A dynamic trap to confine magnetic moments in free space
The magnetic trap project is a new effort led by honors intern Jessica Ryun ‘24 who has accepted a position as a junior staff scientist in the lab and has agreed to lead this challenging project. The goal is to construct a
dynamic trap to confine a small magnetic moment in free space.
Remarkably, the mathematical equations obeyed by the moment only depend on the ratio of moment to mass which fortuituously happens to be the same for small pieces of inexpensive rare earth magnets as for an atom. So it is as if a trap that can confine an atom can also confine a small rare-earth moment and this is a nice chance to study some aspects of atomic physics using relatively large rare-earth moments.
Brief description and layout
The construction of the trap is described is a famous paper ``A magnetic suspension system for atoms and bar magnets" by Sackett, Cornell, Monroe and Wieman, Am. J. Phys., 61, 304 (1993) and we are following their approach with suitable modifications. The physics idea is rather straightforward and can be described as follows: to trap a magnetic moment in stable equlibrium, you need (1) a gradient to overcome the weight of the object, (2) a somewhat large axial field to define the axis of confinement, (3) an ac field with enough curvature such that the effective confinement potential keeps the moment confined to the zr plane and most importantly, (4) the confinement potential has to rotate fast enough that the particle is alternately confined along z and then along r and never really gets the chance to escape along z nor along r. In other words, the ac field rotates faster than the particle can respond.
The equations of motion of the trapped moment are described by the famous Mathieu differential equation whose solutions are bound only for a certain range of parameters. These parameters are commonly referred to as a and q in the mathematics literature but in physics terms a is related to the curvature of the dc field and q is related to the curvature of the ac field. Experimentally, this means that both the dc and ac curvature have to be finely adjusted so the trap operates within the stable zone. The hard part, which we are slowly discovering for ourselves, is that supporting the physics and the mathematics with the correct engineering requires considerable finesse.
Our preliminary work was presented at the UWSP Research Symposium in May 2022 and that poster is available. The basic elements of the trap are in place. Two ring magnets provide a ~ 150 Gauss axial field while a third ring magnet supplies the dc gradient to counter gravity. A prototype ac coil pair has been constructed and we have just completed measuring the field and curvature profile.
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