Use MU Research Reactor on first reference. MURR is acceptable on second reference. 

For more than 50 years the faculty and staff of the MU Research Reactor (MURR) have promoted groundbreaking research and developed life-saving radiopharmaceuticals, providing benefits to people across the country and around the world. MURR is the highest-power university research reactor in the United States, operating at 10 megawatts, 6.5 days a week and 52 weeks a year.

Example: She is a researcher at the MU Research Reactor.