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Submitted on 1 Jan 1978
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RINGS AMONG THE ROTONS : MEASUREMENTS
OF THE VORTEX NUCLEATION RATE FOR
NEGATIVE IONS WHOSE DRIFT VELOCITIES ARE
LIMITED BY ROTON EMISSION
D. Allum, P. Mcclintock
To cite this version:
JOURNAL. D E PHYSIQUE
Colloque C6, suppliment au no 8, Tome
39, aoiit 1978, page
C6-174
RINGS AMONG THE ROTONS
:
MEASUREMENTS OF THE VORTEX NUCLEATION RATE FOR NEGATIVE IONS WHOSE D R I F T V E L O C I T I E S ARE L I M I T E D BY ROTON EMISSIOND.R. ~llum* and P.V.E. McClintock
Physics Department, University o f Lizncaster, Lamaster, England
Rbsum6.- Nous avons mesurd les fr6quences de nucldation
v
d'un anneau vortex pour des ions n6gatifs se ddplasant dans l'He I1 sous l'influence de champs 6lectriques0,8 < E <<I2 kV cm-I, 1 des temp6ratures 0.4 < T < 0.6 K et 1 une pression de 25 bar.
Pour E > 5 kV cm-l, les r6sultats expdrimentaux sont bien ddcrits par une th6orie due 1 Bowley. Une d6pendance anormale de
v
en tempdrature trouv6e pour de petites valeurs de E est attribu6e 1 l'influence d1impuret6s isotopiques.Abstract.- We have measured vortex ring nucleation rates
v
for negative ions moving in He I1 under the influence of electric fields 0.8 < E < 12 kV cm-l, for temperatures0.4 < T < 0.6 K and a pressure of 25 bar. For E > 5 kV cm-l, the experimental data are
well described by a theory due to Bowley. An anomalous dependence of
v
on T found at lower lower E is attributed to the influence of isotopic impurit6es.The only set of conditions under which an the drift space between G p and Gg by means of explicit calculation of nucleation rates v for suitable potentials applied to G 1 and Gp. The charged vortex rings in liquid helium has been size of the current i reaching- the collector C performed /I/ is for negative ions moving in He I1 depends on : (i) the proportion of the ions which under prevsure P > 20 bar, temperature T < 0.7 K : fail to nucleate rings between G 2 and G 3 ; (ii) the ionic drift velocity
;
is then limited almost the magnitude of the current entering the drift exclusively by roton creation 121, and it becomes space at G2.possible to solve the appropriate Boltzmann equa- tion for the distribution function F(v
tantaneous ionic velocities vi in an electric
20 -
fleld E. Assuming that the velocity dependence of
0
the transition rate was of the form
0 d = l O m m
(1
where Ro is a constant, 8 is the unit step func-
-
e
tion and v is a critical velocity 131, Bowley
111
0
was able to calcutate v/R0 for plausible values of vo. We now report what is believed to be first attempt to test this theory systematically over a wide range of electric fields.
The experimental technique involved mea- suring the exponential decay 141 into vortex rings of pulses of bare ions propagating through He I1 under uniform E. Rings move slowly that the ions which they carry are, in effect, completely lost from the pulse. The electrode structure used is shown diagrammatically in the inset to figure 1
(further details are given in 121. Pulses of ions from the field emission source S are gated into
z
Present address : Physics Department, University of Exeter, Exeter, EnglandFig. 1 : Pulse heights i at the collector as a function of electric field E at 0.5 K, 25 bar, for two lengths d of the drift space. Inset, the electrode structure (diagramtic) : S-field emission ion source, G1 G 2 G 3
-
grids, C-
collec- tor.The latter can be written as i g(E ) where
0 d
i is the current arriving at G 2 , Ed is the field in the drift space, and g(Ed) is a function whcch varies smoothly from zero at Ed = 0 to approxima- tely unity when Ed"E the gate field between G1
g' and G 2 151. Thus
i (Ed) = i g(E ) exp(-VT)
0 d (2)
where T is the transit time in G p Gg. By measuring i (E ) for two different values of the G2 Gg sepa-
c d
ration d, values of
v
may then tedetermined from_where subscripts 1 and 2 refer respectively to the long and short drift spaces. A typical set of such data is shown in figure 1. In using (3) to obtain
v(E) from these measurements, we can obtain iO1/ ion by comparing icl and i for small. Ed where
v
c2
is negligible (in fact, iO1/io2 = 1 for the data of figure I); and we can measure TI and ~2 as des- cribed previously 121. This analysis yields abso- lute values of
v
up to the highest Ed (3000 ~.cm-l) for which data are available for both cellkngths.To deduce v(E) for larger E we can use (2) in con- junction with ic2(Ed)measurements, assuming g(E )
d
= I under these conditions and finding iO2 from the measured v(E) near 300 V cm-l
.
By these means we have measured v(E) for 0.8 < E < 12 kV cm-I.
Results for three temperatures are shown
in figure 2, together with Bowley's theoretical curves / I / for Ro = 3.4 x
lo4
s-I with vv = 58 or 59 ms-l.
We note that, for very large E, the measurements are temperature independent within their scatter and in satisfactory agreement withtheory.
-
E-' (cm kv-')
Fig. 2 : Measurements (points) of the vortex ring nucleation rate v as a function of E-l for three temperatures at 25 bar. Bowley's theory /I/ has been fitted (curves) to the temperature indepen- dent part of the characteristics for two plausi- ble / 3 / values of vv.
The anomalous temperature dependence observed at lower E is probably due to condensation of 3 ~ e isotopic impurities on the surfaces of the ions
We conclude that the high field data are in
reasonable agreement with expectation /I/, but that it is highly desirable to repeat the measurements using isotopically purified 4 ~ e in order to check the validity of the theory over a wider range of
E, particularly since pulse shape analyses at higher temperatures /5/ have cast a measure of doubt on the utility of the approximation (I). Efforts directed towards this end 171 are already
under way.
It is a pleasure to acknowledge numerous illuminating discussions with Dr. R.M. Bowley.
References
/ I / Bowley, R.M., J.Phys. C : Solid State Phys.
2
(1976) L367.121 Allum, D.R., McClintock, P.V.E., Phillips, A. and BOwley, R.M., Philos. Trans. R. Soc. Lond. A 2 (1977) 179.
/ 3 / Schwarz, K.W. and Jang, P.S., Phys. Rev.
A 8
(1973) 3199./ 4 / Zoll, R. and Schwarz, K.W., Phys. Rev. Lett. 31 (1973) 1440.
/5/ Allum. D.R. and McClintock, P.V.E., J. Low Temp. Phys. to be published.
161 Allum. D.R. and McClintock, P.V.E., J. Phys.C: Solid State Phys.
9
(1976) L273./7/ McClintock, P.V.E., Proc. LT15.
