Asymptotic analysis of the model of gyromagnetic autoresonance
- 28 Downloads
The system of ordinary differential equations that in a specific case describes the cyclotron motion of a charged particle in an electromagnetic wave is considered. The capture of the particle into autoresonance when its energy undergoes a significant change is studied. The main result is a description of the capture domain, which is the set of initial points in the phase plane where the resonance trajectories start. This description is obtained in the asymptotic approximation with respect to the small parameter that in this problem corresponds to the amplitude of the electromagnetic wave.
Keywordsnonlinear oscillations small parameter asymptotics autoresonance
Unable to display preview. Download preview PDF.
- 4.L. A. Kalyakin, “Asymptotic analysis of the model of the cyclotron gyromagnetic autoresonance,” Vestn. Chelyab. Gos. Univ., Ser. Fizika, No. 21, 68–74 (2015).Google Scholar
- 7.L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 2: The Classical Theory of Fields (Nauka, Moscow, 1973; Pergamon, Oxford, 1975).Google Scholar
- 9.A. A. Kolomenskii and A. N. Lebedev, “Resonance phenomena in the motion of particles in a plane electromagnetic wave,” Zh. Eksp. Teor. Fiz 44, 261–269 (1963).Google Scholar
- 10.V. Ya. Davydovskii, “On the resonance acceleration of charged particles by electromagnetic waves in a constant magnetic field,” Zh. Eksp. Teor. Fiz 43, 886–888 (1962).Google Scholar
- 11.V. I. Veksler, “A new method for the acceleration of relativistic particles,” Dokl. Akad. Nauk SSSR 43, 346–348 (1944).Google Scholar
- 12.V. I. Veksler, “On a new method for the acceleration of particles,” Dokl. Akad. Nauk SSSR 44, 393–396 (1944).Google Scholar
- 14.A. I. Neishtadt, “Crossing the separatrix in the resonance problem with a slowly varying parameter,” Prikl. Mat. Mekh. 39, 621–632 (1975).Google Scholar
- 15.O. M. Kiselev, “Oscillations near the separatrix in the Duffing equation,” Trudy Inst. Mat. Mek. Ural. Otd. Ross. Akad. Nauk. 18 (2), 141–153 (2012).Google Scholar
- 17.G. M. Zaslavsky and R. Z. Sagdeev, Nonlinear Physics: From the Pendulum to Turbulence and Chaos (Nauka, Moscow, 1977; Harwood, New York, 1988).Google Scholar
- 18.A. I. Neishtadt and A. V. Timofeev, “Autoresonance in electron cyclotron heating of a plasma,” Zh. Eksp. Teor. Fiz. 93, 1706–1713 (1987).Google Scholar
- 22.R. N. Garifullin, “An analysis of the growth of solutions to a nonlinear equation depending on the initial data,” in Collected Papers of School–Conference on Mathematics and Physics for Students, Graduate Students, and Young Scientists, Vol. 1: Mathematics (Ufa, 2003), pp. 189–195.Google Scholar