Extraction of Inductances and Spatial Distributions of Currents in a Model of Superconducting Neuron

Abstract A mathematical model and a computational method for extracting the inductances and spatial distributions of supercurrents in an adiabatic artificial neuron are proposed. This neuron is a multilayer structure containing Josephson junctions. The computational method is based on the simultaneous solution of the London equations for the currents in the superconductor layers and Maxwell’s equations, which determine the spatial distribution of the magnetic field, and on a model of the current sheet, which accounts for the finite depth of conducting layers and current contacts. This approach effectively takes into account interlayer contacts and Josephson junctions in the form of distributed current sources. The resulting equations are solved using the finite element method with large dense matrices. Computational results for the model of neuron with a sigmoid transfer function are presented. To optimize the device design, both the operating (planned in the first phase of the design) and parasitic inductances and the distribution of currents are calculated. The proposed methodology and software can be used for simulating a wide range of superconductor devices based on superconducting quantum interference devices.