This proposal outlines a program to develop a vibration-free reverse-Brayton cycle cooling system using specially-tuned magnetic bearings. Such a system is critical for the level of sensitivity required by future electromagnetic and gravitational wave detectors. The nature of magnetic bearings and their accompanying control systems make them ideal for applications that demand zero vibration, low-gravity, and maintenance-free operation. Further integration of these bearings into a reverse-Brayton cycle for cooling instruments is an ideal solution for use in high-sensitivity, long-term operations. In Phase I, Mainstream will develop a control algorithm designed to eliminate virtually all vibration and will be developed and tested on an existing machine operating under similar operating speeds and conditions. Design of the system and individual components will be finalized for immediate fabrication and testing in Phase II.