Quantized Vortex Rings Research Articles

Evidence for an Energy Barrier Impeding the Creation of Quantized Vortices in He II

The rate ν at which negative ions create quantized vortex rings in isotopically pure He II has been measured for temperatures 70<T<500mK, pressures 12<P<19 bar and electric fields 104<E<105Vm-1. The result can be taken to imply the existence of an energy barrier impeding the nucleation process of ∼3K.

The breakdown of superfluidity in liquid 4 He III. Nucleation of quantized vortex rings

We have measured the rate v at which negative ions nucleate charged vortex rings in isotopically pure superfluid 4 He for pressures, P , temperatures, T , and electric fields, E , within the ranges: 15 &lt; P &lt;25 bar; 0.3 &lt; T &lt; 0.9 K; 5 x 10 4 &lt; E &lt; 10 6 V m -1 . The measurements were done by a novel electrostatic induction technique specially developed for the purpose, and this is described in some detail. It was found that: at fixed E and P , v increases rapidly with T for T ca. 0.5 K, but approaches a temperature-independent limiting value v s for T &lt; 0.5 K; at fixed P and T , v at first increases rapidly with E but then passes through a maximum at ca. 7 x 10 5 V m -1 and decreases again for larger values of E ;at fixed E and T , v increases rapidly with decreasing P until, below ca. 15 bar, the signal becomes too small to use. In all cases, v was found to be considerably smaller than had been measured for low E by earlier workers using helium of the natural isotopic ratio ( ca. 2 x 10 -7 ). The same signals were also used for measuring ionic drift velocities, v for v &lt; ca . 3 x 1O 4 s -1 . Values of the matrix element for roton pair emission have been deduced from the v ( E ) measurements for several pressures in the range 17 &lt; P &lt; 25 bar. The pressure dependence of the Landau critical velocity was measured and is compared with predictions based on accepted values of the roton parameters. Analysis of the nucleation data showed that, at fixed v and P ,( v — vs ) oc n r ,where n r is the thermal roton density, suggesting that v is the sum of contributions from two independent nucleation mechanisms: a spontaneous mechanism responsible for v s and a roton driven mechanism responsible for the increase in v with T above 0.5 K. The existence of a maximum in v ( E ) appears to be inconsistent with the peeling model of vortex nucleation; but it is entirely to be expected on the basis of the quantum transition model. It is shown that all the nucleation rate measurements reported herein are consistent with the quantum transition model, provided that due account is taken of the possibility that roton absorption may give rise to a critical velocity v r that is smaller than the critical velocity v v characteristic of the spontaneous nucleation mechanism. Values of v v and v r are deduced from the experimental data for several pressures. The fact that exponential decay of the bare ion signal still occurs even when v &gt; v v (or v r ) constitutes the first experimental evidence that the microscopic mechanisms responsible for vortex nucleation are probabilistic in nature.

Trajectories of quantized vortex rings near an orifice

Using the exact Wallraven calculation for the energy of a vortex ring coaxial with a thin orifice, I have calculated the exact low-temperature trajectories with background flow through the orifice and approximate trajectories when the temperature is finite and mutual friction is important. Closed-form approximations are given for the maximum ring expansion, ring lifetime, and range.

Energy cross term for a quantum vortex ring

The energy cross term Ec between an initial fluid flow v0 and the flow from a vortex ring is normally written as v0⋅P, where P is the momentum of the vortex ring. There is some uncertainty about how to calculate P. Ec is computed exactly for flow around a closed circuit (a ring) in an incompressible fluid where circulation is quantized. v0 is allowed to be a function of position. The vortex rings are assumed not to be created impulsively. The result is that Ec is equal to the circulation times the mass of fluid that v0 causes to flow through the vortex ring per second. This reduces to the usual result P=ρκπr2 when v0 is constant in the neighborhood of the vortex ring.

Impurity ions in liquid helium

A technique for introducing a wide variety of positive ions into liquid helium is described and used to investigate positive atomic ions of K, Rb, Cs, Ca, Sr, and Ba. The zero-field mobilities of the impurity ions were measured in He II in the temperature range 1.2 < T < 1.4 K. The dependence of mobility on ion mass alone was found directly for Ca+ ions by investigating two isotopes. Measurements were made of the ion drift velocities in high electric fields, where nucleation of quantized vortex rings occurs. All the data and its analysis are consistent with the assumptions that all the impurity ions are singly charged, that the size of the cluster surrounding the ion is significantly different for the different ions, and that the ion-roton cross section is approximately geometric. A possible alternative model for the structure of the ion complex is discussed and a mechanism is suggested which may account for the observed variations in ionic radii.

Impulse given to a plate by a quantized vortex ring

It is shown that a quantized vortex ring in superfluid ${\mathrm{He}}^{4}$, moving freely towards a flat plate, gives to it an impulse equal to the fluid impulse of the ring, provided only that the radius of the plate is larger than the initial vortex radius but smaller than the distance to the source of the ring. This is in agreement with experiment, in contradiction to two previous theoretical analyses.

High-field negative-ion persistence currents in superfluid helium

The behavior of negative ions in superfluid helium at high electric fields has been investigated. It is concluded that at sufficiently high fields the negative-ion complex is not an electron trapped on a circular, singly quantized vortex ring. The size of the complex is measured and found to be about 35 \ensuremath{\mu}m. The ion complex is observed to break up at very high fields.

Creation of Quantized Vortex Rings by Charge Carriers in Superfluid Helium

A brief review of the current state of understanding of the vortex-ring transition in superfluid helium leads to a reexamination of the early suggestion that the critical velocity for vortex-ring creation is determined by energy and momentum conservation. The energy and impulse of a sphere and a vortex ring moving coaxially through an ideal fluid are evaluated. This aliows an approximate determination of the velocity at which a moving sphere can create a vortex ring with a given size and location. By minimizing this velocity with respect to the size and location of the ring, one finds that the ring first appears girdling the sphere in the plane perpendicular to the direction of motion. The critical velocity when this ring appears is evaluated for sphere radii and masses dcrived from the usual models of the charge carriers in helium. The results are in good qualitative agreement with the experimentally observed critical velocities. (auth)

Transmission of High-Frequency Phonons through a Solid-Liquid-Helium Interface

S>Heat-pulse experiments at 1.3 K show that the conversion of ballistic high-frequency phonons in a solid into second sound in supefluid helium can be used to study the transmission coeffidient of the phonons through the interface. The transmission coeffidients for longitudinal and transverse phonons in silicon are found to be equal for heater temperatures between 10 and 20 K. (auth) We have produced and observed quantized vortex rings emitted from orifices when superfluid helium is forced through channels at critical velocity. The vortices are identified by measuring their velocity and size, and are found to be in the n= 1 quantum state. (auth)

Creation of Quantized Vortex Rings in Superfluid Helium

We have produced and observed quantized vortex rings emitted from orifices when superfluid helium is forced through channels at critical velocity. The vortices are identified by measuring their velocity and size, and are found to be in the $n=1$ quantum state.

Vortex-ring model of Bose condensation

The partition function of the interacting Bose fluid is represented by an integral over function space and is evaluated approximately by an extension of the saddle-point method. In this way a vortex-ring model is derived from first principles. The superfluid phase of the Bose fluid is represented by a uniform field with a small number of quantized vortex rings of small circumference. In the normal phase the field is in a state of stationary homogeneous turbulence on a microscopic scale. The model leads to a combinatorial problem which, when solved approximately, gives a specific-heat exponent α = 1 3 . The analogy with the droplet model of condensation is discussed.

Quantized vortex ring dynamics and the vortex core radius in He II

Using a newly developed time-of-flight technique, we have determined the temperature dependence of the vortex core radius in the range 0.35 K ≤T ≤ 0.60 K by means of precise measurements of vortex ring dynamics. One of us (W.I.G.) has extended this work to a measurement of the pressure dependence of the vortex core radius. Our results are in agreement with the earlier work of Rayfield and Reif atT=0.28 K and zero pressure 1 and with a model of the vortex core proposed by Glaberson, Strayer, and Donnelly. 2,3 The precision of our measurements enabled us to observe differences in the dynamics of oppositely charged vortex rings in the same electric field configurations. We were able to quantitively account for these differences in a simple way by incorporating the frictional drag associated with the ion bound on the vortex core into the equations of motion. Our results suggest that the negative ion shape is not greatly distorted by its presence on the vortex core, nor is the negative ion strongly shielded by the vortex velocity field. Some of our results have been previously reported. 4–6

Stochastic theory of the nucleation of quantized vortices in superfluid helium

The problem of the appearance of quantized vortex lines and rings in superflow and the modification of that flow by the vortices , is examined in the light of a suggestion by lordanskii, namely that thermal fluctuations may play a vital role in the nudeation process. The view is taken that there exists a distribution of quantized vortex rings in liquid helium and that the smallest of these is a roton. The evolution of these rings in a counterflow is examined by means of a Langevin equation. A Fokker-Planck equation is developed, and a number of examples are presented which illustrate the features of such include nucleation of vortices in an unbounded fluid, nucleation in a finite channel, the thermally activated vortex mill, nucleation of vortices by ions and phonon-roton relaxation times.

Size of Quantized Vortex Rings in Liquid Helium II

Size of Quantized Vortex Rings in Liquid Helium II

Measurement of the Probability of Nucleation of a Vortex Ring in Helium II

An experiment is described which determines the probability of nucleation of a quantized vortex ring by an ion as a function of the ion velocity. The "lifetime edge" produced by a series of such measurements is compared with the theoretical predictions of Donnelly and Roberts.

Evolution of a Pulse of Charged Vortex Rings in Superfluid Helium

Experiments with a pulsed beam of charged, quantized vortex rings show that it evolves into a steady-state distribution. This behavior is shown to follow from the Coulomb interaction among the vortices and a negative effective pressure arising from the vortex dispersion law.

Possible existence of pair-condensate in superfluid helium

An analysis of the lower critical velocity of quantized vortex rings found by Cunsolo and Maraviglia is given on the assumption that pair-condensate exists in superfluid helium. The experimental results are found to agree to within experimental error with the theoretical model proposed earlier.

Deflection of Quantized Vortex Rings by Magnetic Fields

A comparison is made of the predictions of three different theories of quantized vortex rings and the experimental data on the deflection of such rings, containing trapped ions, by magnetic fields.Received 31 December 1969DOI:https://doi.org/10.1103/PhysRevA.1.1549©1970 American Physical Society

Nucleation of Quantized Vortex Rings by Ions in Helium II

We suggest that a quantized vortex ring is formed when a roton, localized near a moving ion, is expanded by stochastic processes to become a small ring, attached to the ion. Calculations based on this notion are compared with experiment.

Critical Velocities of Ions in Liquid Helium

A model using quantized vortex rings is presented to describe the observed temperature dependence of the small quantized changes of ion mobility in He II at low electric fields. The trapping and release of ions by vortices at high fields is also discussed.