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The electron cyclotron maser instability is shown to support backward wave oscillation in a traveling-wave gyrotron. Numerical values for two parameters that identify oscillation thresholds are determined.

The theory of linear and stimulated free-electron lasers using the Smith-Purcell effect is presented. These lasers depend upon the resonant interaction of an electron beam with the longitudinal field of a surface-harmonic wave on a diffraction grating. Detailed design criteria for the linear Smith-Purcell-effect laser are determined. Numerical estimates show that infrared lasers are feasible at beam currents smaller than 1 A and that single-mode operation may be achieved. Saturation estimates determine the power output in the range 102 W. An expression for the gain of the stimulated Smith-Purcell laser is derived. The frequency up-conversion factor for the stimulated interaction may be very large. Its possible use as a soft x-ray laser is limited by the available intensity of the pump wave.

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