Creating a Stable Magnetic Trap in an Intrinsically Unstable Magnetodynamic Field: Concept and Experimental Verification

Author

Denae Arianna Cantrell, Southern Illinois University CarbondaleFollow

Date of Award

8-1-2025

Degree Name

Master of Science

Department

Electrical and Computer Engineering

First Advisor

Komaee, Arash

Abstract

Magnetic drug delivery aims to accumulate a swarm of therapeutic magnetic nanoparticles at sites of disease, but efforts are hindered due to the inherent instability of magnetic fields explained by Earnshaw's theorem, which states that it is impossible to realize a stable equilibrium point to trap a ferromagnetic particle inside a static magnetic field. When exposed to a magnetic field, ferromagnetic domains are immediately aligned with the direction of that field, and consequently, are attracted towards the magnets generating the field rather than a stable equilibrium point. On the other hand, ferromagnetic nanorods have a brief transient period before being completely aligned with the magnetic field, during which, they can be repelled. A previous study exploited this concept to produce a repulsive magnetic force in a process called dynamics inversion. First, by applying a uniform field, a nanorod is aligned in one direction with no magnetic force acting on it. Then, by applying a magnetic field gradient in the opposite direction, the nanorod is repelled for a short time before it can align with the new field. The results from this study indicate that a periodic dynamic magnetic field (magnetodynamic field) can concentrate a swarm of nanorods at a central location between four distinct electromagnets without the use of a feedback loop to stabilize them individually, which is infeasible.With this in mind, this thesis first develops a model consisting of both translational dynamics (referring to movement along a straight line) and rotational dynamics of a nanorod. An open-loop control algorithm exploiting dynamics inversion is applied to an electromagnet array surrounding the nanorod. The control problem is reformulated as a perturbation problem, and through averaging theory, it is determined that the open-loop control may induce a stable limit cycle, as an analysis which is supported by numerical simulations. Next, an experimental testbed is designed to realize the stable magnetic trap, allowing for experimental verification of model dynamics through a comparison with simulation results. Moreover, this thesis discusses dynamics inversion as a means of control for a swarm of particles through variations in the location of the magnetic trap, which serves as the foundation behind future work that aims to build upon the open-loop control for a swarm of nanorods.