On the thermodynamics of the inhomogeneous mixed phase of an ideal type II superconductor

The macroscopic tensor S _ik is defined so as to characterize changes in the structure of the vortex system. This tensor contains only three independent components instead of the six of the strain tensor u _ik which is used commonly to describe deformations of the vortex system. All components of S _ik are independent of the magnetic induction B and can be considered as thermodynamic variables of the system together with B. The stress tensor for an inhomogeneous mixed phase is obtained in these variables. It is shown on the basis of the Ginzburg-Landau current equation that the mixed phase tends to be uniform; inhomogeneities (e.g., macroscopic currents) can penetrate to the uniform phase only up to some distance that diverges at H H _c2. The free energy of a weak inhomogeneous mixed state is discussed; nonlocal features of the vortex system and its special magnetic symmetry are taken into account. This symmetry allows for the existence of contributions to the free energy that are linear in the magnetic field and strains. The equilibrium conditions differ in general from the simple relation j × B = 0, so that the force-free configurations do not correspond to the thermodynamic equilibrium of an ideal material. The connection between the fields B and H is obtained in the form of a differential equation that also includes the structural parameters S _ik. These fields need not be parallel in general. The current distribution in a slab of an ideal type II material in a transverse field is calculated.