A new approach to the inverse problem for current mapping in thin-film superconductors

TL;DR

This paper introduces a detailed mathematical method for solving the inverse Biot-Savart law in thin-film superconductors using Magneto-Optical Imaging, improving accuracy and implementation over previous approaches.

Contribution

It presents a new, detailed approach for current mapping in superconducting thin films, refining previous methods and verifying effectiveness with experimental data.

Findings

Effective inversion of the Biot-Savart law demonstrated on YBa2Cu3O7 films.

Refined methods improve accuracy over previous techniques.

Streamlined iterative technique accounts for in-plane magnetic fields.

Abstract

A novel mathematical approach has been developed to complete the inversion of the Biot-Savart law in one- and two-dimensional cases from measurements of the perpendicular component of the magnetic field using the well-developed Magneto-Optical Imaging technique. Our approach, especially in the 2D case, is provided in great detail to allow a straightforward implementation as opposed to those found in the literature. Our new approach also refines our previous results for the 1D case [Johansen et al., Phys. Rev. B 54, 16264 (1996)], and streamlines the method developed by Jooss et al. [Physica C 299, 215 (1998)] deemed as the most accurate if compared to that of Roth et al. [J. Appl. Phys. 65, 361 (1989)]. We also verify and streamline the iterative technique, which was developed following Laviano et al. [Supercond. Sci. Technol. 16, 71 (2002)] to account for in-plane magnetic fields caused by the bending of the applied magnetic field due to the demagnetising effect. After testing on magneto-optical images of a high quality YBa2Cu3O7 superconducting thin film, we show that the procedure employed is effective.