Simulation of the current dynamics in superconductors: Application to magnetometry measurements

Abstract

A simple model for simulating the current dynamics and the magnetic properties of superconductors is presented. Short simulation times are achieved by solving the differential form of Maxwell's equations inside the sample, whereas integration is only required at the surface to meet the exact boundary conditions. The procedure reveals the time and position dependence of the current density and the magnetic induction $(B)$ making it very convenient to apply field dependent material parameters for the simulation of magnetization loops, relaxation measurements, etc. Two examples, which are important for standard magnetometry experiments, are discussed. First, we prove that evaluating the critical current density $({J}_{\text{c}})$ from experiment by applying Bean's model reveals almost the exact ${J}_{\text{c}}(B)$ behavior if the evaluation is corrected by a simple numerical expression. Second, we show that the superconducting volume fraction of a sample can be directly determined from magnetization loops by carefully comparing experiment and simulation in the field range, where the current loops are differently oriented within the sample.