First Order Vortex Dynamics

TL;DR

This paper introduces a non-dissipative, first-order vortex dynamics model for thin superconductors, simplifying the complex field equations to focus on vortex motion and interactions.

Contribution

It presents a novel first-order differential equation reduction for vortex dynamics derived from a Galilean invariant Ginzburg--Landau model.

Findings

Two vortices exhibit circular orbits at constant speed and separation.

The model simplifies vortex interactions to first-order equations.

It provides insights into vortex behavior in idealized superconducting systems.

Abstract

A non-dissipative model for vortex motion in thin superconductors is considered. The Lagrangian is a Galilean invariant version of the Ginzburg--Landau model for time-dependent fields, with kinetic terms linear in the first time derivatives of the fields. It is shown how, for certain values of the coupling constants, the field dynamics can be reduced to first order differential equations for the vortex positions. Two vortices circle around one another at constant speed and separation in this model.