Comparison between Electromagnetic Models and Magnetic Measurements in the LHC Magnets

Hagen, P.; Auchmann, Bernhard; Todesco, E.

doi:10.1109/tasc.2011.2177054

Cited by 2 publications

(8 citation statements)

References 6 publications

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“…where the Coulomb's gauge condition is added to the initial relation (13). The reason is that (13) consists of 3 equations (one for each vector component), while there are 4 fields to be determined (the 3 components of A and φ). In addition, the Poisson equation for A, ∇ 2 A = −µ 0 J, does not directly imply the continuity equation for J, ∇ · J = 0.…”

Section: J − φ Formulationmentioning

confidence: 99%

“…In the following, we investigate the resulting functional from minimizing the magnetic variable, ∆H or ∆J, and its interpretation. Regarding the J − φ formulation, the system follows the Euler-Lagrange equations of the functional, which correspond to (13) and (22). By using these equations and the relation ∇φ · J = ∇ · (φJ) − φ∇ · J, the minimized functional becomes…”

Section: Thermodynamical Interpretationmentioning

confidence: 99%

“…The dependence from the equation above (actually J c d) fits well to the experimental data from [66] for parallel and perpendicular applied magnetic Figure 11: Magnetic field dependence of J c used in the model for the coil in figure 10. Symbols are measurements at 50 K from Selvanickam et al in [66] and lines are analytical fits from equations (12) and (13).…”

Section: Assumed Magnetic Field Dependence On J C and Coil Critical Cmentioning

confidence: 99%

See 2 more Smart Citations

Electromagnetic modelling of superconductors with a smooth current–voltage relation: variational principle and coils from a few turns to large magnets

Pardo

Šouc

Frolek

2015

Supercond. Sci. Technol.

121

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Many large-scale applications require electromagnetic modelling with extensive numerical computations, such as magnets or 3-dimensional (3D) objects like transposed conductors or motors and generators. Therefore, it is necessary to develop computationally time-efficient but still accurate numerical methods. This article develops a general variational formalism for any E(J) relation and applies it to model coated-conductor coils containing up to thousands of turns, taking magnetization currents fully into account. The variational principle, valid for any 3D situation, restricts the computations to the sample volume, reducing the computation time. However, no additional magnetic materials interacting with the superconductor are taken directly into account. Regarding the coil modelling, we use a power law E(J) relation with magnetic field-dependent critical current density, Jc, and power law exponent, n. We test the numerical model by comparing the results to analytical formulas for thin strips and experiments for stacks of pancake coils, finding a very good agreement. Afterwards, we model a magnet-size coil of 4000 turns (stack of 20 pancake coils of 200 turns each). We found that the AC loss is mainly due to magnetization currents. We also found that for an n exponent of 20, the magnetization currents are greatly suppressed after 1 hour relaxation. In addition, in coated conductor coils magnetization currents have an important impact on the generated magnetic field; which should be taken into account for magnet design. In conclusion, the presented numerical method fulfills the requirements for electromagnetic design of coated conductor windings. * Final version published as E Pardo, JŠouc and L Frolek 2015 Supercond. Sci. Technol. 28 044003, doi:10.1088/0953-2048/28/4/044003. Several minor typos have been corrected in the published version. 1 ReBCO stands for ReBa 2 Cu 3 O 7−x , where Re is a rare earth, typically Y, Gd or Sm. the flux creep exponent and the AC loss. Critial current density and flux-creep exponentIn this article, we use a ReBCO coated conductor tape from SuperPower [49] for all experiments. This tape is 4 mm wide, with a total of 40 µm copper stabilizer layers, a 1 µm thick superconducting layer, and a self-field critical current at 77 K of 128 A.We measured the dependence of the critical current density J c on the magnetic field magnitude |B| ≡ B and its orientation θ (see sketch in figure 3) at 77 K, as detailed in [50]. In order to extract J c from measurements of the tape critical current, I c , we corrected the spurious effects of the self-field, following the method in [50]. The reader can find the I c measurements and extracted J c for the tape used in this article in [30]. For completeness, we include the extracted J c (B, θ) relation, being J c (B, θ, J) = [J c,ab (B, θ, J) m + J c,c (B) m ] 1/m (60) with J c,ab (B, θ, J) = J 0,ab 1 + Bf (θ,J) B 0,ab β ab ,J c,c (B) = J 0,c

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Section: J − φ Formulationmentioning

confidence: 99%

Section: Thermodynamical Interpretationmentioning

confidence: 99%

Section: Assumed Magnetic Field Dependence On J C and Coil Critical Cmentioning

confidence: 99%

See 1 more Smart Citation

Electromagnetic modelling of superconductors with a smooth current–voltage relation: variational principle and coils from a few turns to large magnets

Pardo

Šouc

Frolek

2015

Supercond. Sci. Technol.

121

View full text Add to dashboard Cite

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“…The nonlinear component due to iron saturation has a larger discrepancy between model and measurement: at 7 TeV we expect a reduction of the ratio field/current of 0.78% from the model, whereas the measurements yield only 0.62% [19]. This discrepancy is due to a limited knowledge of the B-H curve of the iron.…”

Section: A Cross-check Between Model and Measurementsmentioning

confidence: 75%

“…The LHC dipoles were constructed with three successive iterations of the coil geometry. Here we recall the results relative to the comparison of a model [18] using the detailed layout of the superconducting strands to the measurements of the so called geometric component of the transfer function (TF) [19]. The geometric TF is defined as the value of the magnetic field divided by the current at 5 kA where nonlinear effects are not present.…”

Section: A Cross-check Between Model and Measurementsmentioning

confidence: 99%

Large Hadron Collider momentum calibration and accuracy

Todesco

Wenninger

2017

Phys. Rev. Accel. Beams

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As a result of the excellent quality of the Large Hadron Collider (LHC) experimental detectors and the accurate calibration of the luminosity at the LHC, uncertainties on the LHC beam energy may contribute significantly to the measurement errors on certain observables unless the relative uncertainty is well below 1%. Direct measurements of the beam energy using the revolution frequency difference of proton and lead beams combined with the magnetic model errors are used to provide the energy uncertainty of the LHC beams. Above injection energy the relative uncertainty on the beam energy is determined to be AE0.1%. The energy values as reconstructed and distributed online to the LHC experiments do not require any correction above injection energy. At injection a correction of þ0.31 GeV=c must be applied to the online energy values.

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Comparison between Electromagnetic Models and Magnetic Measurements in the LHC Magnets

Cited by 2 publications

References 6 publications

Electromagnetic modelling of superconductors with a smooth current–voltage relation: variational principle and coils from a few turns to large magnets

Electromagnetic modelling of superconductors with a smooth current–voltage relation: variational principle and coils from a few turns to large magnets

Large Hadron Collider momentum calibration and accuracy

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