Inverse Biot–Savart Optimization for Superconducting Accelerator Magnets

Abstract

Superconducting (SC) magnets for accelerator concepts are often synthesized by numerically optimizing magnetic field waveforms, a process that requires a subsequent solution of a constrained inverse problem to identify suitable SC magnet windings. When the desired field distribution is intuitive, the inverse process is facilitated by seeding preconceived coil distributions into design optimization methods for refinement. With more complex magnetic field distributions, an initial design may be unknown, and topology optimization tools are required to synthesize current distributions without apriori guidance from a subject matter expert. In this work, we develop a constrained inverse Biot-Savart topology optimization methodology that synthesizes optimal distributions of current density in racetrack-like SC coils. The problem structure is exploited through a computationally efficient quadratic programming formulation, and the method is applied to recently published magnetic field waveforms for a recirculating proton phase shifter, a proton therapy gantry, and dipole magnets with sharp field transitions. The method and results herein identify novel winding configurations that can help magnet designers bring accelerator concepts to fruition.

Current distribution monitoring enables quench and damage detection in superconducting fusion magnets

“…Following the implementation of Ref. 30 , in the absence of magnetic material and sensor positioning errors the measured response at Hall probe k is the sum of Eq. 2 over all cables: Re-writing Eq.…”

“…4 ), the least squares form is considered: This linear system can be solved to obtain the cable current distribution, and Ref. 30 outlines several techniques to improve the stability of the dense and ill-conditioned system. Previously, a similar technique based on Singular Value Decomposition (SVD) was employed to investigate current distributions in ITER cables 31 , however the high levels of current sharing did not permit the methodology employed here.…”

“…It is possible to solve the least squares problem with a net transport current constraint (see Ref. 30 ), however this was not necessary here.…”

Gradient-based optimization of permanent-magnet assemblies for any objective

“…Now we consider the problem of improving the field quality, with respect to any required distribution [24]. In particular, we assume a uniform vertical field as the target.…”