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PROBABILITY OF THE CREEP DISCHARGES
J. Brzosko, E. Zukowski, J. Grudzinski, W. Zukowski, A. Konarzewski
To cite this version:
J. Brzosko, E. Zukowski, J. Grudzinski, W. Zukowski, A. Konarzewski. PROBABILITY OF THE CREEP DISCHARGES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-471-C7-472.
�10.1051/jphyscol:19797229�. �jpa-00219211�
JOURNAL DE PHYSIQUE Colloque C7, suppldment au n07, Tome 40, J u i l l e t 1979, Page c7- 471
PROBABILITY OF THE CREEP DISCHARGES
J.S. Brzosko, E. Zukowski, J. Grudzinski, W. Zukowski and A. Konarzewski.
I n s t i t u t e of Physics, Warsaw University Branch, Bialys tok, Poland.
When a d i e l e c t r i c s a m p l e a f e w c e n t i - p e t e r s i n d i a m e t e r a n d a b o u t 1 mm t h i c k
i s p l a c e d i n a n a.c. f i e l d o f 1 k V a n d f=50Hz b e t w e e n two s t e e l e l e c t r o d e s o f s e - v e r a X m i l i m e t e r s i n d i a m e t e r a c r e e p d i s - c h a r g e o c c u r s u n d e r n o r m a l c o n d i t i o n s i n t h e a i r a t i t s s u r f a c e . T h e d i s c h a r g e s con- c e n t r a t e i n s e v e r a l n a r r o w c h a n n e l s o r i e n - t e d r a d i a l l y w i t h r e s p e c t t o t h a e l e c t r o d e a x i s .
O u r p r e v i o u s i n v e s t i g a t i o n s a s w e l l a s t h o s e p r e s e n t e d h e r e were c o n d u c t e d i n f u - l l y c o n t r o l l e d p h y s i c a l p a r a m e t e r s o f t h e g a s i n t h e e x p e r i m e n t : t h e a i r t e m p e r a t u r e h u m i d i t y a n d p r e s s u r e w e r e 20°c, 30% a n d 1 a m . r e s p e c t i v e l y .The g e o m e t r y o f t h e d e t e c t i o n s y s t e m a s w e l l a s e l e c t r o n i c set -up h a s b e e n s i m i l a r t o t h o s e p u b l i s h e d e a r l i e r [2]. The m e a s u r e m e n t s were d o n e f o r b a k e l i t e , t e f l o n , p l e x i g l a s s , t h e re- s u l t s o b t a i n e d b e i n g q u a l i t a t i v e l y s i m i l a n
The a i m of t h e p r e s e n t work was t h e c o - n t i n u a t i o n of t h e s t u d y o f t h e s t a t i s t i c a l p r o p e r t i e s of t h e c r e e p d i s c h a r g e s .
F i g 1
r n t h e c o u r s e o f t h e i n v e s t i g a t i o n s were d o n e t h e - m e a s u r e m e n t s o f : ( i ) d i s t r i - b u t i o n s ~ ( k t ) o f time e l a p s e d f r o m t h e ze-
.TO c r o s s p o i n t t o t h e o c c u r e n c e o f a d e f i - n e d number, k, of d i s c h a r g e s , F i g . 1 , (ii) t h e i n f l u e n c e o f t h e p r e c e d i n g d i s c h a r g e a m p l i t u d e o n t h e s u c c e s s i v e o n e A, F i g . 2 , (iii) t h e w a i t i n g time, a n d ( i v ) d i s t r i - b u t i o n I ( A ~ ) o f time i n t e r v a l s & b e t w e e n t o
c o n s e c u t i v e d i s c h a r g e c a s c a d e s m e a s u r e d i n number o f v o l t a g e c y c l e s , Fig.3,
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F i g . 3 F i g . 4
The r e s u l t s f o r BC s a m p l e a r e shown i n F i g s . 1-3 by way o f t h e e x a m p l e s . F i g s . l , 2 a r e f o r t h e a p p l i e d v o l t a g e a m p l i t u d e ex- c i d i n g 30% o f t h e i n c e p t i o n v a l u e . T h e re- s u l t s i n F i g . 3 w e r e d o n e f o r 2% o v e r v o l - t a g e w h e r e d i s c h a r g e s o c c u r i n c a s c a d e s o f 6-10 t i m e s e p a r a t e d d i s c h a r g e s w i t h a v e r a - g e r e p e t i t i o n of c a s c a d e s 40 ms.The d a s h e d l i n e s i n F i g s 1 a n d 3 r e p r e s e n t c a l c u l a - t i o n s b a s e d o n ~ o i s s o n % d i s t r i b u t i o n f o r v a r i a t e d a v e r a g e i n t e n s i t y t a k e n f r o m si- m u l t a n e o u s m e a s u r e m e n t s , s o l i d l i n e , The d i s c h a r g e a m p l i t u d e d i s t r i b u t L o n s Fig.2
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Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797229
'were measured f o r t h e k - t h d i s c h a r g e i n t h e c y c l e , We compare t h e a m p l i t u d e d i s t - r i b u t i o n q f o r s m a l l and h i g h a m p l i t u d e s o f t h e p r e c e d i n g d i s c h a r g e s , dashed and s o l i d l i n e s , r e s p e c t i v e l y .
The d i s c u s s e d m a t e r i a l r e v e a l s t h a t t h e d i s c h a r g e p r o b a b i l i t y i s f u l l y d e s c r i - bed i n t e r m s o f t h e ~ o i s s o n ~ s s t a t i s t i c s a s w e l l a s i n d e p e n d e n c e o f t h e d i s c h a r g e a m p l i t u d e d i s t r i b u t i o n f o r t h e s u c c e s s i v e d i s c h a r g e s . T h i s means t h a t a l l p a r e m e t e r s d e s c r i b i n g d i s c h a r g e s a r e i n d e p e n d e n t o f t h e " h i s t o r y " o f t h e d i s c h a r g e s , n o t o n l y t h o s e w h i c h a r e r e l a t e d t o t h e p r o b a b i l i t y o f d i s c h a r g e i n i t i a t i o n .
F o r m a l l y t h e p r o b a b i l i t y o f t h e c r e e p d i s c h a r g e p e r u n i t t i m e P ( r t ) c a n be t a - k e n a s p r o p o r t i o n a l t o t h e number o f f r e e e l e c t r o n s i n t h e e l e c t r i c f i e l d o p e r a t i o n r e g i o n a n d t o t h e p r o b a b i l i t y ( n o r m a l i z e d t o u n i t t i m e ) t h a t t h e a c c e l e r a t e d e l e c t - r o n c a n i n i t i a t e t h e a v a l y n c h e P3 ( r t ) t h i s i s so t h e ~ o i s s o n ~ s s t a t i s t i c h a s been f u l f i l l e d
3P(r t) =zi-rrdl-G,(~ t) pa (T t)
where: r = r + x i s t h e r a d i u s o f t h e r i n g a t t h e d i e l e c t r i c s u r f a c e w h i c h i s u n d e r d i s c u s s i o n . Be i s t h e d e n s i t y o f e- l e c t r o n s i n t h e n e a r t o t h e s u r f a c e a i r l a y e r .
I t h a s been p o s t u l a t e d [2] , (31 t h a t
a c e r t a i n number o f e l e c t r o n s i s a t t a c h e d t o t h e sample s u r f a c e d u r i n g t h e d i s c h a r g e . I n e f f e c t t h e e l e c t r o n s a r e l i b e r a t e d b y way o f t h e r m a l o r f i e l d e m i s s i o n . The e l e - c t r o n d e n s i t y i n t h e gas i s p r o p o r t i o n a l t o t h e f r e q u e n c y o f detachment and expone- n t i a l y d e c r e a s e a s a f u n c t i o n o f t h e t i m e w i t h h a l f - t i m e o f o r d e r o f 1 0 ms.As r e s u l t o f t h e s i m p l i f i c a t i o n c h a i n t h e p r o b a b i l i - t y o f a d i s c h a r g e a t t i m e t c a n be w r i - t t e n a s
P(t) =lTli.',6,(t)2r0~(t) + ~ ' ( t ) ] The e f f e c t i v e r a d i u s o f t h e e l e c t r i c a l f i e l d s R c a n be c a l c u l a t e d o n t h e base o f t h e e q u i v a l e n t c i r c u i t m o d e l [ A ] .
A v e r y s i m p l e f o r m u l a d e s c r i b i n g t h e p r o b a b i l i t y o f t h e d i s c h a r g e phenomenon was o b t a i n e d a t t h e c o s t s o f i n t r o d u c i n g a s s u m p t i o n s a s t o : t h e e f f e c t i v e o f
Pa,
t h e e x p o n e n t i a l c h a r a c t e r o f t h e a t t a c h e - ment e f f e c t , t h e a v e r a g i n g o f t h e s u r f a c e d e n s i t y Ge and v a l i d i t y o f e q u i v a l e n t c i r - c u i t for d e s c r i p t i o n o f t h e e l e c t r i c a l f i e l d s . .
The c o m p a r i s o n o f c a l c u l a t i o n s based on above f o r m u l a and e x p e r i m e n t a l r e s u l t s r e v e a l a good' agreement Fig.4. The d i s c r e - p a n c y i s r e s u l t o f s m a l l knowledge a b o u t h a l f - l i f e o f t h e c a r r i e r e v a R o r a t i o n e f f e- c t ( i n Ge)and p r e l i m i n a r c a r r i e r d e n s i t y p a r a m e t e r ( i n R ) .
R e f e r e n c e s :
1 J.S.Brz'osko,J.Grudzihski,A.Konarzew- s k i , E.~ukowski,~.~ojew6dzka, J o u r n a E
Phys.D: Appl.Phys. 10,1977,2201,
2 J.S.Brzosko,'~.Zukowski,3.Grudzitjski, W.tukowski,A.Konarzewski, I E E E Tran- s a c t i o n , a c c e p t f o r p u b l o i n 1979 3 J.S.Brzosko,J.Grudzitiski,A.Konarzew- ski,A.Wojew6dzka~,E.~ukowski,Journ.
Phy~.D:Appl.Phy~.lO, 1977,1583