Cancellation of Transverse Excitation in Gain Expanded Free Electron Lasers

  • John M. J. Madey
Part of the Ettore Majorana International Science Series book series (SLAP, volume 49)


We define and analyze emittance growth in gain expanded free electron lasers, develop criteria for the minimization of this phenomenon, and present some examples of the application of these criteria.


Synchrotron Radiation Storage Ring Laser Operation Free Electron Laser Quantum Fluctuation 
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References and Footnotes

  1. 1.
    T. I. Smith, J.M.J. Madey, L. R. Elias, and D.A.G. Deacon, Reducing the Sensitivity of a Free Electron Laser to Electron Energy, J. Appl. Phys. 50:4580 (1979).ADSCrossRefGoogle Scholar
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    J.M.J. Madey, Scaling Relations for the Power Output of Gain Expanded Storage Ring Free Electron Lasers, HEPL-853, June 1979.Google Scholar
  3. 3.
    M. Sands, The Physics of Electron Storage Rings — An Introduction, SLAC Report 121 (November 1970), Eqs. (2.42) and (2.45). A preliminary version of these notes was published in Physics with Interacting Storage Rings, B. Touschek, ed. (Academic Press, 1971).Google Scholar
  4. 4.
    M. Sands, ibid.Google Scholar
  5. 5.
    J.M.J. Madey and R. C. Taber, Equations of Motion in a Free Electron Laser Magnet with a Transverse Gradient, in: “Physics of Quantum Electrons, V. 7,” S. Jacobs, H. Pilloff M. Sargent, M. Scully, and R. Spitzer, eds., Addison-Wesley, Reading, MA (1980).Google Scholar
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  9. 9.
    M. Sands, op. cit., Eq. (2.56).Google Scholar
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    M. Sands, op. cit., Eqs. (2.42) and (2.45).Google Scholar
  11. 11.
    M. Sands, op. cit., Eq. (2.29).Google Scholar
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    The members of the ensemble are assumed to be uniformly distributed in the betatron phase.Google Scholar
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    Note that the area A enclosed by ensemble in the two dimensional (x,x’) phase space can also be changed by interactions which rotate the ensemble out of the (x,x’) plane.Google Scholar
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    We assume similar series expansion for \({\rm{\bar \delta }} \) and Δψ \( {\rm{\bar \delta }} \equiv \sum\limits_{{\rm{j}} = 0}^\infty {{{\rm{\delta }}_{\rm{j}}}{\& ^{\rm{j}}}} \;\;\;{\rm{,}}\;\;\;\Delta {\rm{\psi }}\; \equiv \;\sum\limits_{{\rm{j}} = 0}^\infty {\Delta {{\rm{\psi }}_{\rm{j}}}{\& ^{\rm{j}}}} \;\;\;\;{\rm{.}} \) Google Scholar
  23. 23.
    W. B. Colson, Free Electron Laser Theory, Ph.D. dissertation (Stanford University, 1977), unpublished.Google Scholar
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    J.M.J. Madey, D. Deacon, and T. I. Smith, op. cit. Google Scholar
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    F. Reif, “Fundamentals of Statistical and Thermal Physics,” McGraw-Hill, New York (1965), p. 577.Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • John M. J. Madey
    • 1
  1. 1.Physics Department & High Energy Physics LaboratoryStanford UniversityStanfordUSA

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