Velocity Selection for Propagating Fronts in Superconductors

TL;DR

This paper investigates the propagation speed of planar fronts in superconductors after a quench, revealing how magnetic flux influences the speed and providing analytical and numerical methods for its determination.

Contribution

It introduces a comprehensive analysis of front propagation speeds in superconductors, combining numerical solutions with analytical approaches including asymptotic expansions and exact solutions.

Findings

Fronts propagate at a unique speed controlled by trapped magnetic flux.

Linear marginal stability hypothesis applies for small flux.

Matched asymptotic expansions are effective for large flux.

Abstract

Using the time-dependent Ginzburg-Landau equations we study the propagation of planar fronts in superconductors, which would appear after a quench to zero applied magnetic field. Our numerical solutions show that the fronts propagate at a unique speed which is controlled by the amount of magnetic flux trapped in the front. For small flux the speed can be determined from the linear marginal stability hypothesis, while for large flux the speed may be calculated using matched asymptotic expansions. At a special point the order parameter and vector potential are dual, leading to an exact solution which is used as the starting point for a perturbative analysis.