Density distribution in a magneto - plasma system

TÜRKÎYE ATOM ENERJİSİ KURUMU

ÇEKMECE NÜKLEER ARAŞTIRMA VE EĞİTİM MERKEZİ

Araştırma Raporu No: 236

DENSITY DISTRIBUTION IN A MAGNETO—PLASMA SYSTEM

Melih BOSTAN, Ergun GÜLTEKÎN Physics Department

November 1985

İ

TÜRKİYE ATOM ENERJİSİ KURUMU

ÇEKMECE NÜKLEER ARAŞTIRMA VE EĞİTİM MERKEZİ

Araştırma Raporu No: 236

DENSITY DISTRIBUTION IN A MAGNETO—PLASMA SYSTEM

Melih BOSTAN, Ergun GÜLTEKÎN Physics Department

Nowember 1985

C O N T E N T S Pages 1 . INTRODUCTION 1 2 . THEORY 1 3 . EXPERIMENTAL SET-UP 3 4 . MEASUREMENTS 5 5 . CONCLUSION 7 REFERENCES 9 T A B L E S T able 1 . A x ia l d e n s i ty and te m p e ra tu re g r a d ie n t a t th r e e d i f f e r e n t p r e s s u r e s f o r v a r io u s d is c h a rg e c u r r e n t s 5 F I G U R E S

F ig . 1 - Block diagram o f M agneto-plasma I system 4

F i g . 2 - M agneto-plasm a I system 5

F i g . 3 - A x ia l d e n s ity g r a d ie n t $ F i g . 4 - R a d ia l d e n s i ty p r o f i l e ₇

A B S T R A C T

DENSITY DISTRIBUTION IN A MAGNETO-PLASMA SYSTEM

l a a m a g n e to -p la s m a s y s te m , d e n s i t y d i s t r i b u t i o n a n d t e m p e r a t u r e h a v e b e e n m e a s u re d by m ean s o f tiro L an g m u ir p r o b e s w h ic h c a n be moved a x i a l l y a n d r a d i a l l y by a n e l e c t r i c m o to r . A p la sm a co lu m n o f 100 cm l e n g t h * i n a p y r e x c y l i n d e r o f 6 cm i n d i a m e t e r , h a s b e e n p ro d u c e d by i o n i z i n g t h e a r g o n g a s i n t h e magne to - p la s m a s y s te m . D is c h a r g e was m a i n t a i n e d b y a p p l y i n g 3.5 kV , 15 mA a t m ax. r a n g e ■* ' a w a te r - c o o le d h o l l o w c a t h o d e . P la sm a co lu m n w as c o n f i n e d by m eans o f a m a g n e tic f i e l d o f 1 0 0 0 G a u s s . Ö Z E T

BÎR MAGNETO-PLAZMA SÎSTEMÎNDE YOĞUNLUK DAĞILIMININ İNCELENMESÎ Bu ç a l ış m a d a b i r m agneto - p la z m a s i s t e m i n d e y o ğ u n lu k d a ğ ı l ı m ı v e s ı c a k l ı k , m o to r la r a d y a l v e b o y la m s a l o l a r a k h a r e k e t e d e b i l e n i k i L an g m u ir s o n d a s ı y a r d ı m ı y l a i n c e l e n m i ş t i r . Plazm a k o l o n u , u z u n lu ğ u 100 cm, ç a p ı 6 cm o l a n cam b i r s i l i n d i r i ç e r s i n d e , a rg o n g a z ı n ı n iy o n iz a s y o n u i l e e l d e e d i l m i ş t i r . D e ş a r j , su s o ğ u t m a l ı i ç i oyuk k a to d a maksimum 3 . 5 kV, 15 mA u y g u l a n a r a k s a ğ l a n m ı ş t ı r . î y o n i z e o l a n t a n e c i k l e r , maksimum 1000 G a u s s * lu k m a g n e ti k a l a n y a r d ı m ı y l a s ı k ı ş t ı r ı l a r a k p lazm a k o lo n u o l u ş t u r u l m u ş t u r .

1 INTRODUCTION

A f t e r t h e L angm uir and h i s o o w o rk e rs p io n e e r in g w ork, th e p ro b e ■ e th o d a s one o f t h e B o at p o w e rfu l m eans o f p la s n a d i a g n o s t i c s h a s

b e e n u s e d w i d e ly . I n t h e b e g in n in g o f 1960*8 th e e x p e r im e n ta l te c h n iq u e s a n d t h e t h e o r y o f p r o b e s have b e en r e f i n e d by many w o r k e r s .

A tte m p ts h a v e b e en made t o e x te n d th e p ro b e m ethod t o p a ra m e te r r a n g e s f o r w h ich L a n g m u ir's t h e o r y f a l l s . I n t h i s c o n n e c tio n p lasm a s a t h i g h e r g a s p r e s s u r e s and p la s m a s u n d e r th e i n f l u e n c e o f s t r o n g m ag n etic f i e l d s a r e t o be m en tio n e d a s t h e m ost im p o r ta n t e x te n s i o n , *>f c l a s s i c a l p ro b e t h e o r y ( 1 * 2 ) . Compared t o many o t h e r d i a g n o s t i c t o o l s t h e p ro b e i s

d i s t i n g u i s h e d by t h e p o s s i b i l i t y o f d i r e c t l o c a l m easurem ent o f plasm a p a r a m e t e r s . T h is a d v a n ta g e o f p ro b es* however* i s c l o s e l y c o n n e c te d t o o t h e r m ain s h o r tc o m in g s . The l o c a l m easurem ent r e q u i r e s t h e p ro b e t o be i n s e r t e d i n t o th e p lasm a b e in g i n v e s t i g a t e d by means o f a p ro b e h o ld e r w hose s u r f a c e a r e a i n m ost c a s e s i s many tim e s l a r g e r th a n th e p ro b e i t s e l f • The p ro b e sy s te m fo rm s a " w a ll" i n a d d i t i o n to th e a l r e a d y e x i s t i n g plasm a b o u n d a r ie s and a t l e a s t i n i t s c l o s e p r o x im ity th e

p la sm a p a r a m e te r s may d e v i a t e s e r i o u s l y fro m t h e s e i n th e a b se n c e o f th e p r o b e . I n s p i t e o f t h i s Langm uir p ro b e i s th e m o rt im p o r ta n t d i a g n o s t i c t o o l f o r th e l o c a l m e a su re m e n ts. FOr i n s t a n c e * i n f u s i o n r e a c t o r s su c h l o c a l d e n s i t y and te m p e r a tu r e m easu rem en ts have g r e a t im p o rta n c e and th e i n t e r a c t i o n s b etw een t h e plasm a and th e c o n t a i n e r w a ll a r e i n v e s t i g a t e d by th e Langm uir p ro b e m ethod ( 3 ) .

I n t h i s work* t h e d e n s i t y d i s t r i b u t i o n and th e te m p e r a tu re o f a m a g n e tiz e d plasm a sy ste m (M agneto-plasm a 1 ) were m easured by means o f tw o r a d i a l l y and a x i a l l y m ovable Langm uir p r o b e s .

2 . THEORY

An o u t l i n e o f th e e s s e n t i a l s o f th e L angm uir probe m ethod a s commonly u s e d plasm a d i a g n o s t i c method i s b r i e f l y g iv e n a s f o l l o w s .

When a p o t e n t i a l d i f f e r e n c e i s a p p l i e d betw een two e l e c t r o d e s im m ersed i n a p a r t i a l l y i o n i s e d b u t m a c r o s c o p ic a lly ne a t u r a1 gas* th e p o s i t i v e i o n s w i l l be a t t r a c t e d to w a rd s th e n e g a t iv e e l e c t r o d e and

current i s o b t a i n e d . This phenomenon i s the well-known current-voltage c h a r a c t e r i s t i c o f t h e p r o b e . Such a c h a r a c t e r i s t i c c a n b e u s e d t o d e te r m i n e t h e p la sm a p a r a m e t e r s p r o v i d i n g t h a t t h e c e r t a i n c o n d i t i o n s a r e s a t i s f a i d ( 4 ) . I n t h i s e x p e r i m e n t , a c y l i n d r i c a l t u n g s t e n w i r e i s u s e d a s t h e p ro b e an d t h e c i r c u i t i s c o m p le te d t h r o u g h o n e o f t h e d i s c h a r g e e l e c t r o d e s . When no p o t e n t i a l d i f f e r e n c e e x i s t s b e tw e e n t h e p r o b e a n d p la s m a , t h e c a r r i e r c u r r e n t r e a c h i n g t h e p r o b e i s e q u a l t o t h e ra n d o m c u r r e n t d e n s i t y m u l t i p l i e d by t h e p r o b e ' s s u r f a c e a r e a

I = A p

I

4

ik±

K

q

(1)

Where N , c a n d q a r e t h e c a r r i e r d e n s i t y , mean s p e e d an d c c h a r g e r e s p e c t i v e l y . K i s a m u l t i p l i c a t i o n f a c t o r w h ic h d e p e n d s on t h e p r o b e g e o m e tr y . I f t h e p o l a r i t y o f t h e p r o b e t o p la s m a p o t e n t i a l i s s u c h t h a t c a r r i e r s a r e a t t r a c t e d , t h e p ro b e c u r r e n t i s g r e a t e r t h a n t h a t g i v e n b y B q . I . As a r e s u l t o f t h e a p p l i e d p r o b e t o p lasm a p o t e n t i a l , a s p a c e c h a r g e s h e a t h w h ic h c o n s i s t s o f c h a r g e c a r r i e r s o f o p p o s i t e s i g n t o t h e p ro b e p o t e n t i a l i s fo rm e d a ro u n d t h e p r o b e . O u t s i d e o f t h i s s h e a t h r e g i o n t h e c o n c e n t r a t i o n s o f c h a r g e c a r r i e r s a r e a ssu m e d t o b e e q u a l a n d t h e u n d i s t u r b e d p la sm a i s n e a t u a l* The t h i c k n e s s o f t h i s s h e a t h d e p e n d s on t h e t e m p e r a t u r e o f p la s m a p a r t i c l e s (m ean k i n e t i c e n e r g i e s o f c h a r g e c a r r i e r s ) . The e l e c t r o n c o n c e n t r a t i o n H a t s h e a t h b o u n d a ry i s g i v e n b y ; C

N = N exp

_{e - \ k T e !} W here N__ i s t h e e l e c t r o n c o n c e n t r a t i o n i n t h e u n d i s t u r b e d oo d i s c h a r g e , Vp i s t h e p o t e n t i a l d r o p b e tw e e n t h e s h e e t i e d g e a n d t h é u n d i s t u r b e d p la s m a . E l e c t r o n c o n c e n t r a t i o n w i t h i n t h e s h e a t h r e g i o n v a r i e s w i t h t h e v a l u e a n d t h e s i g n o f t h i s p o t e n t i a l d r o p . And t h i s c o n c e n t r a t i o n i s p r o p o r t i o n a l w i t h t h e e l e c t r o n c u r r e n t r e a c h i n g t o t h e p r o b e . T h is c u r r e n t i s g i v e n b y ; W here I0 i s t h e e l e c t r o n c u r r e n t r e a c h i n g t h e p ro b e when t h e 2

-l a t t e r -l a a t p -lasm a p o t e n t i a -l (Vp» 0 ) . The plasm a t o p ro b e p o t e n t i a l i s d e f i n e d b y ;

V =: V ♦ V*«-

_{va V}

(4)

a s

Where ¥ a i s th e a p p li e d p o t e n t i a l and VAg i s th e a n o d e - s h e a th p o t e n t i a l . I t c a n be w r i t t e n a s V 0-VAjg. When th e a p p lie d p o t e n t i a l V i s a d j u s t e d su c h t h a t t h e r e i s no p o t e n t i a l d ro p betw een th e p ro b e a n d d i s c h a r g e (V p= 0), th e e l e c t r o n c u r r e n t I Q i s d e te rm in e d a s th e s a t u r a t i o n c u r r e n t . T h is i s g iv e n by;

^ V N- Ce e A P = N^ Ap (7 Iffü )

'*>

Where Ap i s th e s u r f a c e a r e a o f th e probe* c e i s th e mean th e r m a l sp e e d o f a n e l e c t r o n i n th e d is c h a r g e and T i s th e e l e c t r o n 8 t e m p e r a t u r e . I n o r d e r t o g e t a u s e f u l l e q u a tio n f o r e l e c t r o n c u r r e n t i n te r m s o f a p p l i e d p o t e n t i a l V * u s i n g th e e q .4 * i t c a n be w r i t t e n a s ;

I = I exp fe C V ^ ) 1

* P [ kTe J ( 6 ) T h is e x p o n e n t ia l e q u a tio n i n d i c a t e s t h a t th e g ra p h o f l n l 8 v e r s u s Va i s l i n e a r * h a v in g a s lo p e (e /k T g ) .

lnIe=ln Io*1^fr(v-VAs)

(7)

By u s i n g t h i s graph* th e e l e c t r o n te m p e ra tu re * T and e l e c t r o n e s a t u r a t i o n c u r r e n t c a n be d e te r m in e d . S u b s t i t u t i n g th e v a lu e o f e l e c t r o n s a t u r a t i o n c u r r e n t i n t o th e e q .5 , th e plasm a e l e c t r o n d e n s ity * N c a n eo be f o u n d . 3 . EXPERIMENTAL SET-UP

The e x p e rim e n t was p e rfo rm e d a t th e M agneto-plasm a I sy ste m . A rgon p lasm a was p ro d u ced i n a p y re x c y l i n d r i c a l tu b e 160 cm i n l e n g t h and 6 cm i n d ia m e te r by u s in g a h o llo w -c a th o d e ( 5 ) . The w a te r-c o o le d h o llo w c a th o d e i s a s t a i n l e s s s t e e l c y l i n d e r h a v in g a n i n n e r r a d i u s , r ^ - 3 , 5 mm o u t e r r a d i u s r 0* 1 3 ,5 mm and a l e n g t h o f 120 mm. The d is c h a r g e v o l t a g e and d i s c h a r g e c u r r e n t a r e 3 .5 kV,15 mA r e s p e c t i v e l y a t m a x .ra n g e .

P la sm a co lu m n I s o b t a i n e d by c o n f i n i n g t h e p la s m a p a r t i c l e s by m ean s o f a m a g n e tic f i e l d , o f 1 0 0 0 G a u ss a t m ax. v a l u e . The i n i t i a l p r e s s u r e o f t h e s y s te m i s 10~*^ t o r r . The e x p e r i m e n t a l s e t - u p i s s c h e m a t i c a l l y show n i n F i g . l . The r a d i a l p r o b e h a s b e e n s e t i n a d i s t a n c e o f 6 cm fro m t h e p la sm a s o u r c e an d i t c a n be moved w i t h i n a l e n g t h o f 1 cm r a d i a l l y .

iqf

3İİV Cothode Anode Magnetic Field O I A1 cods

m m

Vacuum Signal 6 enerator

© *

- a - J^ Ry :3H3 36V _ © RECORDER N S w itc h F i g . l . B lo c k d ia g r a m o f t h e H a g n e to -P le s m a I s y s te m

W ith t h i s p r o b e , m e a s u re m e n ts w ere t a k e n f o r e a c h 2 mm. The a x i a l p r o b e w h ic h i s m ounted on a n i s o l a t e d c a r r i a g e c a n b e moved w i t h i n a d i s t a n c e o f 2 0 cm . A x i a l m e a s u re m e n ts w i t h t h i s p r o b e w e re o b t a i n e d a t i n t e r v a l s o f 2 cm . The p r o b e w as b i a s e d a t -3 6 V , f l o a t i n g p o t e n t i a l a n d t h e n a s a w to o th v o l t a g e p u l s e , Vp p c68 V o l t s , w as s u p e rim p o s e d o n t h i s f l o a t i n g p o t e n t i a l . The p r o b e c u r r e n t a s a p o t e n t i a l d r o p a c r o s s t h e l o a d w as p l o t t e d by m ean s o f a 2 -Y r e c o r d e r . H e n c e , t h e c u r r e n t - v o l t a g e c u r v e w h ic h i s c a l l e d t h e p r o b e c h a r a c t e r i s t i c w as o b t a i n e d . By c o n v e y in g t h i s c u r v e o n a s e m i l o g a r i t m i c g r a p h a n d u s i n g t h e s im p le p to b e t h e o r y a s d e s c r i b e d a b o v e , t h e e l e c t r o n t e m p e r a t u r e , T a n d d e n s i t y c a n b e o b t a i n e d . £ G e n e r a l v ie w o f M a g n e to -p la s m a X s y s te m i s shown i n P i g . 2 . 4

-4 . MEASUREMENTS

The a x ia l probe measurements a t th re e d i f f e r e n t p re s s u re s f o r a c o n s ta n t d isc h a rg e c u r r e n t , 1^=6 mA, s r e shown i n P ig .3 . The m easure­ m ents were tak en w ith 2 cm i n t e r v a l s , from 6 cm to 26 cm away from th e plasma so u rc e. At th e same d isc h arg e c u r r e n t , The measurements tak e n by th e r a d i a l probe w ith in a d is ta n c e of 10 mm a t i n t e r v a l s of 1 mm f o r th r e e d i f f e r e n t p re s s u re s a re shown i n P i g .4 . In a d d itio n , a x ia l d e n s ity and tem p eratu re g r a d ie n ts f o r v a rio u s d isc h a rg e c u r r e n ts a t th re e

d i f f e r e n t p re s s u re s a re giv en by th e Table 1. Dis ch ar ge c u r r e n t I d m A A n / A X (x io10) A T / A X ( e V / c m ) 4 x 1 0 2 T o r r 6 x 1 0 2 T o r r 8 x 1 0 2 T o r r 4 x 1 0 2 T o r r 6 x 1 0 2 T o r r 8x 102 T t r r 1 0 . 0 0 9 9 - — 0 . 0 2 6 8 - -2 0 . 0 0 7 3 0 . 0 1 7 4 - 0. 0283 0 . 0 4 3 3 -4 a 0 0 6 5 0 . 0 1 2 6 0 . 0 5 1 6 0. 0 2 3 8 0 . 0 4 0 8 h 0 4 7 3 6 0. 0056 0 . 0 0 8 4 0 . 0 1 2 6 0 . 02 0 9 0 . 0 3 3 2 0 . 0 3 8 4 e 0. 0048 0 . 0 0 6 9 0 . 0 112 0 . 0 2 0 1 0 . 0 3 9 0 0 . 0 3 8 0 10 - 0 . 0 0 6 2 0 . 0 098 - 0 . 0317 0. 0 3 9 2 12 - 0 0 051 0 0061 - 0 . 030 5 0.0361 14 - “ Û 0 0 4 7 - - 0. 0 3 5 6

Table 1. A xial d e n s ity and tem p eratu re g ra d ie n t a t th r e e d i f f e r e n t p re s s u re s f o r v a rio u s d isc h a rg e c u r r e n ts

-The e l e c t r o n te m p e ra tu re computed from th e s lo p e o f İ n i -V g ra p h 6 fi

l i e s , a c c o rd in g t o th e d is c h a r g e c u r r e n t , betw een 1 .0 eV and 2 .5 eV. U sin g th e e l e c t r o n s a t u r a t i o n c u r r e n t e q u a tio n ( e q .5) , e l e c t r o n d e n s i t y c a n be computed by; N = - ^ l £2. _ J _

<?A„ C.

(8) Where I s ta n d s f o r th e e l e c t r o n s a t u r a t i o n c u r r e n t o b ta in e d by 80 «10 g r a p h i c a l m ethod*e=4.8032x10 s ta tc o u lo m b , e l e c t r o n charge*A p *0 *02199 cm p ro b e a r e a and c e =(8kTe/n»e ) th e mean v e l o c i t y . The mean v e l o c i t y c a n he s t a t e d i n te rm s o f te m p e ra tu re (°K ) by t a k in g k«=1.3807xl0-16 ->rg/°K, me * 9 .1 0 9 5 x l0“28 g r .

- 6 1/2

Ce =06212x10 [Te(K)]

cm/sn.

(9)

A n u m e ric a l e q u a tio n f o r th e e l e c t r o n d e n s i t y can be w r i t t e n b y ;

Neo= 18.288x10* leo (A)/Tt ( V )

cm

(10)

10

The computed e l e c t r o n d e n s i ty l i e s betw een 1 .0 x 1 0 cm and 1 . 5x l 010 cm"3 .

-5 . CONCLUSION

As shown i n F ig .3 a x i a l d e n s ity g r a d ie n t i s a p p ro x im ate ly l i n e a r so t h a t th e slo p e c o rre sp o n d in g to each p r e s s u r e i s d i f f e r e n t . D e v ia tio n from th e l i n e a r i t y a t h ig h p r e s s u r e s a r i s e s from th e p resen ce o f th e more n e a t u r e l p a r t i c l e s . As i t can be seen from th e t a b l e 1 , when h ig h

d is c h a r g e c u r r e n t s a re o b ta in e d by i n c r e a s in g th e d is c h a rg e v o lta g e a t h ig h p r e s s u r e s , th e slo p e g r a d u a lly d e c re a s e s and th e r a t e o f d e v ia tio n from l i n e a r i t y a ls o d e c r e a s e s . I t can be s t a te d t h a t th e r e i s a d is c h a rg e c u r r e n t v a lu e which g iv e s smooth d e n s ity d i s t r i b u t i c ; f o r each of th e s e t h r e e p r e s s u r e s . R a d ia l d e n s ity p r o f i l e s f o r th r e e d i f f e r e n t p r e s s u r e s a r e g iv e n i n P i g .4 . These d e n s ity p r o f i l e s f i t i n w ith th e sta te m e n t w hich i s g iv e n , t h e o r e t i c a l l y f o r a lo w -tem p era tu re c y l i n d r i c a l plasm a colum n i n a u n ifo rm m agnetic f i e l d , by

n (r)=n0exp(-r2/r02)

(11)

Where n i s th e c e n t r a l d e n s ity ; r . r a re th e plasma column_{•A O}

-r a d i u s and th e -r a d i a l p-robe p o s i t io n -r e s p e c tiv e ly * In F i g .4 , th e f a s t d e c re a s e o f r a d i a l d e n s ity a t h ig h p r e s s u r e s f o r th e same d is c h a rg e c u r r e n t» 1^=6 mA, can be seen* T his i s due to th e same re a so n to t h a t o f a x i a l d e n s i ty d i s t r i b u t i o n s t a te d above» i . e . th e f r e q u e n t c o l l i s i o n s betw een ch arg ed and n e a t u r a l p a r t i c l e s . For e ach p r e s s u r e , th e r e i s a d is c h a r g e c u r r e n t g iv in g a d e n s ity p r o f i l e which f i t s i n w ith t h e o r e t i c a l e x p o n e n tia l c u rv e . As shown i n Table 1, te m p e ra tu re g r a d ie n t i s c o m p e ra ti- v e ly h ig h where th e g r e a t e r a x i a l d e n s ity v a r i a t i o n o c c u rs . T h is i s due

t o en erg y l o s s o f ch arg ed p a r t i c l e s th ro u g h th e c o l l i s i o n s w ith n e a t u r a l p a r t i c l e s .

C o n seq u en tly , i t i s w e ll u n d e rsto o d t h a t a plasma c o l h av in g sm ooth d e n s ity and te m p e ra tu re g r a d ie n ts can be o b ta in e d by u se o f

-2 -2

M agneto-plasm a I system w ith in th e p re s s u re ra n g e o f 4x10 -8x10 t o r r and a t d is c h a rg e c u r r e n t s from 4 mA to 12 mA.

REFERENCES

( 1 ) B e r t o t t i , B. (1 9 6 2 ) P hys. F lu id s 8f 1010. ( 2 ) N o b a ta, K. (1 9 6 3 ) J a p a n . J .A p p l.P h y s . 2 , 719.

( 3 ) Manos, D ., M cCracken, 6. (1984) NATO Advanced Study I n s t i t u t e , P h y s ic s o f p la s m a -w a ll I n t e r a c t i o n s i n C o n tr o lle d F u sio n

Q uebec, C anada.

( 4 ) S w if t, J . D . , Schw ar, M .J.R . (1970) E l e c t r i c a l P robes f o r Plasm a D i a g n o s t ic s , I l i f f e Books L td .

( 5 ) O ü lte k in , E . (1 9 7 7 ) TÜBÎTAK V I. S c ien c e C o n g re ss, A p p lied S c ie n c e S e c tio n .