Cylindrical Gaussian Eigenmodes Of A Rectangular Waveguide Resonator Three-Dimensional Numerical Calculation Of Gain Per Mode

Avner Amir; Luis Elias; Juan Gallardo

doi:10.1117/12.947102

16 February 1984 Cylindrical Gaussian Eigenmodes Of A Rectangular Waveguide Resonator Three-Dimensional Numerical Calculation Of Gain Per Mode

Avner Amir, Luis Elias, Juan Gallardo

Author Affiliations +

Proceedings Volume 0453, Free-Electron Generators of Coherent Radiation; (1984) https://doi.org/10.1117/12.947102
Event: Free-Electron Generators of Coherent Radiation, 1983, Orcas Island, United States

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.

Citation Download Citation

Avner Amir, Luis Elias, and Juan Gallardo "Cylindrical Gaussian Eigenmodes Of A Rectangular Waveguide Resonator Three-Dimensional Numerical Calculation Of Gain Per Mode", Proc. SPIE 0453, Free-Electron Generators of Coherent Radiation, (16 February 1984); https://doi.org/10.1117/12.947102

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