Theory of relativistic gyro-traveling wave devices

Using a Hamiltonian formalism, nonlinear, fully relativistic, multimode, multifrequency equations are derived which describe gyro-traveling wave devices. Nonuniform waveguides and nonlinearly tapered magnetic fields are incorporated into the analysis. The formalism is used to analyze the effect of velocity spread on Doppler upshifted operation. It is shown that with present technology, gyro-traveling wave devices cannot operate far from cutoff if high efficiency is desired. As an example, the analysis is applied to a 10 GHz, 430 kV, 240 A gyrotwistron operating at the fundamental cyclotron harmonic with a tapered wall radius and magnetic field. A realistic design that achieves over 30% efficiency 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)].