Determination of the Magnetic Penetration Depth from Finite-Element Susceptibility Calculations of Spheroidal and Cylindrical Superconductors
Abstract
The magnetic penetration depth, λ, is a fundamental parameter of the superconducting state and is commonly determined from precision measurements of the magnetic susceptibility, χ, in the Meissner state. However, extracting λ from such measurements requires an accurate treatment of geometry-dependent demagnetization effects, for which analytic results are only available in a limited number of cases. Here we present a finite-element analysis of the magnetic response of three dimensional superconducting spheroids and cylinders with finite penetration depth. By calculating the magnetic moment and susceptibility, χ(λ), over a wide range of aspect ratios, we quantify the shape-dependent Meissner response and extract effective demagnetization factors in the λ→ 0 limit. For small but finite λ, we further determine effective sample dimensions from the initial variation of χ(λ) and propose an improved analytical expression for these. Our results provide a high-precision procedure for determining λ from volume-exclusion based susceptibility measurements and should be directly applicable to the characterization of novel superconducting materials.
Versions
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BibTeX
@misc{grant2026determination,
title = {{Determination of the Magnetic Penetration Depth from Finite-Element Susceptibility Calculations of Spheroidal and Cylindrical Superconductors}},
author = {Morgan Grant and Antony Carrington},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36133},
eprint = {2610.36133},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36133},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Determination of the Magnetic Penetration Depth from Finite-Element Susceptibility Calculations of Spheroidal and Cylindrical Superconductors
AU - Morgan Grant
AU - Antony Carrington
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36133
UR - https://arxiv.org/abs/2610.36133
AB - The magnetic penetration depth, λ, is a fundamental parameter of the superconducting state and is commonly determined from precision measurements of the magnetic susceptibility, χ, in the Meissner state. However, extracting λ from such measurements requires an accurate treatment of geometry-dependent demagnetization effects, for which analytic results are only available in a limited number of cases. Here we present a finite-element analysis of the magnetic response of three dimensional superconducting spheroids and cylinders with finite penetration depth. By calculating the magnetic moment and susceptibility, χ(λ), over a wide range of aspect ratios, we quantify the shape-dependent Meissner response and extract effective demagnetization factors in the λ→ 0 limit. For small but finite λ, we further determine effective sample dimensions from the initial variation of χ(λ) and propose an improved analytical expression for these. Our results provide a high-precision procedure for determining λ from volume-exclusion based susceptibility measurements and should be directly applicable to the characterization of novel superconducting materials.
ER -