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CINEMATOGRAPHIC INVESTIGATION OF BUBBLONS IN SUPERFLUID HELIUM
M. Khaikin
To cite this version:
M. Khaikin. CINEMATOGRAPHIC INVESTIGATION OF BUBBLONS IN SUPER- FLUID HELIUM. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-1295-C6-1297.
�10.1051/jphyscol:19786561�. �jpa-00218051�
JOURNAL DE PHYSIQUE Colloque
C6,
supplkmenr auno
8, Tome 39, aoiir 1978, page C6- 1295CINEMATOGRAPHIC INVESTIGATION OF BUBBLONS IN SUPERFLUID HELIUM
M.S. Khaikin
I i z s t i t u t e for Physical Problems, Academy o f Science of the USSR, Moscow, USSR
Resume.- On a 6 t u d i 6 l a n a i s s a n c e e t l e developpement de l ' i n s t a b i l i t e d e l a s u r f a c e de l ' h e l i u m l i - q u i d e c h a r g e e d ' e l e c t r o n s q u i s o n t l o c a l i s d s au-dessus d e c e t t e s u r f a c e 1 l ' a i d e d ' u n e camdra r a p i d e . On a c o n s t a t 6 que l e s Q l e c t r o n s p a r t e n t de l a s u r f a c e g r z c e B l a n a i s s a n c e d e "bubblons" d e s b u l l e s q u i p l o n g e n t d a n s l 1 h Q l i u m s u p e r f l u i d e e t q u i c o n t i e n n e n t 10' 1 lo8 d l e c t r o n s , a y a n t 0 , 0 5 1 0 , 3 m d e g r a n d e u r . Les b u b b l o n s , d e p e t i t d i a m e t r e s o n t s t a b l e s e t d a n s un champ 2. 1 CGSE i l s e d e p l a c e n t d a n s l ' h d l i u m 2 une v i t e s s e c o n s t a n t e de i l o 4 cm/s.
On a remarqud une p o s s i b i l i t 6 d ' e x i s t e n c e de n i v e a u x s t a t i o n n a i r e s " d i 6 l e c t r i q u e s " d e l ' e l e c - t r o n , l o c a l i s 6 s t o u t p r s s d ' u n e p a r t i c u l e d i d l e c t r i q u e . Le s p e c t r e d e f r d q u e n c e d e s n i v e a u x d i e l e c - t r i q u e s s t e t e n d d e p u i s d e s f r Q q u e n c e s o p t i q u e s ( p o u r d e s i o n s ) j u s q u ' i 10"
+
1011 Hz.A b s t r a c t . - The i n s t a b i l i t y o f t h e l i q u i d h e l i u m s u r f a c e charged w i t h t h e e l e c t r o n s l o c a l i z e d n e a r t h e s u r f a c e i s i n v e s t i g a t e d by means o f a speed camera. The f i l m shows how e l e c t r o n s l e a v e t h e s u r - f a c e i n bubblons d i v i n g i n t o t h e s u p e r f l u i d helium. The word "bubblon" means a b u b b l e c o n t a i n i n g
10' i lo8 e l e c t r o n s and h a v i n g d i m e n s i o n s of 0.05
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0 . 3 m. Small bubblons a r e s t a b l e and i n e l e c - t r i c f i e l d % 1 CGSE t h e y move through h e l i u m w i t h c o n s t a n t v e l o c i t y of 2. 104 t m / s .F u r t h e r m o r e a n i d e a of a n e x i s t e n c e o f " d i e l e c t r i c " e n e r g y l e v e l s of e l e c t r o n s l o c a l i z e d n e a r a s m a l l d i e l e c t r i c p a r t i c l e i s d i s c u s s e d . The s p e c t r u m of d i e l e c t r i c l e v e l s l a s t s from o p t i c a l f r e - q u e n c i e s ( f o r i o n ) up t o 1012 i lo1' c / s ( f o r p a r t i c l e s m e a s u r i n g cm and l a r g e r ) .
The e l e c t r o n i s a t t r a c t e d t o t h e l i q u i d h e l i m s u r f a c e by t h e p o l a r i z a t i o n o f t h e l i q u i d h e l i u m by t h e e l e c t r o s t a t i c e l e c t r o n f i e l d . For p e n e t r a t i o n i n s i d e t h e l i q u i d t h e e l e c t r o n must p a s s t h r o u g h t h e p o t e n t i a l b a r r i e r of
*
1 eV. So t h e p o t e n t i a l w e l l where t h e two-dimensional l a y e r o f e l e c t r o n s may be l o c a l i z e d a r i s e s n e a r t h e h e l i u m s u r f a c e .The d e n s i t y of l o c a l i z e d e l e c t r o n s can n o t b e more t h a n 2. 2 x l o 9 p e r 1 cm2 / I / . The l i m i t i n g den- s i t y of e l e c t r o n s o v e r t h e s u p e r f l u i d h e l i u m f i l m l y i n g op a m e t a l s u b s t r a t e may be one o r d e r b i g g e r 1 2 1 . A t any a t t e m p t t o s u r p a s s t h i s l i m i t t h e s u r - f a c e c h a r g e c o m p l e t e l y d i s a p p e a r s . As t h e o r e t i c a l a n a l y s i s shows t h e f l a t h e l i u m s u r f a c e t u r n s t o be u n s t a b l e when t h e s u r f a c e c h a r g e d e n s i t y e x c e e d s
t h i s l i m i t 15.41. T h i s r e p o r t d e s c r i b e s e x p e r i m e n t s c l e a r i n g up two q u e s t i o n s : when t h e i n s t a b i l i t y of t h e charged helium s u r f a c e d e v e l o p s a n d how e l e c t r o n s l e a v e t h e s u r f a c e 151. The e x c i t a t i o n o f s u r f a c e wa- v e s due t o i n s t a b i l i t y was o b s e r v e d and f i l m e d by a speed camera. The f i l m shows t h e developement of ttie h e l i u m s u r f a c e i n s t a b i l i t y under d i f f e r e n t condi- t i o n s .
Experiments were c a r r i e d o u t i n helium Dewar w i t h o p t i c a l windows. F i g u r e 1A shows t h e i n n e r p a r t o f t h e a p p a r a t u s . The l i q u i d h e l i u m l e v e l h was m a i n t a i n e d (by thermomechanical pump) i n t h e gap d = 1 i 5 m between two h o r i z o n t a l condensor p l a -
t e s o f d i a m e t e r 40 mm. The f i e l d El o v e r t h e h e l i u m
s u r f a c e and t h e r e f o r e t h e s u r f a c e c h a r g e d e n s i t y was d e t e r m i n e d from t h e d i s p l a c e m e n t of t h e p l a t e 5. The p o s i t i o n o f t h i s p l a t e suspentled on s p r i n g s was mea- s u r e d by t h e c a p a c i t y s e n s o r 6. I n s t a b i l i t y o f t h e charged h e l i u m s u r f a c e was a t ~ a i n e d by one of two ways : by s i n k i n g o f t h e h e l i u m l e v e l h o r by i n - c r e a s e i n condensor v o l t a g e V.
C a p i l l a r y - g r a v i t a t i o n a l waves were e x c i t e d on h e l i u m s u r f a c e d u r i n g 0.03 t 0 . 1 s a f t e r excee- d i n g c r i t i c a l c o n d i t i o n s and i n 0.1 i 0 . 3 s t h e s u r - f a c e d i s a p p e a r e d . F i g u r e IB shows t h e c r i t i c a l pa- r a m e t e r ( E ~ + E') c r i t a s a f u n c t i o n of helium d e p t h
1 2
h . T h i s p a r a m e t e r i s d e f i n i t e i n two c a s e s : h = d / 2 of h (< d - h, which took p l a c e a t e x p e r i m e n t s . The r e s u l t s of t h e e x p e r i m e n t s arc! i n agreement w i t h c a l - c u l a t e d c u r v e 141. The change of t h e c u r v e s l o p e a t h = I i 1.5 mm c o r r e s p o n d t o t h e t r a n s i t ion from t h e i n s t a b i l i t y w i t h r e s p e c t t o waves o f l e n g t h .I = 2 i 3 cm a t h 2 0 . 7 mrn t o t h e i n s t a b i l i t y w i t h r e s p e c t t o c a p i l l a r y waves of X c = 3.2 mm a t h 7 1.5 mm. TNese e f f e c t s a r e c l e a r l y seen i n t h e f i l m .
The p r o c e s s of g o i n g away of e l e r t r o n s from t h e h e l i u m s u r f n c c was d i s c l o s e d by mcans o i n speed camera f i l m i n g . S t a h l e and calm charged l i q u i d he- lium s u r f a c e is s e c n on t h e I-st ( u p p e r ) p i c t u r e of f i g u r e 2 .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786561
C6-1296
JOURNAL DE PHYSIQUEF i g . 1
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A. Scheme of a p p a r a t u s :1
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Source of e l e c t r o n s - t u n g s t e n f i l a m e n t ; 2-
Liquid helium s u r f a c e ;3
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Condensor anode surrounded by e q u i p o t e n t i a l r i n g 4 ;5
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Movable condensor cathode w i t h a c a p a c i t y sen- s o r 6B. Values of t h e c r i t i c a l parameter and t h e f i e l d E 2 a t which t h e charged f l a t l i q u i d helium s u r f a c e l o s e t h e s t a b i l i t y a s a f u n c t i o n of t h e li- q u i d d e p t h h.
The 2-nd p i c t u r e shows t h e i n s t a b i l i t y of t h e charged helium s u r f a c e developed a f t e r i n c r e a s e i n condensor v o l t a g e : c o n i c a l d e e p i n g s appeared i n de- p r e s s i o n s of e x c i t e d s u r f a c e waves. Bubblons o f d i - mensions 0.05
+
0.3 m a r e b o r n on t h i s d e e p i n g s(3-rd ~ i c t u r e ) and d i v e i n t o t h e helium (4-th p i c - t u r e ) . Reaching p o s i t i v e bottom p l a t e bubblons d i s - c h a r g e themselves. Then s m a l l b u b b l e s measuring
% 0.05 rnm d i s a p p e a r i n 2 s , b i g bubbles e x i s t d u r i n g
*
s and have time t o come t o t h e s u r f a c e . Each bubblon c o n t a i n s n = lo7+
lo8 e l e c t r o n s ; n i s e s t i m a t e d from t h e f u l l s u r f a c e c h a r g e and t h e num- b e r of bubblons d i s c h a r g i n g t h e s u r f a c e e n t i r e l y(20
+
100 bubblons). Radius of a bubblon may b e de- termined from e q u a l i t y of a n e l e c t r o s t a t i c p r e s s u r e o u t s i d e t o a c a p i l l a r y p r e s s u r e of helium s u r f a c e i n s i d e : r = 3/n2 e 2 / 1 6 n a = 0.08 mm, where e-
elec- t r o n c h a r g e , a-
s u r f a c e t e n s i o n of a l i q u i d helium.Small d i a m e t e r (QJ 0.05 mrn) bubblons move through l i q u i d helium under t h e a c t i o n of e l e c t r i c f i e l d E = lCGSE w i t h c o n s t a n t v e l o c i t y
*
10' cm/s a c c o r d i n g t o s t o k e v i s c o u s motion. The d u r a t i o n of motion t o t h e bottom 2, s i s much l o n g e r t h a n r e l a x a t i o n t i m e s f o r e l e c t r i c and e l a s t i c inhomoge- n e i t i e s i n a bubblon. At t h e same time lower v i b r a -F i g . 2 : F i l m p i c t u r e s show t h e e x c i t i n g of c a p i l l a - r y waves and t h e b i r t h of bubblons t a k i n g o f f e l e c - t r o n s from s u r f a c e i n t o t h e l i q u i d helium. The 1-st (upper) p i c t u r e shows calm charged l i q u i d h e l i u m s u r f a c e (lower b o r d e r o f t h e b l a c k s t r i p e ) , pushed down by a condensor f i e l d on 0 . 2 mm r e l a t i v e t o t h e n e u t r a l l i q u i d helium s u r f a c e o u t of a condensor
(upper b o r d e r o f t h e b l a c k s t r i p e ) .
t i o n a l modes of a bubblon have wave l e n g t h s of t h e o r d e r of magnitude o f a bubblon r a d i u s r =
A c . T h i s means t h a t a bubblon i s r i g i d and t h e more r i - g i d t h e s m a l l e r i t i s . B e s i d e s decay of a s m a l l bub- b l o n is e n e r g e t i c a l l y u n p r o f i t a b l e ( t h e more unpro- f i t a b l e i s t u n n e l i n g of e l e c t r o n s i n t o t h e l i q u i d h e l i u m ) . E v e r y t h i n g t a k e n t o g e t h e r shows t h a t s m a l l bubblons a r e s t a b l e o b j e c t s .
Due t o t h e e l e c t r o s t a t i c i n t e r a c t i o n e l e c - t r o n s i n a bubblon fonn a two-dimensional l a y e r n e a r a l i q u i d s u r f a c e . D e n s i t y of e l e c t r o n s r e a c h t o
1011 9 1 0 ' ~ / e m ~
-
s o h i g n t h a t a l a y e r may b e c o n s i - d e r e d a s f l a t and Wigner c r y s t a l l i z a t i o n of e l e c t r o n s i s v e r y p r o b a b l e 1 6 1 . A t t h e same time l i t t l e bub- b l o n w i t h s m a l l number of e l e c t r o n s must be a t h r e e - dimensional quantum system.I n c o n c l u s i o n l e t u s show a v e r y i n t e r e s t i n g p o s s i b i l i t y c o n c e r n i n g a g e o m e t r i c a l c a s e o p p o s i t e t o c o n s i d e r e d : t h e a p p e a r i n g of s t a t i o n a r y "die- l e c t r i c " e n e r g y l e v e l s o f e l e c t r o n s n e a r l i t t l e he- l i u m d r o p s o r , g e n e r a l l y s p e a k i n g , n e a r s m a l l d i e - l e c t r i c p a r t i c l e s 171. The c a s e o f e x t r e m e l y s m a l l quantum s y s t e m of s u c h t y p e i s w e l l known : t h i s i s a n e g a t i v e i o n . The c a l c u l a t i o n shows t h a t t h e spec- trum of d i e l e c t r i c l e v e l s r a n g e s from o p t i c a l f r e - q u e n c i e s f o r i o n up t o 1012 5 1 0 ' ~ c / s f o r p a r t i c l e s m e a s u r i n g % cm. T h i s s p e c t r u m t r a n s f o r m s i n t o t h e known s p e c t r u m of e l e c t r o n s l o c a l i z e d a t t h e f l a t d i e l e c t r i c s u r f a c e w i t h i n c r e a s i n g o f cur- v a t u r e r a d i i o f a p a r t i c l e s u r f a c e . D i e l e c t r i c l e - v e l s may e x i s t a t cosmic d u s t p a r t i c l e s and a c t a n i m p o r t a n t p a r t i n f o r m a t i o n o f cosmic r a d i a t i o n i n t h e r a n g e mentioned above.
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