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Modelling of Saturation Currents and Dynamic Resistance in High-Temperature-Superconductors

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posted on 14.06.2022, 01:40 by Justin BrooksJustin Brooks

High temperature coated conductors are useful for their large Tc, Jc and Bc2values. They are manufactured in long lengths and are available from numerouscommercial distributors around the world. As a result, they have found use inmany applications that can utilise the large magnetic fields that these materialscan produce.

In any complex circuit that incorporates superconducting components, it can bedesirable to include superconducting analogues of semiconducting power electronics,such as switches, and transistors. The ideal switch in a superconducting circuit haszero resistance when the switch is closed and infinite resistance when open. Onlysuperconductors can provide the zero resistance closed state. Thus it is the onset ofresistive phenomenon, the conditions under which a non zero resistance is inducedin a superconducting tape, stack, or loop, that are the subject of this thesis. The two phenomena that are examined are: geometric current saturation, and dynamicresistance. Both are investigated using existing finite element models employing the H-formulation and a power-law resistivity in the software COMSOL, accompaniedby experimental verification.

Flux flow resistance arises when the transport current in a high temperature superconductor is larger than the critical current I c. This current produces asufficiently large Lorentz force such that there is continuous vortex motion through the superconductor. This results in an effective DC resistance. Today, the criticalcurrent is universally identified using an arbitrary voltage measurement criterion. In this thesis, it is demonstrated that current filling and eventual saturation acrossthe width of a HTS tape can be observed using magnetic field imaging near to the tape surface and correlated with changes in the measured I-V characteristics. Asimple model is presented to explain this behaviour which requires only that the material have a non-linear resistivity. The current filling behaviour is modelledusing numerical methods and validated against experimental data obtained from commercial wires. Finally, it is shown that the saturation determined using eithermagnetic field imaging or voltage measurements is sensitive to the rate of change of current.

Dynamic resistance is a resistive phenomenon that occurs when an AC magnetic field interacts with a high temperature superconductor that is simultaneously carrying aDC transport current lower than the critical current. Dynamic resistance occurs when the AC field amplitude is larger than some sample dependent threshold.

Comparison between numerical models and measured data demonstrate that field dependent Jc values are required to reproduce the experimentally observed transientvoltage waveforms. The finite element models were then used to analyse the transient current distributions inside of vertical stacks of parallel connected tapesand predict values for the threshold magnetic field. The threshold fields exhibit a transition from ’tape-like’ to ’slab-like’ behaviour as the stack aspect ratio varies.

Finally, the effective resistance of a current carrying hollow superconducting strip exposed to an alternating perpendicular magnetic field is presented and analysedvia finite element modelling.


Copyright Date


Date of Award



Te Herenga Waka—Victoria University of Wellington

Rights License

CC BY 4.0

Degree Discipline


Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level


Degree Name

Doctor of Philosophy

Victoria University of Wellington Unit

Robinson Research Institute

ANZSRC Socio-Economic Outcome code

170102 Industrial energy efficiency

ANZSRC Type Of Activity code

3 Applied research

Victoria University of Wellington Item Type

Awarded Doctoral Thesis



Victoria University of Wellington School

School of Chemical and Physical Sciences


Badcock, Rodney; Bumby, Chris