Preservation of beam emittance in the presence of ion motion in future high-energy plasma-wakefield-based colliders.

The preservation of beam quality in a plasma wakefield accelerator driven by ultrahigh intensity and ultralow emittance beams, characteristic of future particle colliders, is a challenge. The electric field of these beams leads to plasma ions motion, resulting in a nonlinear focusing force and emittance growth of the beam. We propose to use an adiabatic matching section consisting of a short plasma section with a decreasing ion mass to allow for the beam to remain matched to the focusing force. We use analytical models and numerical simulations to show that the emittance growth can be significantly reduced.

Dosimetric Evaluation of Metal Artefact Reduction using Metal Artefact Reduction (MAR) Algorithm and Dual-energy Computed Tomography (CT) Method

Purpose: Computed Tomography (CT) is one of the standard diagnostic imaging modalities for the evaluation of a patient’s medical condition. In comparison to other imaging modalities such as Magnetic Resonance Imaging (MRI), CT is a fast acquisition imaging device with higher spatial resolution and higher contrast-to-noise ratio (CNR) for bony structures. CT images are presented through a gray scale of independent values in Hounsfield units (HU). High HU-valued materials represent higher density. High density materials, such as metal, tend to erroneously increase the HU values around it due to reconstruction software limitations. This problem of increased HU values due to metal presence is referred to as metal artefacts. Hip prostheses, dental fillings, aneurysm clips, and spinal clips are a few examples of metal objects that are of clinical relevance. These implants create artefacts such as beam hardening and photon starvation that distort CT images and degrade image quality. This is of great significance because the distortions may cause improper evaluation of images and inaccurate dose calculation in the treatment planning system. Different algorithms are being developed to reduce these artefacts for better image quality for both diagnostic and therapeutic purposes. However, very limited information is available about the effect of artefact correction on dose calculation accuracy. This research study evaluates the dosimetric effect of metal artefact reduction algorithms on severe artefacts on CT images. This study uses Gemstone Spectral Imaging (GSI)-based MAR algorithm, projection-based Metal Artefact Reduction (MAR) algorithm, and the Dual-Energy method.

Materials and Methods: The Gemstone Spectral Imaging (GSI)-based and SMART Metal Artefact Reduction (MAR) algorithms are metal artefact reduction protocols embedded in two different CT scanner models by General Electric (GE), and the Dual-Energy Imaging Method was developed at Duke University. All three approaches were applied in this research for dosimetric evaluation on CT images with severe metal artefacts. The first part of the research used a water phantom with four iodine syringes. Two sets of plans, multi-arc plans and single-arc plans, using the Volumetric Modulated Arc therapy (VMAT) technique were designed to avoid or minimize influences from high-density objects. The second part of the research used projection-based MAR Algorithm and the Dual-Energy Method. Calculated Doses (Mean, Minimum, and Maximum Doses) to the planning treatment volume (PTV) were compared and homogeneity index (HI) calculated.

Results: (1) Without the GSI-based MAR application, a percent error between mean dose and the absolute dose ranging from 3.4-5.7% per fraction was observed. In contrast, the error was decreased to a range of 0.09-2.3% per fraction with the GSI-based MAR algorithm. There was a percent difference ranging from 1.7-4.2% per fraction between with and without using the GSI-based MAR algorithm. (2) A range of 0.1-3.2% difference was observed for the maximum dose values, 1.5-10.4% for minimum dose difference, and 1.4-1.7% difference on the mean doses. Homogeneity indexes (HI) ranging from 0.068-0.065 for dual-energy method and 0.063-0.141 with projection-based MAR algorithm were also calculated.

Conclusion: (1) Percent error without using the GSI-based MAR algorithm may deviate as high as 5.7%. This error invalidates the goal of Radiation Therapy to provide a more precise treatment. Thus, GSI-based MAR algorithm was desirable due to its better dose calculation accuracy. (2) Based on direct numerical observation, there was no apparent deviation between the mean doses of different techniques but deviation was evident on the maximum and minimum doses. The HI for the dual-energy method almost achieved the desirable null values. In conclusion, the Dual-Energy method gave better dose calculation accuracy to the planning treatment volume (PTV) for images with metal artefacts than with or without GE MAR Algorithm.

Capacity Investment in Renewable and Conventional Energy Sources

This dissertation studies capacity investments in energy sources, with a focus on renewable technologies, such as solar and wind energy. We develop analytical models to provide insights for policymakers and use real data from the state of Texas to corroborate our findings.

We first take a strategic perspective and focus on electricity pricing policies. Specifically, we investigate the capacity investments of a utility firm in renewable and conventional energy sources under flat and peak pricing policies. We consider generation patterns and intermittency of solar and wind energy in relation to the electricity demand throughout a day. We find that flat pricing leads to a higher investment level for solar energy and it can still lead to more investments in wind energy if considerable amount of wind energy is generated throughout the day.

In the second essay, we complement the first one by focusing on the problem of matching supply with demand in every operating period (e.g., every five minutes) from the perspective of a utility firm. We study the interaction between renewable and conventional sources with different levels of operational flexibility, i.e., the possibility

of quickly ramping energy output up or down. We show that operational flexibility determines these interactions: renewable and inflexible sources (e.g., nuclear energy) are substitutes, whereas renewable and flexible sources (e.g., natural gas) are complements.

In the final essay, rather than the capacity investments of the utility firms, we focus on the capacity investments of households in rooftop solar panels. We investigate whether or not these investments may cause a utility death spiral effect, which is a vicious circle of increased solar adoption and higher electricity prices. We observe that the current rate-of-return regulation may lead to a death spiral for utility firms. We show that one way to reverse the spiral effect is to allow the utility firms to maximize their profits by determining electricity prices.