3D magnetization currents, magnetization loop, and saturation field in superconducting rectangular prisms

Abstract

Bulk superconductors are used in both many applications and material characterization experiments, being the bulk shape of rectangular prism very frequent. However the magnetization currents are still mostly unknown for this kind of three dimensional (3D) shape, specially below the saturation magnetic field. Knowledge of the magnetization currents in this kind of samples is needed to interpret the measurements and the development of bulk materials for applications. This article presents a systematic analysis of the magnetization currents in prisms of square base and several thicknesses. We make this study by numerical modeling using a variational principle that enables high number of degrees of freedom. We also compute the magnetization loops and the saturation magnetic field, using a definition that is more relevant for thin prisms than previous ones. The article presents a practical analytical fit for any aspect ratio. For applied fields below the saturation field, the current paths are not rectangular, presenting 3D bending. The thickness-average results are consistent with previous modeling and measurements for thin films. The 3D bending of the current lines indicates that there could be flux cutting effects in rectangular prisms. The component of the critical current density in the applied field direction may play a role, being the magnetization currents in a bulk and a stack of tapes not identical.

Fast Fourier transform-based solution of 2D and 3D magnetization problems in type-II superconductivity

“…Appearance of a significant z component of j , necessary for shielding the zero-field core, is an unexpected feature of current density distribution discovered and explained in [16][17][18]. We found that smoothing, employed in the FFT-based method, smears the narrow peaks of z j and, therefore, had to use a weaker Gaussian filter with 0.5d   to arrive at the z j -distribution ( Figure 6) similar to that in [19].…”

“…To make the conducting and non-conducting domains simply connected, we introduced a cutting-hole layer . The iterations(18), intended to eliminate the stray outside current, were applied in out  but not in 0  . For e ( ) (0,0, ) tt  h the resistivity out 200   was sufficient to make the current in 0  negligibly small even without such iterations (see the hole || j levels inFigure 7, left).…”

Cross-field demagnetization of stacks of tapes: 3D modelling and measurements

“…The trapped magnetic field B t during the whole process is calculated 1 mm above the top surface ( figure 11). After relaxation, we applied cross-fields with two different amplitudes, 40 and 240 mT, in order to see the behaviour in the fields below and above the penetration field B p of the stack. The parallel penetration field B p, of 1 tape is 17 mT according to the slab Critical-State model [50,51],…”

3D simulation of superconducting magnetic shields and lenses using the fast Fourier transform

“…Here we solve such a 3D problem for a hollow superconducting cylinder sealed at one end (the configuration considered in [2]) using the Fast Fourier Transform (FFT) based method [6]. This method is an easily implemented alternative to the finite element methods for 3D magnetization problems (see, e.g., [7][8][9][10][11][12]) and we employ it to model also field concentration by a magnetic lens. The configuration of a bulk superconductor in the latter problem is that of the magnetic lenses in [13].…”