Validation of frequency and mode extraction calculations from time-domain simulations of accelerator cavities

TL;DR

This paper validates a frequency extraction algorithm applied to realistic accelerator cavity simulations, demonstrating high accuracy in frequency and mode determination, aiding cavity design without extensive manufacturing costs.

Contribution

It applies and validates a frequency extraction method for realistic accelerator cavities modeled with embedded boundaries, showing its effectiveness and accuracy in practical scenarios.

Findings

Frequency extraction error less than 1 part in 10^5.

Computed and experimental values differ by about 1 part in 10^4, mainly due to machining errors.

Method effectively distinguishes degenerate modes with minimal post-processing.

Abstract

The recently developed frequency extraction algorithm [G.R. Werner and J.R. Cary, J. Comp. Phys. 227, 5200 (2008)] that enables a simple FDTD algorithm to be transformed into an efficient eigenmode solver is applied to a realistic accelerator cavity modeled with embedded boundaries and Richardson extrapolation. Previously, the frequency extraction method was shown to be capable of distinguishing M degenerate modes by running M different simulations and to permit mode extraction with minimal post-processing effort that only requires solving a small eigenvalue problem. Realistic calculations for an accelerator cavity are presented in this work to establish the validity of the method for realistic modeling scenarios and to illustrate the complexities of the computational validation process. The method is found to be able to extract the frequencies with error that is less than a part in 10^5. The corrected experimental and computed values differ by about one parts in 10^$, which is accounted for (in largest part) by machining errors. The extraction of frequencies and modes from accelerator cavities provides engineers and physicists an understanding of potential cavity performance as it depends on shape without incurring manufacture and measurement costs.