Gain Expanded Free Electron Lasers

Abstract

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

$$ {{\rm{\lambda }}_{\rm{r}}}\;{\rm{ = }}\;\frac{{{{\rm{\lambda }}_{\rm{w}}}}}{{{2_{\rm{\lambda }}}}}2\;\;\left( {1\;{\rm{ + }}\;\;\frac{{{{\rm{e}}^2}{{\rm{B}}_{\rm{w}}}{}^2{{\rm{\lambda }}_{\rm{w}}}^2}}{{{{\left( {2{\rm{\pi }}\;{\rm{m}}{{\rm{c}}^2}} \right)}^2}}}} \right)\;\;\; \equiv \;\;\frac{{{}^{\rm{\lambda }}{\rm{w}}}}{{2{\rm{\gamma }}}}2\;\;\left( {1\;{\rm{ + }}\;{{\rm{\alpha }}^2}\;{{\rm{B}}_{\rm{w}}}{}^2} \right) $$

(1)

can be satisfied even for electrons of differing energies if the value of the magnetic field seen by any electron, B_w, 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.

Work supported in part by the Office of Naval Research under contract N00014-78-C-0403.