Topology Optimization Using a Normalized Gaussian Network of Iron Yoke for Magnetic Field Design of an Accelerator Superconducting Magnet

Abstract

Field quality in the order of 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-4}$</tex-math></inline-formula> is required for a superconducting dipole magnet to keep the beam stable in an accelerator. An iron yoke usually is employed to enhance the magnetic field and reduce the fringe field. As the superconducting magnet provides a field that is higher than 2 T, the field quality is distorted by the saturation effect of the iron yoke during the beam acceleration. Field tuning holes are adopted to the iron yoke to adjust the magnetic flux so as to keep the field error variation flat in the region from the injection field to the top field. It is time costly in terms of computing to determine the initial shape and search for the best solution that satisfies design requirements. This paper presents a topology optimization method using a non-dominated sorting genetic algorithm for the iron yoke design of an accelerator superconducting magnet. The shape of the iron yoke is represented by using the normalized Gaussian network to achieve smoothness of the material distribution. This method is applied to a superconducting bending magnet for a compact heavy-ion synchrotron in which the field errors are required to be lower than 2.5 unit and 3.5 unit at the point of injection field and the top field, respectively. As a result, a smooth shape of the iron yoke is obtained by this method; both field error at the top field and the field error variation are mitigated by the method.