Muon Cooling via Ionization and Tests of Muon Acceleration Cavities Don Hartill, Mentor High energy muons can be used to produce a very intense well defined neutrino beam and possibly a very high energy high luminosity collider. Key to this possibility is a method of cooling (reducing the six dimensional phase space) the muon beam by ionization whereby ionization energy loss in a low-Z absorber reduces the beam energy in all three coordinates followed by an acceleration in only the longitudinal coordinate. The transverse size of the beam is thereby reduced while maintaining the energy of the muon beam. Unfortunately, straggling in the energy loss process causes the longitudinal phase space to increase leading to significant particle loss during cooling. Initial results from simulations carried out this past year indicate that by suitable manipulation of the phase of the accelerating cavities, this effect can be significantly reduced or eliminated. The REU student would continue this work to confirm its effectiveness and explore the ultimate reduction in six dimensional phase space using this approach. In addition, the student would assist in the testing of two 500 MHz superconducting rf cavities that are prototypes of the cavities that would be needed to accelerate the muons to high energy after they were successfully cooled. Assisting with these tests would represent about 30% of the student's activity during the summer.