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)1743410.22363/2312-9735-2017-25-4-401-409Research ArticleSolitary Right Hand Polarized Electromagnetic Wavein Relativistic PlasmaDorofeenkoV G<p>Dorofeenko V. G. - professor, Candidate of Physical and Mathematical Sciences, senior researcher of Department of Kinetic Equations of Keldysh Institute of Applied Mathematics, Russian Academy of Sciences</p>dorofeen@gmail.comKrasovitskiyV B<p>Krasovitskiy V. B. - professor, Doctor of Physical and Mathematical Sciences, expert of Department of Kinetic Equations of Keldysh Institute of Applied Mathematics, Russian Academy of Sciences</p>krasovit@mail.ruTurikovV A<p>Turikov V. A. - Candidate of Physical and Mathematical Sciences, assistant professor of Department of Applied Physics of Peoples’ Friendship University of Russia (RUDN University)</p>turikov_va@rudn.universityDepartment of Kinetic Equations Keldysh Institute of Applied Mathematics, Russian Academy of SciencesDepartment of Applied Physics Peoples’ Friendship University of Russia (RUDN University)1512201725440140910122017Copyright © 2017, Dorofeenko V.G., Krasovitskiy V.B., Turikov V.A.2017<p>In this paper of the nonlinear laser wave propagation in the hot plasma along the strong exter-nal magnetic ﬁeld under the electron cyclotron resonance conditions is investigated. The strongnonlinearity of such a process is caused by the relativistic electron movement and resonancewave ponderomotive force acting on the electrons. The system of equations for the enveloperight hand polarized laser pulse is derived using the hydrodynamics and Maxwells equations.The numerical integration of this system for the cold plasma case discovered the soliton solu-tions. This kind of solutions take a form of the envelope solitons containing inside them the plasma oscillations. The analytical expression for the energy density integral in a cold plasma isderived. It follows from the numerical results that for a hot plasma under cyclotron resonanceconditions the soliton solution becomes unstable. In this case the energy density conservationbreaks down, but electron momentum density conserves. It is concluded that the nonlinear sat-uration of the ﬁeld amplitude is due to the plasma charge separation under electromagneticradiation pressure. In this case the discrete set of the envelope soliton carrier frequency is de-termined by the ratio of the frequency of the nonlinear longitudinal electron oscillations to theLangmuir frequency of plasma. For the low density plasma the discrete frequency spectrumobtained by the numerical integration transforms to the continuous one.</p>magnetoactive plasmaright hand polarized waverelativisticelectronsphase and group velocitiessoliton solutionsмагнитоактивная плазмаправополяризованная волнареляти-вистские электроныфазовая и групповая скоростисолитонные решения[А. А. Kolomensky, А. N. Lebedev, Resonance Phenomena During the Particles Movement in a Plane Electromagnetic Wave, JETP 44 (1) (1963) 261–269, in Russian.][V. Ya. Davydovskii, About the Possibility of the Resonance Acceleration of Charged Particles by Electromagnetic Waves in a Constant Magnetic Field, JEPT 43 (3) (1962) 886–888, in Russian.][C. S. Roberts, S. J. Buchsbaum, Motion of a Charged Particle in a Constant Magnetic Field and a Transverse Electromagnetic Wave Propagating along the Field, Physical Review 135 (1964) 381–389.][V. B. Krsovitskiy, V. V. Prudskikh, Autoresonant Soliton in Plasma, Plasma Physics Reports 20 (1994) 564–570, in Russian.][V. V. Prudskikh, Supersonic and Near-Sonic Solitary Ion-Sound Waves in a Magnetized Plasma, Plasma Physics Reports 36 (2010) 1052–1058, in Russian.][S. Poornakala, A. Das, P. K. Kaw, A. Sen, Z. M. Sheng, Y. Sentoku, K. Mima, K. Nishkava, Weakly Relativistic One-Dimensional Laser Pulse Envelope Solitons in a Warm Plasma, Physics of Plasmas 9 (2002) 3802–3810.][D. I. Dzhavakhishvili, N. L. Tsintsadze, Transport Phenomena in a Completely Ionized Ultrarelativistic Plasma, JEPT 64 (1973) 1214–1325, in Russian.]