Cylindrical Circular and Elliptical, Toroidal Circular and Elliptical Multipoles Fields, Potentials and their Measurement for Accelerator Magnets

TL;DR

This paper extends the standard cylindrical multipole field representation to cylindrical elliptical, toroidal, and other coordinate systems, improving measurement and modeling accuracy for accelerator magnets, especially in fully filled beam apertures.

Contribution

It introduces new methods for representing and measuring multipole fields in various coordinate systems beyond the standard cylindrical approach.

Findings

Extended field representation methods for elliptical and toroidal geometries.

Successful measurement techniques demonstrated on SIS100 magnets.

Enhanced accuracy in modeling complex magnet fields.

Abstract

Recent progress in particle accelerator tracking has shown that the field representation is one of the major limits of the prediction accuracy especially for machines, whose aperture is fully filled by the beam and thus higher the artefacts created by higher order modes have to be thoroughly understood. The standard tool for field presentation today are cylindrical circular multipoles due to their straight forward correspondence to the Cartesian coordinates. In this paper we extend the standard approach to other coordinate systems, show how these can be measured next to their realisation in measuring the SIS100 Magnets for the FAIR project.