The Non-Linear Theory of the Free Electron Laser with Transverse Dimensional Effects

  • P. Sprangle
  • Cha-Mei Tang
Part of the Ettore Majorana International Science Series book series (SLAP, volume 49)


This paper treats finite transverse dimensional effects associated with i) the wiggler field, ii) electron beam and iii) radiation beam in a steady state free electron laser (FEL) in an amplifying configuration. Our formulation incorporates various efficiency enhancement schemes such as spatially contouring the wiggler field as well as accelerating the electron beam. Three dimensional effects associated with the wiggler field introduce an axial velocity shear which is equivalent to a beam temperature. For a given amplitude input signal, the transverse gradients in the wiggler places a restriction on the electron beam radius. The restriction on the radius insures that a substantial fraction of beam electrons will be trapped in the ponderomotive brackets. We also find that the radiation field experiences diffraction and refraction effects in such a way that the superposition of the input radiation field and excited radiation field do not destructively interfere. Finally, a 3-D numerical illustration of a 10.6 μm FEL with enhanced efficiency is given.


Electron Beam Radiation Field Free Electron Laser Input Field Refraction Effect 
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  1. 1.
    J.M.J. Madey, J. Appl. Phys. 42, 1906 (1971).ADSCrossRefGoogle Scholar
  2. 2.
    P. Sprangle and V.L. Granatstein, Appl. Phys. Lett. 25, 377 (1974).ADSCrossRefGoogle Scholar
  3. 3.
    W.B. Colson, Phys. Lett. A, 59, 187 (1976).ADSCrossRefGoogle Scholar
  4. 4.
    P. Sprangle, R. A. Smith and V.L. Granatstein, NRL Report No. 3911 (1978) and Infrared and Millimeter Waves, Edited by K. Button (Academic Press, New York, 1979), Vol. 1.Google Scholar
  5. 5.
    N. M. Kroll and W.A. McMullin, Phys. Rev. A 17, 300 (1978).ADSCrossRefGoogle Scholar
  6. 6.
    P. Sprangle and A. T. Drobot, J. Appl. Phys. 50, 2652 (1979).ADSCrossRefGoogle Scholar
  7. 7a.
    P. Sprangle, Cha-Mei Tang and W. M. Manheimer, Phys. Rev. Lett. 43, 1932 (1979), and Phys. Rev. A 21, 302 (1980).ADSCrossRefGoogle Scholar
  8. 7b.
    P. Sprangle and Cha-Mei Tang, Proc. 4th Int’l Conf. on Infrared and Near Millimeter Waves, S. Perkowitz, Ed. Miami Brach, 10–15 Dec 1979, p. 98.Google Scholar
  9. 8.
    P. Sprangle and R.A. Smith, NRL Report No. 4033 (1979) and Phys. Rev. A 21, 293 (1980).ADSCrossRefGoogle Scholar
  10. 9.
    Free-Electron Generators of Coherent Radiation, Physics of Quantum Electronics, Vol. 7, (1980), Edited by S. F. Jacobs, H. S. Pilloff, M. Sargent III, M. O. Scully and R. Spitzer, Addison--Wesley Publishing Co.Google Scholar
  11. 10.
    N. M. Kroll, P. Morton and M. N. Rosenbluth, JASON Tech. Report JSR-79-15, 1980.Google Scholar
  12. 11.
    G. Bekefi and R. E. Shefer, J. Appl. Phys. 50, 5158 (1979).ADSCrossRefGoogle Scholar
  13. 12.
    T. Kwan and J. M. Dawson, Phys. Fluids 22, 1089 (1979).ADSzbMATHCrossRefGoogle Scholar
  14. 13.
    A. T. Lin and J. M. Dawson, Phys. Rev. Lett. 42, 1670 (1979).ADSCrossRefGoogle Scholar
  15. 14.
    R. C. Davidson, H.S. Uhm and R. E. Aamodt, Plasma Fusion Center, MIT Report PFC/JA-80-4 (1980).Google Scholar
  16. 15.
    A. A. Kolomenskii and A.N. Lebedev, Soc. J. Quantum Electron 8, 879 (1978).Google Scholar
  17. 16.
    L. Friedland and J. L. Hirshfield, Phys. Rev. Lett. 44, 1456 (1980).ADSCrossRefGoogle Scholar
  18. 17.
    3-D effects in the FEL have been discussed by i) J. Slater, DARPA FEL Review, Arlington, Va., Dec 3–4, 1979, ii) P. Sprangle and Cha-Mei Tang, DARPA/ONR/AFOSR FEL Program Review, LASL, April 24–25, 1980, and iii) Y. P. Ho, Y. C. Lee and M. N. Rosenbluth, Sherwood Meeting, Tucson, Arizona, April 23–25, 1980.Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • P. Sprangle
    • 1
  • Cha-Mei Tang
    • 2
  1. 1.Naval Research LaboratoryUSA
  2. 2.JAYCORAlexandriaUSA

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