RINGS AMONG THE ROTONS : MEASUREMENTS OF THE VORTEX NUCLEATION RATE FOR NEGATIVE IONS WHOSE DRIFT VELOCITIES ARE LIMITED BY ROTON EMISSION

1978 ◽  
Vol 39 (C6) ◽  
pp. C6-174-C6-175
Author(s):  
D. R. Allum ◽  
P. V.E. McClintock
Keyword(s):  
Nucleation Rate ◽  
Negative Ions ◽  
Vortex Nucleation

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.

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.

Numerical Simulation of Leakage Current on Conductive Insulator Surface

2019 ◽  
Vol 8 (4) ◽  
pp. 9487-9492
Keyword(s):  
Numerical Simulation ◽  
Electric Field ◽  
Leakage Current ◽  
Method Of Lines ◽  
Electron Attachment ◽  
Negative Ions ◽  
Conduction Current ◽  
Insulator Surface ◽  
Finite Difference Approximations ◽  
Positive Ions

The outdoor insulator is commonly exposed to environmental pollution. The presence of water like raindrops and dew on the contaminant surface can lead to surface degradation due to leakage current. However, the physical process of this phenomenon is not well understood. Hence, in this study we develop a mathematical model of leakage current on the outdoor insulator surface using the Nernst Planck theory which accounts for the charge transport between the electrodes (negative and positive electrode) and charge generation mechanism. Meanwhile the electric field obeys Poisson’s equation. Method of Lines technique is used to solve the model numerically in which it converts the PDE into a system of ODEs by Finite Difference Approximations. The numerical simulation compares reasonably well with the experimental conduction current. The findings from the simulation shows that the conduction current is affected by the electric field distribution and charge concentration. The rise of the conduction current is due to the distribution of positive ion while the dominancy of electron attachment with neutral molecule and recombination with positive ions has caused a significant reduction of electron and increment of negative ions.

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