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

TL;DR

This paper presents a computational model for simulating superconductor current dynamics and magnetic properties, enabling efficient analysis of magnetometry data and revealing accurate critical current densities and volume fractions.

Contribution

A simple, fast simulation method solving Maxwell's equations inside superconductors with surface integration for boundary conditions, improving analysis of magnetometry measurements.

Findings

Critical current density J_c(B) can be accurately extracted using a correction to Bean's model.

Superconducting volume fraction can be directly determined from magnetization loops.

Simulation results match experimental data for standard magnetometry experiments.

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. Firstly, we prove that evaluating the critical current density (J_c) from experiment by applying Bean's model reveals almost the exact J_c(B) behavior, if the evaluation is corrected by a simple numerical expression. Secondly, 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.