Cylindrical Gaussian eigenmodes of a rectangular waveguide resonator: three-dimensional numerical calculation of gain per mode. Technical report, 1 October 1983-30 September 1984

Technical Report · Sun Jan 01 04:00:00 EST 1984

OSTI ID:5725252

First we present approximate analytical solutions to the wave equation inside an over-moded metallic retangular waveguide. The cold eigenmodes are expressed in terms of cylindrical Gaussian-Hermite functions times trigonometric functions to insure the boundary conditions. A numerical three-dimensional calculation for a free electron laser (FEL) amplifier is discussed, 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 the gain per resonator mode to be computed.

• Research Organization: California Univ., Santa Barbara (USA). Quantum Inst.
• OSTI ID: 5725252
• Report Number(s): AD-A-164276/8/XAB; TR-24,
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300* -- Engineering-- Lasers-- (-1989)
AMPLIFICATION
CAVITY RESONATORS
DIFFERENTIAL EQUATIONS
EIGENVECTORS
ELECTRONIC EQUIPMENT
ELECTRONS
ELEMENTARY PARTICLES
ELEMENTS
EQUATIONS
EQUIPMENT
FERMIONS
FREE ELECTRON LASERS
GAIN
LASER CAVITIES
LASERS
LEPTONS
LOW TEMPERATURE
METALS
MODE LOCKING
PARTIAL DIFFERENTIAL EQUATIONS
RESONATORS
WAVE EQUATIONS
WAVEGUIDES