Magnetic shielding properties of high- T_c superconducting hollow cylinders: Model combining experimental data for axial and transverse magnetic field configurations

Magnetic shielding efficiency was measured on high- T_c superconducting hollow cylinders subjected to either an axial or a transverse magnetic field in a large range of field sweep rates, dB_app/dt. The behaviour of the superconductor was modelled in order to reproduce the main features of the field penetration curves by using a minimum number of free parameters suitable for both magnetic field orientations. The field penetration measurements were carried out on Pb-doped Bi-2223 tubes at 77K by applying linearly increasing magnetic fields with a constant sweep rate ranging between 10νTs^-1 and 10mTs^-1 for both directions of the applied magnetic field. The experimental curves of the internal field versus the applied field, B_in(B_app), show that, at a given sweep rate, the magnetic field for which the penetration occurs, B_lim, is lower for the transverse configuration than for the axial configuration. A power law dependence with large exponent, n′, is found between B_lim and dB_app/dt. The values of n′ are nearly the same for both configurations. We show that the main features of the curves B _in(B_app) can be reproduced using a simple 2D model, based on the method of Brandt, involving a E(J) power law with an n-exponent and a field-dependent critical current density, J_c(B), (following the Kim model: J_c = J_c0(1+B/B₁)^-1). In particular, a linear relationship between the measured n′-exponents and the n-exponent of the E(J) power law is suggested by taking into account the field dependence of the critical current density. Differences between the axial and the transverse shielding properties can be simply attributed to demagnetizing fields.