Unified Scaling Law for flux pinning in practical superconductors: II. Parameter testing, scaling constants, and the Extrapolative Scaling Expression

Ekin, John W.; Richter, David H.; Goodrich, Loren F.; Bordini, B.; Splett, Jolene D.; Cheggour, Najib

doi:10.1088/0953-2048/29/12/123002

Cited by 21 publications

(25 citation statements)

References 66 publications

(139 reference statements)

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“…Interestingly, C does not practically change with pressure until Test #11. To get further insight into this finding, we start recalling the Hybrid2 variant of the Extrapolative Scaling Expression (ESE) 50 , 51 : …”

Section: Discussionmentioning

confidence: 99%

“…We can simplify the ESE Hybrid2 expression by making the following assumptions: The pinning-force shaping parameters p and q are fixed to the predicted values for grain boundary pinning: p = 0.5, q = 2 51 ; Experimentally, the exponent σ found in most Nb 3 Sn wires is σ ≈ 1.0 ± 0.3 7 . Here, we fix σ = 1 52 ; The exponent η is ≈ 2, as found in many practical multifilamentary Nb 3 Sn composites 9 , 50 . As in the ITER J c ( B , T , ε ) parameterization 52 , this parameter is fixed to η = 2; In Eq.…”

Section: Discussionmentioning

confidence: 99%

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On the mechanisms governing the critical current reduction in Nb3Sn Rutherford cables under transverse stress

Marzi

Bordini

Baffari

2021

Sci Rep

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Within the framework of the HiLumi-LHC project, CERN is currently manufacturing 11 T dipole and quadrupole accelerator magnets using state-of-the-art Nb3Sn Rutherford cables. Even higher magnetic fields are considered by the Hadron Future Circular Collider (FCC-hh) design study, which plans to develop 16 T Nb3Sn bending dipoles. In such high-field magnets, the design pre-stress can reach considerable values (150–200 MPa) and, since Nb3Sn is a brittle compound, this can constitute a technological difficult challenge. Due to the significant impact that a transverse load can have on the performances of a Nb3Sn magnet, CERN has launched a campaign of critical current measurements of reacted and impregnated Nb3Sn cables subjected to transverse pressure up to about 210 MPa. In this paper, results obtained on 18-strand 10-mm-wide cable sample based on a 1-mm-diameter powder-in-tube (PIT) wire are presented. The tests were carried out on a 2-m-long sample by using the FReSCa test station, at T = 4.3 K and background magnetic fields up to 9.6 T. For applied pressures below ≈ 130 MPa, only reversible reductions of the critical current, Ic, are observed. At higher pressures, a permanent Ic reduction occurs; such irreversible behaviour is due to the residual stresses generated by the plastic deformations of the copper stabilizer. This type of current reduction, whether reversible or not, is fully governed by the strain-induced variations of the upper critical field, Bc2. At higher pressures, estimated between 180 and 210 MPa, it is indeed plausible to believe that cracking of filaments occurs, with detrimental consequences for the Nb3Sn cable’s electrical performances. The complete set of critical current data here presented, collected at different pressures and as a function of the applied magnetic field, allows for the first time to investigate the evolution of superconducting parameters such as the upper critical field Bc2 in the irreversibility region, where both the effects of Cu matrix plasticization and/or cracking of filaments may occur. The experimental approach and data interpretation have a general value and can be applied to any typology of Rutherford cable.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

On the mechanisms governing the critical current reduction in Nb3Sn Rutherford cables under transverse stress

Marzi

Bordini

Baffari

2021

Sci Rep

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“…There are various theories of flux pinning that describe J c . Theory 4,5 and experiment 6,7 often lead to the same generalised scaling law of the formwhere B c2 is the upper critical field, κ 1 is the Ginzburg-Landau parameter, b = B / B c2 is the reduced field, μ 0 is the vacuum permeability, ϕ 0 is the magnetic flux quantum, A is a material dependent constant, and n , m , p and q are constants dependent on the specific pinning mechanism operating. The flux pinning scaling law is widely observed in many different types of superconducting materials including low temperature superconductors (LTS) and high temperature superconductors (HTS).…”

Section: Introductionmentioning

confidence: 96%

“…In this canonical description the parameter ε peak specifies the optimum strain state, or equivalently the optimum atomic spacings in the material, for peak superconducting critical parameters such as T c , and therefore should not depend on B and T . Given the very good scaling of F p , it has also been assumed since then that all the material responds to an applied strain in a similar manner and hence measurements of J c provided averaged properties 6,7,15 . However even now, although Nb 3 Sn is to be used in the multi-billion dollar ITER fusion tokamak 36 and the LHC high-luminosity upgrade 37 , uniaxial strain dependent single crystal data (for Nb 3 Sn 38 or any A15 material 39 ) remain very limited.…”

Section: Introductionmentioning

confidence: 99%

Weakly-Emergent Strain-Dependent Properties of High Field Superconductors

Branch

Tsui

Osamura

et al. 2019

Sci Rep

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All superconductors in high field magnets operating above 12 T are brittle and subjected to large strains because of the differential thermal contraction between component parts on cool-down and the large Lorentz forces produced in operation. The continuous scientific requirement for higher magnetic fields in superconducting energy-efficient magnets means we must understand and control the high sensitivity of critical current density Jc to strain ε. Here we present very detailed Jc(B, θ, T, ε) measurements on a high temperature superconductor (HTS), a (Rare−Earth)Ba2Cu3O7−δ (REBCO) coated conductor, and a low temperature superconductor (LTS), a Nb3Sn wire, that include the very widely observed inverted parabolic strain dependence for Jc(ε). The canonical explanation for the parabolic strain dependence of Jc in LTS wires attributes it to an angular average of an underlying intrinsic parabolic single crystal response. It assigns optimal superconducting critical parameters to the unstrained state which implies that Jc(ε) should reach its peak value at a single strain (ε = εpeak), independent of field B, and temperature T. However, consistent with a new analysis, the high field measurements reported here provide a clear signature for weakly-emergent behaviour, namely εpeak is markedly B, (field angle θ for the HTS) and T dependent in both materials. The strain dependence of Jc in these materials is termed weakly-emergent because it is not qualitatively similar to the strain dependence of Jc of any of their underlying component parts, but is amenable to calculation. We conclude that Jc(ε) is an emergent property in both REBCO and Nb3Sn conductors and that for the LTS Nb3Sn conductor, the emergent behaviour is not consistent with the long-standing canonical explanation for Jc(ε).

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“…5. At 5 T, the value of BSF/I was calculated as follows: (BSF/I)Outward = (50 mT)/(477 A) = 0.10 mT•A -1 for the solid annular block of filaments data in Fig 5. V. DISCUSSION AND CONCLUSIONS The ITER barrel geometry is an accepted standard and selffield correction terms have been widely applied to data in the literature [20]- [24]. Our high field measurements of the difference in IC for the two Lorentz force polarities can be compared to those predicted by Eqn.…”

Section: Fea For a Annular Block Of Superconductormentioning

confidence: 96%

Self-Field Effects on JC(B,T) Measurements of Nb–Ti Strands in High Magnetic Fields

Ridgeon

Raine

Lakrimi

et al. 2018

IEEE Trans. Appl. Supercond.

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We have investigated the applied magnetic field, temperature, and self-field dependence of the critical current density of a Nb-Ti strand produced for ITER poloidal field conductor. Measurements were made on a standard ITER barrel in magnetic fields from 4.0 to 8.0 T and temperatures from 3.5 to 6.0 K. We investigated the effect of self-field by changing the direction of the transport current, resulting in an inward or outward Lorentz force acting on the strand. At 4.2 K and 5 T, the difference in the measured JC between the two Lorentz force polarities was about 1%. From this low value, we conclude that self-field effects in the Nb-Ti strand are about 40% of those expected using standard self-field calculations for fully transposed multifilamentary strands, consistent with theoretical considerations for annular filament transposition.Index Terms-Critical current, Finite element methods, Nb-Ti.

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Unified Scaling Law for flux pinning in practical superconductors: II. Parameter testing, scaling constants, and the Extrapolative Scaling Expression

Cited by 21 publications

References 66 publications

On the mechanisms governing the critical current reduction in Nb3Sn Rutherford cables under transverse stress

On the mechanisms governing the critical current reduction in Nb3Sn Rutherford cables under transverse stress

Weakly-Emergent Strain-Dependent Properties of High Field Superconductors

Self-Field Effects on JC(B,T) Measurements of Nb–Ti Strands in High Magnetic Fields

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