An electron beam coupled to an undulator magnet and a radiation field can exhibit a collective instability.1 In this mode the electron beam is micro-bunched at the radiation wavelength and generates coherent radiation. The efficiency of energy transfer from the electron beam to the radiation field is a function of beam current and quality. We examine the effects of both an angular and an energy spread in the incident electron beam on the efficiency. For a 500-MeV electron beam with characteristics obtainable in a storage ring, one can produce coherent radiation in the 10-50-Å region with an efficiency of the order of 0.1 %, peak and average powers of the order of 1 GW and 1 W, respectively, and a linewidth of ~10−6.

© 1984 Optical Society of America

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