powerlaws.hpp File Reference

Inline E–J resistivity models for HTS materials and their Jacobians. More...

#include "cl_Material.hpp"

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Namespaces
namespace	belfem
	USER GUIDES:

Detailed Description

Inline E–J resistivity models for HTS materials and their Jacobians.

This header provides three resistivity models that an HTS-aware Material may evaluate, together with their analytic derivatives for use in the nonlinear (Newton–Raphson) solver:

• Material::rho_powerlaw(): standard E–J power law parallel-combined with the normal-state resistivity;
• Material::rho_piecewise(): three-regime extension that smoothly transitions from the power law into the flux-flow / normal regime through a quadratic Bezier curve in log–log space;
• Material::rho_riva(): the same parallel model as rho_powerlaw(), made total over the full jc/n table range ( Riva 2021 ); selected via ResistivityLaw.

Each model is offered as a family of overloads that differ only in how the critical current density \(J_c\) and exponent \(n\) are obtained (plain constants, function of \((B,\angle)\), function of \((B,\angle,T)\), or user-supplied temperature-only callbacks) and in whether the spatial defect modulation \(d(x,y,z,t)\) is applied to \(J_c\). The math is identical across overloads; only the source of \(J_c\) and \(n\) changes.

References

• J. Rhyner, "Magnetic properties and AC-losses of superconductors with power-law current-voltage characteristics," Physica C 212 (1993) pp. 292–300. — original derivation of the E–J power-law model used throughout the HTS community.
• C. P. Plummer and J. E. Evetts, "Dependence of the shape of the resistive transition on composite inhomogeneity in multifilamentary wires," IEEE Trans. Magn. 23 (2) (1987) pp. 1179–1182. — phenomenology of the n-value characterizing the transition sharpness.
• C. Messe et al., "BELFEM: a finite-element framework for HTS magnet quench analysis," Supercond. Sci. Technol. 36 (2023) 114001. — BELFEM material database (Sec. 2.6) and the convergence strategy that drives the residual below \(10^{-11}\) (Sec. 2.7) for which these derivatives are required.