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The Superconducting Super Collider, to be built in Texas, will provide an energy to 40 TeV from colliding proton beams. This energy is twenty times higher than currently available from the only other cryogenic collider, the Fermilab Tevatron, and will allow experiments that can lead to a better understanding of the fundamental properties of matter. The energy scale and the size of the new machine pose intriguing challenges and opportunities for its vacuum systems. We discuss the effects of synchrotron radiation on cryogenic beam tubes, cold adsorption pumps for hydrogen, methods of leak checking large cryogenic systems, the development of cold beam valves, and radiation damage to components, especially electronics.