Field mapping characterization for axially magnetized, superconducting cylinders in the remanent critical state: theory and experiment

Abstract

Based on the Bean model with a constant critical current density jc, novel and very precise, analytical approximations for the axial induction component Bz(r) inside and outside of a finite, axially magnetized, circular cylinder with arbitrary aspect ratio in the fully penetrated, remanent critical state are presented. Starting from any mapped field profile the possibility to determine the material parameter jc by means of a global optimum fit procedure is demonstrated. Some characteristic results for melt-textured yttrium barium copper oxide material are outlined. We found that jc determined by vibrating sample magnetometry (VSM) exceeds that from mapping at least by about 50%. This systematic discrepancy is discussed on the basis of two independent effects resulting in a local, space-dependent critical current density: the B-dependence of jc and material inhomogeneities. The first effect becomes important for sample radii in the 1-cm-range, although the Bz-profile remains axially symmetric and well fitted by the Bean model. The second one may lead to asymmetric Bz-profile deformations connected with a decreasing fitting significance. For the first and second effect we estimate the considerable ratio of the absolute maximum to absolute minimum of the local, critical current density of 2 and 4, respectively, which explains the observed discrepancies between the effective jc from mapping and VSM measurements.