Excitation Equations for Irregular Waveguides Taking into Account the Finite Wall Conductivity and Their Application for Ultrahigh-Power Microwave Problems. Part 1

Abstract

The article formulates equations for longitudinally irregular waveguide excitation by three-dimensionally phased electron flows taking into account the finite wall conductivity. A.G. Sveshnikov’s method based on using non-orthogonal coordinates for Maxwell’s equations to formulate the excitation equations, which makes it possible to transpose the irregular boundary of the electrodynamic structure to a regular one. Then, Galerkin’s projection method is used for the transformed regular region with a priori known complete system of vector basis functions for this region. A special approach allows one to solve the difficulty arising due to the boundary conditions for the vector basis functions and the solution on the waveguide surface in the case of finite conductivity. As a result, the original three-dimensional boundary value problem is derived to a one-dimensional (two-point) boundary value problem for the amplitudes of normal coupled waves of the electrodynamic structure. This problem formulates an ordinary differential equation (ODE) system with boundary conditions of the third kind on the first and final sections of the waveguide. The excitation equations, together with the equations of electron motion, form a self-consistent mathematical model for calculating and optimizing high-power electronic devices using irregular waveguides: relativistic traveling wave tubes (TWTs), backward wave oscillators (BWOs), klynotrons, gyro-TWTs, gyro-BWOs, and gyrotons.