Bending-wave Instability of a Vortex Ring in a Trapped Bose-Einstein Condensate

TL;DR

This paper analyzes the stability and dynamics of vortex rings in Bose-Einstein condensates, revealing their precession behavior and identifying conditions for stability against bending wave instabilities.

Contribution

It provides an analytical and numerical study of vortex ring stability, deriving stability boundaries and excitation spectra in the Thomas-Fermi limit.

Findings

Vortex rings precess in condensates as predicted.

Stability boundaries for bending wave instabilities are computed.

The excitation spectrum and stable regions are analytically determined.

Abstract

Based on a velocity formula derived by matched asymptotic expansion, we investigate the dynamics of a circular vortex ring in an axisymmetric Bose-Einstein condensate in the Thomas-Fermi limit. The trajectory for an axisymmetrically placed and oriented vortex ring is entirely determined, revealing that the vortex ring generally precesses in condensate. The linear instability due to bending waves is investigated both numerically and analytically. General stability boundaries for various perturbed wavenumbers are computed. In particular, the excitation spectrum and the absolutely stable region for the static ring are analytically determined.