Meissner-London Susceptibility of Superconducting Right Circular Cylinders in an Axial Magnetic Field
Ruslan Prozorov
Abstract
Analysis of magnetic susceptibility of nonellipsoidal 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. Three-dimensional adaptive finite-element modeling is used to calculate the total magnetic moment ($m$) in a wide range of London penetration depth ($\ensuremath{\lambda}$) to sample size ($a$) ratios, $\ensuremath{\lambda}/a$. By fitting numerical solutions, the closed-form empirical magnetic susceptibility is obtained involving only sample dimensions and $\ensuremath{\lambda}$, thus providing a recipe for determining the London penetration depth from the precision measurements of the magnetic susceptibility. Detailed protocols of the experimental data analysis using the developed approach are given. The results can be readily extended to the most frequently used cuboid-shaped samples.