CONDUCTIVITY MEASUREMENTS OF HIGH CURRENT, HIGH PRESSURE DISCHARGES

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Submitted on 1 Jan 1979

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CONDUCTIVITY MEASUREMENTS OF HIGH CURRENT, HIGH PRESSURE DISCHARGES

M. Skowronek, L. Giry, Vu Gia, P. Romeas

To cite this version:

M. Skowronek, L. Giry, Vu Gia, P. Romeas. CONDUCTIVITY MEASUREMENTS OF HIGH CUR-

RENT, HIGH PRESSURE DISCHARGES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-303-

C7-304. �10.1051/jphyscol:19797149�. �jpa-00219123�

JOURNAL DE PHYSIQUE C o l l o q u e C7, suppZ6ment au n 0 7 , Tome 40, J u i l Z e t 1979, page C7- 303

CONDUCTIVITY MEASUREMENTS OF HIGH CURRENT, HIGH PRESSURE DISCHARGES

M. Skowronek, L. Giry, Vu Tien Gia, and P. Rorneas.

E q u i p e "Plusmas d e n s e s " U n i v e r s i t g P. e t M. C u r i e , T o u r 1 2 , E5, 75230 P d s C e d e x 05.

- 1

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Introduction

A v e r y i m p o r t a n t p r o b l e m , f o r the heating of

d e n s e p l a s m a s like l i s e r produced p l a s m a s [l]

o r focus type p l a s m a

[-is

the knowledge of the t r a n s p o r t p r o p e r t i e s . Strong e l e c t r i c a l f i e l d s o r s t r o n g g r a d i e n t s c a u s e the a p e a r a n c e of m i c r o - t u r b u l e n c e s and a f f e c t the conductivities. In t h e following p a p e r , we d e s c r i b e m e a s u r e m e n t s of t h e voltage d r o p o v e r high density d i s c h a r g e s . T h e s e m e a s u r e m e n t s a r e in good a g r e e m e n t with calculations and allow t h e d e t e r m i n a t i o n of t h e conductivity of a p l a s m a a t a density about

-3 7 0

1

o1

9 c m and a t e m p e r a t u r e %bout 1 0 K. Corn- p a r i s o n i s m a d e with theory.

2

-

E x p e r i m e n t a l s e t - u p [3]

In a t m o s p h e r i c a i r , a s t a b l e ionized f i l a m e n t i s e s t a b l i s h e d between two s h a r p needles 3 c m a p a r t . A c a p a c i t o r bank having 2.6 Y F m a x i m u m c a p a c i t y and a c h a r g e voltage v a r i e d f r o m 50kV t o 100 kV i s d i s c h a r g e d into t h e ionized channel through a s p a r k - g a p having 20 n s r i s e - t i m e . T h e intensity i s m e a s u r e d by m e a n s of a Rogowski coil. It r e a c h e s i t s m a x i m u m (100 kA to 300 kA) whitin 1 ps, The r a d i a l expansion of the d i s c h a r - g e is r e c o r d e d by m e a n s of a n e l e c t r o n i c c a m e - r a S. T. L. used in s t r e a k mode : the t e m p o r d l r e - solution i s 4 ns/mrn and the s p a t i a l r e s o l u t i o n s is 0.1 mm. T h e expansion speed i n t h e f i r s t nano- seconds i s 25 km/s. A complex s y s t e m of shock waves i s r e c o r d e d by m e a n s of a s c h l i e r e n - m e - thod. T h e m a i n shock p r o p a g a t e s a t Mach 12 during 1 t o 2 s. Secondary s h o c k s o v e r t a k e t h e m a i n shock and a c c e l e r a t e it. The s p e c t r u m of t h e light e m i t t e d by the outer s h e l l c o r r e s p o n d s t o a p l a s m a whose density i s 1 0 c m - 3 and t h e 21 t e m p e r a t u r e 1 0 K. 50

- 3

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M e a s u r e m e n t s of the voltage d r o p

A K e r r c e l l i s designed f o r t h i s purpose. It i s f i l l e d with c a r b o n sulphur of high purity. The e l e c t r o d e s a r e I 6 0 m m x 1 Omm and 5 m m s p a c e d It i s t r a n s i l l u m i n a t e d by a cw ~ e / l a s e r . T h e ~ e opening of the K e r r c e l l i s c a l i b r a t e d by m e a n s of s q u a r e p u l s e s of known a m p l i t u d e s having 200 n s half-width.

Two p u l s e s given by t h e K e r r c e l l a r e d i s - played on f i g u r e 1 : a ) durhng t h e calibration p r o - c e d u r e ; b ) with the d i s c h a r g e of a 0 . 8 4 p F c a p a - c i t o r , c h a r g e d a t 80 kV

; Imax = 106 kA a t t h e t i m e t = 0.84 P s . T h e f i r s t l a r g e p u l s e i s due t o the r i s e of the applied voltage. The c u r r e n t

s t a r t s s o m e 150 n s a f t e r . P e a k s n u m b e r e d f r o m 1 t o 8 c o r r e s p o n d s t o b u r s t s in the voltage.

Another d e t e r m i n a t i o n of the voltage d r o p i s deduced f r o m the a n a l y s i s of t h e f i r s t a r c h of the c u r r e n t . It is displayed on f i g u r e 2 and a good a g r e e m e n t between t h e two d e t e r m i n a t i o n s i s obtained. On Fig. 3 the calculated t r a n s m i s s i o n i s displayed.

The conductivity i s the c a l c u l a t e d a s s u m i n g a constant t e m p e r a t u r e profile. It is about 200 d ' c m - I a t t h e t i m e t = 130ns.

4

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Conclusions

In o r d e r t o c o m p a r e t h e conductivity with the t h e o r y , t h e c o r e p l a s m a p a r a m e t e r s m u s t b e known. T h e magnetic p r e s s u r e , the kinetic p r e s s u r e , t h e e q u i l i b r i u m p r e s s u r e i n the o u t e r Shell a r e on the o r d e r of lkbar. T h i s g i v e s t h e product NT. If we a s s u m e t h a t N in the c o r e i s about 1 ~ l ~ c r n - ~

,

T i s about 1

o7

K. T M s i s a l s o c o n s i s t e n t with the c a l c u l a t e d e n e r g y depo- s i t e d by joule affect about 2 k ~ / c m 3

.

The e l e c t r i c f i e l d over the d i s c h a r g e i s r a t h e r

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797149

high, about 1 0 kv/cm. This i s not f a r f r o m 4 D r e i c e r c r i t i c a l field about 3 0 4 v/cm. Locally

i t is not s u r p r i s i n g that the e l e c t r i c field m a y exceed it. The value of the conductivity c o r r e s - ponds

,

a t the b e s t , t o the f o r m u l a given by

Sadgeev and Galeev :

U)p

^: p l a s m a frequency

t h m

M o r e p r e c i s i o n i s needed i n o r d e r t o calculate t h e conductivity and t o a s c r i b e i t s value t o m i - croturbulence. A d e t a i l energy balance will give ed

a l s o the t h e r m a l conductivity. It m a y be calcu-

C A L C U L A T E D VOLTAGE

4

lated a l s o by Franz-Widemann law.

.

.Lr

R e f e r e n c e s

."

1 N. G. Basov, O.N. Krokhip, 3e Conf. d'elect.

L,-,-

^{. c}

^{4 .}

^{- -}

quant. P a r i s 1963

2 J.W.Mather,Conf. o n P 1 a s m a P h y s . a n d C o n t . F i u r e 2 . fudion r e s . ~ u l h a m , ' 1965.

3 M. Skowronek, J. Rous, A. Goldstein, F. Cabannes -Phys. F l u i d s 1 2 (1 970) 378 4 R. Z. Sadgeev and A. A. Galeev, Non l i n e a r

p l a s m a theory. Benjamin New-York 1969

KERR CELL TRANSMISSION

C A L C U L A T E D T R A N S M I S S I O N

,/ C A L I E R A T I O R V O L T A G E : 4 2 K V V E R T I C A L S C A L E : O . 1 V / d i v . H O R I Z O N T A L S C A L E : I O O n s / d i v .

P I C N U N B E R : ~ 2 k '4 ' 5 '6 7 8

b / CHARGE V O L T A G E OF C O N D E N S A T O R B X N K : 8 0 K V V E R T I C A L S C A L E : G . I V / d i V .

H O R I Z O N T A L S C A L E : l O O n s / d i v

F i g u r e 3.