Stable Levitation of Superconducting Myxines of Galathea Plasma Traps

Designing magnetic systems of Galathea plasma traps on the basis of levitating superconducting magnetic coils requires searching for their stable levitating states. For this purpose, proceeding from the property of superconductors to preserve the trapped magnetic flux, the potential energy of a system of several coaxial superconducting rings (one of the rings is fixed) with given trapped magnetic fluxes is obtained as an analytic function of the coordinates of the free rings along the system axis and angular deviations of their axes from the common axis of the system in a uniform gravity field in the thin-ring approximation. Computations demonstrate that, under certain values of physical parameters (the trapped magnetic flux and the dimensions and masses of the rings), this dependence has local minima, which correspond to stable equilibrium states of the levitating rings. For high-temperature superconducting (HTSC) rings and short-circuited HTSC coils manufactured for experiments on levitation, equilibrium states are found in different cases by calculating the aforementioned dependence of the potential energy. In the case where the magnetic fluxes trapped by the rings have the same signs, the calculated equilibrium levitating states of an HTSC ring in the field of a short-circuited HTSC coil (or an HTSC ring), namely, states that are stable against vertical displacements and angular deviations of the axis from the vertical, are implemented experimentally.