A generalized nonlinear electron-wave interaction theory has been developed for the crossed-field emitting-sole amplifier in order to explain the physical phenomena involved in the interaction and ultimately to provide a basis for design. The effects of d-c, r-f and space-charge forces are taken into account and secondary emission from the sole electrode is included in the theory. Solution of the system equations on a digital computer involves following a set of N change groups through the interaction region using electron phase position and interaction length as the independent variables. Representative solutions for various d-c and r-f conditions will be presented in terms of the variation of electron generalized coordinates (positions and velocities) and r-f wave variables (amplitude and phase) vs. interaction distance in electronic wavelengths. Operation above and below the magnetron cutoff condition will be discussed and the effects of space charge secondary emission on the saturated gain and conversion efficiency will be illustrated. In addition a closed-form analysis (HKB) has been used to gain better insight into the interaction process. This will be discussed along with the use of nonuniform magnetic field distributions to enhance the saturation gain.
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