Stability of equilibrium of a superconducting ring that levitates in the field of a fixed ring with constant current

In order to develop a plasma trap with levitating superconducting magnetic coils, it is necessary to search for their stable levitating states. An analytical expression for the potential energy of a single superconducting ring that captures a fixed magnetic flux in the field of a fixed ring with constant current versus the coordinate of the free ring on the axis of the system, deviation angle of its axis from the axis of the system, and radial displacement of its plane is derived for uniform gravity field in the thin ring approximation. The calculated stable levitation states of the superconducting ring in the field of the ring with constant current are proven in experiments. The generalization of such an approach to the levitation of several rings makes it possible to search for stable levitation states of several coils that form a magnetic system of a multipole trap.