The mobility of ions trapped on vortex lines in pure4He and3He-4He solutions

Ostermeier, R.M.; Glaberson, W. I.

doi:10.1007/bf00655835

Cited by 55 publications

(13 citation statements)

References 35 publications

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“…1(b), frames (0, (2)]. In the single-phase superfluid region with a low concentration of 3 Vortices in rotating 4 He have been observed by ion imaging [6]. One may hope to see the dimple and the ma-crocore on the 3 He-4 He interface optically [7].…”

Section: Downfall Of the Vortex Dimple In Superfluitiesmentioning

confidence: 99%

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Downfall of the vortex dimple in superfluids

Sonin

Manninen

1993

Phys. Rev. Lett.

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We have studied analytically and numerically the shape of the boundary that separates a superfluid from a gas or another liquid in the presence of a vortex normal to the boundary. Our analysis reveals an instability at which a crater appears in the center of the dimple around the vortex in the superfluid, developing abruptly into a cylindrical macrocore filled by the other liquid. At the interface between two superfluids, there is repulsion between the ends of vortices on different sides of the boundary.PACS numbers: 67.60. Fp, 67.40.Vs, The free boundary of a liquid has usually a rather simple shape: a sphere for a droplet, a plane for the free liquid surface, and a paraboloid for a liquid in rotation. In contrast, the edges of crystals have a variety of shapes, with phase changes like faceting between them. In this Letter we present the first example of a transition in a fluid boundary. At some critical values of the external parameters, the interface that separates a superfluid with a vertical vortex line from a gas or another liquid (normal or superfluid) changes its shape drastically near the vortex: a bottomless crater with an almost vertical wall is formed in the shallow dimple. This downfall has to do with nucleation of a macroscopic vortex core that was discussed in early theoretical studies of the 3 He-4 He mixture without taking into account surface tension and the interface [1],The conditions for the downfall of the dimples exist in the 3 He-4 He mixture, which below 0.87 K separates onto the 3 He-rich and the 4 He-rich phases along the firstorder phase transition line in the concentration-temperature plane [2] [coexistence curve; see phase diagram in Fig. 1(a)]. When the mixture is rotated, an array of vortices appears in the 4 He-rich superfluid phase. It is well known that the cores of vortices attract impurities, neutral or charged [3], According to a number of theoretical and experimental studies [1,4,5], condensation of 3 He into the vortices starts already in very dilute solutions of 3 He in superfluid 4 He, far from the bulk coexistence curve. This results in the formation of macroscopic vortex cores filled by the 3 He-rich liquid. We shall call them macrocores; the liquid inside can be normal or, below 1 mK, superfluid.If the external parameters are varied in the phase coexistence region, the 3 He-4 He interface is always present in the cell and macrocores appear after the downfall of dimples along the interface [ Fig. 1(b), frames (0,(2)]. In the single-phase superfluid region with a low concentration of 3 He condensation of 3 He starts by the formation of a pool of 3 He-rich liquid around each vortex line on the free surface of the 4 He superfluid. The macrocore appears only later, after the downfall of the 3 He-rich pool [see Fig. Kb), (3)-(5)].Vortices in rotating 4 He have been observed by ion imaging [6]. One may hope to see the dimple and the ma-crocore on the 3 He-4 He interface optically [7]. Another possible way to detect the formation of macrocores is by NMR imaging.Let us consider...

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Section: Downfall Of the Vortex Dimple In Superfluitiesmentioning

confidence: 99%

“…[2,3,9,10]. At r=0, the core radius r c in the 4 Herich phase of the mixture is assumed to be the same as for pure 4 (2) using the parameters for a 3 He-4 He interface at r*0, /*=(). Topmost curve: distortion of the interface by a vortex in 3 He-#.…”

Section: Rcr~"mentioning

confidence: 99%

Downfall of the vortex dimple in superfluids

Sonin

Manninen

1993

Phys. Rev. Lett.

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“…Early speculations suggested that the ion is delocalized in a hollow vortex core, or moves about the core by Brownian motion. We now know, however, that the mobility of the ion along the vortex core rapidly decreases with increasing temperature [4]. Assuming the ion diffuses around the vortex ring in a random walk, the ratio of the time / for the ion to diffuse around the ring to the time r for the ring to travel a distance equal to one circumference is…”

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Motion of charged vortex rings in helium II

Samuels

Donnelly

1991

Phys. Rev. Lett.

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We show that an ion carried through an electric field by a quantized vortex ring in helium II will cause a symmetric change in the radius of the ring, even though the ion is located asymmetrically on the core of the vortex ring. The localized force on the ion will combine with a specific series of vortex waves to give a uniform growth of the ring with a small component of drift velocity perpendicular to the applied electric field. This type of energy transfer may also play an important role in superfluid turbulence. Our calculations should be valid for localized forces on thin-core classical vortices as well.PACS numbers: 67.40.VsOne of the key investigations in the study of helium II was the motion of positive and negative ions at temperatures below 1 K. Rayfield and Reif demonstrated conclusively that both positive and negative ions moving through low-temperature helium nucleate quantized vortex rings and become attached to them 111. They were able to measure the dispersion curve of these ion-vortex complexes, establishing the motion unambiguously as that of vortex rings, they measured the quantum of circulation K^h/m, where h is Planck's constant and m is the mass of the helium atom, and they determined the core radius a of the vortex ring. At first it was not clear where the ion was located: Symmetry appears to demand that it be located in the center of the ring. It later became evident, however, that at the core of the ring there is an energy minimum for an ion [2], and that, in fact, the vortex ring begins its existence by "macroscopic" tunneling from one side of the ion [3]. The ion complex, however, moves through the fluid under the influence of an electric field, and it is not clear how the force on the ion can induce the growth and decay of the vortex ring from an asymmetric location. Early speculations suggested that the ion is delocalized in a hollow vortex core, or moves about the core by Brownian motion. We now know, however, that the mobility of the ion along the vortex core rapidly decreases with increasing temperature [4]. Assuming the ion diffuses around the vortex ring in a random walk, the ratio of the time / for the ion to diffuse around the ring to the time r for the ring to travel a distance equal to one circumference iswhere n is the ion mobility on the vortex line and e the ion charge. This ratio is greater than 1 for r>0.4 K and is 20 by T=0.6 K. Consequently, for temperatures greater than 0.4 K, the ion must be considered to be fixed in place. The great success of the Rayfield-Reif experiment rests on the idea that the vortex rings remain circular when an electric field is applied. The purpose of this Letter is to demonstrate how this paradoxical situation can be explained by modern vortex dynamics [5]. To the best of our knowledge there have been no studies of the effects of localized forces on classical vortex rings. These calculations should be applicable to classical thin core vortices of constant circulation as well as to quantized vortices.Consider a vortex ring in the x-y plane m...

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“…The component of the force along the vortex line should, in principle, result in accelerated sliding of the ion in the direction of the force. However, the instability with respect to emitting Kelvin waves will inevitably result in an effective tangential drag force that will saturate the ion's drift velocity at some ∼10 ms −1 [28,29]. We see that in the first case (binormals to vortex segments aligned with the field) the work eEv q of charge drifting with the segment goes into expanding the length of this smooth segment.…”

Section: Dynamics Of Charged Tanglesmentioning

confidence: 98%

“…There are still plenty of unknowns about the details of the ion-vortex interaction and behavior (see the discussion by Pi et al [26] and references therein), especially with low damping at low temperatures and when the ion and vortex are subject to external force and perturbations. For instance, the experimental mobility of ions along vortex lines was found to greatly exceed a theoretical calculations of the effect of scattering of thermal Kelvin waves by an ion in the vicinity of the vortex core [28,29]. It is also unknown whether the capture of bare ions by vortex lines can be efficient at low temperatures [27].…”

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Charged Tangles of Quantized Vortices in Superfluid 4He

2010

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We show that turbulence in superfluid 4 He at low temperatures can be generated and probed by injected ions trapped on vortex cores. The results of our recent experiments, in which negative ions were injected during short and long periods, in different quantities, and into different applied electric fields, are outlined. Three very different mechanisms of vortex-assisted transport of trapped ions were observed: one is on isolated vortex rings while two others are associated with tangles of vortex lines. It seems there are two different types of vortex tangles that can be characterized by the velocity of ion motion through them: a drifting polarized tangle in a low-dissipation state that mainly advects trapped ions, and a more isotropic tangle in a highly-dissipative state, sustained by a continuous forcing by the ion current in an applied electric field, through which trapped ions move rapidly.

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The mobility of ions trapped on vortex lines in pure4He and3He-4He solutions

Cited by 55 publications

References 35 publications

Downfall of the vortex dimple in superfluids

Downfall of the vortex dimple in superfluids

Motion of charged vortex rings in helium II

Charged Tangles of Quantized Vortices in Superfluid 4He

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