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A passive magnetic damper suitable for use as a vibration isolator coupled between two masses, one of which is subject to vibration. The damper includes at least two pairs of rare earth permanent magnets configured to provide a narrow, generally planar gap, and backing plates positioned to complete a magnetic circuit passing through the magnets and the gap. A flat conductor plate is positioned to be freely movable in the gap. Any time-varying force on the conductor plate results in the generation of eddy currents in the plate, and these in turn generate a mechanical force on the plate, which resists the time-varying force and produces a damping effect. With careful selection of materials for the magnets, the backing plates and the conductive plate, the damper is effective over a wide temperature range that includes cryogenic temperatures, and is operable over a wide range of damping levels.