The breakdown of superfluidity in liquid 4 He. IV. Influence of 3 He isotopic impurities on the nucleation of quantized vortex rings

1985 ◽  
Vol 313 (1527) ◽  
pp. 537-606 ◽  
Keyword(s):  
Electric Fields ◽  
Nucleation Rate ◽  
Negative Ions ◽  
Vortex Rings ◽  
Isotopic Ratios ◽  
A Value ◽  
Upward Curvature ◽  
Few Data ◽  
He Atom ◽  
Average Occupancy

We have investigated the rate v at which negative ions nucleate charged vortex rings in a series of extremely dilute superfluid 3 He/ 4 He solutions. Measurements of v were made at a pressure P = 23 bar (23 x 105 Pa) for temperatures, T , electric fields, E , and 3 He/ 4 He isotopic ratios, x 3 , within the ranges: 0.33 < T <0.61 K, 1.0 x 10 4 < E < 1.5 x 10 6 V m -1 , 2.1 x 10 -8 < x 3 < 1.7 x 10 -7 . A few data were also recorded at other pressures within the range 19 < P < 25 bar. For each concentration, and also for nominally pure 4 He ( x 3 = 1.9 x 10 -10 ), v was measured for the same set of E and T . For all the chosen values of x 3 and P , the form of v ( E, T ) was qualitatively much the same, and considerably more complicated than for pure 4 He. It was found that v became equal to the nucleation rate in pure 4 He for large , but that for smaller values of E at low T . The 3 He-influenced contribution to the overall nucleation rate, A v = v — v 0 , passed through a pronounced maximum at a value of E that increased with increasing T ; but the magnitude of A v itself decreased rapidly with increasing T . Plots of v against x 3 for fixed P, E and T show a marked upward curvature for the lower values of E and T , but become linear within experimental error above ca . 0.5 K. A model is proposed (in two variants) in which the complicated behaviour of v ( E, T ) is accounted for in terms of changes in the average occupancy by 3 He atoms of trapping states on the surface of the ion, it being proposed that the nucleation rate v 1 , due to ions each having one trapped 3 He atom, is very much greater than v 0 for bare ions. The nonlinearities in v ( x 3 ) are interpreted in terms of the simultaneous trapping of two (or more) 3 He atoms on a significant fraction of the ions. It is shown that the model can be fitted closely to the experimental data, thereby yielding numerical values of v 1 )of the 3 He binding energy on the ion, and of a number of other relevant quantities. From the form of v 1 ( E ), it is deduced that the addition of a 3 He atom to a bare ion affects its propensity to create vortex rings in two ways: the critical velocity for the process is reduced by ca . 4 m s -1 , and the rate constant is increased by a factor of ca . 10 3 . The implications of these results for microscopic theories of the vortex nucleation mechanism are discussed.

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

1982 ◽  
Vol 307 (1498) ◽  
pp. 201-260 ◽  
Keyword(s):  
Critical Velocity ◽  
Electric Fields ◽  
Isotopic Ratio ◽  
Negative Ions ◽  
Quantum Transition ◽  
Vortex Rings ◽  
Transition Model ◽  
Spontaneous Nucleation ◽  
The Matrix ◽  
Vortex Nucleation

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 < P <25 bar; 0.3 < T < 0.9 K; 5 x 10 4 < E < 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 < 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 < 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 < P < 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 > v v (or v r ) constitutes the first experimental evidence that the microscopic mechanisms responsible for vortex nucleation are probabilistic in nature.

Paraelektrische Resonanz und dielektrische Dispersion von Wasser in Beryll-Einkristallen / Paraelectric Resonance and Dielectric Dispersion of Water in Beryl Single Crystals

1974 ◽  
Vol 29 (11) ◽  
pp. 1558-1571
Author(s):  
H.-J. Rehm
Keyword(s):  
Electric Fields ◽  
Resonance Effect ◽  
Theoretical Description ◽  
Tunnel Effect ◽  
Zero Field ◽  
Zero Field Splitting ◽  
A Value ◽  
Axis Parallel ◽  
Electric Dipoles ◽  
The One

Paraelectric resonance spectra of beryl crystals are observed in the X-band region between 5 and 20 kV/cm under the condition that the external electric field F[101̅0]. Additional dielectric measurements show, that the paraelectric centres are the monomeric water molecules in the beryl cavities. For water dipoles in beryl only two orientations of the molecular a-axis relative to the crystal C6-axis are possible, and only those with their a-axis parallel to the C6-axis contribute to the paraelectric resonance effect. The electric moment vector µ of these latter molecules may rotate in the (0001)-crystal plane, i. e. around their own a-axis, and has a value of (1.9 ± 0.2) D. A theoretical description of paraelectric resonance is presented for a simplified model: the electric dipoles have 6 equivalent equilibrium positions along the [101̅0]-directions, tunnel effect and external electric fields remove the site degeneracy and we observe a molecular Stark splitting. We calculate a value of (2.0 ± 0.4) GHz for the zero-field splitting in the one-parameter Hamiltonian model.

scholarly journals The Variation of Factor of Enhancement in Nucleation Rate with Electric Field for Water Vapour and Ice

2020 ◽  
Vol 10 (2) ◽  
pp. 221-223
Keyword(s):  
Electric Field ◽  
Water Vapour ◽  
Electric Fields ◽  
Nucleation Rate ◽  
Water Molecules ◽  
Saturation Ratio

the nucleation rate is the parameter to judge the effect of electric field on nucleation of water vapour and ice glaciation. In the presence of electric field the total nucleation is the sum of nucleation due to electric field and nucleation due to diffusion of water molecules. Thus we can say the nucleation rate is enhanced by the factor of RE. This is known as factor of enhancement in nucleation rate. In the present work we will calculate the factor of enhancement in nucleation rate for water vapour and ice on temperature 268 K at different electric fields as a function of super saturation ratio.

Continuum Modeling of Charged Particle Transport: RF Breakdown and Discharges of SF6

1986 ◽  
Vol 68 ◽  
Author(s):  
Brian E. Thompson ◽  
Herbert H. Sawun ◽  
Aaron Owens
Keyword(s):  
Electric Fields ◽  
Electron Attachment ◽  
Negative Ions ◽  
Rate Coefficients ◽  
Rf Discharge ◽  
Continuity Equations ◽  
Positive Ions ◽  
Discharge Model ◽  
Rf Breakdown ◽  
Charged Particle Transport

AbstractContinuity equations for the concentration of electrons, positive ions, and negative ions were constructed and solved to predict rf breakdown voltages and the electrical properties of SF, discharges.These balances for the three types of charged species include terms for convection (electric field-driven fluxes), diffusion, and reactions (ionization, electron attachment, and negative-positive ion recombination).The mobilities, diffusivities, and reaction rate coefficients necessary for the rf discharge model are based on reported measurements and calculations of these parameters in dc electric fields.The electric fields developed in the rf discharge are calculated from Poisson's equation and applied voltage conditions.Predictions based on this model are compared with measured rf breakdown characteristics of SF6.

Turbulent vortex rings

1974 ◽  
Vol 64 (2) ◽  
pp. 227-240 ◽  
Author(s):  
T. Maxworthy
Keyword(s):  
Growth Process ◽  
Slow Growth ◽  
Separated Flow ◽  
Vortex Rings ◽  
Experimental Accuracy ◽  
Turbulent Vortex ◽  
Viscous Forces ◽  
A Value ◽  
Entrainment Coefficient ◽  
Scale Turbulence

We consider the motion of the mass of fluid ejected through a sharp-edged orifice by the motion of a piston. The vorticity formed by viscous forces within the separated flow at the sharp edge rolls up to form a concentrated vortex which, after a development period, consists of a core of very fine scale turbulence surrounded by a co-moving bubble of much larger scale turbulence. This bubble entrains outer fluid, mixes with it, and deposits the majority into a wake together with some small fraction of the total vorticity of the ring. Enough fluid is retained to account for the slow growth of the whole fluid mass. A theory which takes account of both the growth process and the loss of vorticity is proposed. By comparison with experimental measurements we have determined that the entrainment coefficient for turbulent vortex rings has a value equal to 0.011 ± 0.001, while their effective drag coefficient is 0.09 ± 0.01. These results seem to be independent of Reynolds number to within experimental accuracy.

A study of the isotopic abundance of boron from various sources

1968 ◽  
Vol 5 (4) ◽  
pp. 921-927 ◽  
Author(s):  
E. K. Agyei ◽  
C. C. McMullen
Keyword(s):  
Boric Acid ◽  
Atomic Weight ◽  
Igneous Rocks ◽  
Tokyo Bay ◽  
Standard Errors ◽  
Isotopic Ratios ◽  
Isotopic Abundance ◽  
A Value ◽  
The Mean ◽  
The Absolute

The absolute ratio of 11B/10B has been determined for boron from different terrestrial sources with a precision of 0.2% (two standard errors) and a reproducibility of 0.2% (half-range). Values fall in the range 4.108 to 3.987 (i.e. 3% variation) and give a corresponding range in the boron atomic weight of 10.814 to 10.810 (0.04% variation). The absolute ratios are 7% lower than those reported by early workers, but are in accord with the results of recent investigations. Igneous rocks and boric acid are found to have high isotopic ratios, whereas Tokyo Bay water possesses a value for 11B/10B near the mean.

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