FPGA-Stabilized Magnetic Levitation of the APEX-LD High-Temperature Superconducting Coil

In this article, we demonstrate in-vacuum magnetic levitation of a compact high-temperature superconducting coil, which has been designed for magnetic confinement of an electron-positron pair plasma. The closed no-insulation rare-earth barium copper oxide coil was energized with a persistent current to generate a dipole magnetic field and then magnetically levitated by a water-cooled copper lifting coil located above. The vertical position of the floating coil was measured by an array of laser position sensors. Stable levitation was achieved by continuous adjustment of the lifting coil current using a 1-kHz proportional-integral-derivative feedback loop implemented by a field-programmable gate array. The feedback parameters were optimized with a 1-D simulation of the levitation system. A levitation time in excess of 3 h was achieved with a mean vertical displacement from the set point position of -\text{3 } \mu \rm {\text{m}} and a standard deviation of \sigma _{z} = \text{18 }\mu \rm {\text{m}}.