Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of the Royal Society of London A Mathematical and Physical Sciences

Stochastic theory of the interaction of ions and quantized vortices in helium II

Russell James Donnelly, Paul Harry Roberts

Published Sep 30, 1969• 113 citations
Publisher

Abstract

Abstract The interaction of ions and quantized vortex lines in helium II is treated by imagining that the motion of the superfluid near a vortex line acts on an ion so as to produce a potential well. The ion itself is looked upon as a Brownian particle immersed in a gas of quasi-particles. The capture of ions is pictured as a process of sedimentation into the well. The escape of the ions from the well is treated as a problem of the escape of a Brownian particle over a potential barrier. A solution of the Fokker-Planck equation for a two-dimensional well is given. Comparison of the theory with a variety of experiments is presented.

DOI
10.1098/rspa.1969.0174

Related papers

INTERACTION OF IONS WITH VORTEX LINES

A. F. Borghesani

Abstract If the superfluid is contained in a rotating bucket, it resembles a solid-body rotation by developing an uniform array of quantized vortex lines. These can capture ions and, thus, rotating superfluid He II shows a strong anisotropy to the motion of ions. This chapter is concerned with the interaction of ions with vortex lines. The ion capture experiments and their results are described. Concepts such as capture width are discussed. A theoretical model of Brownian diffusion has been developed to understand the capture of ions by vortex lines. The competition between the attractive hydrodynamic suction and the thermal diffusion leads to an effective capture rate of ions. The effect of the pressure on the capture of an electron bubble is also discussed.

•May 31, 2007•1 citation

MOTION OF IONS ALONG LINEAR VORTICES

A. F. Borghesani

Abstract Ions and electron bubbles are captured by the vortex lines which occur in a rotating superfluid sample. Once captured, however, the charges can move along the quantized vortex lines. On one hand, this degree of freedom allows the researcher to use ions to detect the appearance of single, quantized vortex lines. On the other hand, the study of the ion motion along the lines gives important pieces of information on the structure and dynamics of vortices. In fact, the ion motion along the lines is limited by scattering on 3He impurities captured by the vorticity field and by vortex waves, i.e., columnar oscillation of the vortex lines. Experiments and theory of vortex wave-, roton, and 3He impurity scattering on vortex lines are described.

•May 31, 2007•0 citations

Collision of a tracer particle and a quantized vortex in superfluid helium: Self-consistent calculations

Demosthenes Kivotides, Carlo F. Barenghi, Yu. A. Sergeev

Recent experiments have shown that micron-size particles can be trapped in quantized vortices in superfluid helium. We present results of a dynamically self-consistent calculation of the nonlinear interaction of a sphere and a vortex. We find that, depending on the regime, the sphere can be trapped in the vortex or break free from it. We also find that, if trapped, the sphere can travel along the vortex. We analyze the role played by the various forces acting on the sphere during the interaction.

Physical Review B•Jun 7, 2007•32 citations

Inelastic scattering of xenon atoms by quantized vortices in superfluids

Ivan A. Pshenichnyuk, Natalia G. Berloff

We study inelastic interactions of particles with quantized vortices in superfluids by using a semiclassical matter wave theory that is analogous to the Landau two-fluid equations, but allows for the vortex dynamics. The research is motivated by recent experiments on xenon-doped helium nanodroplets that show clustering of the impurities along the vortex cores. We numerically simulate the dynamics of trapping and interactions of xenon atoms by quantized vortices in superfluid helium and the obtained results can be extended to scattering of other impurities by quantized vortices. Different energies and impact parameters of incident particles are considered. We show that inelastic scattering is closely linked to the generation of Kelvin waves along a quantized vortex during the interaction even if there is no capture. The capture criterion of an impurity is formulated in terms of the binding energy.

arXiv:1608.04157•Physical review. B./Physical review. B•Nov 15, 2016•18 citations

Motion of Negative Ions Along Quantized Vortex Lines

William I. Glaberson, D. M. Strayer, Russell James Donnelly

The motion of negative ions trapped in quantized vortex lines in rotating helium II has been measured down to 0.8\ifmmode^\circ\else\textdegree\fi{}K by means of a time-of-flight apparatus. Trapped ions always move more slowly than free ions at the same temperature. The contribution of the extra retardation due to the vortex line appears to vary as $\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\Delta}}{\mathrm{kT}})$, where $\frac{\ensuremath{\Delta}}{k}=1.87\ifmmode^\circ\else\textdegree\fi{}$K between 0.8 and 1.5\ifmmode^\circ\else\textdegree\fi{}K.

Physical Review Letters•Jun 17, 1968•52 citations

Modelling of vorticity, sound and their interaction in two-dimensional superfluids

Stefan Forstner, Yauhen Sachkou, Matt Woolley +4 more

Abstract Vorticity in two-dimensional superfluids is subject to intense research efforts due to its role in quantum turbulence, dissipation and the BKT phase transition. Interaction of sound and vortices is of broad importance in Bose–Einstein condensates and superfluid helium. However, both the modelling of the vortex flow field and of its interaction with sound are complicated hydrodynamic problems, with analytic solutions only available in special cases. In this work, we develop methods to compute both the vortex and sound flow fields in an arbitrary two-dimensional domain. Further, we analyse the dispersive interaction of vortices with sound modes in a two-dimensional superfluid and develop a model that quantifies this interaction for any vortex distribution on any two-dimensional bounded domain, possibly non-simply connected, exploiting analogies with fluid dynamics of an ideal gas and electrostatics. As an example application we use this technique to propose an experiment that should be able to unambiguously detect single circulation quanta in a helium thin film.

arXiv:1901.05167•New Journal of Physics•Apr 23, 2019•11 citations
Abstract The interaction of ions and quantized vortex lines in helium II is treated by imagining that the motion of the superfluid near a vortex line acts on an ion so as to produce a potential well. The ion itself is looked upon as a Brownian particle immersed in a gas of quasi-particles. The capture of ions is pictured as a process of sedimentation into the well. The escape of the ions from the well is treated as a problem of the escape of a Brownian particle over a potential barrier. A solution of the Fokker-Planck equation for a two-dimensional well is given. Comparison of the theory with a variety of experiments is presented.
Abstract If the superfluid is contained in a rotating bucket, it resembles a solid-body rotation by developing an uniform array of quantized vortex lines. These can capture ions and, thus, rotating superfluid He II shows a strong anisotropy to the motion of ions. This chapter is concerned with the interaction of ions with vortex lines. The ion capture experiments and their results are described. Concepts such as capture width are discussed. A theoretical model of Brownian diffusion has been developed to understand the capture of ions by vortex lines. The competition between the attractive hydrodynamic suction and the thermal diffusion leads to an effective capture rate of ions. The effect of the pressure on the capture of an electron bubble is also discussed.
Abstract Ions and electron bubbles are captured by the vortex lines which occur in a rotating superfluid sample. Once captured, however, the charges can move along the quantized vortex lines. On one hand, this degree of freedom allows the researcher to use ions to detect the appearance of single, quantized vortex lines. On the other hand, the study of the ion motion along the lines gives important pieces of information on the structure and dynamics of vortices. In fact, the ion motion along the lines is limited by scattering on 3He impurities captured by the vorticity field and by vortex waves, i.e., columnar oscillation of the vortex lines. Experiments and theory of vortex wave-, roton, and 3He impurity scattering on vortex lines are described.
Recent experiments have shown that micron-size particles can be trapped in quantized vortices in superfluid helium. We present results of a dynamically self-consistent calculation of the nonlinear interaction of a sphere and a vortex. We find that, depending on the regime, the sphere can be trapped in the vortex or break free from it. We also find that, if trapped, the sphere can travel along the vortex. We analyze the role played by the various forces acting on the sphere during the interaction.
We study inelastic interactions of particles with quantized vortices in superfluids by using a semiclassical matter wave theory that is analogous to the Landau two-fluid equations, but allows for the vortex dynamics. The research is motivated by recent experiments on xenon-doped helium nanodroplets that show clustering of the impurities along the vortex cores. We numerically simulate the dynamics of trapping and interactions of xenon atoms by quantized vortices in superfluid helium and the obtained results can be extended to scattering of other impurities by quantized vortices. Different energies and impact parameters of incident particles are considered. We show that inelastic scattering is closely linked to the generation of Kelvin waves along a quantized vortex during the interaction even if there is no capture. The capture criterion of an impurity is formulated in terms of the binding energy.
The motion of negative ions trapped in quantized vortex lines in rotating helium II has been measured down to 0.8\ifmmode^\circ\else\textdegree\fi{}K by means of a time-of-flight apparatus. Trapped ions always move more slowly than free ions at the same temperature. The contribution of the extra retardation due to the vortex line appears to vary as $\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\Delta}}{\mathrm{kT}})$, where $\frac{\ensuremath{\Delta}}{k}=1.87\ifmmode^\circ\else\textdegree\fi{}$K between 0.8 and 1.5\ifmmode^\circ\else\textdegree\fi{}K.
Abstract Vorticity in two-dimensional superfluids is subject to intense research efforts due to its role in quantum turbulence, dissipation and the BKT phase transition. Interaction of sound and vortices is of broad importance in Bose–Einstein condensates and superfluid helium. However, both the modelling of the vortex flow field and of its interaction with sound are complicated hydrodynamic problems, with analytic solutions only available in special cases. In this work, we develop methods to compute both the vortex and sound flow fields in an arbitrary two-dimensional domain. Further, we analyse the dispersive interaction of vortices with sound modes in a two-dimensional superfluid and develop a model that quantifies this interaction for any vortex distribution on any two-dimensional bounded domain, possibly non-simply connected, exploiting analogies with fluid dynamics of an ideal gas and electrostatics. As an example application we use this technique to propose an experiment that should be able to unambiguously detect single circulation quanta in a helium thin film.