Graduate Studies

 

First Advisor

Bradley A. Shadwick

Degree Name

Doctor of Philosophy (Ph.D.)

Committee Members

Ilya Fabrikant, Matthias Fuchs, Mikil Foss

Department

Physics and Astronomy

Date of this Version

7-2025

Document Type

Dissertation

Citation

A dissertation presented to the Graduate College of the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Physics and Astronomy

Under the supervision of Professor Bradley A. Shadwick

Lincoln, Nebraska, July 2025

Comments

Copyright 2025, Roland D. Hesse. Used by permission

Abstract

A natural inefficiency in conventional treatment of the plasma distribution arises from indiscriminate consideration of the contributions to field structure that are dynamically sourced from kinetic activity in disparate sectors of phase space. We introduce a range of techniques for model design to maximize representation efficiency without breaking key physical invariants indicative of physical reliability. An overview of varied adaptation to stable time-advance methods is given. Low-dimensional representation of a laser-driven plasma requires some creativity in differential structural modification, while direct efficiency is uncovered through the compression and rarefaction of a nonuniform momentum grid. These numerical models introduce embedded gains in computational efficiency through the implicit and explicit distribution of computational resources where they are required most. With a focus on low-dimensional settings, we outline the algorithmic structure of our numerical methods and the precise arrangement of operations appropriate to implement models variationally consistent with conservation principles in a way that is generalizable in a number of different directions. Comport towards scheme modularity and compatibility with integration-by-parts as a defining principle is demonstrated in all techniques. We apply these models to several problems requiring both accurate representation and detailed resolution of plasma phase-space.

Advisor: Bradley A. Shadwick

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