`Electromaglev' (`active-maglev')—magnetic levitation of a superconducting disk with a DC field generated by electromagnets: Part 3. Theoretical results on levitation height and stability

Abstract

We present Part 3 results of a comprehensive theoretical study of an `electromaglev' (`active-maglev') system, in which a high-temperature superconducting bulk YBCO sample is levitated stably in a DC magnetic field generated by a magnet system. Field solutions have been obtained numerically to compute levitation height and define stability criteria for the superconducting disk sample. Our analysis assumes that the disk, which otherwise obeys the Bean critical-state model, traps flux when cooled in the presence of a field from the normal state to the superconducting state. Indeed it is shown that the trapped flux makes subtle and crucial changes in field distribution (and thus current density distribution) in the disk, which differ from those in a disk strictly obeying the Bean model used in the zeroth-order theory. The analysis confirms a key experimental finding that the trapped flux is another essential element for determining levitation height and ensuring tilt-free stable levitation. For stability, trapped flux is in addition to at least two degrees of freedom for spatial supercurrent flow and the profile conditions imposed on the field generated by the magnet system. Procedures to produce stable, tilt-free levitation are described. Agreement between experiment and analysis on dependence of levitation height on magnet current is quite good. The analysis also shows that to achieve stable levitation, a YBCO ring sample requires a radial build that is sufficiently thick to permit the supercurrent to flow in the radial direction. The minimum radial build required, Δ R min, for a YBCO ring of outside radius 12.5 mm operating at 77 K is typically ∼50 μm. An analytical expression that gives approximate values of Δ R min has also been derived; Δ R min depends inversely on the square of the critical current density of the superconductor.