Impact of random geometric errors in an elliptical superconducting magnet with application to a compact heavy-ion synchrotron

Abstract

A compact heavy-ion synchrotron is under development for next-generation cancer therapy. A superconducting magnet is designed with a main dipole field of 3.5 T and a field error less than 5 $\times$ 10⁻⁴ to maintain compactness. The coil is wound directly with monolithic Nb-Ti wire on a curved elliptical mandrel, comprising 22 laminated layers to achieve the desired magnetic field. Given the critical need for field quality, it is imperative to determine the tolerance of coil fabrication and to devise a method to eliminate field error during the design stage. This paper presents a numerical investigation of possible random geometric errors stemming from fabrication and assembly tolerances in a curved elliptical superconducting magnet. We first provide an analytical formulation derived in a complex plane to estimate the field error of a straight elliptical coil. We then conduct a Monte Carlo simulation to assess cases involving misalignment of individual wires and coil block sectors. Additionally, we compare simulation results with field measurements obtained from a short model magnet tested previously to predict potential random errors in manufacturing. Finally, we calculate the beam dynamic aperture to assess the effects of random geometric errors on beam loss using Monte Carlo simulation results. This method enables the prediction of tolerances for fabricating high-quality high-field magnets and aids in making design decisions concerning the utilization of active shim coils.