Mathematical analysis of a flux-jump model in superconductivity

Summary

The article analyzes a flux-jump model in superconductivity, considering a 1D configuration with three effects: Joule heating, magnetic relaxation, and temperature diffusion. The study examines the influence of different parameters, including heat capacity, pulse magnitude, and duration, on flux jumps and trapped fields.

Highlights

• Flux jumps occur mostly at low temperatures and medium magnetic fields.
• The heat capacity of the sample plays a crucial role in flux jumps.
• A longer pulse duration can prevent the sample from turning normal.
• The trapped field is larger for a duration of 1000 due to dissipated heating.
• Flux jumps are preceded by large increases in temperature.
• The global driving term (1-B)^2T is responsible for flux jumps.
• The Burger's front dynamics of B causes irregular speed and oscillations.

Key Insights

• The interplay between magnetic field and temperature is crucial in understanding flux jumps, with the temperature equation playing a significant role in the process.
• The nonlinearity of the two equations gives rise to interesting effects, such as the global driving term responsible for flux jumps, which is not present in a simple ohmic behavior.
• The dependence of the critical current density on temperature and magnetic field is essential in modeling flux jumps, and the regularized version of the constitutive law used in the study is a key aspect of the model.
• The numerical results show that flux jumps occur mostly at low temperatures and medium magnetic fields, which is consistent with the global driving term.
• The study highlights the importance of considering the heat capacity of the sample, as it affects the temperature evolution and, subsequently, the flux jumps.
• The use of a longer pulse duration can prevent the sample from turning normal, leading to a larger trapped field, which is a desirable outcome in applications.
• The Burger's front dynamics of B causes irregular speed and oscillations, leading to complex behavior in the magnetic field and temperature profiles.

Mindmap

Citation

Caputo, J.-G., & Rouxelin, N. (2024). Mathematical analysis of a flux-jump model in superconductivity (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.14691