Description of electromagnetic fields in inhomogeneous accelerating sections. I Field representation

TL;DR

This paper explores a new method using a homogeneous basis and generalized coupled modes theory to accurately describe electromagnetic fields in inhomogeneous accelerating sections, with practical procedures for derivative calculations.

Contribution

It introduces a novel approach combining homogeneous basis and generalized coupled modes theory for inhomogeneous sections, improving field description accuracy.

Findings

Single mode representation yields small errors in regular sections.

Accuracy in couplers is acceptable for practical calculations.

Procedures for calculating derivatives of fields with respect to geometry are developed.

Abstract

In this work we present the results of a study of the possibility of using a homogeneous basis and a new generalization of coupled modes theory to describe inhomogeneous accelerating sections. It was shown that the single mode representation describes the electromagnetic fields with small errors in the regular part of the section. In the couplers the accuracy is worse, but it is small enough to be used in calculations. Solving the equations of generalized coupled modes theory requires calculating the derivatives of the fields with respect to various geometrical parameters. Procedures for calculating these derivatives have been developed.