Elliptic flux-line-cutting critical-state model

Abstract

An anisotropic model for describing the critical state of hard superconductors subjected to crossed and rotating magnetic fields is proposed.

Behavior of bulk high-temperature superconductors of finite thickness subjected to crossed magnetic fields: Experiment and model

“…Such a procedure avoids the need to consider two critical current densities J cЌ and J cʈ , as required by flux-cutting theory, 23,24 the two-velocity hydrodynamic approach, 12,14 or more sophisticated models. 26,27 In the present model, the electric field E ជ ʈ J ជ is never parallel to the magnetic induction B ជ . This allows one to describe the magnetic behavior of the material using only one parameter J c -i.e., the conventional depinning current density which is directly accessible via experiment.…”

“…Unlike existing models, which aim to calculate the true critical state in type-II superconductors with cross-flow effects, 12,14,[26][27][28][29][30][31][34][35][36][37] the approach adopted here simply considers an E ϰ J n power law ͑with n = 21 in the present case͒. One of the reasons for the good agreement between the predictions of the model and the experimental results is that the n value in real HTSs is finite and probably very close to 21 for melt-textured YBCO at 77 K, although there is significant discrepancy between n values determined by different experimental techniques.…”

“…12,14 This model, however, is limited to small variations of the tilt angle of the total magnetic field, 25 and, as a result, an elliptic flux-line-cutting critical-state model was developed subsequently. 26,27 In these approaches, the length of the sample is assumed infinite in the direction of both crossed fields, which only arises either for ͑i͒ an infinite slab with crossed magnetic fields parallel to the slab surface or ͑ii͒ an infinite cylinder subjected to both azimuthal and axial fields.…”

Flux cutting in high-Tcsuperconductors

“…Clem was probably the first who clearly formulated the ideas of GCSM through a set [14,17]). In crossing or rotating fields there can be a few spatial zones in the sample where vortices are stable, move under transverse currents, experience cutting (and thus rotation), or both move and cut [13].…”

“…This negates flux pumping and instead introduces measurable voltage oscillations along the wire [11]. Although estimates of the currents resulting in the helical instability in [12] were too small, the flux cutting scenario was widely accepted, further developed, and is still considered in various modern models of the critical state [13][14][15][16][17].…”