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Proceedings Paper

Cylindrical Gaussian Eigenmodes Of A Rectangular Waveguide Resonator Three-Dimensional Numerical Calculation Of Gain Per Mode
Author(s): Avner Amir; Luis Elias; Juan Gallardo
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Paper Abstract

First we present approximate analytical solutions to the wave equation inside an over-moded metallic rectangular waveguide. The cold eigenmodes are expressed in terms of cylindrical Gaussian-Hermite functions times trigonometric functions to insure the boundary conditions. Next, we discuss a numerical three-dimensional calculation for a Free Electron Laser (FEL) amplifier which is based on the Lienard-Wiechert solution of the Maxwell's equations cast in an integral form. This approach is readily and efficiently extended to include the effects of the metallic boundaries of the waveguide by means of the method of "image currents". Finally, the radiation field in the cavity emitted by the electrons in the presence of the combined fields of a co-propagating eigenmode wave plus a linearly polarized magnetic undulator is expanded in terms of cavity eigenmodes. This expansion allows us to compute the gain per resonator mode.

Paper Details

Date Published: 16 February 1984
PDF: 9 pages
Proc. SPIE 0453, Free-Electron Generators of Coherent Radiation, (16 February 1984); doi: 10.1117/12.947102
Show Author Affiliations
Avner Amir, University of California at Santa Barbara (United States)
Luis Elias, University of California at Santa Barbara (United States)
Juan Gallardo, University of California at Santa Barbara (United States)

Published in SPIE Proceedings Vol. 0453:
Free-Electron Generators of Coherent Radiation
Charles A. Brau; Stephen F. Jacobs; Marlan O. Scully, Editor(s)

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