Spatial Grading of Critical Current Density and Temperature-Dependent Magnetic Hysteresis in a Model Superconducting Slab

Nazeha Nassar

Abstract


This study uses computer simulation to look at how putting current in different parts of a type‑II superconducting slab changes how magnetic flux enters the slab how the slab becomes magnetised and how much energy is lost due to hysteresis. The researchers used a isothermal Bean critical‑state algorithm. They compared three kinds of profiles: one that is the same everywhere one that is stronger near the surface and one that is stronger near the centre. All three profiles had the average value. To mimic how temperature weakens the material they multiplied the equations by the factor [1 − (T/Tc)²]². They updated the magnetic field while the external field was increased and then decreased and they calculated the area of the magnetic loops by numerical integration. When the reduced temperature T/Tc was 0.30 and the peak normalised field was 0.50 the surface‑enhanced profile made the loop area 34.1% smaller than the profile giving values of 0.0752 and 0.1141 respectively. At a peak field of 1.50 the situation flipped: the loop areas were 1.7596 for the surface‑enhanced case and 1.3145 for the core‑enhanced case. This flip happened close to the field at which the model predicts penetration of the slab. The numerical results matched the result for a uniform slab and the calculations converged as the grid was refined. The study shows that in a graded slab the benefit of shielding the surface can come at the cost of hysteretic loss depending on the field regime. These results are not tuned to any superconductor and should not be taken as experimental predictions, for a particular material.


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References


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