Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Aerospace, Physics, and Space Sciences

First Advisor

Hector M. Gutierrez, Ph.D.

Second Advisor

Chelakara S. Subramanian, Ph.D., P. Eng.

Third Advisor

Hamidreza Najafi, Ph.D.

Fourth Advisor

Jian Du, Ph.D.


A novel parallelizable probabilistic approach to model eddy currents in AC electromagnets is presented in this research. Consequently, power loss associated with the formation of these eddy currents is estimated and validated using experimental data. Furthermore, predicting the effect of ferromagnetic alternating field enhancement on power loss in the source excitation winding has been an active area of research. Unlike a stationary field, an alternating sinusoidal field diffuses partially into the ferromagnetic material leading to a predictably sub-optimal field enhancement. To model these physics, finite element techniques employ nonlinear iterative solvers which are time consuming. A novel method is developed in this research by packing the ferromagnetic domain with variable sized hard spheres. The interaction of these spherical sub-domains with the inducing background field results in a field enhancement that is theoretically identical to enhancement created by the solid ferromagnetic continuum. The evaluated losses in the winding with and without the ferromagnetic material are further employed to evaluate thermal distributions throughout the system. A holistic multiphysics tool has been realized as part of this research which could be employed to estimate field uniformity and engineer active cooling as part of the development and testing of an electromagnetic coil-core system.

Given the current trend in parallel computing, the probabilistic technique developed by the author has been implemented on General Purpose Graphical Processing Units consisting of 2688 processing cores, each of which handles solution of governing equations at an isolated location in the domain independent of one another. By employing the proposed method, a speed gain of 35% over conventional commercial finite element software is guaranteed for simulating commonly employed coil-core electromagnetic systems. In addition to this primary advantage, the resource intensive ( 20 GB RAM memory) matrix inversion techniques employed by these commercial finite element softwares are bypassed. Since probabilistic techniques intrinsically do not require extensive data storage, on-chip GPU memory of 8GB has been realized to be more than adequate for practical winding simulations.

Experimental validation of the probabilistic model is carried out by employing the Lock-in Amplifier loss determination procedure. The phase shift in voltage with respect to current could be precisely determined by the procedure which is key to evaluating winding losses. To isolate losses in the excitation winding due to ferromagnetic field enhancement, an existing inductive voltage cancellation technique using a compensation winding system has been adapted by the author. A sensitive J-type thermocouple and an IR imager are used to measure and compare temperature predictions made by an existing probabilistic model with the addition of the power loss source term for this study. It has been established that across a range of operating frequencies and drive current, the Monte Carlo probabilistic model results in an overall error of 0.7% in winding losses without the ferromagnetic core material and 2.6% with the core material.

Implementation of developed model to determine losses, field enhancement, field uniformity and multipole characteristics at the required reference radius in the aperture of a novel electromagnet to be used for carbon beam therapy is currently underway. Previously inconceivable simulation domains such as stranded litz wires and thin iron laminates have now become a possibility employing the developed model