Abstract
Excitation of a slow space-charge wave and a TM waveguide mode by passage of a relativistic electron beam through a static, spatially periodic, longitudinal electric field is investigated. The non-linear wave equation, free-electron-laser dispersion relation and spatial growth rate formula are derived in the laboratory reference frame. A formula for the energy-conversion efficiency based on saturation by electron trapping in the space-charge wave is also derived. Equations for transformation to the beam reference frame are presented. The results of a numerical study indicate that efficiencies of 25 to 60% and radiation wavelengths in the millimetre range are possible by operation near cut-off of the TM mode. Radiation wavelengths of the order of 100 mu m or less with somewhat lower efficiencies and growth rates may be obtained by operation above cut-off using a 1 cm pump wavelength
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