Vortex Motion In Charged Fluids

TL;DR

This paper investigates the properties and dynamics of topologically stable vortices in charged fluids modeled by a scalar field coupled to electromagnetism, revealing their static configurations, interactions, and response to external forces.

Contribution

It demonstrates the existence of finite-energy vortex solutions supported by electrostatic and potential terms, and analytically characterizes their pinning and movement under external influences.

Findings

Vortices exist with finite energy supported by electrostatic and potential terms.

A vortex with non-zero topological charge is spontaneously pinned.

Vortex velocity in an external current is proportional to the current, moving perpendicular to it.

Abstract

A non-relativistic scalar field coupled minimally to electromagnetism supports in the presence of a homogeneous background electric charge density the existence of smooth, finite-energy topologically stable flux vortices. The static properties of such vortices are studied numerically in the context of a two parameter model describing this system as a special case. It is shown that the electrostatic and the mexican hat potential terms of the energy are each enough to ensure the existence of vortex solutions. The interaction potential of two minimal vortices is obtained for various values of the parameters. It is proven analytically that a free isolated vortex with topological charge $N\ne 0$ is spontaneously pinned, while in the presence of an external force it moves at a calculable speed and in a direction $(N/|N|) 90^0$ relative to it. In a homogeneous external current $\tilde {\bf J}$ the vortex velocity is $\bf V=-\tilde J$. Other theories with the same vortex behaviour are briefly discussed.