceleration and transition to chaos, Physical Review Letters 75 (1995) 4622-4625. doi:10.1103/PhysRevLett.75.4622.][B. Quesnel, P. Mora, Theory and simulation of the interaction of ultraintense laser pulses with electrons in vacuum, Physical Review E 58 (1998) 3719-3732. doi:10.1103/PhysRevE.58.3719.][A. M. Goncharenko, Gaussian light beams [Gaussovy puchki sveta], Nauka i tekhnika, Minsk, 1997, in Russian.][D. R. Bituk, M. V. Fedorov, Relativistic ponderomotive forces, Journal of Experimental and Theoretical Physics 89 (1999) 640-646.][N. B. Narozhny, M. S. Fofanov, Scattering of relativistic electrons by a focused laser pulse, Journal of Experimental and Theoretical Physics 90 (2000) 753-768. doi:10.1134/1.559160.][V. P. Milant’ev, S. P. Karnilovich, Y. N. Shaar, Description of high-power laser radiation in the paraxial approximation, Quantum Electronics 45 (2015) 1063-1068. doi:10.1070/QE2015v045n11ABEH015800.][S. G. Bochkarev, V. Y. Bychenkov, Acceleration of electrons by tightly focused femtosecond laser pulses, Quantum Electronics 37 (2007) 273-284. doi:10.1070/QE2007v037n03ABEH013462.][N. N. Bogoljubov, Y. A. Mitropolskij, Asymptotic methods in the theory of nonlinear oscillations [Asimptoticheskiye metody v teorii nelineynykh kolebaniy], Nauka, Moscow, 1974, in Russian.][V. P. Milant’ev, A. J. Castillo, On the theory of the relativistic motion of a charged particle in the field of intense electromagnetic radiation, Journal of Experimental and Theoretical Physics 116 (2013) 558-566. doi:10.1134/S1063776113040067.][A. J. Castillo, V. P. Milant’ev, Relativistic ponderomotive forces in the field of intense laser radiation, Technical Physics 59 (2014) 1261-1266. doi:10.1134/S1063784214090138.]