Thermomagnetic stability in isotropic type-II superconductors under multicomponent magnetic fields

Abstract

The goal of this research is the study of the thermomagnetic consequences in isotropic type-II superconductors, subjected to multi-component magnetic fields $\mathbf{H}_a = H_{ay}\hat{y}+H_{az}\hat{z}$, because the instability field $\mathbf{H}_{fi}$ is closely related with a flux jump occurrence. At the critical-state model framework, once the Lorentz $\mathbf{F}_L$ and pinning forces $\mathbf{F}_P$ are at equilibrium, the current density reaches a critical value $j_c$ and a stationary magnetic induction distribution $\mathbf{B}$ is established. The equilibrium of forces is analytically solved considering that the pinning force is mainly affected by temperature increments; the energy dissipation is incorporated throughout the heat equation at the adiabatic regime. The theory is able to obtain the instability field according to the thermal bath and applied field values; moreover, it provides of instability field branches comprising both partial and full penetrates states. With this information is possible to construct a field-temperature map. The results are compared with already published experimental data, finding a qualitatively agreement between them. This theoretical study works with a first order perturbation, then the perturbation presents a periodical behavior along the thickness direction; considering this environment it is constructed the magnetic induction distributions which resemble flexible cantilever structures.