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

Superconducting magnets with noncircular apertures are important for handling unconventional beam profiles and specialized accelerator applications. This paper presents an analytical framework for designing superconducting accelerator magnets with quasipolygonal apertures, aimed at generating precise circular field harmonics. In part 1, we explore the relationship between current distributions on quasipolygonal formers and their corresponding magnetic field harmonics. By employing conformal mapping techniques, we establish a connection between the design of quasipolygonal 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 quasipolygonal apertures. This work not only advances the design of superconducting magnets but also broadens the scope of CCT technology to accommodate more complex geometries.