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

Based on the Bean model with a constant critical current density $j_c,$ novel and very precise, analytical approximations for the axial induction component $B_z($ 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 $j_c$ 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 $j_c$ 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 $j_c$ and material inhomogeneities. The first effect becomes important for sample radii in the $\text{1-}\mathrm{cm}$ -range, although the $B_z$ -profile remains axially symmetric and well fitted by the Bean model. The second one may lead to asymmetric $B_z$ -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 $j_c$ from mapping and VSM measurements.