The Vortex-Particle Magnus Effect

TL;DR

This paper investigates how particles affect vortex dynamics in liquid helium using a Magnus force-based model, validated against Gross-Pitaevskii simulations, demonstrating the model's robustness for simple and complex vortex states.

Contribution

It introduces a semi-analytical Magnus force model to accurately predict vortex-particle interactions, validated against numerical GP simulations, for both simple and complex vortex configurations.

Findings

Magnus force model effectively approximates vortex-particle motion.

Semi-analytical model remains robust for complex vortex states.

Model aligns well with Gross-Pitaevskii simulation results.

Abstract

Experimentalists use particles as tracers in liquid helium. The intrusive effects of particles on the dynamics of vortices remain poorly understood. We implement a study of how basic well understood vortex states, such as a propagating pair of oppositely signed vortices, change in the presence of particles by using a simple model based on the Magnus force. We focus on the 2D case, and compare the analytic and semi-analytic model with simulations of the Gross-Pitaevskii (GP) equation with particles modelled by dynamic external potentials. The results confirm that the Magnus force model is an effective way to approximate vortex-particle motion either with closed-form simplified solutions or with a more accurate numerically solvable ordinary differential equations (ODEs). Furthermore, we increase the complexity of the vortex states and show that the suggested semi-analytical model remains robust in capturing the dynamics observed in the GP simulations.