Gain Expanded Free Electron Lasers

  • James N. Eckstein
Part of the Ettore Majorana International Science Series book series (SLAP, volume 49)


Gain expansion is a technique that was proposed to make the operation of an FEL insensitive to energy spread in the electron beam (1,2). To see how this can be done, we note that the basic synchronism condition
$$ {{\rm{\lambda }}_{\rm{r}}}\;{\rm{ = }}\;\frac{{{{\rm{\lambda }}_{\rm{w}}}}}{{{2_{\rm{\lambda }}}}}2\;\;\left( {1\;{\rm{ + }}\;\;\frac{{{{\rm{e}}^2}{{\rm{B}}_{\rm{w}}}{}^2{{\rm{\lambda }}_{\rm{w}}}^2}}{{{{\left( {2{\rm{\pi }}\;{\rm{m}}{{\rm{c}}^2}} \right)}^2}}}} \right)\;\;\; \equiv \;\;\frac{{{}^{\rm{\lambda }}{\rm{w}}}}{{2{\rm{\gamma }}}}2\;\;\left( {1\;{\rm{ + }}\;{{\rm{\alpha }}^2}\;{{\rm{B}}_{\rm{w}}}{}^2} \right) $$
can be satisfied even for electrons of differing energies if the value of the magnetic field seen by any electron, Bw, is correlated with its energy, γ. This leads to energy independent gain. Gain expanded magnets accomplish this correlation by incorporating a transverse gradient to the wiggler field and dispersing the electrons injected in the FEL to match the intrinsic dispersion of the wiggler.


Optical Field Maximum Gain Gain Curve Small Signal Gain Phase Slippage 
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  1. 1.
    T. I. Smith, J. M. J. Madey, L. R. Elias and D. A. G. Deacon J. Appl. Phys. 50, 4580 (1979).ADSCrossRefGoogle Scholar
  2. 2.
    J. M. J. Madey and R. C. Taber, in Physics of Quantum Electronics, V. 7, ed. S. Jacobs, H. Pilloff, M. Sargent, M. Scully and R. Spitzer, Addison-Wesley (1980).Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • James N. Eckstein
    • 1
  1. 1.W. W. Hansen Laboratories of PhysicsStanford UniversityStanfordUSA

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