Modeling of mesoscopic superconducting suspensions by the method of integral equations

A mathematical model of the current density distribution in an axially symmetric system of superconductors in an external magnetic field is formulated within the framework of the integral form of London equations. The discretization of the model is carried out and the stability and convergence of the computational scheme are investigated. The distribution of magnetic induction, the density of currents in the ring and the sphere and the attractive force between them are calculated. The possibility of stable levitation of the sphere near the center of the ring is shown.