A nonlinear non-stationary self-consistent theory of the wave interaction with helical electron beam in a longitudinally inhomogeneous cylindrical waveguide with impedance walls has been developed. Within this theory, the excitation problem for an inhomogeneous impedance waveguide has been reduced rigorously to a system of partial differential equations.
A computer code has been developed to compute the efficiency and the output power of terahertz gyrotrons, taking into account ohmic wall losses and mode conversion in the gyrotron cavity. Specific numerical calculations have been performed for the 0.46-THz gyrotron at the University of Fukui (UF, Japan) and the 1-THz 5-kW gyrotron at the Institute of Applied Physics (IAP, Russia). Calculations have also been compared with the results of the conventional (non-self-consistent) consideration of the ohmic losses and with the available experimental data.
Fig. 1 - Gyrotron output power for the IAP (à) and the UF (b) gyrotrons versus magnetic field intensity, where 1 - calculated power in the lossless case; 2 - calculation results for the non-self-consistent treatment of the ohmic losses, 3 - results of calculations, which take into account ohmic losses self-consistently; point with a horizontal error bar is the measured output power of the IAP gyrotron; 3* is the measured output power of the UF gyrotron in arbitrary units.
The self-consistent consideration of the ohmic losses makes it possible to reveal an additional mechanism of the power degradation in the gyrotron cavity. It is associated with a decrease in the total quality factor due to the ohmic losses. The decrease in the quality factor, in its turn, leads to increase in the starting current and thus shortens the operation region. Besides it shifts the optimal (with respect to efficiency) operating parameters and lowers the gyrotron efficiency and output power.
In the case of self-consistent consideration of the ohmic losses, calculations are in better agreement with the experimental data. For the IAP gyrotron, they yield the output power, which is close to the measured value of about 5.5 kW (Figure 1a). For the UF gyrotron, such calculations make it possible to determine the operation regime, which is close to one observed in experiments (Fig. 2a).
Fig. 2 - UF gyrotron output power (à) and example of mode conversion (b) in the IAP gyrotron cavity. In Fig. 2a, 1 - results of calculations, which take into account ohmic losses self-consistently; 2 - measured output power of the UF gyrotron in arbitrary units
The mode conversion in the cavities of the UF and the IAP gyrotron is small and has little effect on their efficiency and output power. This is due to the weak cavity inhomogeneity. Moreover, the mode conversion is negligible in the central parts of both cavities, where the beam-wave interaction is the most intensive. The mode conversion becomes more evident at the cavity output (Fig. 2b). The resulting mode composition must be taken into consideration when optimizing the output systems for gyrotrons.