Magnetic field distribution around a superconducting torus

The distribution of the static magnetic field around a superconducting torus is obtained. The superconductor is assumed to be an ideal diamagnet. Under this assumption an analytical expression for the magnetic field distribution around a torus is derived for the first time. This also takes into account magnetic flux trapping. The current density distribution on the torus surface and the magnetic field distribution around the superconducting torus were calculated for three cases: (1) when the torus is cooled down far below the critical temperature T c in zero external magnetic field and then the external magnetic field is switched on; (2) when the torus is cooled down in non-zero external field; (3) when the torus was cooled down as in the previous case and then the external field was switched off. All these cases are illustrated by diagrams. The magnetic flux quantization effect is deduced from classical electrodynamics and gauge symmetry.