In this article, electromagnet layouts are presented, which generate a magnetic field with a magnitude gradient that does not vary significantly in a horizontal plane but decreases monotonically with the vertical height above the magnet. Such a one-direction magnetic field gradient is a specific requirement for magnetic density separation (MDS), a novel recycling technology that combines a vertical magnetic field gradient with a ferrofluid to separate a mixture of non-magnetic materials based on their mass density. We are assembling the first superconducting magnet to be used for this application. In contrast to other separation technologies that use ferrofluid, multiple products can be separated in a single process step. First, the idealized current distribution is introduced that produces such a magnetic field with a magnitude that decays only in one direction. This ideal field can be approximated with practical coil configurations, which are evaluated with a Fourier analysis to derive an optimal cross-sectional layout based on flat racetrack coils. The analysis concludes with a discussion of the effect of winding pack thickness on the value of the magnetic field above the magnet system and the peak field inside the winding pack. The conclusions of this study are applicable not just for MDS but for any application that requires a magnetic field gradient that changes only in one direction. @en

This article discusses the optimum layout of coils of a superconducting magnet system for magnetic density separation (MDS). MDS is a novel separation technology that combines a vertical magnetic field gradient with a ferrofluid to separate mixtures of non-magnetic particles based on their mass density. The MDS process can separate more than two types of particles in a single process step, thereby distinguishing it from other separation techniques using a ferrofluid. The authors are currently constructing a superconducting MDS demonstrator. Ideally, the gradient of the magnetic field magnitude should change only with the distance above the magnet but remain constant in a horizontal plane. In principle, such an ideal field profile can be generated with an infinite harmonic sheet current. In practice, edge effects appear due to the necessity of using a finite number of coils. These cause a horizontal component in the field gradient and also change the vertical component. We compare the vertical magnetic field gradient of various coil layouts to see which configuration performs best. To facilitate ease of production, the analysis is restricted to flat racetrack coils. The main result is that the specific shape of a racetrack coil has a larger influence on the vertical gradient than the number of coils. The feed particles need to be pushed through the separation chamber from the insertion to the collection point. One option to realize this is to use an MDS setup in which the magnet is inclined with respect to the horizontal plane. This tilting results in a horizontal magnetic force component, which drives feed particles through the fluid bed. We show that a three-coil layout provides the largest usable fluid bed depth for a wide range of tilt angles. @en