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THE SPECTROSCOPY OF TOKAMAKS
M. Klapisch
To cite this version:
M. Klapisch. THE SPECTROSCOPY OF TOKAMAKS. Journal de Physique Colloques, 1980, 41
(C3), pp.C3-187-C3-190. �10.1051/jphyscol:1980329�. �jpa-00219848�
JOURNAL DE PHYSIQUE
Colloque
C3,supplkment au n o
4,Tome
41,avril
1980,page
C3-187THE S?ECT!?OSCO?Y OF TOKAMAKS
Klapisch, r 4 .
Racah ~ n s t i t u t e of Physics,Hebrew U n i v e r s i t y , Jerusalem, I s r a e l
A b s t r a c t
-
The importance of l i n e s p e c t r a o f h i g h l y i o n i z e d heavy a t o m i n , Tokamak plasma i s r e c a l l e d . A s h o r t review i s given o f methods, mostly t h e o r e t i c a l , used f o r i d e n t i f y i n g l i n e s : ab i n i t i ocomputation of wavelengths and i n t e n s i t i e s . The c a s e of u n r e s o l v e d t r a n s i t i o n a r r a y s i s d e s c r i b e d . These methods a r e i l l u s t r a t e d by i d e n t i f i c a t i o n of forbidden l i n e s . The need f o r more d a t a on atomic c o e f f i c i e n t s i s underlined.
I . INTRODUCTION t h a t t h e important s p e c t r a l r e g i o n i s 500 8-10
8.
A review of t h e e x p e r i m e n t a l methods i n t h i s range The p r e s e n t g e n e r a t i o n of Tokamaks a r e
i s given by Breton ( 9 ) r a t h e r l a r g e machines, t o r u s e s w i t h s m a l l r a d i i
o f %15-50 cm and l a r g e r a d i i ~ 8 0 - 1 5 0 cm. m i c a 1 los
magnetic f i e l d s a r e *2-5T, and plasma c u r r e n t a r e T ~ I ~ V )
0.1-1 MA. The e l e c t r o n d e n s i t y ne l i e s between 10 3-1~14 cm- 3 , and e l e c t r o n temperature T between
IW: ~d
0.5-2 keV. The main f e a t u r e t h a t SLstinguishes Tokamak spectroscopy i s t h e very s t r o n g l i n e r a d i a t i o n o f h i g h l y i o n i z e d heavy i m p u r i t i e s .
Drawin ( 1 , 2 ) h a s shown very c l e a r l y t h e dramatlc 1W 13'
importance o f t h i s r a d i a t i o n f o r t h e energy balance. It can be deduced from f i g u r e 1 4 , r e f . ( 1 )
,
t h a t f o r n =1014 t h e powerr a d i a t e d by an i m p u r i t y (MO) d e n s i t y , o f 10 10'
1011 ~ m - ~ , (0.1%) i n 1 m3 i s 1 MW! For t h i s r e a s o n , i t i s v i t a l f o r t h e f u t u r e o f thermo- n u c l e a r r e s e a r c h t o i d e n t i Q t h e h e a ~ l y i m p u r i t i e s
appearing i n t h e s p e c t r a , a s w e l l a s t o measure
'
v x xv x x xxv Jl0i
t h e i r i o n i z a t i o n s t a g e s , t h e i r p r o p o r t i o n ,
t e m p e r a t u r e , s p a t i a l and temporal d i s t r i b u t i o n e t c . Fig.
-
range Oft r a n s i t i o n s o f Fe a s a f u n c t i o n of i o n i z a t i o n and T
.
I m p u r i t i e s a r e u s u a l l y c l a s s i f i e d as
" l i g h t " (O,C,N,c!Z) o r "heavy" ( ~ e , C r , N i , ~ o , w ) . S e v e r a l mechanism a r e r e s p o n s i b l e f o r t h e contamination o f t h e deuterium plasma by t h e s e i m p u r i t i e s from t h e w a l l s (3). The degree of i o n i z a t i o n may b e very high
-
e . g . MoXXXIII (41, WxXXV ( 5 , 6 ) . F i g u r e 1 shows approximately i n which s p e c t r a l range l i e t h e resonant t r a n s i t i o n sof t h e d i f f e r e n t i o n i z e d s p e c t r a of i r o n
(71.
S(Te) shows t h e mean i o n i z a t i o n s t a t e of Fe a s a f u n c t i o n o f Te (8). A s T d e c r e a s e s from t h e c e n t e r of t h e plasma t o t h e b o r d e r , s o does t h e i o n i z a t i o n s t a g e , and one s e e s u s u a l l y a super- p o s i t i o n of t h e s e i n t h e spectrum. It i s seen
11. METHODS FOR SPECTRAL LINES IDENTIFICATION
1 ) Experimental
-
The v a s t m a j o r i t y of t h e l i n e s recorded i n V.U.V. and s o f t X-rays were completely unknown a few y e a r s ago. I n o r d e r t o i d e n t i f y t o which element t h e y belong, and t o a c e r t a i n e x t e n t t o which i o n i z a t i o n s t a g e , Tokamak s p e c t r a can be compared w i t h s p e c t r a o b t a i n e d from h i g h power vacuum s p a r k(4) ,
o r l a s e r produced plasma ( 1 0 ) . However, t h e s e s p e c t r a themselves were n o t s t u d i e d p r e v i o u s l y , and one h a s t o r e l y on t h e o r e t i c a l e v a l u a t i o n s o f wavelengths,t r a n s i t i o n p r o b a b i l i t i e s , and l i n e i n t e n s i t i e s t o
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980329
C3-188
JOURNAL DE PHYSIQUE e s t a b l i s h t h e complete c h a r a c t e r i z a t i o n ofeach t r a n s i t i o n .
2 ) Ab-initio Wavelengths Computations
-
It can b e shown by t h e Z-expansion method ( 1 1 ) t h a t , f o r h i g h l y i o n i z e d atoms t h e r e l a t i v e con- t r i b u t i o n s of c o r r e l a t i o n energy decreases a s
z - ~ .
On t h e o t h e r hand, r e l a t i v i s t i c c o r r e c t i o n s behave as ( IXZ) (k2O). k Thus, a model l i k e t h e r e l a t i v i s -
t i c p a r a m e t r i c p o t e n t i a l CRELAC) (12,131
,
which t a k e s f u l l account o f r e l a t i v i s t i c e f f e c t s b y s o l v i n g Dirac e q u a t i o n s i n a c e n t r a l f i e l d , i n c l u d e s t h e B r e i t magnetic i n t e r a c t i o n s , c o n f i g u r a t i o n i n t e r a c t i o n s and Lamb s h i f t may achieve g r e a t accuracy i n p r e d i c t i n g wavelengths, s p e c i a l l y f o r An=l t r a n s i t i o n s . A c t u a l l y t h e discrepancy from measured wavelengths i s only%0.1% on An=l t r a n s i t i o n s , and ~ 1 % f o r An=O.
The same argument a p p l i e s t o t h e HXR method o f Cowan ( 1 4 ) which f e a t u r e s an approximative exchange p o t e n t i a l and f i r s t o r d e r r e l a t i v i s t i c c o r r e c t i o n s t o t h e r a d i a l wavefunctions. A
comparison of t h e r e s u l t s of t h e two methods can Be found i n r e f . ( 1 5 ) . Quite e x t e n s i v e computations were performed on atoms of Tokamak i n t e r e s t w i t h b o t h methods ( 1 6 , 1 7 ) .
3 ) T r a n s i t i o n Arrays
-
I n many o f t h e s e heavy i o n s , 3d, 4d o r 4f s h e l l s may be p a r t i a l l y open, and i n t h e An=l t r a n s i t i o n s , t h e spectrum shows "bands", each one i n c l u d i n g a g r e a t number o f unresolved l i n e s , and corresponding t o a given t r a n s i t i o n a r r a y i n a given i o n i z a t i o n s t a g e ( 4 , 1 0 ) o r i n a s u p e r p o s i t i o n of t h e s e ( 5 , 6 ) . For t h i s c a s e , a s t a t i s t i c a l model of wavelength d i s t r i b u t i o n weighted by o s c i l l a t o r s t r e n g t h i n t r a n s i t i o n a r r a y s has been developed ( 1 8 ~ 1 9 ) . I t allows a b - i n i t i o computations of mean wave- l e n g t h s and s p e c t r a l widths o f each a r r a y . F i g u r e 2 shows a comparison o f t h e s e computations w i t h a Mo spectrum o b t a i n e d from a high power vacuum spark ( 19 ).
4)
E n e r v Level P o p u l a t i o n and Line I n t e n s i t i e s-
Line i d e n t i f i c a t i o n i s impossible w i t h o u t e v a l u a t i o n of W e n s i t i e s a s f u n c t i o n s of ne and Te. This i s u s u a l l y performed i n two s t e p s . F i r s t , t h e r e l a t i v e abundance o f e a c h i o n i z a t i o n s t a t e i s computed. Owing t o t h e low n and h i g h Te, t h e corona e q u i l i b r i u m ( C E ) model can be w e d ( 2 0 ) . The r e s u l t s t h e n depend only on Te. This model was e x t e n s i v e l y used f o rFig. 2
-
Comparison o f t h e s t a t i s t i c a l model f o r t r a n s i t i o n a r r a y s ( r e f . (19) ) w i t h e x p e r i m e n t a l Mo spectrum.a l l atoms t h a t can b e found i n Tokamaks ( 8 ) . The second s t e p i s t o o b t a i n p o p u l a t i o n s of e x c i t e d l e v e l s i n each ion. CE means h e r e c o l l i s i o n a l e x c i t a t i o n s from ground s t a t e and r a d i a t i v e decay.
However, t h i s i s not always s u f f i c i e n t , e s p e c i a l l y i n t h e presence of m e t a s t a b l e s t a t e s . Then t h e c o l l i s i o n a l - r a d i a t i v e model must b e used (211.
Tt i n c l u d e s a l l c o l l i s i o n a l e x c i t a t i o n s and d e e x c i t a t i o n s , a s w e l l a s a l l p o s s i b l e r a d i a t i v e t r a n s i t i o n s between a l l energy l e v e l s . I o n i z a t i o n and recombination from and t o e x c i t e d s t a t e s may be a l s o i n c l u d e d ( 2 2 ) . Line i n t e n s i t y r a t i o s now may depend on ne a s w e l l a s on Te. I n a l l t h e s e e q u a t i o n s , very many r a t e c o e f f i c i e n t s f o r e x c i t a t i o n , i o n i z a t i o n , recombination e t c . , o f h i g h l y i o n i z e d atoms i n t e r v e n e . Although a c c u r a t e methods f o r t h e i r computation e x i s t (23,241 t h e s e a r e p r o h i b i t i v e l y t i m e consuming. Even t h e Coulomb-Born approximation, which s h o u l d g i v e good r e s u l t s (26) i s n o t of common use. Usually, e x t e n s i v e c a l c u l a t i o n s a r e made w i t h t h e h e l p of very simple a n a l y t i c a l approximations t o c r o s s s e c t i o n s ( 2 0 , 2 6 ) .
111. APPLICATION TO FORBIDDEN TRANSITIONS
1. I d e n t i f i c a t i o n
The above mentioned methods have been used t o i d e n t i e forbidden t r a n s i t i o n s i n TFR 'spectrum ( 2 7 , 2 8 ) . F i g u r e 3 shows t h e e x p e r i m e n t a l
C3-
189 s p e c t r u m between 48 and 608
and t h e o r e t i c a l M O ~ r e a s o n s , t o s t u d y l a r g e wavelen&hs. Thus, t h e r e t r a n s i t i o n s . The r e c o r d e d l i n e s t h a t a p p e a r i s g r e a t i n t e r e s t i n " f o r b i d d e n " M 1 l i n e s , which between 508
and 578
have s i n c e b e e n a t t r i b u t e d a r e t r a n s i t i o n s w i t h i n c o n f i g u r a t i o n s . The l i n e a l s o t o E2 t r a n s i t i o n s , i n MoXVI 3d9-3d8 4s ( 1 0 ) . FcXXCI 2p3 2 ~ 5 , 2 - 2 ~ a t 26658
h a s been u s e d3 / 2
s u c c e s s f u l l y f o r t h i s p u r p o s e (311, and s u c h l i n e s a r e s y s t e m a t i c a l l y b e i n g l o o k e d f o r ( 1 6 , 3 2 ) .
T F R Spectrum
F i g . 3
-
E2 t r a n s i t i o n s Pn TFR s p e c t r u m compared w i t h t h e o r e t i c a l r e s u l t s .The agreement w i t h e x p e r i m e n t a l i n t e n s i - t i e s may b e f o r t u i t i o u s , s i n c e l a r g e u s e was made o f s e m i - e m p i r i c a l f o r m u l a s f o r c r o s s s e c t i o n s , a l t h o u g h t h e E i n s t e i n c o e f f i c i e n t s o b t a i n e d by RELAC a r e q u i t e a c c u r a t e . However, i n t h i s c a s e , c a s c a d e s a r e r e s p o n s i b l e f o r 2 / 3 o f t h e E2 l i n e s i n t e n s i t y , and t h e r e i s p r o b a b l y a
s t a t i s t i c a l c a n c e l l a t i o n o f e r r o r s i n t h e t h o u s a n d s o f c o e f f i c i e n t s t h a t c o n n e c t t o g e t h e r t h e 144 e n e r g y l e v e l s i n c l u d e d i n t h e "atomic model". On f i g u r e 4, one s e e s t h e r a t i o o f M2 f o r b i d d e n t o r e s o n a n c e l i n e s 2p6-2p53s 3 ~ 1 / 2p6-2p53s 3F'2 i n t h e Ne i s o e l e c t r o n i c s e q u e n c e C r X I V , FeXVII, N i X I X ( 3 0 ) . Here t h e c a s c a d e s a r e l e s s i m p o r t a n t , t h e s p e c t r u m b e i n g much s i m p l e r . However, t o g e t h e r w i t h c o l l i s i o n a l d e e x c i t a t i o n t h e y a r e r e s p o n s i b l e f o r t h e s m a l l maximum o f t h e c u r v e s , which would n o t have been o b t a i n e d i n t h e CE model.
2. Use f o r Measurement o f T.
Measurements o f t h e i o n t e m p e r a t u r e Ti by Doppler b r o a d e n i n g does n o t s u f f e r from t h e drawbacks o f more c l a s s i c a l methods (29,301.
Moreover, t h e use o f l i n e s o f d i f f e r e n t d e g r e e s o f i o n i z a t i o n a l l o w s a r a d i a l p r o f i l e o f Ti t o b e d e t e r m i n e d ( 3 0 ) . I t i s d e s i r a b l e f o r e x p e r i m e n t a l
F i g . 4
-
T h e o r e t i c a l and rceasured i n t e n s i t y r a t i o f o r M2 t o E l t r a n s i t i o n s i n Ne i s o e l e c - t r o n i c s e q u e n c e . ( s e e t e x t1.
I n t h i s r e v i e w , we d e s c r i b e d v e r y b r - l e f l y some a s p e c t s o f Tokamaks p l a s m a s p e c t r o s c o p y . The c o n t r i b u t i o n o f t h e o r e t i c a l a t o m i c p h y s i c s was u n d e r l i n e d . I t s h o u l d b e s t r e s s e d t h a t t h e r e i s a g r e a t n e e d i n f u r t h e r developments i n t h i s f i e l d . R e l i a b l e c o e f f i c i e n t s f o r i o n i z a t i o n , r e c o m b i n a t i o n , e x c i t a t i o n , e t c . , would, f o r i n s t a n c e , e n a b l e a more d e t a i l e d a n a l y s i s o f i m p u r i t i e s f l u x from t h e w a l l s b y comparing a c t u a l s p a t i a l d i s t r i b u t i o n o f i o n i z a t i o n s t a t e s w i t h CE c o m p u t a t i o n s . T h i s i s j u s t one o f t h e many p o s s i b l e c o n t r i b u t i o n s o f a t o m i c s p e c t r o s c o p y t o t h e a c h i e v e n e n t o f e n e r g y p r o d u c t i o n by t h e r m o n u c l e a r r e a c t i o n s .
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