Macroscopic and microscopic models of i n s i t u superconductors

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Abstract
It is argued that a macroscopic formalism similar to that for continuous filament material can be applied to in situ superconductors, providing an elongated volume element is used for averaging over the microscopic fields and currents. The difference between in situ and continuous filament materials is found in the constitutive equations. For an in situ tape these consist of a specification of three critical current densities for the macroscopic superconducting state, together with three conductivities for the nonsuperconducting state, and, under some conditions, three magnetization components. The interesting region of the nonsuperconducting state occurs when the material is macroscopically nonsuperconducting, but superconducting microscopically. A microscopic model based on the proximity effect is developed for computing the constitutive equations. For calculating the axial current density the model assumes that chains of filaments run through the conductor. When the superconducting proximity layers surrounding a pair of chains overlap, the chains can carry macroscopic supercurrent. In general, a conductor can be superconducting in one, two, or three directions. The critical current densities are expected to be highly anisotropic.