Exploration of stable and unstable vortex patterns in a superconductor under a magnetic disc

TL;DR

This paper investigates the stability of vortex patterns in a 2D superconductor influenced by a magnetic disc, using numerical methods to identify how solutions gain or lose stability as magnetic field strength varies.

Contribution

It introduces a numerical approach combining Newton-Krylov solver and continuation methods to analyze vortex stability in superconductor models under magnetic fields.

Findings

Identified stability loss and regain scenarios for vortex states.

Mapped vortex pattern stability as a function of magnetic field strength.

Abstract

The stable and unstable solutions of a square 2D extreme type-II superconductor are studied in the field of a magnetic disc. We use a preconditioned Newton-Krylov solver to find the solutions and use numerical continuation to track the solutions as the field strength varies. For a disc with a small radius, we have identified generic scenarios through which the state loses and regains its stability.