SQUID sensor-based ultra low-field magnetic resonance apparatus with ${mu}T$-level measurement field requires a strong prepolarization magnetic field ($B_p$) to magnetize its sample and obtain magnetic resonance signal with a high signal-to-noise ratio. This $B_p$ needs to be ramped down very quickly so that it does not interfere with signal acquisition which must take place before the sample magnetization relaxes off. A MOSFET switch-based $B_p$ coil driver has current ramp-down time ($t_{rd}$) that increases with $B_p$ current, which makes it unsuitable for driving high-field $B_p$ coil made of superconducting material. An energy cycling-type current driver has been developed for such a coil. This driver contains a storage capacitor inside a switch in IGBT-diode bridge configuration, which can manipulate how the capacitor is connected between the $B_p$ coil and its current source. The implemented circuit with 1.2 kV-tolerant devices was capable of driving 32 A current into a thick copper-wire solenoid $B_p$ coil with a 182 mm inner diameter, 0.23 H inductance, and 5.4 mT/A magnetic field-to-current ratio. The measured trd was 7.6 ms with a 160 ${mu}F$ storage capacitor. trd was dependent only on the inductance of the coil and the capacitance of the driver capacitor. This driver is scalable to significantly higher current of superconducting $B_p$ coils without the $t_{rd}$ becoming unacceptably long with higher $B_p$ current.