Publication Date


Document Type


First Advisor

Erdelyi, Bela

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Physics


The high-intensity, high-brightness and precision frontiers for charged particle beams are an increasingly important focus for study. Electron microscopy has demonstrated high quality beams from a single nanotip emitter, and cathodes of structured nanoscale arrays show promise as ultracold electron sources. Optimization of the cathode design for precision applications necessitates a detailed treatment of the interplay between the structure geometry, quantum mechanical emission mechanism, and electromagnetic interactions between the emitted electrons and the boundary interface. This dissertation details the numerical tools developed to simulate these processes efficiently with enough fidelity to be accurate even in the ultracold regime.

Conventional simulation methods combine a particle-in-cell framework with an ad hoc current density approach to model electron emission, which are inefficient computationally and reliant on assumptions that are not valid for the type of cathodes studied in this work. I designed a novel computational framework called HiPE that is capable of modeling field electron emission from nanoscale structures on a substrate, with the precision to handle the ultracold regime. HiPE incorporates three primary tools: a Poisson integral solver, a collisional N-body numerical integrator, and a first-principles field electron emission routine.

I optimized the Poisson Solver to run more accurately and efficiently in parallel on a distributed machine, and developed an adaptive regularization approach to solve an existing numerical instability for near-boundary evaluation. The novel numerical integrator was already extensively optimized to be accurate to machine precision with a relatively modest computational expense. I derived a computationally efficient form of the electron distribution function, and utilize a high-order transformation to map the electrons to the physical structure, resulting in an embarrassingly parallel routine.

Consequently, HiPE is the first and only tool of its kind currently available in the whole field, with the potential to aid in increasing the performance of future electron sources by orders of magnitude. This efficacy is showcased by using HiPE to obtain emission characteristics for several cathode designs. Each nanotip emitter in the array generates an independent beamlet initially, and the array of beamlets will then merge to form the final beam. I conclude by presenting analysis of the merger of various beamlet configurations leading to insights regarding the optimal geometric configuration of the cathode and the potential for a method to experimentally infer beam metrics that are not accessible with the current technology.


241 pages




Northern Illinois University

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