Magnetic Vortex in Superconducting Wire

The solutions of a non-linear system of Ginzburg–Landau equations, which describe the order parameter and magnetic field of a vortex in a long superconducting wire of finite radius, are studied. It is found, that the vortex can exist only if the radius of a wire r1 > rc, where rc is some critical radius, which depends on the parameter κ of the Ginzburg–Landau theory. The solutions, describing the vortex in a type I superconducting wire with κ < 1/√2 are also studied. The interpolation formulas, describing the order parameter and magnetic field around the vortex in sufficiently thick superconducting wire, which are valid for arbitrary κ and distances r from the vortex axis, are proposed.