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

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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: mark.ainslie@eng.cam.ac.uk

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)