Microwave Tube High-frequency System Time-domain Analysis And Research

The feature of the high-frequency system will directly affect the microwave tube's working-frequency, bandwidth, conversion efficiency and output power, as well as other properties of a series of the entire tube. Therefore, research and analysis of the high-frequency system of microwave tube, are critical to the design and optimization of the structure, and provide a guidance role for the development of microwave tubes. In this paper, the feature of axisymmetric variable cross-section waveguide high-frequency system was studied theoretically and analysed numerically in time-domain.Based on orthogonal function unfolding theory, the transverse fields can be represented as a superposition of waveguide modes. And according to coupled-wave theory, the time-dependent multi-mode coupling-wave equations (or the generalized telegrapher's equations) and the coupling coefficients among the different modes (TE and TM) were deduced. The generalized telegrapher's equations are a set of coupled one-dimensional partial differential equations (time and axial coordinates) for the amplitudes of the modes. Therefore, the calculations of the electromagnetic fields are based on the waveguide modal representation, which allows the solution of a relatively small number of coupled one-dimensional partial differential equations for the amplitudes of the modes, instead of the full solution of Maxwell's equations.Aim at the special case when the electromagnetic fields in the structure get a stable status, the steady-state model of the coupling-wave equations was founded. The numerical algorithm of it was analysed, and the code of the steady-state model was compiled, which can be used for simulating numerically the multi-mode transmission feature of waveguide transmission system with variable cross-section. Firstly, to show the effect of the finite conductivity of the metallic wall in the research of the multi-mode transmission feature of waveguide transmission system with variable cross-section in THz wave-band, the problem of mode-attenuation in circular waveguide was simulated numerically by using the code. Then, the examples for operation of the code, namely the waveguide couplers and the waveguide transitions, were presented. Next, the numerical algorithm of the time domain model was analysed in particular. Firstly, the system of coupled first-order(in axial position) differential equations of the generalized telegrapher's equations was converted to a system of second-order differential equations. Then, the time evolution of the amplitude was solved using a semiimplicit finite difference predictor–corrector scheme. Because the complex amplitudes of the modes evolve slowly in time on the scale of the basic wave period, we are not bounded by the Courant condition, and can use relatively large time steps even when the required geometry resolution is high and the spatial grid size is small.Lastly, the code of the time domain model was compiled, which can be used for simulating numerically "cold cavity" feature of the high-frequency system with variable cross-section waveguide, besides the multi-mode transmission characteristics of waveguide transmission system. The examples for operation of the code, namely the waveguide couplers, the waveguide transitions and the three-stage gyrotron oscillator, were presented.