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Applications: produce high magnetic fields for
As of the early 2020s, superconducting magnets predominantly use low temperature superconductors Nb-Ti and Nb-Sn, see also most important superconductor materials, but there were efforts underway to create practical high-temperature superconductor-based magnets as well: Section "High temperature superconductor superconducting magnet (HTS magnet)".
Wikipedia has done well for once:
The current to the coil windings is provided by a high current, very low voltage DC power supply, since in steady state the only voltage across the magnet is due to the resistance of the feeder wires. Any change to the current through the magnet must be done very slowly, first because electrically the magnet is a large inductor and an abrupt current change will result in a large voltage spike across the windings, and more importantly because fast changes in current can cause eddy currents and mechanical stresses in the windings that can precipitate a quench (see below). So the power supply is usually microprocessor-controlled, programmed to accomplish current changes gradually, in gentle ramps. It usually takes several minutes to energize or de-energize a laboratory-sized magnet.
Video 15. Superconductivity: magnetic separation by University of Cambridge. Source.

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