Optimization of Coreless Electromagnets to Maximize Field Generation for Magnetic Manipulation Systems

Magnetic manipulation systems typically take the form of a set of stationary electromagnets surrounding, and projecting their fields into, a common workspace. The electromagnets are typically wound with cylindrical geometries, sometimes with a tapered end for tighter packing. Motivating this study was the conjecture that an optimal general electromagnet designed with minimal constraints on the allowable geometry would outperform an optimal (tapered) cylindrical electromagnet in terms of maximizing field generation at a given point on the axis of the electromagnet for a given amount of power. In this letter, we provide a method to calculate the optimal general geometry in the case of coreless electromagnets, and verify that it is not cylindrical, as expected. However, we also find that the optimal general electromagnet negligibly outperforms the optimal (tapered) cylindrical electromagnet for any parameter set. Because of the added complexity in fabricating an optimal general electromagnet, designers of magnetic manipulation systems using coreless electromagnets can limit their design space by considering only simple (tapered) cylindrical electromagnets, with confidence that their design will be very close to the optimal general design.