Comparison Between Modeling and Experimental Results of Magnetic Flux Trapped in YBCO Bulks

Abstract

An electromagnetic simulation of YBCO bulks was performed and the resulting trapped magnetic flux density was compared to Field Cooling experimental measurements for an applied magnetic flux density up to 3 T. The simulation relied on an axisymmetric problem implementing an A-formulation of the Maxwell's equations solved by means of the Finite Element Method so that the time evolution of the magnetic flux density was computed over the cross section of the bulk. To derive its electrical conductivity, a classic power law was adopted that includes the dependence of the critical current density upon temperature and external magnetic field modelled on the basis of a Modified Kim-Anderson relation. It was found that this model tends asymptotically towards the critical state for which the n-value becomes a free parameter that should be then estimated experimentally. The experimental results could be fairly reproduced at different operating temperatures with the best trapping at temperatures below 77 K benefiting from an increasing critical current density. Index Terms-Modified Kim-Anderson relation, trapped magnetic flux, YBCO bulk modelling.

Characterization of High-Temperature Superconductor Bulks for Electrical Machine Application

“…A suitable magnetization method exists called pulse field magnetization (PFM). In this method, the HTS YBaCuO bulk is cooled down and then submitted to magnetic field pulses [ 28 , 29 , 30 ]. It traps less of the magnetic field than the ZFC method but it requires only a small copper magnetization coil.…”

Distribution of Current Density, Temperature, and Mechanical Deformation in YBCO Bulks Under Field-Cooling Magnetization

“…A brief summary of the electromagnetic and thermal models and a more detailed description of the mechanical one are provided in the next paragraphs. a) Electromagnetic model: A detailed description of the electromagnetic model is given in [4]. This model expresses the Maxwell equations using the magnetic vector potential A.…”

“…is the temperature and magnetic flux density dependent strain-free critical current density given in the shape of a modified Kim-Anderson relation [4], [12], and J c,m ( eq ) is the strain-dependent critical current density. Their respective expressions as well as the definition of the n-value are given below,…”

“…The different values appearing in the above equations were obtained by using available plot of normalized critical current versus background magnetic field and by fitting the experimental data of the field-cooling magnetization over time at various operating temperatures, as described in [4]; and…”

“…The proposed model describes the coupled electromagnetic, thermal and mechanical behaviour of a homogeneous YBCO pellet. The electromagnetic model which relies on the Aformulation of the Maxwell equations was presented in [4]. This model was modified to include both the dependence of the critical current density upon mechanical strain and temperature, in addition to the original dependence upon magnetic flux density, and the dependence of the n-value upon temperature and magnetic flux density as well.…”