Macroscopic current in a wire of an ideal type II superconductor in a longitudinal field

The problem formulated in the title is solved. We take into account the dependence of the free energy density on (a) the structure, (b) nonlocal properties, and (c) the special magnetic symmetry of the vortex system. It turns out that inhomogeneities (current density, deformations) have maxima on the wire surface and attenuate exponentially with penetration into the wire. The present solutions distinguish between two different physical situations, when the current and the external field are parallel or antiparallel. All the above results contradict the “force-free” model, in which the current density oscillates a s a function of distance from the axis, and the magnetization of the wire is symmetric with respect to the change of the current direction under the fixed external field.