Meissner-London susceptibility of superconducting right circular cylinders in an axial magnetic field

TL;DR

This paper provides a universal formula for the magnetic susceptibility of superconducting right circular cylinders in an axial magnetic field, enabling accurate determination of the London penetration depth from experimental measurements.

Contribution

The authors derived a closed-form universal susceptibility formula for superconducting cylinders, validated it with finite-element modeling, and demonstrated its application in experimental data analysis.

Findings

Derived a universal susceptibility formula involving sample dimensions and mbda

Validated the formula using finite-element simulations across various mbda/sample size ratios

Provided a practical method for extracting London penetration depth from susceptibility measurements

Abstract

Magnetic susceptibility of non-ellipsoidal samples is a long-standing problem in experimental studies of magnetism and superconductivity. Here the quantitative description of the Meissner-London response (no Abrikosov vortices) of right circular cylinders in an axial magnetic field is given. The three-dimensional adaptive finite-element modeling was used to calculate the total magnetic moment, m, in a wide range of London penetration depth, \lambda, to sample size ratios. By fitting the numerical data, the closed-form universal magnetic susceptibility is formulated involving only sample dimensions and \lambda, thus providing a recipe for determining the London penetration depth from the accurate magnetic susceptibility measurements. Detailed examples of the experimental data analysis using the developed approach are given. The results can be extended to the frequently used cuboid-shaped samples.