Fracasso Michela

Gozzelino Laura

Napolitano Andrea

Torsello Daniele

English

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

21 December 2022POLITECNICO DI TORINORepository ISTITUZIONALESuperconductive and hybrid shielding design: a 3D-modeling study / Fracasso, Michela; Napolitano, Andrea; Torsello,Daniele; Gozzelino, Laura. - ELETTRONICO. - (2021). ((Intervento presentato al convegno 7th International Workshopon Numerical Modelling of High Temperature Superconductors (HTS 2020).OriginalSuperconductive and hybrid shielding design: a 3D-modeling studyPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2973814 since: 2022-12-13T14:52:22ZKevin Berger (Université de Lorraine - GREEN)HAL Id: hal-03296077https://hal.archives-ouvertes.fr/hal-03296077Submitted on 22 Jul 2021HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Superconductive and hybrid shielding design: a3D-modeling studyMichela Fracasso, Andrea Napolitano, Daniele Torsello, Laura GozzelinoTo cite this version:Michela Fracasso, Andrea Napolitano, Daniele Torsello, Laura Gozzelino. Superconductive and hybridshielding design: a 3D-modeling study. 7th International Workshop on Numerical Modelling of HighTemperature Superconductors (HTS 2020), Kévin Berger (Université de Lorraine - GREEN), Jun2021, Nancy (Virtual), France. ￿hal-03296077￿Superconductive and hybrid shielding design: a3D-modeling study1st Michela FracassoPolitecnico di Torino, DISATTorino, Italymichela.fracasso@polito.it2nd Andrea NapolitanoPolitecnico di Torino, DISATTorino, Italyandrea.napolitano@polito.it3rd Daniele TorselloPolitecnico di Torino, DISATTorino, Italydaniele.torsello@polito.it4th Laura GozzelinoPolitecnico di Torino, DISATTorino, Italylaura.gozzelino@polito.itAbstract—Superconducting materials are promising forfabrication of high-performance magnetic shields. For thispurpose, a computational approach is crucial to guidethe shielding devices’ design. In this work, we exploita 3D modeling procedure based on a vector potentialformulation to calculate the shielding properties of cup-shaped superconductors (SC) with and without the su-perimposition of a ferromagnetic (FM) shield. Relying onthe past validation of the model, the efficiency of differentshielding solutions was investigated in both axial-field (AF)and transverse-field (TF) configurations.Keywords—magnetic shielding, 3D numerical modelling, bulksuperconductorI. INTRODUCTIONMagnetic shielding is essential for several applications.Its goal is twofold, aiming at the reduction of stray fieldand electromagnetic noise, and at the achievement of lowmagnetic field background. Superconductors are key materialsfor shielding quasi-static magnetic fields [1] - [3]. Recentlytested solutions included active [4] and passive layouts [1],[5], [6] . Focusing on the latter, a successful approach toimprove shielding ability have combined growth techniqueable to manufacture properly shaped products with high andhomogeneous critical current density, and suitable simulationtools, guiding the whole optimization process [7], [8].Furthermore, improvements in superconductors (SC) shield-ing performance have been proved by superimposing a sheet offerromagnetic (FM) material [9] - [11]. In order to investigatethe non-trivial action of adding a FM sheet around the SC [12]and to optimize the shield design under realistic working con-ditions [13], i.e. for different orientations of applied magneticfield, a 3D modelling is needed.In this work, we applied the numerical procedure based onthe 3D magnetic vector-potential (A) formulation described in[14] to predict the shielding properties of a cup-shaped MgB2bulks with small height/outer radius aspect ratio, studying theeffect of the superimposition of different iron shields in bothaxial-field (AF) and transverse-field (TF) configurations.II. MODELLINGTo model superconductor shielding properties, a numericalprocedure based on the magnetic vector potential formalism[14] was applied by a finite element calculation using COM-SOL Multiphysics® [15]. As presented in [16], ensuring thecollinearity between the current density and the local electricfield and considering an isotropic Jc, the following equationcan be introduced to relate the current density to the electricfield, and, therefore to the time derivative of A.J =Jc|E|(|Ex|tanh(ExE0)i+ |Ey|tanh(EyE0)j++ |Ez|tanh(EzE0)k) (1)where E0 is the conventional criterion taken usually as10−4V m−1 [14].Based on a previous validation of this model to reproduceshielding experiment outputs [17], a Jc dependence on theinduction field need also to be taken into account. A pre-vious experiment [18] evidenced that the experimental Jccurves (obtained from magnetic induction cycles measuredat different temperatures) were successfully fitted by theexponential relation Jc(B) = Jc,0exp[−(B/B0)γ ], whereJc,0 = 5.02 × 108A/m2, B0 = 0.98T and γ = 3.78 werethe constant parameters at T = 30K. The same parameterswere used to model the superconducting shield in all thecomputations reported in the following.The magnetic properties of the FM material were definedby the interpolation of the magnetic induction versus appliedfield curve measured experimentally on a small piece of thesoft iron already used to fabricate magnetic shield [11].The source term for the applied magnetic field, Happl, wasconsidered through the boundary conditions: at a large distancefrom the shield(s), B was set to be equal to µ0Happl. Theapplied field was always assumed increasing monotonically.III. NUMERICAL RESULTSThe model validation presented in [17] allows us to imple-ment the computational procedure in order to explore newhybrid (SC+FM) configurations. Based on previous studyoutcomes [12], [19], the performances of three different cup-shaped arrangements (Fig.1) were investigated in both AF andTF configurations. The data are then compared with thoseobtained computing the shielding properties of the SC cuponly, whose dimensions are the same as for the MgB2 cupstudied in [18].Fig. 1. Design of cup-shaped hybrid (SC+FM) configurations. SC lateralthickness: 3.15 mm, base thickness: 4.20 mm; FM edge thickness: 2.50 mm,base thickness: 2.50 mm; ∆h=3.50 mm.For each configuration, the induction field curves alongz-axis and y-axis (shown in the insets of Fig.2 and Fig.3,respectively) were computed and the shielding efficiency wasestimated using the shielding factor, calculated as the ratiobetween the applied magnetic field and corresponding compo-nent of the local magnetic induction (SF = µ0Happ/Bz(y)).Fig.2 and Fig.3 show the SF behaviors obtained at 5 pointsalong the cup axis in both in AF and TF mode. As one cansee, the ferromagnetic sheet addition actually improves theshielding performances.In particular, for AF configuration and with only SC so-lution, SF > 102 and SF > 104 can be reached up toµ0Happ ≈1.0 T in the inner half of the shield and near theclosed extremity, respectively (symbols in Fig.2). Adding FMsheet enlarges the high-shielding region up to a field of ≈ 1.2T, even though at lower fields higher values of SF can not begained (Fig.2).Fig. 2. Comparison between the SFs of configuration1, 2 and 3 in AFmode considering for the superconductors the same Jc(B) dependence asthat measured in [18] at T = 30 K. Assuming (x,y,z) = (0,0,0) the coordinateof the shield center, the plotted curves were calculated at z1 = 1 mm, z2 =5 mm, z3 = 9.2 mm, z4 = 13.7 mm and z5 = 18.3 mm.On the other hand, greater enhancements are achieved in TFconfiguration. The improvements due to the FM addition aretwofold. Firstly, likewise in AF geometry, it allows extendingthe zone where higher SF values are achieved up to above 1.0T. Secondly, for low values of applied magnetic field, near theclosest extremity of the shield, the screening performancesimprove from a SF ≈ 50 with only SC (symbols Fig.3) toa SF ≈ 120 with configuration2 and to a SF ≈ 140 withconfiguration3 (Fig.3).Fig. 3. Comparison between the SFs of configuration1, 2 and 3 in TFmode considering for the superconductors the same Jc(B) dependence asthat measured in [18] at T = 30 K. Assuming (x,y,z) = (0,0,0) the coordinateof the shield center, the plotted curves were calculated at y1 = 1 mm, y2 =4.6 mm, y3 = 9.2 mm, y4 = 13.7 mm and y5 = 18.3 mm.These results show how the hybrid system can greatlyimprove the shielding performances obtained with only super-conductor system and evidence how 3D modelling is crucialfor achieving a complete information. To this end, the chosenmodeling procedure was found to be a valuable tool to drivethe design of future magnetic shields with small aspect ratioof height/lateral size and improved shielding performances forvarious orientations of the applied magnetic field.ACKNOWLEDGMENTWe wish to thank Fedor Gömöry and Mykola Solovyov fortheir help in the 3D modelling approach.REFERENCES[1] L. Wéra et al., IEEE Trans. Appl. Supercond., 27, 6800305, (2017).[2] Ł. Tomków et al., J. Appl. Phys., 117,. 043901, (2015).[3] Y. Terao et al., IEEE Trans. Appl. Supercond., 21, 1584-1587, (2011).[4] K. S. Haran et al., IEEE Trans. Appl. Supercond., 26, 98-105, (2016).[5] Barna D et al., IEEE Trans. Appl. Supercond., 29, 4101310, (2019).[6] J. Durrell et al., Superconductor. Sci. Technol. 31, 103501, (2018).[7] L. Wéra et al., IEEE Trans. Appl. Supercond, 29, 6801109, (2019).[8] L. Gozzelino et al., Supercond. Sci. Technol., 32, 034004, (2019).[9] A. Omura et al., Physica C, 386, 506–511, (2003).[10] F. Gömöry et al., Science, 335, 1466–1468, (2012).[11] L. Gozzelino et al., Supercond. Sci. Technol., 25, 115013, (2012).[12] L. Gozzelino et al., Supercond. Sci. Technol., 29, 034004, (2016).[13] J. F. Fagnard et al., Supercond. Sci. Technol., 32, 074007, (2019).[14] M. Solovyov et al., Supercond. Sci. Technol., 32, 115001, (2019).[15] COMSOL Multiphysics®5.4 software (http://www.comsol.com).[16] F. Gomory et al., Supercond. Sci. Technol., 22, 034017, (2009).[17] L. Gozzelino et al., Digest HTS2020(sciencesconf.org:htsmod2020:316157).[18] L. Gozzelino et al., Supercond. Sci. Technol., 33, 044018, (2020).[19] G. P. Lousberg et al., IEEE Trans. Appl. Supercond., 20, 33-41, (2010).

Superconductive and hybrid shielding design: a 3D-modeling study

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Superconductive and hybrid shielding design: a 3D-modeling study

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