A non-local power-law baseline for transient flux penetration in YBCO films: parameter degeneracy and constitutive limitations
We assess whether a non-local thin-film model with a bounded, constant-exponent power law can reproduce high-speed magneto-optical measurements of transient flux penetration in a $3\times3$~mm$^2$ YBa$_2$Cu$_3$O$_{7-δ}$ film. The model is solved forward in physical units and used as a controlled constitutive baseline. The critical sheet current is constrained by the final penetration geometry, while the criterion field and creep exponent are constrained by the turnover and relaxation times. The calibration reveals an intrinsic degeneracy: the turnover time depends primarily on the product of the criterion field and saturation parameter, equivalently on the saturated sheet resistivity, so these quantities cannot be identified independently. After parameterizing this degeneracy, the model captures a guarded-current turnover near 22~ms, a relaxation constant of 41.2~ms compared with the measured 37.5 and 43.7~ms, and a late maximum approximately 0.92~mm from the film edge. The amplitude remains discrepant: the calculated transient maximum is $1.90J_{c0}$ and the peak-to-225-ms ratio is 2.13, compared with the reported 1.20. This excess persists under changes in the creep exponent, the degenerate parameter direction, the Kim field dependence, and mesh resolution. Matching the measured ratio through the criterion field would require a value about three orders of magnitude below the conventional scale, while spatial exclusion sufficient to match it would remove the edge peak itself. We also decompose the electric field into irrotational and solenoidal parts and quantify the boundary layer where spectral and finite-difference forms of Faraday's law disagree. The results establish a reproducible non-local power-law baseline and identify limitations of the bounded, constant-exponent constitutive family rather than of non-local thin-film electrodynamics.