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UBC Theses and Dissertations

Spectroscopic studies of dense plasmas Nelson, Robert Howard 1967

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SPECTROSCOPIC STUDIES OP DENSE PLASMAS BY ROBERT HOWARD NELSON B.Sc, University of B r i t i s h Columbia, 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THE DEPARTMENT OP PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OP BRITISH COLUMBIA APRIL, 1967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y o f B r i t i s h C o l u m b i a Vancouver 8, Canada ABSTRACT Spectroscopic measurements vrere made on a l o n g - l i v e d Ar-gon plasma to determine the e l e c t r o n temperature and density and to examine the v a l i d i t y of the thermal e q u i l i b r i u m r e l a -t i o n s used. The derived r e s u l t s when compared w i t h Griem's e q u i l i b r i u m c r i t e r i a i n d i c a t e that a complete thermal e q u i l i -brium was not e s t a b l i s h e d . i i T A B L E OF C O N T E N T S P a g e A B S T R A C T i i L I S T OF F I G U R E S i v ACKNOWLEDGEMENTS . . v C H A P T E R I - - I n t r o d u c t i o n 1 C H A P T E R I I - - T h e o r y 6 C H A P T E R I I I - - A p p a r a t u s 11 1) D i s c h a r g e C i r c u i t 11 2) P l a s m a V e s s e l 13 3) S p e c t r o s c o p i c I n s t r u m e n t s 13 E l e c t r o n i c s 15 5) C o m p a r a t o r 15 C H A P T E R I V - - R e s u l t s 17 1) S p e c t r a l A n a l y s i s 17 2) M e a s u r e m e n t s w i t h M o n o c h r o m a t o r a n d P h o t o m u l t i p l i e r 18 3) M e a s u r e m e n t o f t h e I n s t r u m e n t B r o a d e n i n g F u n c t i o n 19 ]+) D e t e r m i n a t i o n o f H ^ C P r o f i l e 25 5) M e a s u r e m e n t o f R e l a t i v e I n t e n s i t i e s . . . . 27 6) C a l c u l a t i o n o f P l a s m a P a r a m e t e r s 30 C H A P T E R V - - D i s c u s s i o n o f R e s u l t s 36 C H A P T E R V I - - C o n c l u s i o n 38 A P P E N D I X I — C o m p u t a t i o n o f W a v e l e n g t h s f r o m a P l a t e l+O A P P E N D I X I I — F o r w a r d D i f f e r e n c e I n t e r p o l a t i o n F o r m u l a I4.2 B I B L I O G R A P H Y Kk-i i i LIST OP FIGURES Figure Page 1 Discharge C i r c u i t 12 2 Plasma Vessel lk 3 Optical Arrangement 18 i| Possible Instrument P r o f i l e s 20 5 Experimental Arrangement for Measuring Instrument P r o f i l e s 22 6 Measured Instrument P r o f i l e s 23 7 Ho^ P r o f i l e 26 LIST OP TABLES Table Page 1 Argon lines measured 29 2 Computed Parameters 35 i v ACKNOWLEDGEMENTS I w i s h t o thank my s u p e r v i s o r , Dr. A. J . B a r n a r d , f o r h i s k i n d h e l p and s u p p o r t t h r o u g h o u t t h i s work. Thanks are due a l s o t o the t e c h n i c a l s t a f f of the plasma p h y s i c s group f o r t h e i r h e l p i n the c o n s t r u c t i o n and mainten-ance of the apparatus and t o Mr. John Lees and Mr. E r n i e W i l -l i a m s f o r t h e i r h e l p w i t h the g l a s s b l o w i n g . The f i n a n c i a l a s s i s t a n c e of an NRC s t u d e n t s h i p i s g r a t e -f u l l y acknowledged. v I INTRODUCTION I n the f i e l d of plasma p h y s i c s c o n s i d e r a b l e s t u d y has gone i n t o the problem of d i a g n o s t i c s . D i a g n o s t i c s are i m p o r t a n t i n the s t u d y of atomic p r o c e s s e s such as the S t a r k b r o a d e n i n g or s h i f t i n g of s p e c t r a l l i n e s i n a plasma, where one needs t o know the e l e c t r o n temperature and number d e n s i t y as w e l l as the den-s i t y of the v a r i o u s i o n s p r e s e n t . S p e c t r o s c o p i c o b s e r v a t i o n s are w e l l s u i t e d f o r the d e t e r -m i n a t i o n of plasma parameters s i n c e the measurement does not p e r t u r b the plasma. However, i t i s i n g e n e r a l d i f f i c u l t t o i n -t e r p r e t t h e s e o b s e r v a t i o n s s i n c e the p o p u l a t i o n s of the e x c i t e d s t a t e s (and hence the i n t e n s i t i e s of the e m i t t e d l i n e s ) are governed by a l a r g e number of p r o c e s s e s whose r a t e s are not ac-c u r a t e l y known. One u s e f u l c o n d i t i o n i s t h a t of a l o c a l t h e r m a l e q u i l i b r i -urn ( L T E ) . F o r dense plasmas (Ne ^ 10 cm--5) of moderate tem-p e r a t u r e (kT ^ 5 eV) the e l e c t r o n r e l a x a t i o n times are s u f -f i c i e n t l y s m a l l ( o f the o r d e r of 10~^r^usec) so t h a t the v e l o c -i t y d i s t r i b u t i o n of f r e e e l e c t r o n s i s almost always M a x w e l l i a n even f o r t r a n s i e n t and/or s p a t i a l l y inhomogeneous c a s e s . The f r e e e l e c t r o n s can then be d e s c r i b e d by a k i n e t i c t e m p e r a t u r e . Then i f the d i s t r i b u t i o n s over the v a r i o u s bound s t a t e s and i o n i z a t i o n s t a g e s and the v e l o c i t y d i s t r i b u t i o n s of atoms and i o n s are i n a thermodynamic e q u i l i b r i u m of the same t e m p e r a t u r e , 1 2 and i f m a c r o s c o p i c a l l y the plasma i s of u n i f o r m mass d e n s i t y and c h e m i c a l c o m p o s i t i o n one d e s c r i b e s the system as b e i n g i n a s t a t e of complete l o c a l t h e r m a l e q u i l i b r i u m . Such systems can be d e s c r i b e d by a s m a l l number of parameters w h i c h are r e -l a t e d by the e q u a t i o n s of e q u i l i b r i u m s t a t i s t i c a l mechanics (see Chapter I I ) . These parameters can then be determined by a s m a l l number of measurements. Whether or not the v a r i o u s bound s t a t e s and i o n i z a t i o n s t a g e s are i n t h e r m a l e q u i l i b r i u m i s m a i n l y dependent on the f r e e e l e c t r o n d e n s i t y as w e l l as on the e l e c t r o n temperature and v a r i o u s c o l l i s i o n c r o s s s e c t i o n s and t r a n s i t i o n p r o b a b i l i -t i e s . Now the p o p u l a t i o n of a g i v e n bound s t a t e i s d e s c r i b e d by v a r i o u s r a t e e q u a t i o n s i n v o l v i n g the e x c i t a t i o n and i o n i z a -t i o n by e l e c t r o n c o l l i s i o n s and r a d i a t i v e p r o c e s s e s and the de-e x c i t a t i o n and r e c o m b i n a t i o n by c o l l i s i o n , r a d i a t i v e and spon-taneous p r o c e s s e s . I n o r d e r f o r the p o p u l a t i o n of the s t a t e t o be d e s c r i b e d by e q u i l i b r i u m r e l a t i o n s , c o l l i s i o n a l p r o c e s s e s must dominate a l l o t h e r p r o c e s s e s f o r the . p o p u l a t i o n and de-636 p o p u l a t i o n of t h a t s t a t e . Griem d e r i v e s e q u a t i o n s t o e s -t i m a t e the r a d i a t i v e and c o l l i s i o n a l decay r a t e s for- v a r i o u s l e v e l s i n orde r t o determine whether or not t h i s c o n d i t i o n i s met. I n t h i s experiment the g o a l has been t o o b t a i n an LTE plasma f o r which parameters such as e l e c t r o n temperature and d e n s i t y can be r e a d i l y d e t e r m i n e d . Chapter I I p r e s e n t s , f o r 3 reference well known equilibrium equations r e l a t i n g plasma parameters with the experimental quantities measured. Chapter III describes the discharge c i r c u i t , the plasma vessel, which was of a novel construction, as well as associat-ed electronic and spectroscopic equipment used i n the experi-ment. The c i r c u i t was constructed to produce a slow o s c i l l a -tory discharge with a period of 500-1000 .^sec. and a peak current of Jkk. Other workers^N have constructed devices producing a constant current for periods of 100 ^{sec or more in attempts to produce reasonably steady conditions in the plasma. It was hoped, however, that the simpler o s c i l l a t o r y c i r c u i t would have a period long enough so that for a short i n t e r v a l near the current maximum the current would be f a i r l y constant and conditions in the plasma, f a i r l y steady. If the i n i t i a l pressure of the gas were high enough, a l o c a l thermal equilibrium could be expected. Chapter IV describes the various spectroscopic measure-ments taken and their analysis. I n i t i a l l y spectral plates were taken with a spectrograph in order to i d e n t i f y the lines present. Later, observations were made with a monochromator and photomultiplier to measure the r e l a t i v e i n t e n s i t i e s of sev-era l argon lines and the p r o f i l e of the H a l i n e . The instrument p r o f i l e of the monochromator-photomultiplier combination was also determined. Values for the electron density, electron k t e m p e r a t u r e and the i o n d e n s i t i e s were computed from the d i f -f e r e n t s e t s of r e a d i n g s . Chapter V p r e s e n t s a d i s c u s s i o n of the r e s u l t s o b t a i n e d and an e x a m i n a t i o n of e q u i l i b r i u m c r i t e r i a . On the b a s i s of e q u a t i o n s d e r i v e d by G r i e m ^ G i t was concluded t h a t o n l y f o r the upper i o n i c l e v e l s ( p r i n c i p a l quantum number, "Y\ ^  3 f o r A r I I , r\~2k f o r A r l l l and f o r A r - I V ) were LTE r e l a t i o n s v a l i d . F o r most of the A r i l and A r l l l l i n e s s t u d i e d the c o r -r e s p o n d i n g upper l e v e l s s a t i s f i e d t h i s c r i t e r i o n . However, the f a c t t h a t the p o p u l a t i o n s of the l o w e r (TV = 1 , 2 ) l e v e l s were not determined m a i n l y by c o l l i s i o n a l p r o c e s s e s i n v a l i d a t e d the use of Saha's e q u a t i o n i n d e t e r m i n i n g the r e l a -t i v e p o p u l a t i o n s of the v a r i o u s i o n s . F u r t h e r m o r e , at the ap-p a r e n t e l e c t r o n t e m p e r a t u r e , kT = 2.\\<~jz-l Saha's e q u a t i o n p r e -d i c t s t h a t o n l y 0,1% of the hydrogen would e x i s t i n the un-i o n i z e d s t a t e . Hence most of the H<* l i n e r a d i a t i o n , used i n the' d e t e r m i n a t i o n of e l e c t r o n d e n s i t y , must have come from the o u t e r ( c o o l e r ) r e g i o n s of the plasma which need not have the same e l e c t r o n d e n s i t y as the r e g i o n s at the core under s t u d y . The p r e c e d i n g and o t h e r c o n s i d e r a t i o n s i n d i c a t e t h a t f u r -t h e r work i s n e c e s s a r y t o o b t a i n a plasma i n p a r t i a l t h e r m a l e q u i l i b r i u m . A h i g h e r e l e c t r o n d e n s i t y can be a c h i e v e d t h r o u g h h i g h e r i n i t i a l p r e s s u r e s ; however, i t i s d o u b t f u l t h a t the e l e c -t r o n d e n s i t y w i l l be such t h a t c o l l i s i o n a l p r o c e s s e s w i l l dom-i n a t e ground s t a t e l e v e l s , t h e r e b y j u s t i f y i n g the use of Saha's e q u a t i o n i n d e t e r m i n i n g r e l a t i v e i o n p o p u l a t i o n s . I I THEORY In t h i s c h a p t e r th e b a s i c e q u a t i o n s used i n t h e d e t e r m i n a -t i o n o f t h e e l e c t r o n t e m p e r a t u r e , t h e e l e c t r o n and i o n d e n s i t i e s w i l l be b r i e f l y r e v i e w e d . The e l e c t r o n t e m p e r a t u r e i s e x p r e s s e d as a weak f u n c t i o n o f t h e e l e c t r o n d e n s i t y and t h e r e l a t i v e i n -t e n s i t i e s o f two a r g o n s p e c t r a l l i n e s w h i l e t h e e l e c t r o n den-s i t y i s f o u n d as a f u n c t i o n o f t h e H a l i n e p r o f i l e . Some o f t h e e q u a t i o n s g i v e n depend s t r o n g l y on t h e a s s u m p t i o n o f t h e r m a l e q u i l i b r i u m . I f one c o n s i d e r s a p a r -t i c u l a r l i n e e m i t t e d by t h e v-N . i ^ k s t a g e i o n s (where i- 1 i s p r o p o r t i o n a l t o t h e n e t c h a r g e c a r r i e d by t h e i o n ) t h e n i t s r e l a t i v e i n t e n s i t y J i w i l l be g i v e n by J i = N'J A I hV i (1) where N"£ = number d e n s i t y o f i s t a g e i o n s e x c i t e d t o t h e u p p e r l e v e l f o r t h i s p a r t i c u l a r l i n e o n l y ( v a r -i o u s s u b s c r i p t s t o i d e n t i f y t h e l e v e l have been o m i t t e d ) 6 7 A^ = t r a n s i t i o n p r o b a b i l i t y per unit time that a t r a n s i t i o n w i l l occur to the lower l e v e l for this p a r t i c u l a r l i n e Vl = frequency of the l i n e = c/p^i for X i the wave-length h = Planck's constant Usually one does not know However, i f a l l i t n stage levels are in quilibrium with the free electrons then N£ i s given by N£ = N , £i(Te) exp (2) where g£ = s t a t i s t i c a l weight of upper l e v e l corresponding to the p a r t i c u l a r l i n e Ej_ = energy of the upper l e v e l measured i n v o l t s , (lowest energy state of the . i ^ n stage ions i s zero) Nj_ = number density of a l l i ^ * 1 stage ions kT e = thermal energy of the free electrons (elec-tron volts) +• h 2.j_(Tg) = p a r t i t i o n function for the i stage ions 2 i ( T e ) = S i ( ^ ) e x P ( ^ E i ( ^ / k T J (3) where the summation i s over the various levels- of the i ^ n stage ion* The summation i s truncated at some l e v e l s when 8 Ej_(s) exceeds the lowered i o n i z a t i o n p o t e n t i a l . (See Chapter IV f o r the computation of the p a r t i t i o n f u n c t i o n s . ) The t r a n s i t i o n p r o b a b i l i t y i s more conveniently expressed by where Sj_ i s the l i n e s t r e n g t h f o r t h i s p a r t i c u l a r t r a n s i t i o n . The l i n e strength f o r various t r a n s i t i o n s are tabulated Condon and S h o r t l e y and Griem Then, s u b s t i t u t i n g equations ( 2 ) , (li) i n t o (1) gives J i o< N l S i exp T-Ei/kT J ( 6 ) Now i f one considers a d i f f e r e n t l i n e emitted by the ( i + l ) s ^ ions then i t s r e l a t i v e i n t e n s i t y w i l l be given by N. S, J'i+1 1 + 1 • • • exp f-E i + 1 /kT ( (7) assuming the energy l e v e l s of the i + l s t stage ions are a l s o i n thermal e q u i l i b r i u m . (The subscripted v a r i a b l e s have a corres-ponding meaning to the v a r i a b l e s i n equation ( 6 ) . ) Taking the r a t i o of i n t e n s i t i e s , one f i n d s J i + i = ^ i + i H i fi+i / jg j j J i Z i + i N i ' s i WJ ( 8 ) ll. exp ~{E1+1-Eim)/\xTi 9 N Again assuming e q u i l i b r i u m , Saha's equation, 3 / 2 i+1 Zl+1 i Z i N e mQ kT e e 2 7 T K exp p IiA TeJ (9) t h can be a p p l i e d . Here I i = i o n i z a t i o n p o t e n t i a l of the i " " stage ions ( v o l t s ) mg = mass of the e l e c t r o n N. = number de n s i t y of free e l e c t r o n s A = h/27T Then '1+1 2 m e k T e 271^ 3 / 2 S / t • b i + l / X i \ exp s i U + i (10) -(Ii+El+l-Ej.) / kT, Taking logarithms and s o l v i n g f o r kT e ( I D kT e - ( I i + E i + 1 - E i } / 2 ' 3 ° 3 21.79 + l o g 1 0 " l Si+1 J i N e S± J 1 + 1 ( M _ w " i 1 0 8 1 0 kTe where k.Te, I i , E i , E i + i are i n e l e c t r o n v o l t s , N e i s i n cm -3 The e l e c t r o n d e n s i t y N e can be found from the broadening of the E-Qi, l i n e . According to the theory developed by Griem^G" the e f f e c t i v e d e n s i t y i s given by N e f f = C ( N e f f V ' U N X ^ ( ° m " 3 ) ( 1 2 ) 10 where (13) N p f,~ = N + 2 3 / / % 0 + 3 3 / / 2N 0^ + =SH i 3 / / 2 N . ( c m - 3 ) e i J - J- ^ 3 i+ 1 x N i = number d e n s i t y of n e u t r a l p a r t i c l e s N 2 = number d e n s i t y o f s i n g l y c h a r g e d i o n s A?S>= h a l f w i d t h o f t h e B<* p r o f i l e G ; ( N e f f , T e ) i s a weak f u n c t i o n o f N e f f and T @ and i s t a b -u l a t e d by G r e i m 6 1 + G . The c o n d i t i o n o f c o n s e r v a t i o n o f c h a r g e i s t h e n a p p l i e d . N e = N 2 + 2 N 3 + 3 N ^ + w Then i f one c o n s i d e r s o n l y t h e f i r s t , s e c o n d and t h i r d s t a g e i o n s one has t h e 6 unknowns k T e , N e f f , N e , N 2 , N3, N]^ c o n t a i n e d i n t h e 6 e q u a t i o n s ( 1 1 ) , ( 1 2 ) , ( 1 3 ) , (111) and (9) ( a p p l i e d t w i c e ) . F o r e a c h a d d i t i o n a l i o n d e n s i t y N i c o n s i d e r e d one has Saha's e q u a t i o n (7) f o r t h i s i o n . Hence t h e e q u a t i o n s m e n t i o n e d a r e a c l o s e d s y s t e m and t h e unknowns c a n be s o l v e d f o r u s i n g an i t e r a t i v e p r o c e s s . I l l APPARATUS T h i s c h a p t e r p r e s e n t s a d e s c r i p t i o n of the apparatus b u i l t f o r t h i s e x p e r i m e n t , i n c l u d i n g the d i s c h a r g e c i r c u i t and the plasma v e s s e l . The more s t a n d a r d e l e c t r o n i c and s p e c t r o s c o p i c i n s t r u m e n t s w i t h the e x c e p t i o n of the a u t o m a t i c comparator are not d e s c r i b e d i n d e t a i l . D i s c h a r g e C i r c u i t The d i s c h a r g e c i r c u i t (see F i g . 1) c o n s i s t e d of a c a p a c i -t o r bank (22l|^qF), an i n d u c t o r ( L ^ ^ H ) and an a i r s p a r k gap s w i t c h S]_.placed i n s e r i e s w i t h the d i s c h a r g e t u b e . A second s w i t c h S2, p l a c e d i n p a r a l l e l w i t h the c a p a c i t o r bank was used t o s h o r t out the o s c i l l a t o r y d i s c h a r g e a f t e r one h a l f c y c l e ( 250 4^ sec ). Each s w i t c h c o n s i s t e d of two h e m i s p h e r i c a l b r a s s e l e c t r o d e s one i n c h i n d i a m e t e r e n c l o s e d i n a b r a s s can. The e l e c t r o d e at ground p o t e n t i a l had been d r i l l e d out t o r e c e i v e a t u n g s t e n t r i g g e r p i n surrounded w i t h i n s u l a t i o n of b a k e l i t e and epcxy r e s i n . E l e c t r o d e s p a c i n g f o r a w o r k i n g range of 2.5 - V was 1/8" f o r S x and l / l 6 " f o r S 2 . To t r i g g e r s w i t c h S-j_ a f a s t ( l O n s e c r i s e t i m e ) , h i g h v o l t -6CT age (H;kV) p u l s e g e n e r a t e d ' b y a t h e o p h a n i s c i r c u i t was ap-p l i e d between the e l e c t r o d e and the t r i g g e r p i n . A s m a l l e r s i g n a l from the t h e o p h a n i s c i r c u i t was d e l a y e d 250 ju.sec and f e d i n t o a second t h e o p h a n i s c i r c u i t w h i c h then t r i g g e r e d S2. 11 TO SPECTROGRAPH OR MONOCHROMATOR 12 OlSCHARGE TUBE s, : c BANK n MANUAL \ TRIGGER TO VACUUM SYSTEM H.V. A PULSE THEOPHANIS TRIGGERING CIRCUIT D E L A Y UNIT THEOPHANIS TRIGGERING CIRCUIT H.V. PULSE F i g . 1 - - D i s c h a r g e C i r c u i t 13 The i n d u c t o r c o n s i s t e d of 2I4. t u r n s of -|" copper t u b i n g , 7 i n c h e s i n d i a m e t e r , wound and clamped on a frame of •§•" l u c i t e . A f t e r s e v e r a l thousand f i r i n g s no damage t o the i n d u c t o r was a p p a r e n t . Plasma V e s s e l The d i s c h a r g e tube (see P i g . 2) was made from t w o - i n c h " ;Kimax" ( p y r e x ) t u b i n g p u l l e d out t o a diameter of 3/V' (O.D.) i n the c e n t r e p o r t i o n and f i t t e d w i t h s t a n d a r d t a p e r e d ends. The c o n s t r i c t e d r e g i o n was about irg-" i n l e n g t h . The a luminium e l e c t r o d e s were s e a l e d t o the tube w i t h neopreme "0" r i n g s and s t a n d a r d f i t t i n g s . An aluminium v i e w i n g tube w i t h a q u a r t z window was a t t a c h e d t o the p o s i t i v e e l e c t r o d e ; e x t e n d i n g the window reduced s c a r r i n g t o a minimum. In a normal shot the bank: was charged t o a v o l t a g e of 3^V and the tube was f i l l e d w i t h argon t o 0.3 t o r r . The maximum c u r r e n t a c h i e v e d was then 7^A» The c u r r e n t was monitored by o b s e r v a t i o n of the i n t e g r a t e d s i g n a l from a s m a l l p i c k u p c o i l p l a c e d i n the i n d u c t o r . S p e c t r o s c o p i c I n s t r u m e n t s I n i t i a l l y the d i s c h a r g e was examined w i t h a H i l g e r E742 g l a s s s p e c t r o g r a p h ( r e c i p r i c a l d i s p e r s i o n : lj.-10 S/mm). When most of the s p e c t r a l l i n e s i n the v i s i b l e r e g i o n had been i d e n -t i f i e d the d i s c h a r g e was examined w i t h a J a r r e l l Ash (type 82-010) g r a t i n g monochromator w i t h an RCA IP-28 p h o t o m u l t i p l i e r Ik m a P i g . 2 - -Plasma Vessel QUARTZ WINDOW ALUMINUM TUBE O-RING ALUMINUM ELECTRODE PYREX TUBE ALUMINUM ELECTRODE SCALE •  HALF- SIZE 15 a t the e x i t s l i t . The monochromator had a r e c i p r o c a l d i s p e r -s i o n of 16 S/mm and was s u p p l i e d w i t h f i x e d s l i t s of 10, 25 and 50 m i c r o n s . A l l o b s e r v a t i o n s were made a l o n g the a x i s of the d i s c h a r g e t u b e . E l e c t r o n i c s A T e k t r o n i x 551 d u a l t r a c e o s c i l l o s c i p e was used to observe the s i g n a l s from the p i c k u p c o i l and the p h o t o m u l t i p l i e r . How-ever owing t o the l e n g t h of the ( c o a x i a l ) c a b l e f rom t h e photo-m u l t i p l i e r , i n d u c t i v e n o i s e from the bank d i s c h a r g e was l a r g e (~*10 v o l t s ) . To reduce the n o i s e an e x t r a (dummy) c a b l e was used w i t h a d i f f e r e n t i a l ( t y p e G-) p r e a m p l i f i e r t o s u b t r a c t o f f the n o i s e s i g n a l . The n o i s e was thus reduced t o about 0.5 v o l t s peak t o peak. The p r e s s u r e was measured w i t h an Edwards P i r a n i gauge w h i c h was l a t e r checked w i t h a MacLeod gauge. Comparator The s p e c t r o s c o p i c p l a t e s were read u s i n g a Grant L i n e M e a s u r i n g Comparator. T h i s i n s t r u m e n t , w h i c h measures the p o s i -t i o n of l i n e s on a p l a t e t o an a c c u r a c y of a mi c r o n , u t i l i s e s : a p r e c i s e measuring engine w i t h substage i l l u m i n a t i o n and ground g l a s s v i e w i n g s c r e e n ; a s c a n n i n g system c o n s i s t i n g of a r o t a t -i n g p r i s m , a s e r i e s of a d j u s t a b l e prisms and thr e e p h o t o m u l t i -p l i e r s ; and a p r o c e s s i n g u n i t c o n s i s t i n g of a d u a l beam o s c i l -l o s c o p e , a d i g i t a l v o l t m e t e r and an IBM keypunch machine.!-16 I n the s c a n n i n g system the l i n e p r o f i l e r e c o r d i n g photo-m u l t i p l i e r sees l i g h t t h a t has passed t h r o u g h the p l a t e , the r o t a t i n g p r i s m and v a r i o u s s l i t s . The s i g n a l , which r e p r e s e n t s a sweep a c r o s s a l i n e on the p l a t e , i s then a m p l i f i e d and ap-p l i e d t o b o t h beams of the c o n t r a - s w e e p i n g d u a l beam o s c i l l o s -cope. To c e n t r e on a l i n e , i t i s o n l y n e c e s s a r y t o move the comparator s t a g e so t h a t the two l i n e p r o f i l e s on the s c r e e n c o i n c i d e d . ( I f the l i n e i s a s y m m e t r i c a l one a l i g n s j u s t the peaks o f the l i n e s . ) The t r a n s m i s s i o n r e c o r d i n g p h o t o - m u l t i p l i e r , w h i c h has i t s own s e t of s l i t s , sees l i g h t w h i c h has passed t h r o u g h a s m a l l f i x e d r e g i o n i n the c e n t r e of the f i e l d o f view. The t h i r d p h o t o m u l t i p l i e r i s used t o s y n c h r o n i z e the o s c i l l o s c o p e sweep w i t h the r o t a t i n g p r i s m . The comparator was equipped w i t h a d e v i c e w h i c h , when a b u t t o n was p r e s s e d , caused the keypunch machine t o punch out on an IBM c a r d the p o s i t i o n of the c a r r i a g e ( s i x f i g u r e s ) and the t r a n s m i s s i o n of the p l a t e at t h a t p o i n t ( t h r e e f i g u r e s ) . IV RESULTS S p e c t r a l A n a l y s i s Time i n t e g r a t e d s p e c t r a were t a k e n u s i n g Kodak I F p l a t e s and an i r o n a r c f o r the r e f e r e n c e spectrum. A Hartmann d i a -phragm was used t o p l a c e the unknown spectrum i n the c e n t r e band w i t h the i r o n a r c spectrum a d j a c e n t t o i t . I n the a n a l y -s i s of the p l a t e w i t h the a u t o m a t i c comparator, the comparator r e a d i n g of e v e r y l i n e i n the unknown spectrum t o g e t h e r w i t h t h o s e of s i x t y known i r o n l i n e s ( f o r a range of 3 0 0 0 A.U.) were the n punched out on IBM c a r d s . Then u s i n g a F o r t r a n IV p r o -gram (see Appendix 1) the wavelengths of a l l the unknown l i n e s were computed and p r i n t e d o u t . The computed wavelengths were compared w i t h the m u l t i p l e t ^ 9 M t a b l e s ' ' and c e r t a i n l i n e s were r e a d i l y i d e n t i f i e d . Most of the l i s t e d A r i l and A r l l l l i n e s p l u s the H<<and Ep l i n e s were p r e s e n t . I m p u r i t y l i n e s observed were those of C I I and C I I I p l u s most of t h e l i s t e d l i n e s of O i l , O I I I , S i l l , S i l l l and S i l V . On the f i r s t p l a t e the computed wavelengths of the i d e n t i -f i e d l i n e s were c l o s e t o the l i s t e d v a l u e s ( w i t h i n 0 . 1 A . ) ; how-ever a l l the l i n e s appeared t o be s h i f t e d t o the r e d . T h i s s h i f t i n g was o r i g i n a l l y a t t r i b u t e d t o some plasma p r o c e s s ; how-ever on a second p l a t e i n a d i f f e r e n t r e g i o n the i d e n t i f i e d l i n e s appeared t o be s h i f t e d i n the o t h e r d i r e c t i o n by a s i m i l a r 1 7 18 amount. The a p p a r e n t s h i f t i n g must a r i s e i n some o t h e r p r o c e s s , e i t h e r i n a l i g n i n g t h e s t a n d a r d i r o n a r c o r i n r e a d i n g t h e p l a t e on t h e c o m p a r a t o r . ( E r r o r s may a r i s e i n r e a d i n g t h e s t a n d a r d i r o n l i n e s and t h e a r g o n s p e c t r u m i n s u c c e s s i v e sweeps.) Once t h e m a j o r i t y o f l i n e s had been i d e n t i f i e d i t was t h e n p o s s i b l e t o s e l e c t s e v e r a l a r g o n I I and I I l i n e s f o r f u r t h e r s t u d y w i t h t h e t i m e r e s o l v i n g monochromator and p h o t o m u l t i p l i e r . P r e l i m i n a r y s t u d i e s were made w i t h A r i l 3868 and A r l l l 3858. Measurements w i t h Monochromator and P h o t o m u l t i p l i e r The o p t i c a l a r r a n g e m e n t i s shown i n P i g . 3 ( p l a n v i e w ) . P i g . 3 O p t i c a l A r r a n g e m e n t 19 The s t a n d h o l d i n g the monochromator was s e c u r e l y a t t a c h e d and braced t o the main frame. The h o r i z o n t a l o p t i c a l a l i g n m e n t was made w i t h m i r r o r M]_ whi c h was f r e e t o r o t a t e on a v e r t i c a l a x i s and t o move a l o n g the a x i s of the tub e . I n P i g . 3 ?1 a n d i S 2 . a r e f i x e d (removeable) s l i t s , M 2 and M3 are curved ( c y l i n d r i c a l ) m i r r o r s , G i s the g r a t i n g and P i s a red f i l t e r ( f o r s c a n n i n g the H o t l i n e o n l y ) . The red. f i l t e r was n e c e s s a r y at the h i g h e r wavelengths t o p r e v e n t l i n e s of lower w a v e l e n g t h from the s e c -ond o r d e r spectrum from r e a c h i n g the e x i t s l i t S 2 . C e r t a i n p r e c a u t i o n s were t a k e n i n measuring the r e l a t i v e i n t e n s i t y of p a i r s of l i n e s . Large day t o day v a r i a t i o n s (~|?0^ ) vrere n o t i c e d i n the p h o t o m u l t i p l i e r s i g n a l s so t h a t i n t e n s i t i e s t o be compared were measured as c l o s e t o g e t h e r as p o s s i b l e . S i n c e the response curve of the m o n o c h r o m a t o r - p h o t o m u l t i p l i e r c o m b i n a t i o n had not been p l o t t e d , a l l l i n e s t o be compared l a y c l o s e t o g e t h e r ( s e p a r a t e d by 80 angstroms or l e s s ) . Care was ta k e n t o ensure t h a t the p h o t o m u l t i p l i e r measured the e n t i r e i n t e n s i t y of the l i n e , t h a t ' t h e e n t i r e l i n e f e l l w i t h i n the e x i t s l i t S g . B e f o r e the i n t e n s i t y of a l i n e was measured a rough p r o f i l e was found by s c a n n i n g a c r o s s the l i n e u s i n g the narro w e s t (10//) s l i t s . Measurement of the Instrum e n t Broadening F u n c t i o n For two reasons i t was n e c e s s a r y t o measure the i n s t r u m e n t b r o a d e n i n g f u n c t i o n f o r v a r i o u s s l i t w i d t h s . I n the f i r s t p l a c e i t was n e c e s s a r y t o check t h a t the p h o t o m u l t i p l i e r d e t e c t e d the 2 0 e n t i r e l i n e i . e . t h a t the measured i n t e n s i t y would be g i v e n by o f t h e l i n e . S e c o n d l y , i t was not known q u a n t i t a t i v e l y how t h e f i n i t e s c a n n i n g w i d t h o f t h e monochromator would a f f e c t t h e measured p r o f i l e of t h e H<=>c l i n e . I n t h e f i r s t c a s e one would want a l a r g e s c a n n i n g w i d t h and i n t h e se c o n d c a s e , a s m a l l s c a n n i n g w i d t h . The i n s t r u m e n t b r o a d e n i n g f u n c t i o n c a n be d e f i n e d as t h e t r a n s m i s s i o n c u r v e H ( f )') f o r w a v e l e n g t h s d i f f e r i n g by a s m a l l amount jf f r o m t h e c e n t r a l w a v e l e n g t h p\0 . T h i s f u n c t i o n i s d e -p e n d e n t on the v a r i o u s s l i t s u sed and on t h e f i x e d g e o m e t r y o f t h e i n s t r u m e n t and i s a weak f u n c t i o n o f t h e c e n t r a l wave-"a where 1 ( A ) i s t h e d i s t r i b u t i o n o f i n t e n s i t y l e n g t h A c M(5) F(X) 5. k HCS) c F i g . i+ 21 The i n s t r u m e n t b r o a d e n i n g f u n c t i o n H ( ^ ) and the a c t u a l l i n e p r o f i l e F(^\)'' might be as shown i n P i g . I c, a c o n s t a n t f o r ( ? ) ^ T, > where H( $ }• = < e [ 0 f o r | f | > \ x I f the c e n t r a l w avelength i s "^\0 t h e n the i n t e n s i t y meas< ured i s the c o n v o l u t i o n i n t e g r a l oo (1) I ( ^ \ o ) = I H ( t ) P ( A o + f ) df — « = < » F o r measuring i n t e n s i t i e s one would l i k e the w i d t h 2 f o f t h e f l a t r e g i o n of H( ~f ) t o be g r e a t e r t h a n " ^ 1 * Then i f the monochromator i s p r o p e r l y c e n t r e d on the l i n e ( i .e . P\ Q = ^ ) one has ' «s' * * * * , e <• I ( X J- = / C. F ( * + f ) d f c. y F( A> d A w h i c h i s the t o t a l i n t e n s i t y of the l i n e . F o r measuring l i n e p r o f i l e s one would l i k e t h e s c a n n i n g w i d t h 2f , t o be s m a l l compared w i t h t h e l i n e w i d t h . Then K ? \ © ) ^ r 1 c. F ( ? V , + ? ) d f - r , 2 J] • C P ( A o ) ( I n r e a l i t y the measured p r o f i l e I ( ^ \ a ) would be broader t h a n the a c t u a l p r o f i l e P ( A o ) . ) 2 2 I n o r d e r t o measure the i n s t r u m e n t b r o a d e n i n g f u n c t i o n H( I" ) one c o u l d scan a c r o s s a n e a r l y monochromatic l i n e p roduc-ed by a l a s e r or a G - e i s s l e r t u b e . I n t h i s case and iUo) = f H( f ) o f ( A o + f - ^ ) d f = H ( ? \ ' - ? V o ) . The e x p e r i m e n t a l arrangement i s shown i n F i g . 5>. F i g . 5 E x p e r i m e n t a l Arrangement f o r Measuring I n s t r u m e n t P r o f i l e s 23 The l a s e r beam was modulated by a l i g h t chopper t o p e r m i t the use of an A.C. a m p l i f i e r w i t h the p h o t o m u l t i p l i e r . The l e n s system L-j_, L 2 , L-j was used t o ensure even i l l u m i n a t i o n of the m i r r o r M 2 and thence the g r a t i n g G . The p r o f i l e s o b t a i n e d f o r v a r i o u s s l i t c o m b i n a t i o n s are shown i n F i g . 6 . | | F i g . 6 -- Measured Instrument P r o f i l e s Hence the c o m b i n a t i o n u s i n g 1 0 ^ s l i t s ( F i g . 6a) would be be s t f o r measuring l i n e p r o f i l e s w h i l e the c o m b i n a t i o n of F i g . £ (g) h a v i n g a f l a t r e g i o n of 0.1+>r/, would be bes t f o r measur-i n g t o t a l l i n e i n t e n s i t i e s . The h a l f w i d t h s (the w i d t h s at h a l f i n t e n s i t y ) f o r these c o m b i n a t i o n s are t a b u l a t e d below a l o n g w i t h the e s t i m a t e d v a l u e s . S l i t Combina-t i o n (-^f)->-10/10 10/25 25/10 25/25 10/50 50/10 25/50 50/25 C a l c u - o l a t e d (A) 0.17 0.1+2 0.1+ 0.1+2 0.81+ 0.78 0.81+ O.78 E x p e r i - o mental (A) 0.27 0.1+ 0.32 0.35 0.7 ' 0.6 0.7 0.53 25 D e t e r m i n a t i o n of P r o f i l e The Hoc l i n e was p r e s e n t as an i n t e n s e l i n e on p l a t e s of the argon d i s c h a r g e and was due t o i m p u r i t i e s i n the d i s c h a r g e v e s s e l . (The hydrogen p r o b a b l y came from the vacuum grease used ..at the ends of the tube.) The p h o t o m u l t i p l i e r gave a weak s i g n a l a t t h i s w a velength (6562.88) due t o i t s poor s e n s i t i v i t y i n t h i s r e g i o n . " The peak s i g n a l was about 2 v o l t s a t 6562 $ u s i n g 2S^t( s l i t s and a pho-toca t h o d e p o t e n t i a l of 1050 v o l t s . ( N o r m a l l y 800 v o l t s was used f o r the photocathode p o t e n t i a l . I n c r e a s i n g the v o l t a g e however a m p l i f i e d the shot n o i s e as w e l l as the s i g n a l . ) The peak s i g n a l o c c u r r e d l a t e r i n time than the c u r r e n t maximum as d i d the peak s i g n a l s f o r a l l the observed i m p u r i t y l i n e s . The c u r r e n t maximum and peak s i g n a l o c c u r r e d about 125 ^ sec and 250^" sec r e s p e c t i v e l y a f t e r t he s t a r t o f the d i s -c h a r g e . The peak s i g n a l s f o r the observed Argon I I and I I I l i n e s o c c u r r e d e a r l i e r , near t = 100 ^ s e c so t h a t t h i s time was chosen f o r measurement. The H^ l i n e was then scanned, u s i n g the s l i t s , i n inc r e m e n t s of 0.5 S. S i n c e the n o i s e s i g n a l was a p p r e c i a b l e ( s i g n a l t o n o i s e r a t i o was about 3), s e v e r a l s e t s of r e a d i n g s were t a k e n and averaged. The h a l f w i d t h of the p r o f i l e o b t a i n e d "The IP-28 has a quantum e f f i c i e n c y of 0.5^Qor l e s s a t 6560 A compared w i t h a peak v a l u e of 1%% at 35°0 A. 26 when t h e background i n t e n s i t y had been s u b t r a c t e d o f f was 2.08-0.05 angstroms. S i m i l a r r e s u l t s were o b t a i n e d when the e x i t s l i t iiras r e p l a c e d w i t h a 5 0 ^ / s l i t . Next a m i x t u r e of 90$ argon and 10% hydrogen was i n t r o - , duced i n t o the tu b e . I t was hoped t h a t the a d d i t i o n a l h y d ro-gen would g i v e a s t r o n g e r s i g n a l w i t h o u t p e r t u r b i n g the c o n d i -t i o n s i n the plasma a p p r e c i a b l y . The l i n e was a g a i n scanned s e v e r a l times w i t h the 25U/ -$0yCf s l i t arrangement and the averages p l o t t e d . T h i s time the h a l f w i d t h was 2.13 X. 0 6551 52 53 5¥ 55 56 57 1 1 1 1 1 1 1 1 1 5Z 59 60 61 62 63 64- 65 66 P i g . 7 - - - H K Prof i l e 27 When s e v e r a l a v a i l a b l e TP-28 tubes were compared one was found t o be s i x times more s e n s i t i v e at 6562 8 than the o t h e r s . W i t h t h i s tube i t was p o s s i b l e t o scan the l i n e u s i n g l C U c ^ s l i t s . W i t h the s m a l l e r r e s u l t a n t i n s t r u m e n t p r o f i l e the measured h a l f w i d t h of the Hc?c l i n e was 2.00 8. The f i n a l value was taken as 2.02 ±0.05 8 (see F i g . 7). Measurement of R e l a t i v e I n t e n s i t i e s I n t he p r e l i m i n a r y i n v e s t i g a t i o n s w i t h A r i l 3868 and A r l l l 3858, shots were t a k e n w i t h v a r i o u s bank v o l t a g e s and i n i t i a l p r e s s u r e s . The bank v o l t a g e s were 2.5 kV, 3*0 kV, 3.5 kV, 4.0 kV, I4..5 kV and the i n i t i a l p r e s s u r e s were 200, 350 and 500 m i l l i t o r r . The peak s i g n a l v o l t a g e f o r each l i n e was s t r o n g l y dependent on ( i . e . i n c r e a s e d w i t h ) p r e s s u r e and was o n l y x-jeakly dependent on bank v o l t a g e . However, f o r h i g h e r v o l t a g e s the s i g n a l was of s h o r t e r d u r a t i o n . On the b a s i s of these s h o t s i t was d e c i d e d t o take r e a d i n g s w i t h a bank v o l t a g e of 3*0 kV and an i n i t i a l p r e s s u r e of 3 5 0 ^ . W i t h these c o n d i -t i o n s the Argon I I I l i n e reached a maximum between 75 and 100 ^ a e c a f t e r time z e r o ; hence the time t = 100 ^ / s e c was s e l e c t -ed f o r r e c o r d i n g r e a d i n g s . The l i s t s of wavelengths t a k e n from the p l a t e s were then searched f o r a d d i t i o n a l A r i l and A r l l l l i n e s s u i t a b l e f o r f u r -t h e r s t u d y . Nine l i n e s were s e l e c t e d (see T a b l e 1 ) . The c r i - • t e r i o n was t h a t each l i n e had t o be i s o l a t e d by l 8 on each s i d e 28 and t h a t any two l i n e s chosen f o r comparison would be s e p a r a t e d o by no more than 80 A. The i n t e n s i t i e s of th e s e l i n e s were then measured f o l l o w -i n g a d e f i n i t e p r o c e d u r e . F i r s t the r e g i o n a d j a c e n t to each l i n e was scanned i n 0 . 5 ^ increments u s i n g the 1 0 ^ / s l i t s i n o r d e r t o check t h a t the l i n e s d e t e c t e d corresponded t o the wavelengths from the p l a t e s or from the t a b l e s . N e x t , each of the l i n e s was scanned i n 0.1 8 increments u s i n g the 1 0 « X / s l i t s t o check t h a t i t s p r o f i l e was not t o o wide. (With the 1 C W - 5 0 > ^ s l i t c o m b i n a t i o n t o be used ( f o r measuring i n t e n s i t i e s ) the i n s t r u m e n t p r o f i l e was 0.i| £ wide. Argon l i n e p r o f i l e s had t o be no w i d e r than t h i s . ) F i n a l l y r e a d i n g s were t a k e n u s i n g the ICUc/- s l i t c o m b i n a t i o n when the monochromator had been p r o p e r l y c e n t r e d on the l i n e . Readings t o be compared were t a k e n as c l o s e t o g e t h e r i n time as p o s s i b l e t o reduce e r r o r s from l o n g term v a r i a t i o n i n s i g n a l s t r e n g t h s . The e x p e r i m e n t a l r e s u l t s are t a b u l a t e d below. " I f t h e r e were any doubt c o n c e r n i n g the i d e n t i t y of a l i n e the d i s c h a r g e tube was pumped down and f i l l e d w i t h n i t r o -gen. The s h o t s vrere then r e p e a t e d to check whether or not the l i n e v a n i s h e d . 29 T a b l e 1 — Argon L i n e s Measured L i n e M u l t i p l e t E x c i t a t i o n P o t e n t i a l ( V o l t s ) L i n e S t r e n g t h ( C a l c ' d ) R e l a t i v e I n t e n s i t y (Observed) A r i l 3868.53 A r m 3858.52 90 5 2 3 . 0 7 2 9 . 6 6 2 3 . 6 0 0 . 1 3 1 6 . 7 0 5.90 A r i l 3 5 2 1 . 2 7 A r i l 3 5 2 0 . 0 0 A r l l l 3 5 0 3 . 5 8 56 56 2 2 2 . 9 2 2 2 . 9 7 2 7 . 7 9 6 . 6 6 8 . 5 3 16.50 2 . 0 6 2 . 9 0 2 1 . 3 0 A r i l 3388.51+ A r l l l 3358.1+9 96 3 • 2 3 . 5 3 2 7 . 9 7 9 . 2 0 20 .00 2.55 2 l r . 3 0 A r i l 3388.51+ A r l l l 3391.85 96 6 23 .53 30.05 8.1+1+ 2 .80 2.35 3 . 8 5 A r i l 3 2 8 1 . 7 2 A r l l l 3 2 8 5 . 8 5 47 1 22 .98 25.28 0 . 6 3 25.20 0.35 2 7 . 6 0 A r i l 3 3 7 0 . 9 7 J A r l l l 3358.1+9 57 3 2 3 . 0 7 27.91+ 0.71+ 2 0 . 0 0 0 . 3 3 25.70 ! A r I I I 3021+.05 A r l l l 3 0 5 4 . 8 7 A r l l l 3078.15 A r l l l 306I+.77 A r l V 3 0 3 7 . 9 8 k k k k 2 I 2 9 . 6 6 2 9 . 6 6 • 29 .65 2 9 . 6 5 35 .83 3 5 . 2 0 1 8 . 9 0 8 . 3 9 6 . 2 9 2 7 . 2 0 3.54 3 . 2 0 1 .36 1.04 0.54 1 30 Calculation of Plasma Parameters The various parameters were determined using the LTE as-sumption discussed e a r l i e r (see Chapters 1 5c 2 ) . The six equa-tions, (11), (12), (13), (li+), and (9) (applied twice) were solved for the s i x unknowns by an i t e r a t i v e process: (1) The i n i t i a l values were chosen, N e = N e f f =~ 2 x l 0 l 6 c m " 3 , kT = 2.75 ev 1 Then B =21.79 + l o S 1 0 was calculated. h S i + 1 J i + 1 S i -16 (2) A new value of kT was found by i t e r a t i n g equation (11): j^rp = A g -y B ' - l o g ^ ^ N e j + 3/2 l o g 1 0 kT e (where A = {It + E i + 1 -E i)/(2.303) u n t i l a consistent value of kT e was attained. (Because of the logarithmic dependence this equation converged rapidly.) (3) A new value of ^eff was found by i t e r a t i n g equation (12): 3 /2 - 3 N e f f = C ^ N e f f ^T1) ' (^ ) cm u n t i l consistent values of N Qf£ were obtained. (Here J\ ?\ = observed half width of Hoc • l i n e , C ( N Q f f ; kT g) = weak function of N f f and kT @, tabulated by Griem.) Since only 9 values of C x\rere given 31 (for T Q = 1 0 0 0 0 , 2 0 0 0 0 , [+0000 ° K , N = 1 0 l 6 , 1 0 1 7 , 1 0 l 8 cm"3) an interpolation procedure was needed to find G for given value; of kT Q and N e f f encountered during the i t e r a t i o n . A forward difference interpolation was applied f i r s t for one argument and then for the other. (See appendix2) (1+) The p a r t i t i o n function P max £ - ( T e ) = i L _ gi(p)|exp - E i(p)/kT < (15) was then calculated for each ion considered ( A r i l , A r l l l , A r l V ) . It i s clear that the summation i f carried out over an i n -f i n i t e number of levels would diverge. This is because the energy E^(p) approaches a constant value 1^ (the ionization potential) as p — w h e r e a s the s t a t i s t i c a l weight gj_(p) i s 2 roughly proportional to 2n , for n the p r i n c i p a l quantum num-ber. However, because of the e l e c t r i c f i e l d s in the plasma, only a f i n i t e number of ionic levels w i l l e x i s t . The Debye theory predicts a lowering of the i o n i z a t i o n potential /\ I i = — n volts for = 1.6 x 10 "^coul -12 {_ o - 8 . 8 5 x 10 coul/volt m. (16) = Debye Length • e • 32 E o k T e e 2 (N, + 7 % ) 2, 2 m (16) whereas t o f i r s t o r d e r t h e energy l e v e l s are unchanged. The summation i s then c a r r i e d out over energy l e v e l s E l ( p ) . £ I . - A I ± F o r the v a l u e s of N , i n t h i s experiment the changes i n i o n i z a t i o n p o t e n t i a l s y\ I . were s m a l l so t h a t the l i s t e d energy l e v e l s E^(p) d i d not extend t o the c u t o f f v a l u e I ^ - ^ I ^ . Kence th e e n e r g i e s and s t a t i s t i c a l w e i g h t s of the upper l e v e l s had t o be e s t i m a t e d . I t x\ras assumed t h a t the upper l e v e l s were h y d r o g e n i c , i . e . t h a t the energy of the ri^1 l e v e l ( f o r n = p r i n c i p a l quantum number) would be g i v e n by 2 E i ( n ) = i I H (1 - 1_) V n 2 / (17) I f max f o r i - l = charge on i o n Ijj = i o n a z a t i o n p o t e n t i a l of hydrogen = 13.53 v o l t s f o r the h i g h e s t l e v e l 2 ~ i IH  i 2 I H - E± ( n m a x ) n = n max x s JL 3 The s t a t i s t i c a l w e i g h t s f o r the upper l e v e l s were th e n 33 e s t i m a t e d by (2L + 1)(2S + 1) X 2xi (18) s t f o r L = t o t a l o b i t a l a n g u l a r momentum of the i = l i o n i n the ground s t a t e S = t o t a l s p i n of the i = l s t i o n i n the ground s t a t e . To c a l c u l a t e iTj>(T) the summation (15) i s c a r r i e d out t o the h i g h e s t p r i n c i p a l quantum number n^ f o r which the l i s t e d l e v e l s are thought t o be complete. To t h i s v a l u e i s then added max W = ^2 2n (2L+1)(2S+1) exp | - p 1 - i 2 I H j / k T n n l + l n 2 _ j (19) (5) The Saha r a t i o s R = K 3 = Z 3 ( T ) 2 IT2 and R[|_3= - _2 3 N S m kT e ^2 exp 2-n« m kT e - I 2 / k T 3/2 exp ^ - I ^ / k T y (20) (21) were then c a l c u l a t e d . (6) U s i n g e q u a t i o n (13) N 2 , N - j , and N @ were c a l c u l a t e d . N ? = N e f f / ( 2 3 / / 2 + 3 3 / 2 R^p + 8 R , ,^ R ^ P ) 32 \3 32 (22) = R ^ 2 N 2 N„ = No + 2N 0 + (23) (2i|) 3N^ 31+ (7) The l a t e s t v a l u e s of N e j f and k T e were th e n compared w i t h the p r e v i o u s v a l u e s N e r-f and kT, ( p r e c e d i n g the i t e r a t i o n i n (2)). I f ^ kT - kT I <^  10 N e f f " N e f f U 10~k and - " ' - ^ N e f f kT the i t e r a t i o n was t e r m i n a t e d . Otherwise the i t e r a t i v e p r o c e d -ure was r e p e a t e d from (2). I n p r a c t i c e v a l u e s of N e f f and kT from s u c c e s s i v e i t e r a -t i o n s were found t o form o s c i l l a t i n g sequences, c o n v e r g i n g s l o w l y . F a s t e r convergence was a t t a i n e d by a v e r a g i n g f o u r s u c -c e s s i v e v a l u e s of N e f f and kT, c a r r y i n g out t h r e e c y c l e s of the i t e r a t i o n , a v e r a g i n g a g a i n and so on. The i t e r a t i o n s f o r the r e m a i n i n g d a t a vrere c a r r i e d out w i t h a computor program. The r e s u l t s are l i s t e d below: 35 T a b l e 2 — Computed Parameters L i n e ( m u l t i p l e t ) kT (ev) N e ( c m - 3 ) N 2 (cm" 3) N3 (cm" 3) N 4 ( c m - 3 ) A r i l 3868 .5 (90) A r l l l 3858.3 ( 5) 3.25 1 . 5 8 x l 01 6 3 . 8 2 x l 0 1 2 7.37x10 1 1^ 4 . 7 6 x l 0 1 ^ A r i l 3521.3 (56) A r l l l 3503.6 ( 2) 2 .48 1 . 2 3 x l 01 6 1 . 2 6 x 1 0 ^ 5.28x10^ 5.48xio 1 [ <-A r i l 3520.0 (56) A r l l l 3503.6 ( 2) 2 .46 1 . 2 2 x l 01 6 1.37xl0 l l+ 5.32x10^ 4.77x10^ A r i l 3388 .5 (96) A r l l l 3358.5 ( 3) 2 .45 1 . 2 2 x l 01 6 1.42x10^ 5 . 3 3 x l 0 1 ^ 4 . 5 5 x 1 0 ^ A r i l 3388 .5 (96) A r l l l 3391.9 ( 6) 2 .64 1 . 3 2 x l 01 6 6 . 3 8 x l 0 1 3 4.54x10^ 1.34x10^ A r i l 328I.7 (1+7) A r l l l ,3285.9 ( 1) 2.17 1 . 0 3 x l 01 6 4.78xl0 1 [^ 4 .87x1 o 1 ^ 4 . 3 9 x l 0 1 3 A r i l /'3371.0 (57) A r l l l 3358.5 ( 3) 2 . 4 2 1 . 1 9 x l 01 6 1.65x10^ 5.37x10^ 3.49x1O 1^ A r l l l 3024.1 ( I4.) A r l V 3038.0 ( 2) 2.91 1 . 4 4 x l 01 6 1 . 9 1 x l 0 1 3 2.41x10^ 3.18x10^ 1 j-*-A r l l l 3054.9 ( 4) A r l V 3038.O ( 2) 2.82 1 . 4 0 x l 01 6 2 . 9 8 x l 0 1 3 3 . l 6 x l 0 1 ^ i 2.53x10^ A r m 3078.2 ( 4) A r l V 3038.0 ( 2) 2.81 1 . 4 0 x l 0 1 6 2 . 9 5 x l 0 1 3 3.14x1o 1^ 2 . 5 5 x i o ^ A r l l l 3064.8 ( l i ) A r l V 3038.0 ( 2) 2.82 1 . 4 0 x l 01 6 2 . 9 5 x l 0 1 3 3.14x10^ 2 . 5 5 x i o 1 ^ ] V DISCUSSION OP RESULTS In Chapter I c r i t e r i a f o r the existence of l o c a l thermal e q u i l i b r i a were discussed. G r i e m ^ 3 G has derived equations to check the v a l i d i t y of LTE r e l a t i o n s i n d e s c r i b i n g the popula-t i o n of the n ^ l e v e l and the ground stat e l e v e l s . For the pop-u l a t i o n of the n i o n i c l e v e l to be described by the Boltzmann r e l a t i o n , the e l e c t r o n d e n s i t y must s a t i s f y the r e l a t i o n N e 7.1+ x 1 01 8 i 7 / k T ^ cm - 3 (25) ^ - -f o r i - l = i o n i c charge (atomic u n i t s ) n = p r i n c i p a l quantum number I H = i o n i z a t i o n p o t e n t i a l of hydrogen = 1 3 . 5 3 v o l t s In t h i s case f o r kTc= 2.1L5 eV, N e - = 1 . 2 5 x 1 0 l 6cm" 3 (25) becomes 1 n r" "1 ol8 • 6 / 8 . 5 N 3-15 x 10 1 /n n 1 7 / 2 ^ 3 . 1 5 x 1 0 1 8 i 6 / N = 253 I 6 ( 26 ) Then f o r A r i l (1=2). n ^ 3 . 1 f o r A r l l l n ^  I| .2 f o r A r l V n ^  5 . 1 The c r i t e r i o n f o r c o l l i s i o n dominated processes at the ground s t a t e i s that N e -3 9 . 2 x 1 0 1 7 / kT^l * / E 2 - E 1 V cm"3 (27) , % ' V I H 36 37 S e t t i n g kT = 2.1+5 eV, IJJ = 13»53 v o l t s , gives N e ^ 1.58 x 10 l i + (E2-E1P cm"3 where E 2 and E]_ are the energies f o r the upper and lower states of the resonance l i n e . For A r i l , the t r a n s i t i o n lis ^ "P~^ 3p^ 2P i s used where E 1 = 0, E 2 = 16.1+0 v o l t s . 17 -3 Then N e ^? 6.95 x 10 cm I t i s seen that only f o r very dense plasmas w i l l c o l l i s i o n -a l processes dominate the ground state l e v e l s . (This i s i n the absence of resonance a b s o r p t i o n ) . Hence f o r the plasma produced i n t h i s experiment Saha's equation cannot be a p p l i e d . VI CONCLUSION Gene r a l l y speaking the goal of the experiment has not been achieved. Although i t i s true that the d i f f e r e n t values f o r the e l e c t r o n d e n s i t y and temperature, c a l c u l a t e d from the E<=< p r o f i l e and the various i n t e n s i t y measurements, agreed to w i t h -i n 12$, some doubt e x i s t s as to the v a l i d i t y of the technique'.' In the f i r s t place the expression f o r kT was dependent '•" upon two assumptions. F i r s t l y , the populations of the upper : bound states f o r each l i n e had to be p r o p o r t i o n a l to the B o l t z -mann f a c t o r . This would be true i f c o l l i s i o n a l processes dom-inated the population and depopulation of these states and i n p a r t i c u l a r i f equation (25), which expresses t h i s c o n d i t i o n , were met. A l t e r n a t i v e l y , f o r a f i x e d value of N e, equation (25) expresses f o r each i o n i c stage a minimum p r i n c i p a l quantum num-ber n f o r which the Boltzmann f a c t o r a p p l i e s . In t h i s case f o r the A r i l i o n s , n = 3; f o r A r l l l , n = I4.; and f o r A r l V , n = 5. This c o n d i t i o n i s not too r e s t r i c t i v e and was met f o r a l l the A r i l and A r l l l l i n e s s t u d i e d . The second assumption f o r equa-t i o n (11) was that the r e l a t i v e populations of the d i f f e r e n t ions could be described by Saha's equation. This would be true i f the populations of the ground sta t e l e v e l s f o r each type of ion were determined by c o l l i s i o n a l processes. This c o n d i t i o n i s expressed by equation (27) which f o r argon x^rould r e q u i r e N e ^ 6.95 x 1 0 1 7 cm"3 C l e a r l y t h i s c o n d i t i o n i s not s a t i s f i e d i n t h i s experiment where 38 3 9 N e l . l i x 10' L Dcra"^. The o t h e r d i f f i c u l t y i n v o l v e d u s i n g t h e h a l f w i d t h o f t h e H<=< l i n e t o d e t e r m i n e N Q . F o r an e l e c t r o n t e m p e r a t u r e o f 2.1\. ev most o f t h e h y d r o g e n i n t h e p l a s m a would e x i s t i n t h e i o n i z e d s t a t e . Saha's e q u a t i o n p r e d i c t s t h a t o n l y 0.1$ o f t h e h y d r o g e n would be n e u t r a l . Hence most of t h e H l i n e r a d i a t i o n must have come-from t h e o u t e r ( c o o l e r ) r e g i o n s o f p l a s m a w h i c h need n o t have t h e same e l e c t r o n d e n s i t y as the r e g i o n u n d e r s t u d y . Hence f u r t h e r work i s r e q u i r e d t o o b t a i n an L T E p l a s m a f o r w h i c h N e and kT c a n be r e a d i l y d e t e r m i n e d . A h i g h e r e l e c t r o n d e n s i t y , w h i c h can be a c h i e v e d w i t h a h i g h e r i n i t i a l p r e s s u r e i n t h e d i s c h a r g e t u b e , w i l l I n c r e a s e t h e number o f bound s t a t e s whose p o p u l a t i o n c a n be d e s c r i b e d by L T E r e l a t i o n s . However, i t i s d o u b t f u l i f t h e e l e c t r o n d e n s i t i e s a t t a i n a b l e w i l l be h i g h enough f o r c o l l i s i o n a l p r o c e s s e s t o d o m i n a t e ground s t a t e popu-l a t i o n s t h e r e b y p e r m i t t i n g t h e use o f Saha's e q u a t i o n . I f Saha's e q u a t i o n c a n n o t be used i t w i l l be n e c e s s a r y t o f i n d kT f r o m r a t i o o f i n t e n s i t i e s o f l i n e s e m i t t e d by one t y p e o f i o n . The S t a r k b r o a d e n i n g o f a r g o n I I l i n e s w o u l d seem t o be a b e t t e r method f o r f i n d i n g the e l e c t r o n d e n s i t y . APPENDIX I C o m p u t a t i o n o f W a v e l e n g t h s f r o m a P l a t e The program, w h i c h works o v e r a r a n g e o f 1000 A . U . f i r s t t a k e s t h e c o m p a r a t o r r e a d i n g s and c o r r e s p o n d i n g w a v e l e n g t h s o f t h r e e s t a n d a r d i r o n l i n e s " and f i t s a Hartmann d i s p e r s i o n equa-t i o n t o t h e s e v a l u e s . (The t h r e e c o n s t a n t f o r m u l a ^= + C d 0 - d g i v e s t h e w a v e l e n g t h ?\ as a f u n c t i o n o f c o m p a r a t o r r e a d i n g d. Here Q , C, d Q a r e t h e c o n s t a n t s ) . The a p p r o x i m a t e wave-l e n g t h s f o r t h e o t h e r s e v e n t e e n s t a n d a r d i r o n l i n e s a r e t h e n computed. The computed (Hartmann) w a v e l e n g t h s and t h e c o r r e s -p o n d i n g known w a v e l e n g t h s u s u a l l y d i f f e r ( s y s t e m a t i c a l l y ) by two a n g s t r o m s o r l e s s . The p r o g r a m t a k e s t h e computed d i f f e r -e n c e s w i t h the c o r r e s p o n d i n g c o m p a r a t o r r e a d i n g s and f i t s (by l e a s t s q u a r e s ) a f o u r t h d e g r e e p o l y n o m i a l . A c o r r e c t i o n p o l y -n o m i a l t o t h e Hartmann e q u a t i o n i s t h e n known as a f u n c t i o n o f c o m p a r a t o r r e a d i n g . The p r o g r a m r e c a l c u l a t e s t h e w a v e l e n g t h o f e v e r y i r o n s t a n -d a r d l i n e i n t h e r e g i o n and compares i t w i t h t h e a c t u a l wave-l e n g t h . The s t a n d a r d d e v i a t i o n i s t h e n f o u n d . I f the r e c a l c u l -"The t h r e e l i n e s a r e e v e n l y s p a c e d o v e r t h e r e g i o n w i t h t h e f i r s t and t h i r d a t t h e extreme e n d s . i i i a t e d w a v e l e n g t h o f any l i n e d i f f e r s f r o m t h e a c t u a l v a l u e by more t h a n t w i c e t h e s t a n d a r d d e v i a t i o n t h i s l i n e i s r e j e c t e d as a s t a n d a r d . I f t h i s l i n e was one o f t h e f i r s t t h r e e t h e e x e c u -t i o n i s t e r m i n a t e d . I f t h e l i n e was one o f t h e l a s t g r o u p t h e n t h e p o l y n o m i a l c o n s t a n t s a r e r e c a l c u l a t e d w i t h one fewer s t a n -d a r d . T h i s p r o c e d u r e i s r e p e a t e d u n t i l a l l t h e d e v i a t i o n s a r e l e s s t h a n t w i c e the s t a n d a r d d e v i a t i o n o r u n t i l t h e s t a n d a r d d e v i a t i o n i s l e s s t h a n 0 . 0 5 (The p r o g r a m s e l d o m r e j e c t s more t h a n one o r two s t a n d a r d l i n e s . ) T h e n u s i n g t h e f i n a l v a l u e s f o r t h e Hartmann c o n s t a n t s and t h e p o l y n o m i a l c o n s t a n t s t h e p r o g r a m computes and p r i n t s out t h e w a v e l e n g t h s of a l l t h e l i n e s i n t h e unknown s p e c t r u m . These v a l u e s a r e a c c u r a t e t o 0 . o r b e t t e r . O PROGRAM TO COMPUTE UNKNOWN WAVELENGTHS GIVEN THE COMPARATOR READ-c INGS OF STANDARD IRON LINES. THE PROGRAM FIRST COMPUTES THE HART-c MANN CONSTANTS (USING THREE STANDARD LINES) AND THEN APPLIES A c POLYNOMIAL CORRECTION, THE COEFFICIENTS OF WHICH ARE COMPUTED FROM c THE REMAINING STANDARD LINES (USING A LEAST SQUARES F I T ) . DOUBLE PRECISION AY,BE,CDO»ELO,DO,.C,DB»ELFS»DIFF,A,DE,B,DP,DEP,D> 1 EL,CORR,ELL,DEV,ESUM,E,DC,COR,ELF,DPS, DPCDEPC DIMENSION D(60),EL(60),DP(60),A(11,10),B(10),ELFS(60) ,DIFF(60) DIMENSION DE(60),DEP(60),SD(60),SEL(60),DEV(60) 21 WRITE (6,88) READ (5,1) (SD(I),SEL(I),I = 1,3) READ (5,90) N,NDATA WRITE (6,89) N,NDATA M = NDATA + 3 • NN = N + 1 READ (5,1) (SD(I)•SEL(I)»I = 4,M) DO 999 K = 1,M D(K) = DBL E(SD(K) ) 999 E L(K) = DBLE(SEL(K) ) 301 WRITE (6,31 ) WRITE (6,32) (SEL(I),SD(I),I = 1,M) IF( D ( 3 ) - D ( D ) 7,8,8 C 8 PROGRAM FIRST COMPUTES THE HARTMANN CONSTANTS AY= (D(2)-D(1) )/(EL(2)-EL(1 ) ) BE= (D(3)-D(1))/(EL(3)-EL(1)) CDO = (D(3)-D(2))/(AY-BE) ELO = EL(1) -CDO DO =AY*(EL(2)-EL0) C = CD0*D0 DB = DO + D(1) WRITE (6,33) EL0,C,DB • C NOW COMPUTES THE POLYNOMIAL COEFFICIENTS DO 28 I = 4,M ELhS(I) = LLO + C/(DB-D(I)) 28 DIFF(I) = EL(I) - ELFS(I) DO 48 I = 1 ,M 48 DE(1) = 0(1)/10.D0 DO 22 I = 1,NN DO 22 J = 1,NN A( J , I ) = O.DO DO 22 K = 1,M 22 A(J,I) = A(J,I) + DE(K)**(I + J -2) DO 23 I = ltNN A(NN + 1* I ) = 0.D0 DO 23 K = 4»M 23 A(NN+1.I )=A(NN+1»I ) + DIFF<K)*DE(K)**(I-1) CALL GAUSSC(A»NN+1»B) WRITE (6*91 ) ( I»B( I ) * I = 1»NN) WRITE (6,87) C NOW RECALCULATES STANDARD -WAVELENGTHS AND THE STANDARD DEVIATION DO 801 I = 1 ,3 801 ELFS( I) = EL( I ) ESUM = O.DO DO 802.I = 1•M CORR = O.DO DO 803 K = 1,NN 803 CORR = CORR + B(K)*DE (I)**(K-1) ELL = ELFS(I) + CORR - . DEV( I ) = ELL - EL(I ) SELL = SNGL(ELL) WRITE (6,92) SD(I ) ,SELL,DEV( I ) 802 ESUM = ESUM + DEV( I )**2 E =DSQRT ( ESUM/FLOAT.( M-l ) ) WRITE (6,93) E IF(E.LT.5.0D-02)GO TO 861 DO 804 L = 1,3 IF(DABS(DEV(L)).GT.2.0*E) GO TO 210 804 CONTINUE DO 80 5 L = 4,M IF(DABS(DEV(L)).GT.2.0*E) GO TO 211 805 CONTINUE 861 WRITE (6,88) WRITE (6,14) 6 READ (5,2) SDCINTY DC = DBLE(SDC) IF(DC)21,11,4 4 ELF = ELO + C/(DB-DC) DEC = DC/10.D0 COK = O.DO • DO 913 I = 1,NN 913 COR = COR + B(I ) * D E C * * ( I - l ) ELF = ELF + COR SELF = SNGL(ELF) INTY = 1000 - INTY WRITE (6,13) SDC,INTY,SELF GO TO 6 c SECOND HALF OF THE PROGRAMM FOR REVERSE ORIENTATION OF THE PLATE 7 DPS = D(1) + D(3) DO 24 I = 1,M 24 DP(I) = DPS - D(I) C PROGRAM FIRST COMPUTES THE HARTMANN CONSTANTS AY= (DP(2)-DP(1) )/(EL(2)-EL(1 ) ) BE= (DP(3)-DP(1) )/(EL(3j-EL(1) ) CDO = (DP(3 )-DP(2) )/(AY-BE) ' ELO = EL(1) - CDO DO =AY*(EL(2) - ELO) C = CDO*DO DB = DO + DP(1) WRITE (6,33) ELO,C,DB C NOW COMPUTES THE POLYNOMIAL COEFFICIENTS DO 29 I = 4,M ELFS(I) = ELO + C/(DB-DP(I)) I 1 29 DIFF( I ) = EL( I) - ELFS( I ) DO 49 I = 1»M 49 DEPM ) = DP ( I J/10.D0 DO 2 6 I = 1,MN DO 26 J = 1,NN A(J,I) = O.DO DO 26 K = 1,M 26 A(J,I) = A(J,I) +DEP(K)**(I+J-2) DO 27 I = 1,NN A(NN+1,I) =0.D0 DO 2 7 K = 4,M 27 A(NN+1,I)=A(NN+1,I) + DIFF(K)*DEP(K)**(I-l) CALL GAUSSCtA,NN+1,B) WRITE (6,91 ) ( I,B( I ) , I = 1 ,NN) WRITE (6,87) C NOW RECALCULATES STANDARD WAVELENGTHS AND THE STANDARD DO 810 I = 1,3 DEVIATION 810 ELFS( I ) = EL( I ) ESUM = O.DO DO 812. I = 1,M CORR = O.DO DO 813 K = 1,NN 813 CORR = CORR + B(K)*DEP(I>**(K-1) ELL = ELFS(I) + CORR * DEV(I) = ELL - EL(I) 9 SELL = SNGL(ELL) . ci WRITE (6*92) SD ( I ) >SELL,DEV( I )• 8 812 ESUM = ESUM + 'DEV( I )**2 6 E =DSQRT(ESUM/FLOAT(M-l ) ) oi WRITE (6,93) E Ti IF(E.LT.5.OD-02) GO TO 860 zi - DO 814 L- = 1,3 fi IF(DABS(DEV(L) ).GT.2.0*E ) GO TO 210 1 8 14 CONTINUE DO 815 L = 4,M IF(DABS(DEV(L)>.GT.2.0*E) GO TO 211 815 CONTINUE 860 WRITE (6,88) WRITE (6,14) C NOW COMPUTES THE UNKNOWN WAVELENGTHS 9 READ (5,2) SDCINT'Y DC = DBLE(SDC) IF(DC) 21,11,5 5 DPC = DPS - DC DEPC = DPC/10.D0 ELF = ELO + C/(DB-DPC) COR = 0.D0 DO 914 I = 1,N N -914 COR = COR + B(I)*DEPC#*(1-1) ELF = ELF + COR SELF = SNGL(ELF) INTY = 1000 - INTY . WRITE (6,13) SDC,INTY,SELF GO TO 9 2 10 WRITE (6,94) L,DEV(L) GO TO 11 C PROGRAM REJECTS BAD STANDARDS 211 WRITE (6,94) L,DEV(L) MM = M-l IF(L.EQ.M) GO TO 470 DO 850 K = L,MM r SD(K) = SD(K+1) 1 SEL(K) = SEL(K+l) 1 D(K) = D(K+l) 850 E L(K) = EL(K+l) 470 NDATA = NDATA - 1 M = M-l IF(M.LT.2*N) GO TO 500 WRITE (6,88) WRITE (6,89) N,NDA TA GO TO 301 500 WRITE (6,95) 11 STOP 1 FORMAT(F6.3,5X,F7.3) , " 2 FORMAT(F6.3,14) 3 FORMAT(1X,F10.3,I6,10X,F10.3,5X,F10.1) 13 FORMAT(13X,F10.3,I9,F13.3,5H A.U.) 14 FORMAT(1H-,15X,8HPOSITION,5X,3HINT,6X,1OHWAVELENGTH) 3 1 FORMAT( 1H-,14HSTANDARDS USED) 32 FORMAT(16X,F10.3,1X,1HA,5X,2HAT,3X,F10.3,1X,2HMM) 33 FORMAT(1H-,9HCONSTANTS,5X,6HELO = ,D13.7,4X,4HC = ,D13.7,4X, 1 5HDB = ,D13.7/) . 87 • FORMAT(lH-,5X,8HPOSITION,5X,13HST.WAVELENGTH,2X,15HCALC.WAVELENGTH 1»4X,9 HDEV I AT I ON) 88 FORMAT(1 HI) 89 FORMAT(1H0,16X,4HN = ,I 2,5X,8HNDATA = ,12) 90 FORMAT(2I3) 91 FORMAT(15X,2HB(,11,3H) =,D14.7) 92 FORMAT(1X,F12.3,F16.3,F16.3,D18.4) 93 FORMAT(1H0,42HSTANDARD DEVIATION FOR LEAST SQUARES FIT =,D11.4) 94 FORMAT!1H-,4HDEV( , 12,3H) =,D12.4,45H IS GREATER THAN TWICE THE STA 1NDARD DEVIATION) 95 FORMAT(IH-, 14HDATA EXHAUSTED) END $ FORTRAN SUBROUTINE GAUSSC(ANO,MN,X )  DOUBLE PRECISION ANO,X,RM,ATRI,AA,AC,AB,AD,Y,Z NN = MN - 1 DIMENSION- A (J17_,_16 ) , RM ( 17,16) , X( 16 )  DIMENSION ATRI(17,16)» AN0(17,16), IR(16) DO 5 N=2,NN M = N M'M^ TF"! AA = ANO(MM,MM) AC = DABS ( AAJ_ lT^ACTC'TTlToT:r4rr~<SIT TO~T9 I R ( N ) = 0 DO 44 J=1,NN CT> -~~~> OO CO o z < i! —> cn »—* •* -4" i—i <f — o <J~ »—i I— QC O r- O Q < CD QC Z z :£ » 51 — II O _ l z < cn II O cQ Q < cn cn O c9 i n cn I L U — O CO • < r-H -— • LO t-CQ —I < • Q Q II < Q LL. < i-" O L U <f ZD O O LO vO L U I— t—i OC CM cn LO LD _ l _ l _ l O z < Z II «\ -—-•-H :> II :> _ i _J _ i _j cn — cn >-i o vt cn O L U —> Z O - _ J r-H ' • II o —) L U • cn — O L L Q i— O Z < II ~5 L U - « Z i n — i—i Cn i— r-oc z O h- O •Q < u cn cn cr: < z ct: z h-* < 2: 11 11 ~ o 5: o O CT O cr 1 —> — #v r-H 1—1 cr o h- z < < -) r-H L U I—I I—1 I— cr cr z I— r— O < < m z z <t -d- — o z < o z < I— z z II O I O ll Q _ l QC I— < O ~ I » z a z < i J: s + x ~) + 11 > Q_ II ~ ) > - M isi : 11 cr — ZD _J r— — L U x cr L, CHUN LIMITED cr> 0 0 r-* ir> '^ n V I 12 13 [ 9 : 8 I 7 5 L 5 ' 1 3 i t i S "56 FORMAT ( 1X»21HEQUATI ON S INTRACTABLE) ; ' 9 END <• SENTRY 8 6 01 T T APPENDIX 2 Forward D i f f e r e n c e I n t e r p o l a t i o n Formula Suppose that the f u n c t i o n Y(x) i s tabulated w i t h the d i f -f e r e n t values of the dependent v a r i a b l e xo, xx, x 2 , e q u a l l y spaced. I t i s desired to f i t an a n a l y t i c expression to the tabulated values of x and Y. C l e a r l y an i n f i n i t e number of fu n c t i o n s can be f i t t e d to a f i n i t e number of points (x, Y ) ; however, i t i s usual to s e l e c t a smooth f u n c t i o n . I f n points are used the forward d i f f e r e n c e i n t e r p o l a t i o n formula f i t s a polynomial of degree n-1. When successive d i f -ferences of the dependent v a r i a b l e Y are taken one gets the f o l l o w i n g array: Independent v a r i a b l e Dependent v a r i a b l e Y, i f ^ °Y k = Y k Then c l e a r l y Y 0 + ZX Y 0 Y 2 Y 3 Y 0 =• 3 ^ Y 0 Y 0 + 2A Y 0 + ^ 2 Y , +' 3 ^ 2 Y 0 + ^ 3 Y 0 o 1+2 h3 hence f o r Y^ where K i s an i n t e g e r one can w r i t e s y m b o l i c a l l y Y k = ^ Y o (28) T h i s f o r m u l a i s t h e n extended t o n o n - i n t e g r a l v a l u e s of k. I f f o u r p o i n t s are used Y k = Y Q + k<AY0 + k ( k - l ) ^2YQ + k ( k - I ) ( k - 2 ) A 3?r, 2 3} and Y k i s seen t o be a p o l y n o m i a l i n k of degree 3. Hence i f one has a v a l u e of x and w i s h e s t o e s t i m a t e the c o r r e s p o n d i n g v a l u e o f Y, t h e n k w i l l be found by k = x ' x o h where h = x^ - x Q = x 2 - x^ = c o n s t a n t . E q u a t i o n (28) i s then a p p l i e d . BIBLIOGRAPHY 35C Condon, E.U., and S h o r t l e y , G.H., Theory of Atomic  S p e c t r a , Cambridge (1935) 59M Moore, C.E., A M u l t i p l e t T a b l e of A s t r o p h y s i c a l I n t e r e s t , NBS T e c h n i c a l Note 36, (1959) 60T Theophanis, G.A., Rev. S c i . I n s t r . 31, IL27 ( I 9 6 0 ) S p i t z e r , L., P h y s i c s of F u l l y I o n i z e d Gases, I n t e r s c i e n c e (1962) — 63G Griem, H.R., Phys. Rev. 131, 1170 (1963) 6J4.G Griem, H.R., Plasma S p e c t r o s c o p y , M c G r a w - H i l l (1961L) N e u f e l d , C.R., M.Sc. T h e s i s , U n i v e r s i t y of B r i t i s h Colum-b i a (1963) James, H.G., M.Sc. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia (1965) 6 7 N N e u f e l d , C.R., Ph.D. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia (1967) kk 

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