This grant supports research and development of a new type of linear accelerator structure, the superconducting Radio Frequency Quadrupole (SRFQ). Both superconducting linac techniques and RFQ technology have reached a sufficiently advanced state so that the combination of the two may be tried with a large degree of confidence. This research will advance the science of superconducting accelerators and provide a new and unique tool for many important applications such as the 100% duty factor acceleration of very low velocity ion beams. The goal of the proposed project is to design, build and test a complete prototype unit. The design study will investigate the problem of longitudinal and radial matching between the ion source and the RFQ as well as between RFQ units, fringe fields problems, and the accelerating field variation along the RFQ. Resonator studies, also will be carried out. These will include analytic and numerical investigations of the 4-rod RFQ parameters and comparison with the 4-vane RFQ. Following the design studies, a prototype unit will be constructed. Tests of the RFQ in the normal-conducting and superconducting states, including bead tests, calibration of the probes, test for multipactoring, low field Q and high field performance, will be carried out. The project will culminate in beam tests of the superconducting RFQ.