Hierarchical Asymptotic Methods in the Theory of Cluster Free Electron Lasers

  • Victor V. Kulish
  • Alexander V. Lysenko
  • Alla Ju. Brusnik


We describe an algorithm for the hierarchic method of averaged characteristics and discuss a practical application of this concept. The application of this method opens new prospects for the solutions of many difficult electrodynamic problems, which, until recently, were considered “unsolved”. We illustrate this method with the example of the effect of plural multi-harmonic parametric resonance of electron-beam waves. This effect can take place within high-current electron beams in the case of the realization of two-stream instability. The considered relativistic beam-model is treated as a model for the transit section of relevant klystron Cluster Two-stream Free Electron Laser (CTSFEL).


Hierarchic method of averaged characteristics Plural multi-harmonic parametric resonance Two-stream instability Cluster free electron laser 


  1. 1.
    V.V. Kulish, Hierarchic Electrodynamics and Free Electron Lasers (CRC Press, Taylor & Francis Group, 2011).CrossRefGoogle Scholar
  2. 2.
    V.V. Kulish, Hierarchic Methods. Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics. Vol. 1 (Kluwer Academic Publishers, Dordrecht/Boston/London, 2002).Google Scholar
  3. 3.
    V.V. Kulish, Hierarchic Methods. Undukative Electrodynamic Systems. Vol. 2 (Kluwer Academic Publishers, Dordrecht/Boston/London, 2002).Google Scholar
  4. 4.
    King-Yuen Ng, Physics of Intensity Dependent Beam Instabilities (World Scientific Publishing Company, Incorporated, 2006).Google Scholar
  5. 5.
    N.A. Krall, and A.W. Trivelpiece, Principles of Plasma Physics (San Francisco Press, New York, 1986).Google Scholar
  6. 6.
    “Report to the APS of the Study Group on Science and Technology of Directed Energy Weapons: Executive Summary and Major Conclusions”, Phys. Today, 40, S3 (1987)Google Scholar
  7. 7.
    T.C. Marshall, Free electron laser (MacMillan, New York, London, 1985).Google Scholar
  8. 8.
    H.P. Freund, and T.M. Antonsen, Principles of Free Electron Lasers (Springer, Berlin-Heidelberg-New York-Tokyo, 1996).Google Scholar
  9. 9.
    F.P. Miller, A.F. Vandome, J. McBrewster. Free Electron Laser. (VDM Publishing House Ltd., 2010).Google Scholar
  10. 10.
    V.V. Kulish, A.V. Lysenko, V.I. Savchenko, “Two-Stream Free Electron Lasers: General Properties,” Int. J. Infrared Millim. Waves 24, 129 (2003).CrossRefGoogle Scholar
  11. 11.
    V.V. Kulish, A.V. Lysenko, V.I. Savchenko, “Two-Stream Free Electron Lasers: Physical Analysis of the Systems with Monochromatic Pumping,” Int. J. Infrared Millim. Waves 24, 285 (2003).CrossRefGoogle Scholar
  12. 12.
    V.V. Kulish, A.V. Lysenko, V.I. Savchenko, “Two-stream free electron lasers. Physical and project analysis of the multiharmonic models,” Int. J. Infrared Millim. Waves 24, 501 (2003).CrossRefGoogle Scholar
  13. 13.
    B.W.J. McNeil, G.R.M. Robb, “Two-beam free-electron laser”, Phys. Rev. E 70, 035501 (2004).CrossRefGoogle Scholar
  14. 14.
    W. Liu, Z. Yang, Z. Liang, “Instability of Two-stream Free-electron Laser with an Axial Guiding Magnetic Field”, Int. J. Infrared Millim. Waves 27, 1073 (2006).CrossRefGoogle Scholar
  15. 15.
    H. Mehdian, N. Abbasi, “Dispersion relation and growth in a two-stream free electron laser with helical wiggler and ion channel guiding”, Phys. Plasmas 15, 013111 (2008).CrossRefGoogle Scholar
  16. 16.
    V.V. Kulish, A.V. Lysenko, A.Ju. Brusnik, “Active FEL-klystrons as formers of Femto-second clusters of electromagnetic field,” J. Nano- Electron. Phys. (Ukraine) 2, No2, 50 (2010).Google Scholar
  17. 17.
    V.V. Kulish, A.V. Lysenko, V.I. Savchenko, I.G. Majornikov, “The Two-Stream Free Electron Laser as a Source of Electromagnetic Femto-Second Wave Packages,” Laser Physics 15, 1629 (2005).Google Scholar
  18. 18.
    V.V. Kulish, A.V. Lysenko, I.G. Mayornikov, “The two-stream multi-harmonic FEL as a powerful source of Femto-second wave package,” Proceedings of the National Aviation University (Ukraine), 126 (2005).Google Scholar
  19. 19.
    J. Weiland, H. Wilhelmsson, Coherent non-linear interaction of waves in plasmas (Pergamon, Oxford, 1977).Google Scholar
  20. 20.
    D.I. Trubetskov, A.E. Khramov Lections on the microwave electronics for physicists (Fizmatlit, Moscow, 2003).Google Scholar
  21. 21.
    S.A. Akhmanov, V.A. Vysloukh, A.S. Chirkin, Physics of the Femto-second laser pulses (Nauka, Moscow, 1988).Google Scholar
  22. 22.
    C. N. Lashmore-Davies, “Two-stream instability, wave energy, and the energy principle”, Phys. Plasmas 14, 092101 (2007).CrossRefGoogle Scholar
  23. 23.
    D.V. Rose, T.C. Genoni, D.R. Welch, E.A. Startsev, R.C. Davidson, “Two-stream instability analysis for propagating charged particle beams with a velocity tilt”, Phys. Rev. ST Accel. Beams 10, 034203 (2007).CrossRefGoogle Scholar
  24. 24.
    E.A. Startsev, R.C. Davidson, “Two-stream instability for a longitudinally compressing charged particle beam”, Phys. Plasmas 13, 062108 (2006).CrossRefGoogle Scholar
  25. 25.
    P. Schmuser, M. Ohlus, and J. Rossbach, Ultraviolet and Soft X-Ray Free Electron Lasers: Introduction to Physical Principles, Experimental Results, Technological Challenges (Springer, Berlin-Heidelberg-New York-Tokyo, 2008).Google Scholar
  26. 26.
    E.L. Saldin, E.V. Schneidmiller, and M.V. Yurkov, The Physics of Free Electron Lasers (Springer, Berlin-Heidelberg-New York-Tokyo, 2000).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Victor V. Kulish
    • 1
  • Alexander V. Lysenko
    • 2
  • Alla Ju. Brusnik
    • 1
  1. 1.National Aviation UniversityKievUkraine
  2. 2.Sumy State UniversitySumyUkraine

Personalised recommendations