Surface currents of a superconducting axisymmetric body that screen an external coaxial magnetic field

A time-saving method to find currents on the surface of a superconducting axisymmetric body is suggested for the case when the axis of the body and the symmetry axis of an external magnetic field coincide. The method is based on solving a one-dimensional integral equation. Analytical solutions are derived for the superconductor in the form of an ellipsoid of revolution that is placed in a uniform magnetic field and in the form of a sphere placed in a magnetic field varying as a polynominal at the symmetry axis. To find the current density on the surface of an arbitrarily shaped axisymmetric body placed in an arbitrarily varying magnetic field, a method of numerically solving the integral equation is proposed. It is a combination of the iterative regularization method and the projective method with a projector in the form of B splines. The results of numerical reconstruction of the sought functions by the latter method for a number of particular cases are presented.