Equivalent-circuit model of vircators with step circular waveguides

Summary form only given. A rigorous microwave equivalent-circuit model is elaborated to study vircators with step circular waveguides. It makes use of well-defined equivalent voltages and currents for which equivalent circuit representations can be used. In the first part of this work, we have determined the empty cavity vircator oscillation modes, i.e., the Q factors, resonance frequencies, and field distributions in an axisymmetric vircator with a waveguide step. The method is based on the field representation in terms of local normal waveguide modes. Matrix equations in these modes for two different uniform sections of circular waveguides are formulated. Along with the open resonator boundary conditions, these equations form an eigenvalue problem. The eigenvalues are the complex frequencies and can be solved by Newton´s method in singular value decomposition type. The eigenvectors correspond to the field distributions. The resonance frequencies and contributing waveguide modes of some of these oscillation modes of our investigated vircator will be presented. Once these oscillation modes are known, the electromagnetic field in the presence of the electron beam can be expanded in terms of them and the Maxwell equations with a localized current source can then be solved to determine the excitation coefficients. In our model, the current distribution can be simply approximated by our two-dimensional particle-in-cell simulation results. By comparing the field structure, the dominant resonant frequency, and the power flow as a function of the distance of the waveguide step, the physical mechanism of power enhancement by vircators with an abrupt discontinuity in circular waveguides can be elucidated.