Accurate Transfer Maps for Realistic Beamline Elements: Part I, Straight Elements

TL;DR

This paper develops accurate transfer maps for straight beamline elements by extracting detailed field models from 3D data, enabling precise orbit and transfer map calculations considering nonlinear effects.

Contribution

It introduces surface fitting methods to derive realistic interior and fringe fields from 3D data for use in transfer map computations of straight magnetic elements.

Findings

Validated methods with a challenging model field

Achieved high-accuracy transfer maps for straight elements

Provided benchmarks for future studies

Abstract

The behavior of orbits in charged-particle beam transport systems, including both linear and circular accelerators as well as final focus sections and spectrometers, can depend sensitively on nonlinear fringe-field and high-order-multipole effects in the various beam-line elements. The inclusion of these effects requires a detailed and realistic model of the interior and fringe fields, including their high spatial derivatives. A collection of surface fitting methods has been developed for extracting this information accurately from 3-dimensional field data on a grid, as provided by various 3-dimensional finite-element field codes. Based on these realistic field models, Lie or other methods may be used to compute accurate design orbits and accurate transfer maps about these orbits. Part I of this work presents a treatment of straight-axis magnetic elements, while Part II will treat bending dipoles with large sagitta. An exactly-soluble but numerically challenging model field is used to provide a rigorous collection of performance benchmarks.