Self-consistent non-linear theory of TWT gyrotron

A multi-stage gyrotron traveling wave amplifier is needed to increase the stability in the output section and lower the gain ripple, and to isolate the input source from the load return signal. Following the wideband proof-of-principle experiment with the tapered waveguide circuit [1], another gyrotron amplifier experiment is underway at the Naval Research Laboratory by using two-stage gyrotron. In this paper we present a self-consistent large signal theory and a computer code for a two-stage gyro-TWT with a sever. The theory is developed for waveguides of rectangular cross-section with an annular electron beam. A mildly tapered waveguide cross-section in a non-uniform external magnetic field is also considered for increased bandwidth. The dynamics of the gyro-TWT are represented by a system of coupled, nonlinear differential equations for the electrons and the rf fields. The beam current modulation acts as a source term in the rf field equations. These equations are solved self consistently by satisfying proper boundary conditions. The output power and the gain are calculated and optimized for the various physical parameters, i.e., input power, magnetic field, frequency, beam power, length and taper angle of the waveguide, etc. A computer code for the large signal theory has been tested for the rectangular gyrotron amplifier circuit with the sever where the rf wave is completely terminated For waveguides of uniform cross-section we find 50% efficiency and 52dB gain when there is no axial velocity spread. At 10% axial velocity spread, the efficiency becomes 37%. The tapered two-stage gyro-TWT gives rise to 40% bandwidth and 40dB total gain for zero axial velocity spread. The tapered case is much more sensitive to the beam velocity spread than the uniform guide case.