Discrete and Continuous Models and Applied Computational ScienceDiscrete 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)4010610.22363/2658-4670-2024-32-1-122-127BBLNGKArticlesСтатьиResearch ArticleOn cyclotron damping of longitudinal waveО циклотронном затухании продольной волныhttps://orcid.org/0000-0002-7669-7030KarnilovichSergey P.КарниловичС. П.

Candidate of Sciences in Physics and Mathematics, Assistant professor of Institute of Physical Research and Technology

karnilovich-sp@rudn.ruhttps://orcid.org/0000-0002-3645-1060LovetskiyKonstantin P.ЛовецкийК. П.

Candidate of Sciences in Physics and Mathematics, Associate Professor of Department of Computational Mathematics and Artificial Intelligence

lovetskiy-kp@rudn.ruhttps://orcid.org/0000-0002-1856-4643SevastianovLeonid A.СевастьяновЛ. А.

Professor, Doctor of Sciences in Physics and Mathematics, Professor at the Department of Computational Mathematics and Artificial Intelligence of Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University), Leading Researcher of Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research

sevastianov-la@rudn.ruhttps://orcid.org/0000-0002-2588-504XStrashnovaSvetlana B.СтрашноваС. Б.

Candidate of Chemical Sciences, Associate Professor at the Department of General and Inorganic Chemistry

strashnova-sb@rudn.ruhttps://orcid.org/0000-0003-4951-5657ShaarYahya N.ШаарЯ. Н.

PhD in Physics and Mathematics, Assistant professor of Institute of Physical Research and Technology

al-shaar-ya@rudn.ruRUDN UniversityРоссийский университет дружбы народовJoint Institute for Nuclear ResearchРоссийский университет дружбы народовRUDN UniversityОбъединённый институт ядерных исследований30062024321VOL 32, NO1 (2024)ТОМ 32, №1 (2024)12212719072024Copyright ©; 2024, Karnilovich S.P., Lovetskiy K.P., Sevastianov L.A., Strashnova S.B., Shaar Y.N.Copyright ©; 2024, Карнилович С.П., Ловецкий К.П., Севастьянов Л.А., Страшнова С.Б., Шаар Я.Н.2024Karnilovich S.P., Lovetskiy K.P., Sevastianov L.A., Strashnova S.B., Shaar Y.N.Карнилович С.П., Ловецкий К.П., Севастьянов Л.А., Страшнова С.Б., Шаар Я.Н.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/40106

Average equations of motion of relativistic charged particles in the field of HF (high frequency) wave packets are obtained in the range of cyclotron resonance in the case of strong LF (low frequency) electric field. Strong electric field means that the characteristic velocity of the particle comparable with the electric drift velocity \((v \sim v_E)\). It is shown that with taking into account the electric drift velocity, new mechanisms of damping of longitudinal waves become possible. The effect of a strong electrostatic field on the resonant interaction of relativistic particles with high-frequency waves, as well as the relativistic effect, on cyclotron resonance for a longitudinal wave, is analyzed. The analytical solution of the averaged system of equations in the quasi-relativistic approximation is analyzed, as well as a numerical experiment for the Langmuir wave under the condition of cyclotron resonance in the case of a strong electric field.

Выведены усредненные уравнения движения для релятивистских заряженных частиц в ВЧ поле (высокочастотных) волновых пакетов в диапазоне циклотронного резонанса в случае НЧ (низкочастотного) сильного электрического поля, где сильное электрическое поле означает, что характерная скорость частицы сравнима со скоростью электрического дрейфа \((v \sim v_E)\). Показано, что при учете скорости электрического дрейфа становятся возможными новые механизмы затухания продольных волн. Проведен анализ влияния сильного электростатического поля на резонансное взаимодействие релятивистских частиц с высокочастотными волнами, а также влияние релятивизма на циклотронный резонанс для продольной волны. Получено аналитическое решение усредненной системы уравнений в квазирелятивистском приближении, а также проведен численный эксперимент для Ленгмюровской волны в случае циклотронного резонанса с учетом сильного электрического поля.

Electric drift velocitydampingrelativistic charged particlesstrong electric fieldlongitudinal waveshigh frequency wave packetscyclotron resonanceСкорость электрического дрейфазатуханиерелятивистские заряженные частицысильное электрическое полепродольные волнывысокочастотные волновые пакетыциклотронный резонансThis research was funded by the RUDN University Scientific Projects Grant System, project No. 021934-0-000 (K.P. Lovetskiy, L.A. Sevastianov). This research was supported by the RUDN University Strategic Academic Leadership Program (S.P. Karnilovich, S.B. Strashnova, Yahya N. Shaar).Karnilovich, S. P. & Milantiev, V. P. Effect of strong electric-field on resonance interaction between particles and HF waves. Journal of Experimental and Theoretical Physics 94, 537-545 (1989).Karnilovich, S. P. & Milantiev,V. P. On cyclotron damping of longitudinal wave in XIX International Conference on Phenomena in Ionized Gases 4 (1989), 810-811.O’Neil, T. Collisionless Damping of Nonlinear Plasma Oscillations. The Physics of Fluids 8, 2255- 2262. doi:10.1063/1.1761193 (Dec. 1965).Karnilovich, S. P. & Milantiev, V. P. The effect of a strong quasi-stationary electric field on the resonant wave-particle interaction in a magnetized plasma in Mat. of the 6th All-Union Conference on the interaction of electromagnetic radiation with plasma, Dushanbe (1991).Karnilovich, S. P. & Milantiev, V. P. Collection of scientific papers “Problems of quantum. and the stat. Physics” in. Chap. Dynamics of resonant particles in RF fields in the MHD approximation (UDN, Moscow, 1989).Karnilovich, S. P., Milantiev, V. P. & Bespalov, S. V. Effects of the electric drift on the resonant wave-particle interaction in Proc. XXIV Int. Conf. On Phenomena in Ionized Gases - ICPIG-99, Warsaw 2 (1999), 81-82.Karnilovich, S. P., Milantiev, V. P. & Konovalseva, L. V. The influence of the electric drift on resonant wave-particle interaction in Proc. 1992 ICPP Innsdruck. Austria (1992).Karpman,V. I., Istomin, J. N. & Shklyar, D. Nonlinear theory of a quasi-monochromatic whistler mode packet in inhomogeneous plasma. Plasma Physics 16, 685-692. doi:10.1088/0032-1028/16/8/001 (1974).Pocobelli, G. Damping of an electron plasma wave with detrapping of the electrons. The Physics of Fluids 24, 2177-2182. doi:10.1063/1.863334 (1981).Nishida, Y. & Sato, N. Observation of high-energy electrons accelerated by electrostatic waves propagating obliquely to a magnetic field. Physical Review Letters 59, 653-656. doi:10.1103/PhysRevLett.59.653 (1987).Sugawa, M. & Sugaya, R. Nonlinear Interaction between Electrostatic Electron Cyclotron Harmonic Waves and Electrons. Journal of the Physical Society of Japan 54, 1339-1347. doi:10. 1143/JPSJ.54.1339 (1985)