Advertisement

Regular and Chaotic Dynamics

, Volume 15, Issue 4–5, pp 564–574 | Cite as

Regular and chaotic charged particle dynamics in low frequency waves and role of separatrix crossings

  • A. I. NeishtadtEmail author
  • A.V. Artemyev
  • L.M. Zelenyi
Special Issue: Valery Vasilievich Kozlov-60

Abstract

We consider interaction of charged particles with an electromagnetic (electrostatic) low frequency wave propagating perpendicular to a uniform background magnetic field. The effects of particle trapping by the wave and further acceleration of a surfatron type are discussed in details. Method for this analysis based on the adiabatic theory of separatrix crossing is used. It is shown that particle can unlimitedly accelerate in the trapping in electromagnetic waves and energy of particle does not increase for the system with electrostatic wave.

Key words

surfatron acceleration separatrix crossings adiabatic invariant 

MSC2000 numbers

70H11 70K55 70K70 37N05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Artsimovich, L.A. and Sagdeev, R.Z., Plasma Physics for Physicists, Moscow: Atomizdat, 1979 (Russian).Google Scholar
  2. 2.
    Sagdeev, R.Z., Usikov, D.A., and Zaslavsky, G.M., Nonlinear Physics: From the Pendulum to Turbulence and Chaos, New-York: Harwood Academic Publishers, 1988.zbMATHGoogle Scholar
  3. 3.
    Zaslavsky, G.M., Neishtadt, A.I., Petrovichev, B.A., and Sagdeev, R.Z., Mechanism for Enhanced Diffusion in a Wave-particle Interaction in a Weak Magnetic Field, Sov. J. Plasma, 1989, vol. 15, pp. 638–641.Google Scholar
  4. 4.
    Neishtadt, A.I., Artemyev, A.V., Zelenyi, L.M., and Vainchtein, D.L., Surfatron Acceleration in Electromagnetic Waves with Low Phase Velocity, Pisma Zh. Eksp. Teor. Fiz., 2009, vol. 89, no. 9, pp. 528–534 [JETP Lett., 2009, vol. 89, pp. 441–447].Google Scholar
  5. 5.
    Arnold, V.I., Kozlov, V.V., and Neishtadt, A.I., Mathematical Aspects of Classical and Celestial Mechanics, Berlin: Springer, 2006.zbMATHGoogle Scholar
  6. 6.
    Lifshits, I.M., Slutskin, A.A., and Nabutovskij, V.M., On the Phenomenon of Scattering of Charged Quasi-Particles at Singular Points in a p-space, Dokl. Akad. Nauk SSSR, 1961, vol. 137, no. 3, pp. 553–556 (Russian).Google Scholar
  7. 7.
    Lifshits, I.M., Slutskin, A.A., and Nabutovskij, V.M., Motion of Charged Quasiparticles in a Varying Inhomogeneous Electromagnetic Field, Sov. Phys., JETP, 1962, vol. 14, pp. 669–675.Google Scholar
  8. 8.
    Gurevich, A.V. and Tsedilina, E.E., Long Distance Propagation of HF Radio Waves, Berlin: Springer-Verlag, 1985.Google Scholar
  9. 9.
    Neishtadt, A.I., Passage Through a Separatrix in a Resonance Problem with a Slowly-varying Parameter, Prikl. Mat. Meh., 1975, vol. 39, nos. 4–6, pp. 1331–1334 [J. Appl. Math. Mech., 1975, vol. 39, pp. 594–605].MathSciNetGoogle Scholar
  10. 10.
    Büchner, J. and Zelenyi, L.M., Regular and Chaotic Charged Particle Motion in Magnetotaillike Field Reversals. 1: Basic Theory of Trapped Motion, J. Geophys. Res., 1989, vol. 94, no. A9, pp. 11821–11842.CrossRefGoogle Scholar
  11. 11.
    Henrard, J., The Adiabatic Invariant in Classical Mechanics, in: Dynamics Reported, Expositions in Dynamical Systems, vol. 2, Berlin: Springer, 1993, pp. 117–235.Google Scholar
  12. 12.
    Landau, L.D. and Lifshitz, E.M., Course of Theoretical Physics, Vol. 1: Mechanics, Oxford: Pergamon, 1988.Google Scholar
  13. 13.
    Sagdeev, R.Z., Reviews of Plasma Physics. Volume 4, New York: Consultants Bureau, 1966.Google Scholar
  14. 14.
    Katsouleas, T. and Dawson, J.M., Unlimited Electron Acceleration in Laser-driven PlasmaWaves, Phys. Rev. Lett., 1983, vol. 51, pp. 392–395.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. I. Neishtadt
    • 1
    • 2
    Email author
  • A.V. Artemyev
    • 1
  • L.M. Zelenyi
    • 1
  1. 1.Space Research Institute (IKI)MoscowRussia
  2. 2.Dept. of Math. SciencesLoughborough UniversityLoughboroughUK

Personalised recommendations