Generation of circular field harmonics in quasi-polygonal magnet apertures using superconducting canted-cosine-theta coils

TL;DR

This paper introduces an analytical method for designing superconducting magnets with quasi-polygonal apertures that produce precise circular field harmonics, expanding the application scope of CCT technology.

Contribution

It develops a conformal mapping-based framework linking quasi-polygonal and circular bore magnet designs, enabling precise harmonic control in complex geometries.

Findings

Established a relationship between current distributions and magnetic harmonics.

Applied conformal mapping to simplify complex magnet design formulations.

Designed analytic winding schemes for quasi-polygonal CCT magnets.

Abstract

Superconducting magnets with non-circular apertures are important for handling unconventional beam profiles and specialized accelerator applications. This paper presents an analytical framework for designing superconducting accelerator magnets with quasi-polygonal apertures, aimed at generating precise circular field harmonics. In Part 1, we explore the relationship between current distributions on quasi-polygonal formers and their corresponding magnetic field harmonics. By employing conformal mapping techniques, we establish a connection between the design of quasi-polygonal bore magnets and traditional circular bore configurations, facilitating the simplification of complex mathematical formulations. Part 2 applies the derived current distributions to the canted cosine theta (CCT) coil magnet concept, focusing on designing analytic winding schemes that generate single or mixed circular harmonics within quasi-polygonal apertures. This work not only advances the design of superconducting magnets but also broadens the scope of CCT technology to accommodate more complex geometries.