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FARADAY ROTATION APPLIED TO A REVERSE FIELD PINCH
D. Muir, P. Carolan
To cite this version:
D. Muir, P. Carolan. FARADAY ROTATION APPLIED TO A REVERSE FIELD PINCH. Journal
de Physique Colloques, 1979, 40 (C7), pp.C7-833-C7-834. �10.1051/jphyscol:19797402�. �jpa-00219402�
JOURNAL DE PHYSIQUE CoZZoqm C7, sqp2d&nt au n07, Tome 40, JuiZZet 2979, page
! C7- 833
FARADAY ROTATION APPLIED TO A REVERSE FIELD PINCH
D.G. ~ u i r * end P.G. Carolan.
CuZham Laboratory, Abingdon, Oxon, OX14 3DB, U K (EURATOM/UKAEA Fusion A s s o c i a t i o n ) .
INTRODUCTION when t h e F a r a d a y r o t a t i o n a n g l e e x c e e d s some
l o U .
T h e r e a r e now a v a r i e t y o f t e c h n i q u e s f o r meas- The r o t a t i o n a n g l e , $, i s d e s c r i b e d by t h e r e l a t i o n : u r i n g i n t e r n a l m a g n e t i c f i e l d s i n tokamaks, t h a t
have been s u c c e s s f u l l y d e v e l o p e d , e.g. l i g h t s c a t - t e r i n g , [' ] [ * ] Zeeman s p l i t t i n g [ 3 1 and F a r a d a y
The p o l o i d a l f i e l d . Bo. was t h e q u a n t i t y o f i n t e r e s t s i n c e i t s d i s t r i b u t i o n d e t e r - mines t h e plasma e q u i l i b r i u m and s t a b i l i t y p r o p e r t i e s
Cthe t o r o i d a l f i e l d d i s t r i b u t i o n , B Z ( r ) d i f f e r s only s l i g h t l y from t h a t produced e x t e r n a l l y ] . I n r e v - e r s e d f i e l d p i n c h plasmas, b o t h t h e B z [ r ) and B e ( r l f i e l d d i s t r i b u t i o n s a r e m a i n l y g e n e r a t e d i n t e r n a l l y and p l a y and e q u a l r o l e i n t h e plasma s t a b i l i t y . T h e r e f o r e , b o t h B and BZ a r e t h e q u a n t i t i e s of
e
i n t e r e s t .
The F a r a d a y r o t a t i o n method g i v e a c o n t i n u o u s i n t e g r a l measurement o f t h e i n t e r n a l p o l o i d a l mag- n e t i c f i e l d a l o n e when t h e beam i s i n t h e v e r t i c a l p l a n e , b u t o t h e r w i s e g i v e s a c o n t i n u o u s i n t e g r a l measurement of b o t h i n t e r n a l m a g n e t i c f i e l d s . The i n t e g r a l i s o v e r a s t r a i g h t p a t h and t h e measure- ment o f t h e Faraday r o t a t i o n a n g l e i s done by simple p o l a r i m e t r y e x t e r n a l ' t o t h e machine. I t i s proposed t o u s e t h e Faraday r o t a t i o n t e c h n i q u e , employing a n HCN/DCN l a s e r ( h = 337/190 pml t o m e a s u r e b o t h d i s - t r i b u t i o n s i n t h e HBTXIA plasma.
The HBTXIA machine i s a r e v e r s e d f i e l d p i n c h [RFP) u n d e r c o n s t r u c t i o n a t Culham. I t has a m a j o r r a d i u s o f 0.8m and minor r a d i u s o f 0.26m. The ex- p e c t e d plasma p a r a m e t e r s a r e : T a50-150eV: nea
20 - 3 .
1 . 5 x 1 0 ~ ~ - 4 x 1 0 m
.
c u r r e n t % 4;OkA: <B> a 0.5T.THE CHOICE OF WAVELENGTH AND SOURCE
The c h o i c e o f a s u i t a b l e w a v e l e n g t h f o r Faraday r o t a t i o n i s governed e s s e n t i a l l y by c o n s i d e r i n g what s o u n c e s a r e a v a i l a b l e , and whether t h i s s o u r c e h a s s u f f i c i e n t power f o r an a c c u r a t e measurement o f t h e F a r a d a y r o t a t i o n a n g l e o b t a i n e d a t t h e s o u r c e wave- l e n g t h . O t h e r i m p o r t a n t e f f e c t s which have t o be c o n s i d e r e d a r e r e f r a c t i o n , l o s s o f t r a n s m i t t e d power due t o t u r b u l e n c e [ 5 1 and d e g r a d a t i o n o f t h e beam p o l a r i s a t i o n due t o t h e p e r p e n d i c u l a r component o f magnect f i e l d
[ G I
[71We have found t h a t b e c a u s e of t h e low t o r o i d a l m a g n e t i c f i e l d i n RFP p l a s m a s , t h e d e p o l a r i s a t i o n e f f e c t i s n e g l i g i b l e . T h i s i s i n c o n t r a s t t o tokamak p l a s m a s where b e c a u s e o f t h e l a r g e t o r o i d a l f i e l d , t h e d e p o l a r i s a t i o n e f f e c t becomes i m p o r t a n t
where X i s t h e l a s e r wavelength: ne and B a r e t h e e l e c t r o n d e n s i t y and m a g n e t i c f i e l d r e s p e c t i v e l y ; and L i s t h e p a t h l e n g t h . T h i s r e l a t i o n i s n o t v a l i d when d e p o l a r i s a t i o n i s p r e s e n t .
I f t h e plasma c a n be c o n s i d e r e d t o be a h o r i - z o n t a l c y l i n d e r , o f r a d i u s a , w i t h c y l i n d r i c a l sym- m e t r y , t h e n f o r a beam of w a v e l e n g t h h p r o p a g a t i n g t h r o u g h t h e plasma w i t h an i m p a c t p a r a m e t e r , h, and a t an a n g l e ,
a,
from t h e v e r t i c a l p l a n e , t h e n t h e F a r a d a y r o t a t i o n a n g l e ,JI,
i s f o u n d t o be g i v e n by:= $, + JI, ( 1 1
where Bo and BZ a r e t h e p o l o i d a l and l o n g i t u d i n a l m a g n e t i c f i e l d s r e s p e c t i v e l y : A = 2.62 x 1 0 -13 r a d t e s l a -1 : and $e and $= a r e t h e r o t a t i o n a n g l e s due t o t h e i n d i v i d u a l m a g n e t i c f i e l d s Be and B r e s p e c - t i v e l y , and a r e g i v e n by t h e i n t e g r a l i n c o r p o r a t i n g t h e a p p r o p r i a t e m a g n e t i c f i e l d .
The F a r a d a y r o t a t i o n a n g l e , t h e r e f o r e s c a l e s a s h2, a s d o e s r e f r a c t i o n . Numerical c a l c u l a t i o n s o f t h e e x p e c t e d a n g l e o f r o t a t i o n , and r e f r a c t i v e dev- i a t i o n f o r v a r i o u s s o u r c e w a v e l e n g t h s a r e g i v e n i n T a b l e I . The a x i a l e l e c t r o n d e n s i t y used was 1 . 5 x 1020m-3 and t h e plasma c u r r e n t 40OkA. The r a t i o o f a x i a l t o c r i t i c a l e l e c t r o n d e n s i t y , n /nc, i s a measure o f t r a n s m i s s i o n o f t h e beam. A r a t i o g r e a t e r t h a n 0.2 c o u l d i n d i c a t e v e r y h i g h a t t e n u a t i o n due t o t u r b u l e n c e and a r a t i o l e s s t h a n 0.02 would be d e s i r a b l e L 5 ' . From T a b l e I t h e w a v e l e n g t h g i v i n g r i s e t o t h e l a r g e s t F a r a d a y r o t a t i o n a n g l e w i t h an ne/nc r a t i o o f l e s s t h a n 0.02 and w i t h a t o l e r a b l e beam d e f l e c t i o n i s 337um produced by a n HCN l a s e r . A t t h i s w a v e l e n g t h t h e r o t a t i o n e x p e c t e d i s t y p i c - a l l y 10' w i t h a beam d e v i a t i o n l e s s t h a n 5mm. The minimum m e a s u r a b l e a n g l e a t t h i s w a v e l e n g t h d e t e r - mined by d e t e c t o r and a m p l i f i e r n o i s e i s a b o u t 0.1' v e r i f i e d e x p e r i m e n t a l l y a t Fontenay-aux-Roses 143
.
- 3 A t a h i g h e r a x i a l e l e c t r o n d e n s i t y of 4 x lo2' m t h e DCN l a s e r w a v e l e n g t h o f 190pm would a l s o g i v e a
0 .
F a r a d a y r o t a t i o n a n g l e o f t y p i c a l l y 10 and a beam d e v i a t i o n l e s s t h a n 5mm. The s o u r c e p r o d u c i n g r a d -
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797402
i a t i o n a t t h e s e w a v e l e n g t h s a l s o has s u f f i c i e n t power f o r a m u l t i c h a n n e l Faraday r o t a t i o n d i a g n o s t i c . DATA INVERSION
From e q u a t i o n ( 1 ) t h e Faraday r o t a t i o n a n g l e ,
I), f o r a beam p r o p a g a t i n g a t an a n g l e , S?, f r o m t h e v e r t i c a l p l a n e , i s t h e sum o f two r o t a t i o n s . I)e and
I)=, a r i s i n g f r o m t h e two m a g n e t i c f i e l d s Be and BZ.
The p o l o i d a l f i e l d r o t a t i o n , I)e, c a n be measured a l o n e when Q=O. The t o r o i d a l f i e l d r o t a t i o n , I)=,
can a l s o be measured when S l # 0, b u t t h i s r e q u i r e s t h a t t h e a p p r o p r i a t e be known. here fore, f o r m e a s u r i n g t h e t w o r o t a t i o n a n g l e s , we must have two beams p r o p a g a t i n g t h r o u g h t h e plasma s i m u l t a n e o u g l y , a t t h e same i m p a c t parameter, and one beam h a v i n g Q=0. I t i s b y t h i s method t h a t t h e i n t e r n a l mag- n e t i c f i e l d s o f HBTXIA w i l l be measured. To o b t a i n t h e f i e l d p r o f i l e s t h e d i a g n o s t i c must be a m u l t i - c h a n n e l one. The p i t c h p r o f i l e c a n be d e t e r m i n e d w i t h o u t any knowledge o f t h e e l e c t r o n d e n s i t y , s i n c e by A b e l i n v e r s i o n o f I)e and I)=:
I ,(%)dh
AX^
t a n Q neBz =- , Jr dh
and f r o m t h e d e f i n i t i o n o f t h e p i t c h , P = rBZ/Be and t h e above e q u a t i o n s :
w h i c h does n o t i n v o l v e t h e e l e c t r o n d e n s i t y . The s a f e t y f a c t o r p r o f i l e i s a l s o g i v e n s i n c e q = P/R where R i s t h e plasma m a j o r r a d i u s .
CONCLUSIONS
We have c o n c l u d e d t h a t a Faraday r o t a t i o n d i a g n o s t i c u s i n g an HCN/DCN l a s e r i s a p r a c t i c a l d i a g n o s t i c method f o r m e a s u r i n g t h e i n t e r n a l mag- n e t i c f i e l d s o f a RFP and i n p a r t i c u l a r t h e HBTXIA plasma. W i t h t h e w a v e l e n g t h s a v a i l a b l e w i t h t h i s l a s e r system, 337ym o r 190ym, and t h e e x p e c t e d
r a n g e o f e l e c t r o n d e n s i t y (1.5 x
l o z 0
- 4 xl o z 0 ~ 3 ,
Faraday r o t a t i o n a n g l e s o f t y p i c a l l y 10' w i l l be.
observed w i t h n e g l i g i b l e r e f r a c t i o n , d e p o l a r i s a t i o n . o r l o s s o f t r a n s m i t t e d power.
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[3] McCORMICK K, KIRK
H,
OLIVAIN J: P r o c 8 t h E u r Conf on C o n t r o l l e d F u s i o n and Plasma P h y s i c s , Prague,1
[ I 9 7 7 1 140[ 4 ] KUNZ W: E q u i p e TFR, Nuc Fus,
18,
12 [ I 9 7 8 1 1729151
WORT 0 J H: Plasma Phys, (19661 79[6] CRAIG AD: Plasma Phys., (19761 777
[7]
SEGRE S E: Plasma Phys.,2
(19781 295TABLE I
SOURCE OF WAVELENGTHS, ROTATION AND DEFLECTION ANGLE FOR HBTXIA
a n g l e : a = maximum d e f l e c t i o n a n g l e .
* A t t a c h e d f r o m R o y a l H o l l o w a y C o l l e g e , U n i v e r s i t y o f London
SOURCE
REFERENCES
[ I ] FORREST M J, CAROLAN P G , PEACOCK N J : N a t u r e 271. 5647 (19783 718
-
n = 1.5 x 1 0 ~ ' m - ~ : I) = t y p i c a l F a r a d a y r o t a t i o n ne'nc
0.13 0.032 OL015 0.005 0.002 5 x 1 0 - ~ I mm
CH3F ,-.HCN
D CN M e t h a n o l CQ2
y-waite 496pm 337pm 190urn 118p 10.6pm
I)
88O 22O 1
oa
3O lo O.O1°
a
20°
5O 2O lo 0.3' 0. 002O
r
, '
