Inductance computation of microscopic superconducting loop

Aimed for the design of superconducting digital circuits, a direct method is proposed to estimate the inductance of three-dimensional microscopic superconducting loop. This method directly computes current-density distribution by using the Maxwell equations and the expression of the momentum, which are both discretized; without free-energy minimization technique, we just solve a set of linear equations considering a spatially-discrete model. Computer simulation was carried out for various shapes of superconductors, and the simulated results agreed well with the Chang's formula in a model which can be regarded as two-dimensional. The magnetic field distribution also agreed well with the theoretical value.