The Large-Signal Behavior of Crossed-Field Traveling-Wave Devices

A large-signal theory for the interaction between a slow wave and a beam of electrons traveling in crossed dc electric and magnetic fields is formulated. The adiabatic equations of motion are used, space-charge forces are neglected, but phase focusing by the rf field and loss of the beam at the anode and sole plate are taken into account. The limits of validity of the conventional small-signal theory are obtained, and an analog computer is employed to follow the interaction to power saturation. Results are presented for a forward-wave amplifier, backward-wave amplifier, and backward-wave oscillator. It is shown that for very short lengths the backward-wave amplifier may give superior results to the equivalent forward-wave amplifier but that otherwise greater gain and efficiency can be obtained with a forward-wave amplifier. However, it is shown that there is a mode of operation for a backward-wave tube equivalent to an oscillator started by and then locked to the input signal, a condition unlike anything obtained in the equivalent longitudinal twt. Also, it is shown that in a forward-wave or backward-wave tube, the gain is dependent on the input signal and may increase as the input signal level is increased. However, it is apparent that this type of device has inherently a low gain, especially when designed for high efficiency. Consequently, some suggestions which have been made for improving this deficiency are examined.