THRESHOLD FIRST SOUND AMPLITUDES FOR THE GENERATION OF VORTEX LINES IN He II

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THRESHOLD FIRST SOUND AMPLITUDES FOR THE GENERATION OF VORTEX LINES IN He II

R. Carey, J. Rooney, C. Smith

To cite this version:

R. Carey, J. Rooney, C. Smith. THRESHOLD FIRST SOUND AMPLITUDES FOR THE GENER-

ATION OF VORTEX LINES IN He II. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-176-C6-

177. �10.1051/jphyscol:1978678�. �jpa-00218358�

JOURNAL DE PHYSIQUE

Colloque C6, supplhnent au no 8, Tome 39, aozit 1978, page C6-176

THRESHOLD FIRST SOUND AMPLITUDES FOR THE GENERATION OF VORTEX LINES IN He I 1

R.F. Carey, J.A. Rooney and C.W. Smith

Department o f Physics, University o f Maine, Orono, Maine, 04473, U.S.A.

Rdsum6.- Nous avons observe des attgnuations trSs fortes des courants d'ions negatifs par le premier son de haute amplitude dans l'hdlium liquide pour 1,30 K

<

T

<

1,70 K et w / 2 ~

=

1, 3, et

10

MHz. Nos rdsultats sont en accord avec ceux obtenus par capture des ions sur lignes de vortex dans un tube

P

contre courant. En outre, pour chaque frdquence, nous pouvons ddterminer un seuil de l'amplitude du ddplacement du transduceur, Ac, qui marque le ddbut de la capture. Pour les tempgratures et frdquen- ces utilisdes, nous trouvons.que wAc est la vitesse critique ndcessaire pour engendrer des lignes de vortex dans He 11. Ltanalyse de nos rdsultats,

P

l'aide de la thgorie de la turbulence de Vinen donne WAC

=

0,15 + 0,05 cm/s.

Abstract.- We have observed strong negative ion current attenuations in high amplitude first sound fields in liquid helium for 1.30 K

<

T < 1.70 K and w/2m

=

1,3 and

10

megahertz. Our experimental re- sults agree with those for ion trapping on vortex lines in counter-flow tubes. In addition, for each frequency we are able to identify a threshold transducer displacement amplitude, Ac, for which trap- ping begins. For the temperatures and frequencies studied, we find that wAc is the bulk critical ve- locity necessary for the generation of vortex lines in He 11. Analysis of our data using dinen's di- mensional theory of turbulence yields wA

=

0.15

?

0.05 cm/s.

Vinen/l/ first proposed a physical basis for

1.00

the Gorter-Mellink mutual friction force/2/, sugges-

5

^0.98

ting that turbulent He I1 was penetrated by quanti-

w . K

zed vortex lines which interact with the normal

^LT _{3 0.96}

0

fluid. This characterization of superfluid turbulen-

0

cehas been quite successful in describing the re- /

0.94

- 1

sults of flow and counterflow experiments/3/. In

Q Z 0.92

such studies channel size constraints and the onset

^K ₀

of normal fluid turbulence can make interpretation

Z 0.90

difficult. In this paper we describe measurements which provide information about the onset of super- fluid turbulence in bulk He I1 which avoids these complications. Our method uses ultrasound in the

0 0 0.5 LO 1.5

VE LOC l TY (CM/S)

Fig. -

1 :

Normalized collector current as a function megahertz frequency range to generate superfluid of maximum fluid velocity in the applied sound field

for three frequencies at T

=

1.60 K.

turbulence/4/ which is detected bye the trapping of negative ions on quantized vorticity associated with the turbulent state. The apparatus consists of a grounded grid triode cell with a t'wo Curie tritium source. Data presented here were obtained for an electric field intensity of 50 volts/cm. Matched pairs of PZT4 ceramic thickness mode transducers (w/2n.

=

1, 3 and

10

megahertz) are positioned in the grid-collector region to generate and receive first sound transverse to the ion drift velocity.

An off-null signal from a capacitance bridge, one arm of which is the sound source transducer, is a direct measure of the displacement amplitude, A, of the transducer/5/ and the maximum fluid velocity,

v =

wA.

tive ion current below T

=

1.70 K due to trapping of ions on vortex lines. Figure

1

shows current-sound characteristics at T

=

1.60 K for the three frequen- cies studied. We observe a threshold velocity v c ~ A C . below which no trapping occurs. We interpret this to indicate that there exists a critical fluid veloci- ty above which vortex lines can be generated by first sound. In the small attenuation regime,

a

linear ex- trapolation to zero current attenuation yields

0

v

=

0.25

?

0.05 centimeters/second (Ac

=

4.0 A,

C 0 0

1.3 A, and 0.4 A for w/2a

= 1 ,

3 and

10

MHz). Below T

=

1.70 K, where thermally activated escape of trapped charge in unimportant/6/, the dynamic balan-

- .

ce between growth and annihilation of vortex line In general, we observe an attenuation of nega-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978678 Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978678

can be analyzed i n a f a s h i o n s i m i l a r t o t h e a n a l y s i s of counterflow experiments by Ashton and Northby/7/.

The s t e a d y s t a t e i s c h a r a c t e r i z e d by t h e e q u i l i b r i u m l e n g t h of v o r t e x l i n e p e r u n i t volume, L = K l ( ~ n - v L ) 2 where ( v -vL) i s t h e d i f f e r e n c e v e l o c i t y between t h e

n

normal f l u i d and t h e v o r t e x l i n e . The a n n i h i l a t i o n r a t e of v o r t e x l i n e , and hence t h e r a t e of trapped charge r e l e a s e , i s given by

t

⁼ K~L;. I f we choose a model i n which vL

"

0 / 8 / (we assume t h a t t h e l i n e s t o f i r s t o r d e r , do n o t respond t o t h e sound f i e l d i n t h e megahertz range) and t a k e i n t o account a t h r e s h o l d v e l o c i t y wA = vc, we f i n d t h e c u r r e n t d e n s i t y change, A j , t o b e given by

where D i s t h e source t o g r i d d i s t a n c e , E t h e per- m i t t i v i t y of f r e e s p a c e , (dj/dVs)o t h e s l o p e of t h e j(Vs) curve a t zero sound l e v e l , V t h e source b i a s v o l t a g e ,

o

t h e c a p t u r e width of e l e c t r o n s on v o r t e x l i n e s , and !Z t h e l e n g t h of l i n e obscured by a t r a p - ped ion. The f u n c t i o n a l form of e q u a t i o n ( 1 ) i s in- s e n s i t i v e t o t h e choice of vL. For small A j

,

e q u a t i o n (1) p r e d i c t s a l i n e a r r e l a t i o n s h i p between ( ~ j ) - ' and (v-vC)-'. Figure 2 shows d a t a a t 1 MHz f o r f o u r t e m p e r a t u r e s . The s t r a i g h t l i n e s through t h e d a t a a r e b e s t f i t s t o e q u a t i o n (1) w i t h vC, o, and K1 used a s f i t t i n g parameters. T y p i c a l v a l u e s of

cr

and K1 d e r i v e d from t h e s e f i t s a r e 50 ym and l o 5 r e s p e c t i v e l y . A s i n g l e b u l k c r i t i c a l f l u i d v e l o c i t y v = 0.15 f. 0.05 cm/s g i v e s t h e b e s t f i t f o r each d a t a s e t i n t h e temperature and frequency ranges s t u d i e d

.

These experiments show t h a t Vinen's d e s c r i p - t i o n of t h e t u r b u l e n t s t a t e provides a model from which t h e c a p t u r e width o can b e determined and i n d i -

c a t e s t h a t u l t r a s o u n d i n t h e megahertz range i s an e f f i c i e n t g e n e r a t o r of t u r b u l e n c e (we f i n d K1 appro- ximately an o r d e r of magnitude l a r g e r t h a n v a l u e s d e r i v e d from c o u t e r f l o w experiments). I n a d d i t i o n we observe a w e l l d e f i n e d c r i t i c a l f l u i d v e l o c i t y a s s o c i a t e d w i t h i n i t i a t i o n of t h e t u r b u l e n t s t a t e .

T h i s workwassupported by a g r a n t from t h e U.S. A i r Force O f f i c e of S c i e n t i f i c Research.

References

/ I / Vinen,W.F., Proc. R. Soc. S e r .

2

(1958) 400 / 2 / Gorter,C.J. and Mellink,J.H., Physica

2

(1949)

285

/3/ See, f o r example, Keller,W.E., i n Helium-3 and Helium-4 (Plenum P r e s s , New York) 1969, c h a p t e r 8

/4/ Carey,R.F., Rooney,J.A. and Smith,C.W., Phys.

L e t t . t o appear

/ 5 / F i l l , E . E . , IEEE Trans. BME-16 (1969) 165 / 6 / Douglass,R.L., Phys. Rev. L e t t .

2

(1964) 791 /7/ Ashton,R.A. and Northby,J.A., Phys. Rev. L e t t .

30 (1973) 1119

-

/8/ See P i o t r o w s k i C . and Tough,J.T., Phys. Rev.

B17

(1978) f o r a d i s c u s s i o n of t h e choice f o r vL i n counterflow experiments.

F i g . 2 : Reciprocal change i n c u r r e n t d e n s i t y v e r s u s r e c i p r o c a l of ( V - V , ) ~ f a f o u r temperatures a t ~ 1 2 7 1

= 1.0 MHz. The s t r a i g h t l i n e s a r e f i t s of t h e d a t a t o e q u a t i o n ( 1 ) . T y p i c a l e r r o r b a r s a r e shown.