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Nonrelativistic Dynamics of the Charged Particles at Cyclotron Resonances


V. A. Buts, E. S. Voitsenya, A. P. Tolstoluzhsky

The new mechanicm of stochastization of movement nonrelativistic charged particles in conditions of an isolated cyclotron resonance is studied. Is investigated both dynamics of the separate charged particle, and dynamics of their ensemble, which by a self-consistent way excite of an electromagnetic wave. The interactions of a type a wave – particle underlie physics of plasma, physics of beams of the charged particles and in a basis of other directions of physics. The special role at such interaction is belong to resonances. their number is small. Among resonances the greatest role are play Cherenkov resonance and cyclotron resonances. Conditions of occurrence of dynamic chaos in conditions of all known resonances now are formulated, the scenario of transition from regular dynamics to chaotic dynamics is determined. At this was shown, that in all cases slow dynamics of the charged particles can be described by model of a mathematical pendulum. The transition to dynamic chaos in such model arises at overlapping nonlinear resonances (criterion Chirikov). Thus, in all cases was considered, that the dynamic chaos arises only as result of interaction of nonlinear resonances, i. e. at an essential role in dynamics of several resonances. In the work is shown, that the dynamic chaos can develop in conditions of a isolated cyclotron resonance. Under this condition the slow dynamics of particles is described not by model of a mathematical pendulum, but with model other new nonlinear oscillator. The phase portrait this oscillator, in generally, contain three special points: two points such as “centre” and one point such as “saddle”. He is similar to a phase portrait of Duffing oscillator, but is not identical to him. The important feature of this oscillator is that fact that at increase of amplitude of a wave two special points (point such as “centre” and point such as “saddle”) merges and disappears. If now intensity of a field of a wave will fall, these points again are born. thus, if the amplitude of a field of a wave will be modulated, the phase portrait will undergo periodic bifurcations. Is shown, what just these bifurcations are the reason of occurrence of dynamic chaos in conditions of a isolated cyclotron resonance. Thus, the main results of work are: the formulation of model new nonlinear oscillator, and also new mechanism of occurrence of dynamic chaos in conditions of an isolated cyclotron resonance. Besides in work the results of the numerical analysis of dynamics of ensemble charged particles in conditions of an isolated cyclotron resonance are given. Is shown, that as soon as density of the charged particles appears enough large – such, that the amplitude of a raised wave becomes enough large and the level of its modulation also is great enough – that qualitatively picture of collective process of excitation of oscillation and script of birth of a chaotic mode it appear similar to a picture at study of dynamics of one particleю.
June 24, 2020
May 29, 2020

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