If a beam of electrons propagates over the surface of a waveguide and interacts with its mode, amplification of a weak signal is impossible owing to complete symmetry of the processes of radiation and absorption of photons.1 This degeneration can be removed if a waveguide is placed in a gas medium1 or in a constant magnetic field directed along the waveguide axis. In the latter case using the conservation laws of pulse and energy we find that the electrons taking part in absorption and radiation have different pulses. That is why, for a beam of electrons with Gaussian pulse spread, it is possible to obtain population inversion (where the number of radiating electrons is larger than that of absorbing ones) and to amplify a signal.

© 1990 Optical Society of America

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