Abstract :
[en] The goal of this thesis is to comprehend the influence of the inhomogeneity of the magnetic field distribution on the low frequency shielding performances of passive bulk high-temperature superconducting magnetic shields. We aim at gaining a better understanding of the magnetic field penetration, of the shape of the flux front and of the shielding current distribution within the superconducting shield. We also seek to locate spots where the local magnetic flux density is the strongest, i.e. corresponding to the location of the easiest “flux entry gates”.
The inhomogeneity of the magnetic field distribution is characterized using two parameters - its gradient and the curvature of flux lines - which are interdependent because of Gauss law. For our investigation we consider three shielding problems of increasing complexity in terms of loss of symmetry between the magnetic screen and the field distribution, thus increasing the inhomogeneity of the magnetic field and the distribution of shielding currents. Each configuration corresponds to a given magnetic field source for which the magnetic field experienced by the superconducting shield is characterized and analyzed. The superconductors investigated experimentally are all made of bulk Bi-based high-temperature superconductors (either Bi2Sr2CaCu2O8 [Bi-2212] produced by melt-cast process or polycrystalline Bi2Sr2Ca2Cu3O10 [Bi-2223]).
With the first problem, we consider a bulk superconducting tube subjected to the inhomogeneous magnetic field generated by a coil placed inside the shield, which corresponds de facto to an “emission” problem configuration.
We show, in the axisymmetric situation where the source coil is placed coaxially to the tube and at its center, that the maximum applicable magnetic field that can be shielded can be approximated analytically with a simple 1D model based on magnetic flux conservation, and is in remarkably good agreement with the experimental data. This model predicts and quantifies the phenomenon of magnetic flux concentration occurring between the source coil and the inner surface of the superconductor and originating from the diamagnetic behavior of the superconductor. Unlike a superconducting magnetic shield placed in a uniform external field, for which the maximum field to be screened depends primarily on the wall thickness, our results show therefore it is necessary to take into account the total volume of the shield for an optimal design in an “emission” configuration.
The second problem involves a magnetic shield subjected to the inhomogeneous stray field of a solenoidal coil placed at moderate distance (of the order of the height of the coil) and such that the field is quasi-axial. We show that the magnetic field experienced by the superconductor can be approximated as the field generated by an equivalent magnetic dipole at the center of the coil, thus generalizing our results to situations where the dipolar approximation stands valid.
We compare this situation to that of a tube subjected to an oblique homogeneous magnetic field and observe similarities in the shielding current distribution. Our results give evidence that the characteristics of the shielding currents in an inhomogeneous field are primarily related to the orientation of the local applied field. Moreover, we observe that, when considering oblique fields, portions of the magnetic shield act to reduce the magnetic flux density within the superconductor but not necessarily within the inner space delimited by the shield.
The third investigated configuration involves the magnetic field generated by a pancake coil placed at very short distance of the magnetic shield. In this situation the superconductor is subjected to a quasi-transverse magnetic field.
We show how the inhomogeneity of the magnetic field affects the shielding current distribution within the superconductor by comparing our results to those obtained when considering a similar shield subjected to an uniform transverse field. We also observe how the location of the strongest magnetic flux density points is affected.
In this configuration the temperature dependence of the shielding performances is also examined thanks to a bespoke variable temperature measurement system. We point out the difficulty to analyze the superconductor behavior using a creep exponent as the measured properties result from two effects acting together: the temperature dependence of the creep exponent and the effective volume of the magnetic shield penetrated by the magnetic flux lines, which is directly related to the degree of inhomogeneity of the magnetic field.
Two finite element models are developed: a 2D axisymmetric model based on an A formulation and a 3D model using an H-φ formulation. Both offer results in agreement with analytical results and results obtained with the Brandt method. Moreover, they are in good agreement with the experimental results and provide relevant information regarding the flux penetration and the shielding current distribution. In particular, the 3D model permits the treatment of the general case of a superconducting shield which can be multiply connected, i.e. containing holes, subjected to inhomogeneous magnetic fields.
Finally, we carry out a magnetic shield topology analysis for the design of a magnetic shield for a real practical application: an ultra-sensitive particle detector operating at very low temperature.
