Description of electromagnetic fields in inhomogeneous accelerating sections. IV couplers

TL;DR

This paper introduces a new analytical approach to modeling electromagnetic coupling in inhomogeneous accelerating sections, simplifying complex integro-differential equations into manageable differential systems for improved design and simulation.

Contribution

It presents a novel method that reduces complex coupled integro-differential equations to simpler differential equations for electromagnetic coupling analysis.

Findings

Reduced input reflection coefficient to 8E-3 without additional matching

Developed a computer code for matching loop couplers in X-band sections

Validated the analytical model through simulation results

Abstract

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.