THEORY OF RELATIVISTIC GYRO-TRAVELING WAVE DEVICES

Using a Hamiltonian formalism, nonlinear, fully relativistic, multimod e, multifrequency equations are derived which describe gyro-traveling wave devices. Nonuniform waveguides and nonlinearly tapered magnetic f ields are incorporated into the analysis. The formalism is used to ana lyze the effect of velocity spread on Doppler upshifted operation. It is shown that with present technology, gyro-traveling wave devices can not operate far from cutoff if high efficiency is desired. As an examp le, the analysis is applied to a 10 GHz, 430 kV, 240 A gyrotwistron op erating at the fundamental cyclotron harmonic with a tapered wall radi us and magnetic field. A realistic design that achieves over 30% effic iency is produced. The issue of stability of this device with respect to competition from parasitic modes is taken up in a companion paper [ Phys. Plasmas 2, 3511 (1995)]. (C) 1995 American Institute of Physics.