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The Levitated Dipole Experiment (LDX) is a new, innovative magnetic confinement fusion experiment being designed and installed in collaboration with Columbia University at the Massachusetts Institute of Technology (MIT). The primary objective of the experiment is to investigate the possibility of steady-state, high-beta plasma confinement with near classical transport. The main component of the experiment is a levitated cryostat with a 5.7 T Nb/sub 3/Sn superconducting magnet, housed in an Inconel high pressure helium vessel. The pressure vessel is surrounded by a large thermal mass radiation shield and an outer vacuum shell, all of which are magnetically levitated inside a much larger vacuum chamber. The cryostat, now under construction is described in this paper. The cryostat keeps the magnet temperature between 5 and 10 K during 8 hours of levitated operation.