Superconductivity in MgB2 Khalil Ziq Physics Department KFUPM April 12 2003.
Numerical modelling & comparison of MgB2 bulks fabricated by HIP & infiltration growth
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Transcript of Numerical modelling & comparison of MgB2 bulks fabricated by HIP & infiltration growth
Numerical modelling & comparison of
MgB2 bulks fabricated by HIP &
infiltration growth
Bulk Superconductivity Group, Department of Engineering
Dr Mark Ainslie
Royal Academy of Engineering (UK) Research Fellow
Bulk MgB2
• Bulk MgB2 is an alternative to bulk (RE)BCO materials
• Cheaper, lighter
• More homogeneous Jc (pinning sites) distribution
• Relatively easier to fabricate, many processing techniques exist
• Up to 5.4 T trapped at 12 K (hot-pressing ball-milled Mg & B)
• Disadvantages:
• Lower operating temperature (15–20 K)
• More complex cryogenics
• Thermal instability flux jumps
B S G
Bulk MgB2 Modelling
• Numerical modelling of bulk MgB2 is simpler than (RE)BCO
• Simplified assumptions regarding geometry and Jc
distribution can be made
• Can use measured Jc(B,T) characteristics of a single, small specimen
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Numerical Modelling of Bulk Magnetization
• Finite Element Method (FEM)
using commercial software
Comsol Multiphysics
• Governing equations:
• Electromagnetic equations
(Maxwell’s equations,
H formulation)
• Thermal equations
• Jc(B,T)
• E-J power law
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Numerical Modelling of Bulk Magnetization
• Conventional materials non-
linear permeability, linear
resistivity
• Superconductors linear
permeability, non-linear
resistivity
• Non-linearity is extreme:
power law with n > 20
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E-J Power Law
Bulk MgB2 Modelling – Sample Information
• Four samples measured:
• Trapped field (FC) between ~ 5-15 K and 40 K
• Jc(B,T) of single, small specimen
B S GZou, Ainslie, Fujishiro et al. Supercond. Sci. Technol. 28 (2015) 075009
Bulk MgB2 Modelling – Jc(B, T) Data Fitting
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HIP#22 HIP#38
HIP-Ti20% IG1
Zou, Ainslie, Fujishiro et al. Supercond. Sci. Technol. 28 (2015) 075009
Bulk MgB2 Modelling – Jc(B, T) Data Fitting
B S GZou, Ainslie, Fujishiro et al. Supercond. Sci. Technol. 28 (2015) 075009
Bulk MgB2 Modelling – Field Cooling Magnetization
• Simulating FC magnetization process:
• FC with Bapp = Btrap:
1) 0 ≤ t ≤ x1 Apply ramped field to Bapp = Btrap at T = Tex > Tc
2) x1 ≤ t ≤ x2 Slow cooling of bulk to operating temp. T = Top
3) x2 ≤ t ≤ x3 Slowly ramp applied field Bex 0
• In electromagnetic model, we need to define ρ for all temperatures:
• For T > Tc, need to define ρnormal (ρnormal = 3 x 10-8 Ωm)
• For T < Tc, ρsc defined from E-J power law, where E = ρJ:
• To avoid non-convergence of ρ at Tc:
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Bulk MgB2 Modelling – Thermal Properties
• Can choose constant parameters for C, κ for
T = Top
• When temperature change is insignificant
• Case study #1 used constant parameters at
T = 77 K
• Here, T changes from Tex = 100 K (> Tc) to
Top = 5 – 30 K
• Measured experimental data from 0 – 100 K
for each sample input directly into model
(direct interpolation)
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Thermal equation:
Bulk MgB2 Modelling – Comparison of Results
• Simulation reproduces
experimental trapped field
measurements extremely well
• Samples have excellent
homogeneity
• Model is validated as a fast &
accurate tool to predict
trapped field performance
• Any size of bulk MgB2 disc
• Any specific operation
conditions
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Comparison of simulation & experimental
results for trapped field in different bulk
MgB2 samples
Zou, Ainslie, Fujishiro et al. Supercond. Sci. Technol. 28 (2015) 075009
Topical Review – Bulk Superconductor Modelling
Available at Superconductor Science and Technology
http://iopscience.iop.org/0953-2048/28/5/053002/
Topics include:
Calculating trapped fields; practical magnetization techniques;
AC losses & demagnetization; novel & hybrid bulk superconductor structures
Thank you for listening
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Contact email: [email protected]
Website: http://www.eng.cam.ac.uk/~mda36/
Co-authors:
• Jin Zou (University of Cambridge)
• H. Fujishiro, T. Naito (Iwate University)
• A. G. Bhagurkar, N. Hari Babu (Brunel University)
• J-F. Fagnard, P. Vanderbemden (University of
Liege)
• A. Yamamoto (University of Tokyo)