Blow-up instability in the vortex sate of type II superconductors

TL;DR

This paper presents a theoretical analysis of flux jump instabilities in type-II superconductors, deriving explicit solutions for temperature and electromagnetic field evolution during flux creep, highlighting blow-up phenomena.

Contribution

It introduces a new explicit blow-up solution modeling flux jump instabilities in the flux creep regime of type-II superconductors.

Findings

Derived explicit blow-up solutions for electromagnetic and thermal fields.

Identified conditions leading to flux jump instabilities.

Showed the evolution of temperature and electric field during flux jumps.

Abstract

A theoretical study of small thermal and electromagnetic perturbations in type-II superconductors is studied in the flux creep regime with a power-law voltage-current characteristics. The space-time evolution of temperature and electric field was calculated using the heat diffusion equation, coupled with Maxwell's equations and material law, assuming that heat diffusion is small that the magnetic diffusion. An explicit blow-up-like solution is obtained, which describes the time and space evolution of the electromagnetic field and temperature due to flux jump instabilities.