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MOTION OF IONS ALONG LINEAR VORTICES

A. F. Borghesani

Published May 31, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1093/acprof:oso/9780199213603.003.0012

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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.
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.
The mobility of negative ions trapped on linear vortices in rotating superfluid helium has been measured by a time-of-flight technique in the temperature range $0.8\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}<T<1.6\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. Measurements could not be extended below 0.8\ifmmode^\circ\else\textdegree\fi{}K because, contrary to the present theory, the ion escape rate became too large. No evidence of direct trapping of positive ions by vortex lines was observed down to 0.4\ifmmode^\circ\else\textdegree\fi{}K. The trapped-ion mobility is interpreted in terms of scattering of the ion by thermal distributions of quantized vortex waves and rotons localized about the vortex axis.
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.
We give a general review of recent developments in the theory of vortices in superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superfluid. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and masses of quantized vortices. We think that one can get unambiguous answers by considering a broken symmetry state that consists of one vortex in an infinite ideal system. We argue for a Magnus force that is proportional to the superfluid density, and we find that the effective mass density of a vortex in a neutral superfluid is divergent at low frequencies. We have generalized some of the results for a neutral superfluid to a charged system.
The lifetimes of both positive and negative ions trapped on quantized vortex lines in rotating 3He^{3}\mathrm{He}3He-4He^{4}\mathrm{He}4He mixtures have been measured at temperatures down to 0.1 K. Evidence is found that the 3He^{3}\mathrm{He}3He condenses at the vortex core, and possibly at the surface of the electron bubble.
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.