Radio-frequency cavities are at the heart of particle accelerators used for nuclear and high-energy physics research, medical treatment, pollution control, clean energy production, development of new materials, and national security. The most advanced accelerators utilize cavities that are made from superconducting materials. However, the performance of these cavities is reaching a fundamental limit, and they are very expensive to fabricate and operate. Hence, next-generation accelerators require development of advanced cavities. One promising approach to greatly improving the performance and reducing cost is to coat the inner surfaces of these cavities with superconducting thin film materials having certain critical properties. Magnesium diboride is a superconductor that can meet these requirements. Depositing thin films of this compound is challenging, though an approach based on reactive evaporation has yielded superb results.We propose to develop equipment and methods that will advance the state-of-the-art of this thin- film coating technology and extend its capability in order to enable deposition of high-quality magnesium diboride thin films onto the inner surfaces of real-world elliptical superconducting radio-frequency cavities. During Phase I of this project we will produce and test simple three- dimensional cavity resonators coated with our material. We will also explore and model hardware designs and process methodologies to produce more complicated real-world resonators that have been developed for advanced accelerators.Successful deployment of this technology in a Phase II or Phase III project will result in the ability to produce the worldâs most advanced and cost-effective superconducting radio-frequency cavities in order to enable a host of beneficial applications outlined above