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For this purpose, a levitated dipole trap (APEX-LD) has been constructed. The magnetically levitated, compact (7.5-cm radius), closed-loop, high-temperature superconducting floating (F-)coil consists exclusively of a no-insulation rare-earth barium copper oxide winding pack, solder-potted in a gold-plated-copper case. A resealable in-vacuum cryostat facilitates cooling (via helium gas) and inductive charging of the F-coil. The 70-min\u00a0preparation cycle reliably generates persistent currents of \u223c60 kA-turns and an axial magnetic flux density of B0 \u2248 0.5 T. We demonstrate levitation times in excess of 3\u00a0h with a vertical stability of \u03c3z &amp;lt; 20 \u03bcm. Despite being subjected to routine quenches (and occasional mechanical shocks), the F-coil has proven remarkably robust. 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