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Physical Review A
Volumn 32, Issue 1, 1985, Pages 460-471
Plasma-wave generation in the beat-wave accelerator
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EID: 0001131104     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.32.460     Document Type: Article
Times cited : (60)
References (14)
  • 8
    • 84927181749 scopus 로고    scopus 로고
    • D. J. Sullivan and B. B. Godfrey, in Laser Acceleration of Particles (Los Alamos, 1982) (AIP, New York, 1982), p. 43; The Challenge of Ultra-High Energies, edited by J. Mulvey (European Committee for Future Accelerators 83/68, Rutherford Appleton Laboratory, Oxford, 1983), p. 209.
  • 11
    • 84927181748 scopus 로고    scopus 로고
    • A. I. Akhiezer, I. A. Akhiezer, R. V. Polovin, A. G. Sitenko, and K. N. Stepanov, Plasma Electrodynamics, Vol. 2 (Pergamon, New York, 1975).
  • 12
    • 84927181746 scopus 로고    scopus 로고
    • L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Course of Theoretical Physics, Vol. 2, 4th ed. (Pergamon, New York, 1975), p. 118.
  • 13
    • 84927181744 scopus 로고    scopus 로고
    • A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981). For the benefit of the reader unfamiliar with this technique, we note that the KBM method applied to Eq. (4.3) seeks a uniform expansion (i.e., no secular or small divisor terms) for the solution as a series y( τ )=ε a cos φ + ε2y2(a, φ ) + .., where epsilon is a perturbative bookkeeping device set to unity at the end of the calculation. The amplitude-phase equations are series of the form da/d( ωpτ )= ε A1(a) + ε2A2(a) + .. and d φ /d ( ωpτ )=1 +ε Φ1(a) + ε2Φ2(a)+ ... Using these expansions in Eq. (4.3) and solving for the yn, An, and Φn order by order in epsilon, one finds that the scaling Rppd2== ε3f ensures uniform behavior of the series y( τ ). The amplitude-phase equations (4.5) have relegated secular terms to O( ε5ωpτ ), involving terms proportional to a5ωptau and a2Rppd2ωptau. Consequently the solution (4.4) is uniformly valid for all ωpτ

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