Inductance calculation of 3D superconducting structures

Abstract

We propose a method for inductance calculation of three-dimensional superconducting structures by using software designed for high-frequency normal metal cases. By examining the analytical expressions for the current density distributions of the same ideal parallel plane structure in both the high-frequency normal metal case and the superconductor case, we obtain a correction factor for the kinetic inductance calculation in the latter. It is then assumed that this correction factor can be applied to real superconducting layers with finite widths. The total inductance of any superconducting structure can be obtained by finding the magnetic field energy in the high-frequency normal metal case with the same configuration, and adding the kinetic energy with the correction factor applied. Normal metal field simulators, such as MAXWELL, can readily be used. A SQUID loop inductance is simulated as a test case on MAXWELL, and 3% agreement is achieved with the experimental result.