Energy of Magnetic Vortices in Rotating Superconductor

TL;DR

This paper analytically examines the energy of magnetic vortices in a rotating superconductor, revealing that rotation does not alter the total vortex energy and clarifying the relation between magnetic field strength and vortex configuration.

Contribution

It provides a systematic analytic analysis of vortex energies in rotating superconductors, showing the cancellation of rotational effects on total energy and clarifying the magnetic field relations.

Findings

Total vortex energy per unit length is unaffected by rotation.

The macroscopic magnetic field H equals the external London field, not the average B.

Rotation modifies magnetic and kinetic energy contributions separately, but not the total energy.

Abstract

We carry out a systematic analytic investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible non-relativistic superconductor in a rigidly rotating background. It is shown that although the magnetic and kinetic contributions to the energy per unit length of such a vortex are separately modified by the background angular velocity, its effect on the total energy per unit length cancels out. For a type II superconductor threaded by a parallel array of such vortices, this result implies that the relevant macroscopic magnetic field strength H will not be equal to the large scale average <B> of the local magnetic induction B (as has previously been suggested) but instead that H will simply be equal to the external London field that characterizes the value of B outside the vortices.