D E T E R M I N A T I O N O F E M I S S I O N S H A P E

Lc~ L I N E B Y T H E G R A D U A T E D

A B S O R P T I O N M E T H O D

V. V . S k i d a n , V . I . G l a d u s h c h a k , a n d E . Y a . S h r e i d e r

O F T H E

UDC 535.34

The dens i ty of hyd rogen a toms in a p l a s m a can be d e t e r m i n e d by the g radua ted abso rp t ion method. To use this one m u s t know the e m i s s i o n line shape. The p r e s e n t pape r d e s c r i b e s two methods for d e t e r - mining e m i s s i o n l ine shape .

In the vacuum s p e c t r a l r eg ion the defects of h i g h - r e s o l u t i o n i n s t rumen t s compe l s one to use ind i rec t me thods of de t e rmin ing e m i s s i o n l ine shape . One such method is tha t p r o p o s e d by Zemansk i i fo r sma l l opt ical th i ckness . It is based on m e a s u r e m e n t of the p a r a m e t e r c~ (the ra t io of the e m i s s i o n to abso rp t ion l ine widths) [1, 2]. This method is a l so used i m p r o p e r l y fo r l a rge opt ical th ickness [3, 4]. The p a r a m e t e r a is de t e rmined using r e f e r e n c e mix tu re s in an abso rp t ion tube [4]. However , a is not cons tant fo r l a rge opt ical t h i cknes se s .

We d e s c r i b e the l ine shape in t e r m s of a t w o - l a y e r model [5-7], s ince this model accounts for p l a s m a nonun i fo rmi ty and includes the p r e s e n c e of a cof ivers ion l aye r . We shal l show below that a t w o - l a y e r mode l al lows a de sc r ip t i on of exper imen ta l abso rp t ion c u r v e s . Table 1 shows values of the abso rp t ion (A), computed f r o m the t w o - l a y e r mode l using the fo rmula

. i l l - - e -k'~176 e -s [1 - - e -ko't``',,] &o A - o , (1)

. i [ l - - e - '~ e-~;c't'~ 0

T T~ ?I where k0l , k0/ , k0/ a r e the opt ical t h i c knes se s of the emis s ion , conver s ion , and abso rp t ion l a y e r s , r e - spee t ive ly (see Fig. 1); w = (2,;ln2/AUD)(U--u0); f (w)= e - w 2 - (2a/,/-rc) [1-- 2wF(co)]; F(w) is a funct ion de sc r ib ing the abso rp t i on l ine for a < 0.01 [2] ; a = (AUe/AVD) , / ln2 ; Au c and 2xu D a r e the d i spe r s ion and Doppler l ine widths, r e s p e c t i v e l y ; and u 0 is the l ine cen t e r f r equency .

Values of a a r e ehosen for the ca lcu la ted absorp t ion . It can be seen f r o m Table 1 that even fo r opt ical th ickness l e s s than 10, the quant i ty a changes m a r k e d l y when t h e r e is a conve r s ion l ayer , as the opt ical th ickness of the abso rp t i on l a y e r changes , and cannot uniquely d e s c r i b e the e m i s s i o n line shape.

I 1 "Zl l l ' . a,,, i h~il . -

Fig. 1. A r r a n g e m e n t of the emis-" s ion (1), c o n v e r s i o n (2), and ab - s o r p t i o n (3) l a y e r s in the e m i s s i o n (4) and abso rp t ion tubes .

The p a r a m e t e r s k~l ' and k~ l " , c o r r e s p o n d i n g to the two- l a y e r model , can be chosen f r o m abso rp t ion m e a s u r e m e n t for a l a r g e r ange of opt ical t h i ckness . Such m e a s u r e m e n t s were made for the I ~ l ine on a fac i l i ty d e s c r i b e d e a r l i e r [8]. Norma l hy - d r o g e n a toms , c r e a t e d by a h igh - f r equency d i s cha rge , a r e pumped out th rough an abso rp t ion cell . A d i s c h a r g e in a mix tu re of h y d r o g e n and he l ium at a p r e s s u r e of ~0.5 t o r t and c u r r e n t dens i ty of ~500 m A / c m 2 e n s u r e s comple te hyd rogen d i s soc ia t ion , and so the dens i ty of n o r m a l h y d r o g e n a toms in the cel l was known.

T r a n s l a t e d f r o m Zhurnal P r ik ladno i Spektroskopi i , Vol. 20, No. 4, pp. 588-591, Apr i l , 1974. Original a r t i c l e submi t t ed March 19, 1973.

�9 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.

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T A B L E 1. Abso rp t i on A and P a r a m e t e r ~ as a Func- t ion of Optical Th ickness of the C o n v e r s i o n and Ab- s o r p t i o n L a y e r s

ko!

0,25 1,00

10 100

k'O/'=lO a=0,0025 . , ; , ' = , ~

i1-�9 �9 ~- _~ A c~

0,102 I 2,0 0,377 1,55 0,872 1,40 0,983 1,25

0,078 ~9 0,456 ~4 0,892 2,0

A h i g h - f r e q u e n c y d i s c h a r g e (cu r ren t dens i ty 200 m A / c m 2) was made to o c c u r in the e m i s s i o n tube, conta in ing a m i x t u r e of h y d r o g e n a nd he l ium at a p r e s s u r e of ~1 t o r t . The r ad ia t ion was r e c o r d e d by an open- type pho tomul t ip l i e r , i n sens i t ive to l ong-wave rad ia t ion . Under t he se condi t ions the pho tomul t ip l i e r s igna l is d e t e r m i n e d in p r a c t i c e by the in tens i ty of the La l ine, s ince the s h o r t - w a v e e m i s s i o n is cut off by the l i th ium f luor ide window.

The r ad ia t ion f r o m the e m i s s i o n tube was modula ted and r e c o r d e d by m e a n s of a synch ronous d e t e c - to r . The r e l a t i v e m e a n squa re e r r o r of the abso rp t i on method did not exceed 3%~

F igu re 2�9 the expe r imen ta l va lues of a b s o r p t i o n for t h r e e d i f fe ren t e m i s s i o n l a y e r s . If one t r i e s to d e s c r i b e the e m i s s i o n l ine shape us ing the p a r a m e t e r a , c u r v e s a r e obtained analogous to those shown by b r o k e n l ines on Fig . 2. T h e s e can be b rough t to a g r e e with t h e expe r imen ta l c u r v e only within a v e r y n a r r o w r ange of values of k0l .

Conve r se ly , if one d e s c r i b e s the e m i s s i o n l ine shape by means of p a r a m e t e r s k'0l' and k~ l " , then with an a p p r o p r i a t e choice of t he se p a r a m e t e r s one can d e s c r i b e the comple t e se t of m e a s u r e d abso rp t ions , and this is c o n f i r m e d by the expe r imen ta l points fal l ing c lo se to the cont inuous c u r v e computed for each l a y e r with a p p r o p r i a t e va lues of k'0l' and k~' l" . Thus, the abso rp t ion m e a s u r e d fo r a l a r g e r ange of opti- cal t h i ckness can be used to d e t e r m i n e the e m i s s i o n line shape .

F o r the Lc~ l ine we s u c c e e d e d in applying ano the r me thod of de t e rmin ing the shape, based on Stark b roaden ing of the L a l ine. This me thod has been d e s c r i b e d e a r l i e r [9] and is analogous to the method of scann ing in a magne t i c f ield [10]. The a b s o r p t i o n cel l is p laced in an e l e c t r i c field whose s t r eng th can be va r i ed . One m e a s u r e s the ra t io of a b s o r p t i o n in the p r e s e n c e of the f ield to that with the f ield absent , AE /A E = 0. The cu rves of A E/A E = 0 as a funct ion of the field s t r eng th should have a m a x i m u m , due to the

A

/ / " - / J . z "

o m e,o ~ r,% t~

J,~ .~

4a

46

I,o

1,0 ~^ ~-,,

Fig. 2 Fig. 3

Fig. 2. Abso rp t i on as a funct ion of the l oga r i t hm of opt ica l t h i ckness of the abso rp t i on l aye r , k~l ' = 300 (I), 100 (II), 50 (HI); k~'l" = 5 (I), 7 (II), 2.5 (HI); ~ = 2 (1), 2.5 (2) and 5(3).

Fig. 3. A b s o r p t i o n as a funct ion of the potent ia l d i f f e rence be tween the p la tes k~l ' = 300 (I), 100 (II) and 50 (HI); k~ l" = 5 (1), 7 (II) and 2.5 (III).

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fact that the components of the absorption line displaced by the field coincide with the maxima of the self- conversion emiss ion line. Thus, the shape of the curves depends on the emission line shape.

(1), expanding 1-- e-k0/e-w2 in a se r i e s* and using the f i rs t two t e rms of the expansion

t e -1~~ [1 - - e -k~ ~ ci e-'o~2 do) Ae o ,=t

F rom Eq. we obtain

AE=O ~e -k~ [ 1 - e-kot'. H(~ e - `~ do~ o

(2)

3 2

, - - 0 ) - ~ , where ~ ci e-' 'i -- 1 b [fie -t- e -('~ e_(,,j_a~,,~-] ~=~ 2 [ ! ; b is a factor depending on the rat io of the geometr ic

dimensions of the cell to those of the plates generating the e lectr ic field; b -- 2 if all of the absorption cell is located in the electr ic field, and b > 2 if part of the cell is outside the field; Aw is the line shift due to the field. Equation (2) is applicable for low values of absorption. For large values of absorption the quantity A E / A E =o will depend on the optical thickness of the absorbing layer .

Figure 3 shows the values of AE/AE = 0 measured for different e lectr ic field strengths and for the same emiss ion layers as in Fig. 2. The absorption cell contained a plane capaci tor whose plates were covered with a thin Teflon layer to reduce recombination of hydrogen atoms. The flux of hydrogen atoms was created f rom dissociat ion of hydrogen molecules on an incandescent tungsten filament. The hydrogen atom density was controlled by changing the filament temperature~ Here we verified that the pa rame te r A E / A E = o was independent of the density of absorbing atoms, i. e~ that Eq. (2) is applicable.

A check was made that the emission line shapes chosen from the absorption curves corresponded to the experimental data shown in Fig. 3. The curves presented were calculated for the emission line shapes found above. For curves I and II the agreement can be considered sa t is factory. The descending par t of curve III shows noticeable discrepancies which a re apparently due to targe measurement e r r o r s for lines with weak se l f -convers ion. The relat ive mean square e r r o r of measurement was ~7%.

Thus, it has been shown that the same line shape descr ibes the dependence of absorption on optical thickness of the absorption layer and the dependence of absorption on the e lectr ic field strength.

It should be noted that the method of investigating emission line shape by means of an e lectr ic field is applicable only for lines whose width is comparable with the Stark broadening, while the method of in- vestigation using a re fe rence absorption layer is applicable for any resonance line.

In conclusion the authors thank Pro fesso r A. N. Zaidel for discussion of resul ts and A. V. Tarakanov, a student at LGU, for help in conducting the experiment.

L I T E R A T U R E C I T E D

1. S . E . Fr isch, Collection: Gas Discharge Plasma Spectroscopy [Russian translation], edited by S. E. Frisch, Nauka, Leningrad (1970), p. 7.

2. A. Mitchell and M. Zemanskii, Resonance Radiation and Excited Atoms [in Russian], ONTI, Mos- cow (1937).

3. J . K . Barker and J. M. Michael, J . Opt. Soc~ Am., 58, 1615 (1968). 4. A . L . Myerson and W. S. Watt, J . Chem. Phys. , 49, 425 (1968). 5. W. Bleeker, Z. Physik, 52, 808 (1929). 6. W. Braun and T. Carrington, J. Quant. Spectr. Rad. Trans . , 9, 1133 (1969). 7. N . G . Preobrazhenski i , Spectroscopy. of an Optically Thick Plasma [in Russian], Nauka, Novosi-

b i r sk (1971). 8. V . V . Skidan and E. Ya. Shreider, Opt. i Spektr., 27, 532 (1969); Opt. i Spektr. 28, 627 (1970). 9. J. Vanier, Appl. Opt., 6, 167 (1967).

10. M . N . McDermot and R. Novick, Phys. Rev., 131, 707 (1963).

*We consider the absorption line shape to be Doppler.

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