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Three-dimensional theory of the free-electron laser in the collective regime

Physical Review A, ISSN: 1050-2947, Vol: 28, Issue: 6, Page: 3438-3449
1983
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  • Citations
    87
    • Citation Indexes
      87

Article Description

A fully self-consistent theory of the free-electron laser is derived in the collective regime which includes all transverse variations in the wiggler field as well as the effects of a finite waveguide geometry. A general orbit theory is derived by perturbation about the steady-state trajectories in a configuration which consists of an axial guide field in addition to the helical wiggler field, and used to obtain the source current and charge density for the Maxwell-Poisson equations. By this means, a set of coupled differential equations is found which describes an arbitrary radial beam profile. A dispersion equation is obtained under the assumption of a thin monoenergetic beam, and solved numerically for the growth rates of the TE11 and TM11 modes in a cylindrical waveguide. A selection rule is found by which the TElm or TMlm modes are resonant at the lth free-electron-laser Doppler upshift. © 1983 The American Physical Society.

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