Title: Computational Modeling of Magnetic Field Interaction with Superconductors Under High-Field and High-Dissipation Conditions: A TDGL Approach Applied to Nb and Nb3Sn

Abstract: Superconducting radiofrequency (SRF) cavities are essential components in modern particle accelerators, enabling the efficient acceleration of charged particles for various applications in physics, medicine, materials science, and beyond. The performance of these cavities is significantly influenced by the properties of superconducting materials, such as niobium (Nb) and triniobium-tin (Nb\textsubscript{3}Sn), and the defects and surface features present within the material. This dissertation presents a computational study focused on understanding the behavior of SRF cavities, using a sample-specific time-dependent Ginzburg-Landau (TDGL) framework to simulate their performance under realistic material conditions. The research integrates experimental data and density functional theory (DFT) calculations to model the impact of various defects, including hydrides, Sn-deficient islands, grain boundaries, and surface roughness. The calculations reveal how these defects contribute to performance degradation, particularly in terms of dissipation and quality factor ($Q$). We also investigate the impact of surface layers and roughness on the behavior of Nb\textsubscript{3}Sn, finding that surface features play a significant role in influencing cavity performance. In addition, the dissertation explores the generalized TDGL (GTDGL) model, which offers an extension to traditional TDGL theory and enables improved predictions of frequency-dependent phenomena. This work contributes to the development of more accurate computational tools for analyzing SRF cavity performance, providing insights that can guide future efforts in material optimization and accelerator technology.