Dynamics of the magnetic flux penetration into type II superconductors

TL;DR

This paper derives an exact analytical solution for the nonlinear magnetic flux diffusion in type II superconductors, revealing how magnetic flux penetrates over space and time under a power-law increasing external field.

Contribution

It provides a novel exact solution for magnetic flux penetration dynamics considering nonlinear flux flow resistivity in superconductors.

Findings

Analytical expression for magnetic flux distribution over space and time.

Describes flux penetration behavior under power-law increasing magnetic field.

Enhances understanding of flux dynamics in superconductor applications.

Abstract

The magnetic flux penetration into the half-space superconductor sample is studied in the flux flow regime in parallel geometry assuming that an external magnetic field increasing with time in accordance with the power law. Assuming that the flux flow resistivity as a power-law function of the magnetic field induction we found an exact analytical solution for the nonlinear local magnetic flux diffusion equation. The obtained solution describes space-time distribution of the magnetic induction in the sample.