Date of Award

Spring 1-1-2016

Document Type


Degree Name

Doctor of Philosophy (PhD)


Applied Mathematics

First Advisor

Scott Parker

Second Advisor

Thomas Manteuffel

Third Advisor

Scott Parker

Fourth Advisor

Thomas Manteuffel

Fifth Advisor

Yang Chen


This thesis focuses on the development of simulation models, based on fully resolving the gyro-motion of ions with the Lorentz force equations of motion, for studying low-frequency phenomena in well-magnetized plasma systems. Such models, known as fully kinetic ion models, offer formal simplicity over higher order gyrokinetic ion models and may provide an important validation tool or replacement for gyrokinetic ion models in applications where the gyrokinetic ordering assumptions are in question. Methods for dealing with the added difficulty of resolving the short time scales associated with the ion gyro-motion in fully kinetic ion models are explored with the use of graphics processing units (GPUs) and advanced time integration algorithms, including sub-cycling, orbit averaging and variational integrators. Theoretical work is performed to analyze the effects of the ion Bernstein modes, which are known to cause difficulties in simulations based on fully kinetic ion models. In addition, the first simulation results for the ion temperature gradient driven instability in toroidal geometry using a fully kinetic ion model are presented. Finally, during the course of this work, a method for analyzing the effects of a finite time step size and spatial grid in the delta-f approach to the particle-in-cell method was developed for the first time. This method was applied to an implicit time integration scheme and has revealed some unusual numerical properties related to the delta-f method.