This project investigates a new type of high Q resonant structure, which has recently been demonstrated, to develop high gradient, superconducting accelerator cavities. Based on the concept of a Photonic Band Gap (PBG) resonator, these new structures are physically significantly different from the resonant cavities currently used in normal superconducting devices. A resonant mode suitable for accelerating charged particle beams arises from the presence of a defect in a two-dimensional lattice of dielectric obstacles placed between two conducting sheets. PBG resonators have two unique properties that may overcome many of the limitations in the present state of the art: (1) it may be possible to obtain a structure with no higher order modes and with the single resonant frequency energy distributed in a pure monopole mode, thereby reducing beam instabilities and also reducing energy losses; and (2) it is expected that one could achieve Q > 106 at 4K using presently available niobium material, with particular ease, because only flat sheets of superconductor are required, with no joints or bends. In Phase I, optimum configurations of PBG structures for accelerator applications are being established through numerical simulations. Suitable means will be established for coupling fields between adjacent resonators and for coupling radio frequency power into a PBG accelerator structure. The construction of a cryogenic test facility suitable for experimental evaluation of PBG configurations will be specified and its cost anytime requirements planned. This project is evaluating the potential applicability of PBG resonant structures for very high gradient, high energy electron accelerators as well as for high gradient, high current proton and heavy-ion accelerators. The findings will be incorporated in a report on the potential performance and applicability of PBG resonant structures for very high gradient, high Q acceleration structures, including the design of a high power test structure. The Phase II project would build and test a room temperature model to verify design features and would build and test a superconducting version. Anticipated Results/Potential Commercial Applications as described by the awardee: This project should evaluate and demonstrate the benefits of using a new resonant structure based on the concept of a PBG with defect. This structure should allow more efficient, smaller footprint, and higher gradient electron and proton linear accelerators. In addition to being used in government laboratories, this structure has projected commercial applications, including sources for x-ray lithography, production of medical radionuclides, uses in medical proton therapy, and uses in nuclear waste transmutation.