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Submitted on 1 Jan 1978
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DIRECT OBSERVATION OF ORBITAL DISSIPATION
AND SUPERFLOW COLLAPSE IN 3He-A
M. Bagley, P. Main, J. Hook, D. Sandiford, H. Hall
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-13
DIRECT OBSERVATION OF ORBITAL DISSIPATION AND SUPERFLOW COLLAPSE IN 3He~A
M. B a g l e y , P . C . Main, J . R . Hook, D . J . S a n d i f o r d and H . E . H a l l
Schuster Laboratory, University of Manchester, Manchester M13 9PL, England.
Résumé.- Des expériences de pendule de torsion dans lesquelles le temps de relaxation orbitale est comparable à la période d'oscillation montrent une atténuation fortement dépendante de l'amplitude dans 3He-A qui est absente dans 3He-B. A forte amplitude, la densité superfluide apparente tend
vers zéro, suggérant l'effondrement du courant superfluide comme l'ont décrit Bhattacharyya, Ho et Mermin.
Abstract.- Torsion pendulum experiments in which the orbital relaxation time is comparable with the oscillation period show strong amplitude dependent damping in 3He-A that is absent in 3He-B. At
large amplitudes the apparent superfluid density decreases towards zero, suggesting collapse of superflow as described by Bhattacharyya, Ho and Mermin.
In our previous torsion pendulum experiments /I,2/ on superfluid 3He the width d of the flow
Cha-nel was such that the relaxation time of the orbi-tal texture T = (u/p )(2md/K)2 was very much longer
than the period of oscillation. In these circums-tances we observed an essentially static texture controlled by the mean square relative velocity,
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vs
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V
-With the object of observing dynamic textu-res and the concomitant dissipation by orbital vis-cosity, we have reduced d so that the orbital rela-xation time is of the same order as the period of oscillation. The construction of the torsion pendu-lum is essentially as described previously, but the CMN pill is now surrounded by a stack of 25 toroi-dal flow channels, each of which is 49 ym in height and 0.75 mm in radial extent. The channels were formed by casting Stycast 1266 around aluminium foil and etching away the aluminium after machining was completed.
As before, the oscillation amplitude was controlled by a feedback loop, and the drive level was used as a measure of damping. To facilitate the measurement of absolute amplitudes a capacitance bridge (GR 1621) operating at 10 kHz was used to detect the oscillations, and the suitably phase-shifted output at the pendulum frequency (about 60 Hz) was used to trigger the drive voltage. In this self-oscillating mode the oscillation frequency could be read continuously on a frequency counter. Our basic experimental data are thus additional re-sonance width and frequency shift relative to the normal state ; both are of the order of mHz. All the
measurements were carried out at the pressure of the melting curve minimum (29.7 bar) to avoid pressure fluctuations.
Figure 1 shows two recorder traces of drive level as a function of time during the final stages of demagnetisation and the subsequent warmup. The only difference is that in figure 1(a) the liquid remained in supercooled A-phase throughout, whereas in figure 1(b) it entered the B-phase. It is clear that at this amplitude (though not at the lowest amplitudes) there is a substancial excess damping in the A-phase but not the B-phase ; this alone is strongly suggestive of dissipation by orbital vis-cosity. The small hydrodynamic damping in the B-phase is attributable to normal shear viscosity. Another feature worthy of note in figure 1(b) is that when the liquid returns to the A-phase the dis-sipation builds up to its full value only rather slowly and in a somewhat erratic manner.
Both damping and frequency shift are roughly proportional to (1 - T/T ) . We therefore show in figure 2, as a function of velocity amplitude at (1 - T/T ) = 0.1, the values of these quantities, normalised to the low amplitude frequency shift. Two features are noteworthy :
(1) the damping maximum, suggesting that we pass through the condition 0)T ^ 1 as the amplitude in-creases ;
(2) the great reduction in frequency shift at large amplitudes (which was not observed in the B-phase), implying that the whole liquid is tending to follow the motion of the pendulum.
The second observation, taken together with the slow and erratic return of dissipation after
a B + A t r a n s i t i o n , s t r o n g l y s u g g e s t s t h a t we a r e o b s e r v i n g t h e c o l l a p s e d s u p e r f l o w d e s c r i b e d by B h a t t a c h a r y y a , Ho and Mermin / 3 / ; t h e d e l a y e d r e - t u r n o f damping would b e a s s o c i a t e d w i t h t h e d i f f i - c u l t y o f surmounting t h e f r e e energy b a r r i e r t o f o r m a t i o n of t h e c o l l a p s e d s t a t e . 1 hour F i g . 1 : Recorder t r a c e s of damping a s a f u n c t i o n o f t i m e a t a n a m p l i t u d e of 3.0 mm/s d u r i n g t h e f i - n a l s t a g e s of d e m a g n e t i s a t i o n and t h e s u b s e q u e n t warmup. I n ( a ) t h e l i q u i d remained i n s u p e r c o o l e d A-phase, whereas i n (b) i t e n t e r e d t h e B-phase.
We t h e r e f o r e compare o u r r e s u l t s w i t h n u m e r i c a l s o l u t i o n s o f t h e e q u a t i o n of m c t i o n proposed by H a l l / 4 / The f u l l c u r v e s i n f i g u r e 2 a r e c a l c u l a t e d f o r a2 = 5.0 and (Bp/ps) = 1.2 x 10-'cm2s-', which w i t h t h e measured v a l u e o f p /5/ g i v e s B = 4.0. These p a r a m e t e r s g i v e a b o u t t h e b e s t o v e r a l l f i t ; l a r g e r v a l u e s f i t t h e low a m p l i t u d e damping b e t t e r , and s m a l l e r v a l u e s f i t t h e h i g h a m p l i t u d e f r e q u e n c y s h i f t b e t t e r . I n view of t h e c o n s i d e r a b l e o v e r s i m p l i f i c a t i o n i n v o l v e d i n u s i n g t h e s i n g l e p a r a m e t e r t o des- c r i b e changes i n s u p e r c u r r e n t r e s u l t i n g from t h e e f f e c t of t e x t u r e s on s ,
gs,
and c u r l8,
we c o n s i - d e r t h a t eq. ( I ) d e s c r i b e s o u r r e s u l t s a s w e l l a s can r e a s o n a b l y b e e x p e c t e d . C e r t a i n l y , t h e agreement o v e r t h e g e n e r a l form of t h e r e s u l t s g i v e u s c o n s i - d e r a b l e c o n f i d e n c e t h a t t h e i d e a s of s u p e r f l o w c o l - l a p s e and o r b i t a l r e l a x a t i o n on which eq. ( I ) i s based a r e e s s e n t i a l l y c o r r e c t .R e f e r e n c e s
/ I / Main, P.C., K i e w i e t , C.W., Band, W.T., Hook, J.R., S a n d i f o r d , D . J . , and H a l l , H.E., J. Phys. C
9
(1976) L 397.121 Main, P.C., Band, W.T., Hook, J.R., H a l l , H.E. and S a n d i f o r d , D . J . , Quantum F l u i d s and S o l i d s , ed. T r i c k e y S.B., Adams E . D . , and Duffy J . W . (Plenum 1977) p. 117.
-
-
w i t h t h e boundary c o n d i t i o n s v = 0 a t t h e w a l l s / 3 / B h a t t a c h a r y y a , P., Ho T-L, and Mermin, N.D., Phys. Rev. L e t t .
2
(1977) 1290, 1691. and vn = v s i n a t everywhere. From t h e s o l u t i o n we/ 4 / H a l l , H.E., p a p e r a t t h i s c o n f e r e n c e . compute t h e r a t e o f change of momentum and hence
/ 5 / Paulson, D.N., K r u s i u s , M. and Wheatley, J . C . ,
t h e t o r q u e on o u r t o r s i o n pendulum. Phys. Rev. L e t t .
36
(1976) 1322.F i g . 2 : Normalised f r e q u e n c y s h i f t 6v ( s o l i d p o i n t s ) and e x t r a r e s o n a n c e w i d t h 6~ Bopen p o i n t s )
W
