Tai, TaminNiobium-based Superconducting Radio Frequency (SRF) particle accelerator cavity performance is sensitive to localized defects that give rise to quenches at high accelerating gradients. In order to identify these material defects on bulk Nb surfaces at their operating frequency and temperature, it is important to develop a new kind of wide bandwidth microwave microscopy with localized and strong RF magnetic fields. A novel near-field magnetic field microwave microscope that enables mapping of the local electrodynamic response in the multi-GHz frequency regime at liquid helium cryogenic temperatures was successful built via the combination of a magnetic writer and a near field-microwave microscope [1] [2]. This magnetic writer can create a localized and strong RF magnetic field and should achieve a condition with Bsurface ~150 mT and sub-micron resolution (Chapter 3). Our objective is to study the extreme and local electrodynamic properties of Niobium (Nb), and to relate these properties to specific defects that limit the ultimate RF performance of superconducting radio frequency cavities made from Nb. Therefore, in this dissertation, many superconducting materials, especially the candidate materials for superconducting RF cavities, were tested at a fixed location to analyze the local electrodynamic response through linear and nonlinear microwave measurements. For the linear measurement (Chapter 4), many fundamental properties of RF superconductivity such as the critical temperature Tc and penetration depth lambda can be identified. For the nonlinear response measurement (Chapter 5), both the intrinsic and extrinsic nonlinearities from the superconductors are excited by our magnetic write head probe. Many models are introduced to identify the measured nonlinearity, including the intrinsic nonlinearity from the modulation of the superconducting order parameter near Tc, and the extrinsic nonlinearity from the moving vortex model, weak-link Josephson effect, and the possible nonlinear mechanism from switching events between the Meissner state and the mixed state. These models of extrinsic nonlinearity are studied in Chapter 6. The high transition temperature and low surface resistance of MgB2 attracts interest in its potential application in superconducting radio frequency accelerating cavities. However, compared to traditional Nb cavities, the viability of MgB2 at high RF fields is still open to question. Hence, in Chapter 7, two-gap high quality MgB2 films with thickness 50 nm, fabricated by a hybrid physical-chemical vapor deposition technique on dielectric substrates, are measured at a fixed location to investigate its RF properties. The third harmonic measurement on MgB2 films shows different nonlinear mechanisms compared to the bulk Nb measurement [3] . We conclude that the nonlinear response for the high quality MgB2 films at temperature less than Tc shows the nonlinearity from the moving vortices and from the following possible mechanisms: First, an intrinsic nonlinearity from the proximity-induced second Tc. Second, the intrinsic nonlinearity arising from Josephson coupling between the sigma and pi bands of the two gap nature of MgB2. Third: The potential nonlinearity from the reported superconducting nodal gap properties. Finally the future plan to raster scan on the SRF candidate materials is proposed to relate the nonlinear electromagnetic images to the physical defects on the superconductor surface. These efforts can finally feed back to the cavity processing techniques and suggest new thoughts for alternate surface processing treatment in the future. [1] T. Tai, et al., IEEE Trans. Appl. Supercond. 21, 2615, (2011). [2] T. Tai et al., IEEE Trans. Appl. Supercond. 23, 7100104, (2013). [3] T. Tai et al., Phys. Rev. ST Accel. Beams 15, 122002, (2012).DissertationPhysicsElectrical engineeringMaterials ScienceBulk Niobiummagnesium diboridemagnetic probenear field microwave microscopeSuperconducting Radio Frequency Cavitysuperconductivity