Passive magnetic shielding by machinable MgB₂ bulks: measurements and numerical simulations

Abstract

We report on a combined experimental and modelling approach towards the design and fabrication of efficient bulk shields for low-frequency magnetic fields. To this aim, MgB2 is a promising material when its growing technique allows the fabrication of suitably shaped products and a realistic numerical modelling can be exploited to guide the shield design. Here, we report the shielding properties of an MgB2 tube grown by a novel technique that produces fully machinable bulks, which can match specific shape requirements. Despite a height/radius aspect ratio of only 1.75, shielding factors higher than 175 and 55 were measured at temperature T = 20 K and in axially-applied magnetic fields μ0Happl = 0.1 and 1.0 T, respectively, by means of cryogenic Hall probes placed on the tube’s axis. The magnetic behaviour of the superconductor was then modelled as follows: first we used a two-step procedure to reconstruct the macroscopic critical current density dependence on magnetic field, Jc(B), at different temperatures from the local magnetic induction cycles measured by the Hall probes. Next, using these Jc(B) characteristics, by means of finite-element calculations we reproduced the experimental cycles remarkably well at all the investigated temperatures and positions along the tube’s axis. Finally, this validated model was exploited to study the influence both of the tube’s wall thickness and of a cap addition on the shield performance. In the latter case, assuming the working temperature of 25 K, shielding factors of 105 and 104 are predicted in axial applied fields μ0Happl = 0.1 and 1.0 T, respectively.

Modelling and Performance Analysis of MgB2 and Hybrid Magnetic Shields

“…As we already reported in our previous works [43,54], a J c dependence on the magnetic field also needs to be taken into account. A previous experiment [48] evidenced that the experimental J c curves were successfully fitted by the following exponential relation:…”

“…The infield behavior of the material was taken into account via the dependence of its critical current density J c on the magnetic field, as detailed in the next subsection. To this aim, we considered the critical current density values achieved at T = 30 K from magnetic flux density measurements carried out on the axis of tube-and cup-shaped shields while the applied field was cycling [48,54]. These shields were obtained by carving fully machinable MgB 2 cylinders, fabricated by spark plasma sintering of BN-added MgB 2 powders [48,49].…”

“…To this aim, we considered the critical current density values achieved at T = 30 K from magnetic flux density measurements carried out on the axis of tube-and cup-shaped shields while the applied field was cycling [48,54]. These shields were obtained by carving fully machinable MgB 2 cylinders, fabricated by spark plasma sintering of BN-added MgB 2 powders [48,49]. We chose the working temperature of 30 K because it guarantees a negligible flux-jump occurrence, thus allowing the J c calculation [49], joined with still noteworthy shielding properties (by way of example, the cup shielding performances are still comparable with those found at 20 K on a YBa 2 Cu 3 O 7 cup with similar aspect ratio [8]).…”

“…Then, focusing on the applied field range 0-0.5 T where the shielding effect is more significant, we calculated the magnetic flux density assuming the applied field tilted of 7.5°, 15°, 30°, 45°, and 60°with respect to the shield axis. To model the superconductor, the parameters J c,0 = 3.01 × 10 8 A/m 2 , B 0 = 0.83T and γ = 2.52, experimentally found at T = 30 K for a similar MgB 2 tubular shield [48], were employed in Equation (2). In Figure 2, the data calculated in the tube axis center O are shown.…”

“…The material choice was driven by the MgB 2 specific features, such as the low-cost, the use of non-toxic precursors (e.g., not containing rare earth elements), the low weight density, and the long coherence length. In particular, the last characteristic implies that boundaries among well connected grains do not prevent the flow of high current densities, thus opening to the employment of large polycrystalline manufacts-fabricated by in situ or ex situ sintering processes [45][46][47][48][49] or by infiltration processes [9,50,51]-for large scale applications.…”