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Andrews, H. L.

Paper Title Page
MOPPH025 Three-dimensional Theory of the Cerenkov Free-Electron Laser 73
 
  • C. A. Brau, H. L. Andrews
    Vanderbilt University, Nashville, Tennessee
 
  We present an analytical theory for the operation of a Cerenkov free-electron laser which includes diffraction of the optical mode in the direction transverse to the electron beam. Because the width of the optical mode depends on the gain, the usual cubic dispersion relation is replaced by a 5/2-power dispersion relation, however, only two of these roots are allowed. These two roots both have positive real parts, indicating that they are slow waves. For a narrow electron beam, the optical mode is much wider than the beam, thus reducing the gain by an order of magnitude from that predicted by the two dimensional theory. In the limit of a wide electron beam, the two dimensional theory is recovered.  
MOPPH026 Three-Dimensional Theory of the Smith-Purcell Free-Electron Laser 77
 
  • H. L. Andrews, C. A. Brau, J. D. Jarvis
    Vanderbilt University, Nashville, Tennessee
 
  We present an analytic theory for the operation of a Smith-Purcell free-electron laser (SPFEL) that includes transverse diffraction of the optical beam. For the case of an infinitely wide electron beam, this theory agrees with previous two-dimensional analyses. When the electron beam is narrow compared to the mode, the gain (amplifier regime) is substantially reduced by diffraction, while its dependence on the beam current is increased due to gain guiding. A 5/2-power dispersion relation replaces the conventional cubic dispersion relation. Additionally, the constituent waves of the laser mode are found to have different transverse decay rates. An estimate of the start current (oscillator regime) of the device is obtained by satisfying the appropriate boundary conditions on the beam axis.