Description of electromagnetic fields in inhomogeneous accelerating sections. IV couplers
A new approach to incorporating coupling elements into a generalized coupled mode theory is presented. The simplest model of coupling of a structured waveguide with an external RF power source and load through loops and transmission lines was used. Even such a simple model significantly complicated the system of coupled equations. It turned into a coupled integro-differential system of the Barbashin type with degenerate kernels. Since the integral kernels are degenerate, this system is reduced to three independent systems of differential equations. Instead of solving a system of coupled integro-differential equations, we need to find solutions to three systems of ordinary differential equations. Two systems describe the distribution of the field excited by one loop and the specified value of the excitation current in it. In the first system the loop is located at the section's input, and in the second, at the section's output. The third system does not depend on the loop parameters at all. It describes the distribution of the field excited by an electron beam in a section without loops. Based on the developed analytical model, the computer code was developed for matching the loop couplers for the uniform accelerating sections of X-band. The calculation results were used to simulate the non-uniform section. Without additional matching, we obtained an input reflection coefficient of 8E-3.