Levitating states of superconducting rings in the field of a fixed ring with constant current

We consider the possibility of designing a plasma trap with a magnetic system formed by super-conducting rings and coils levitating in the field of a fixed coaxial coil carrying constant current. An analytic dependence of the potential energy of such a system with one or two levitating superconducting rings having trapped preset magnetic fluxes on their coordinates in the uniform gravitational field is obtained in the thin ring approximation. Calculations performed in the Mathcad system show that equilibrium states of such a system exist for certain values of parameters. Levitating states of a single superconducting ring and two superconducting rings in the field of the coil with constant current are observed experimentally in positions corresponding to calculated values.