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Mosc. Math. J., 2011, Volume 11, Number 3, Pages 531–545 (Mi mmj431)  

This article is cited in 9 scientific papers (total in 9 papers)

Resonance-induced surfatron acceleration of a relativistic particle

A. I. Neishtadtab, A. A. Vasilievb, A. V. Artemyevb

a Department of Mathematical Sciences, Loughborough University, Loughborough, United Kingdom
b Space Research Institute, Moscow, Russia

Abstract: We study motion of a relativistic charged particle in a plane slow electromagnetic wave and background uniform magnetic field. The wave propagates normally to the background field. The motion of the particle can be described by a Hamiltonian system with two degrees of freedom. Parameters of the problem are such that in this system one can identify slow and fast variables: three variables are changing slowly and one angular variable (the phase of the wave) is rotating fast everywhere except for a neighborhood of a certain surface in the space of the slow variables called a resonant surface. Far from the resonant surface dynamics of the slow variables may be approximately described by the averaging method. In the process of evolution of the slow variables the particle approaches this surface and may be captured into resonance with the wave. Capture into this resonance results in acceleration of the particle along the wave front (surfatron acceleration). We study the phenomenon of capture and show that a captured particle never leaves the resonance and its energy infinitely grows. Passage through the resonant surface without capture leads to scattering at the resonance, i.e. a small phase-sensitive deviation of actual motion from the motion predicted by the averaging method. We find that repeated scatterings result in diffusive growth of the particle energy. The considered problem is a representative of a wide class of problems concerning passages through resonances in nonlinear systems with fast rotating phases. Estimates of accuracy of the averaging method in this class of problems were for the first time obtained by V. I. Arnold

Key words and phrases: adiabatic invariants, passage through resonance, surfatron acceleration.

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MSC: 34E10, 34D10, 37N05
Received: January 6, 2011

Citation: A. I. Neishtadt, A. A. Vasiliev, A. V. Artemyev, “Resonance-induced surfatron acceleration of a relativistic particle”, Mosc. Math. J., 11:3 (2011), 531–545

Citation in format AMSBIB
\by A.~I.~Neishtadt, A.~A.~Vasiliev, A.~V.~Artemyev
\paper Resonance-induced surfatron acceleration of a~relativistic particle
\jour Mosc. Math.~J.
\yr 2011
\vol 11
\issue 3
\pages 531--545

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    This publication is cited in the following articles:
    1. Artemyev A.V., Vasiliev A.A., Mourenas D., Agapitov O.V., Krasnoselskikh V.V., “Nonlinear Electron Acceleration by Oblique Whistler Waves: Landau Resonance Vs. Cyclotron Resonance”, Phys. Plasmas, 20:12 (2013), 122901  crossref  isi  scopus
    2. A. I. Neishtadt, “Averaging, passage through resonances, and capture into resonance in two-frequency systems”, Russian Math. Surveys, 69:5 (2014), 771–843  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Artemyev A.V., Vasiliev A.A., Mourenas D., Neishtadt A.I., Agapitov O.V., Krasnoselskikh V., “Probability of Relativistic Electron Trapping By Parallel and Oblique Whistler-Mode Waves in Earth's Radiation Belts”, Phys. Plasmas, 22:11 (2015), 112903  crossref  isi  elib  scopus
    4. Artemyev A.V., Mourenas D., Agapitov O.V., Vainchtein D.L., Mozer F.S., Krasnoselskikh V., “Stability of Relativistic Electron Trapping By Strong Whistler Or Electromagnetic Ion Cyclotron Waves”, Phys. Plasmas, 22:8 (2015), 082901  crossref  mathscinet  isi  elib  scopus
    5. Artemyev A.V., Vasiliev A.A., “Resonant Ion Acceleration By Plasma Jets: Effects of Jet Breaking and the Magnetic-Field Curvature”, Phys. Rev. E, 91:5 (2015), 053104  crossref  isi  elib  scopus
    6. Artemyev A.V., Neishtadt A.I., Vasiliev A.A., Mourenas D., “Probabilistic Approach to Nonlinear Wave-Particle Resonant Interaction”, Phys. Rev. E, 95:2 (2017), 023204  crossref  isi  scopus
    7. Artemyev A.V., Neishtadt A.I., Vainchtein D.L., Vasiliev A.A., Vasko I.Y., Zelenyi L.M., “Trapping (Capture) Into Resonance and Scattering on Resonance: Summary of Results For Space Plasma Systems”, Commun. Nonlinear Sci. Numer. Simul., 65 (2018), 111–160  crossref  mathscinet  isi  scopus
    8. Vainchtein D., Zhang X.-J., Artemyev A.V., Mourenas D., Angelopoulos V., Thorne R.M., “Evolution of Electron Distribution Driven By Nonlinear Resonances With Intense Field-Aligned Chorus Waves”, J. Geophys. Res-Space Phys., 123:10 (2018), 8149–8169  crossref  isi  scopus
    9. Mourenas D., Zhang X.-J., Artemyev A.V., Angelopoulos V., Thorne R.M., Bortnik J., Neishtadt A.I., Vasiliev A.A., “Electron Nonlinear Resonant Interaction With Short and Intense Parallel Chorus Wave Packets”, J. Geophys. Res-Space Phys., 123:6 (2018), 4979–4999  crossref  isi  scopus
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