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Measurements of the Stark widths of N II and N III spectral lines at variable electron densities Purcell, Stephen T. 1982

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MEASUREMENTS OF THE STARK WIDTHS OF N II AND N III SPECTRAL LINES AT VARIABLE ELECTRON DENSITIES B.Sc, Dalhousie University, 1978 THESIS SUBMITTED IN PARTIAL FULFILMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Physics We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA c) Stephen Thomas P u r c e l l , 1982 by Stephen T. Purc e l l July 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of VriYSl C S  The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date ZTVL. V 2.3 , 1^32. . DE-6 (3/81) i i ABSTRACT The Stark widths of seventeen N II and ten N III spectral l i n e s , emitted by plasmas with free electron densities of .9 ± .1 x 10 1 7, 2.2 ± .3 x 10 1 7 and 2.9 ± .4- x 10 1 7 cm"3, were measured. Nine of the N II linewidths and four of the N III linewidths have not been previously measured. The plasma source was a wall s t a b i l i z e d discharge f i l l e d with 50% helium and 50% nitrogen. The d i f f e r e n t electron densities were produced by varying the f i l l i n g pressure and charging voltage. The electron temperature was determined from the in t e n s i t y r a t i o of several N II to N III l i n e s . The electron densities were estimated by measuring the Stark widths of He I 5876 and 6678. The nitrogen l i n e s were measured at d i f f e r e n t plasma conditions to check li n e a r scaling of Stark width vs electron density on the same device. However, the large errors in both the Stark widths and the electron density measurements, about half of which came from appreciable o p t i c a l depths, made i t d i f f i c u l t to check the scaling even over the limited range of t h i s experiment. TABLE OF CONTENTS i i i Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES iv LIST OF FIGURES v ACKNOWLEDGEMENTS v i CHAPTER 1 INTRODUCTION 1 CHAPTER 2 THEORY OF LINE BROADENING 4 CHAPTER 3 EXPERIMENTAL APPARATUS AND TECHNIQUE 15 3-1 The Plasma Source 15 3-2 The Optical Spectroscopic System 19 3-3 The Timing System 21 3-4 Calibr a t i o n 24 3-5 F i r i n g Procedure 27 3- 6 Data Handling 28 CHAPTER 4 PLASMA DIAGNOSTICS 29 4- 1 Local Thermodynamic Equilibrium 29 4-2 Plasma Homogeneity 34 4-3 Reproducibility 36 4-4 Time Dependence 37 4-5 Optical Depth 37 4-6 LTE Computations 45 4-7 Temperature Measurements 46 4- 8 Electron Density Measurements 49 CHAPTER 5 LINEWIDTH MEASUREMENTS AND CONCLUSIONS 54 5- 1 Preliminary Work 54 5-2 Stark Widths And Conclusions 56 5-3 Improvements And Further Work 62 BIBLIOGRAPHY 67 i v L I S T OF TABLES Page TABLE (3-1) E x p e r i m e n t a l C o n d i t i o n s .18 T a b l e (4-1) I o n i c D e n s i t i e s At T e = 3.1 ev 31 T a b l e (4-2) E q u i l i b r a t i o n T i m es From R e s o n a n c e E x c i t a t i o n R a t e s 34 T a b l e (4-3) E r r o r In T 0 42 T a b l e (4-4) Plasma D e n s i t i e s 46 T a b l e (4-5) W i d t h s Of He I L i n e s And C o r r e s p o n d i n g N e ' s .52 T a b l e (5-1) N I I And N I I I S t a r k W i d t h s F o r Run 1 56 T a b l e (5-2) N II And N I I I S t a r k W i d t h s F o r Run 2 57 T a b l e (5-3) N II And N I I I S t a r k W i d t h s F o r Run 3 58 T a b l e (5-4) O p t i c a l D e p t h s From I n t e n s i t y R a t i o s 62 V L I S T OF FIGURES Page F i g u r e (3-1) L a y o u t Of E x p e r i m e n t W i t h o u t T i m i n g System .16 F i g u r e (3-2) Q u a r t z D i s c h a r g e Tube 17 F i g u r e (3-3) A r c C u r r e n t T r a c e And T i m i n g 19 F i g u r e (3-4) T i m i n g System 23 F i g u r e (4-1) C o r r e c t e d S t a r k W i d t h To M e a s u r e d W i d t h R a t i o (w /w ) v s O p t i c a l D e p t h 41 F i g u r e (4-2) N II To N I I I I n t e n s i t y R a t i o s From The Saha E q u a t i o n 48 F i g u r e (4-3) He I 5876 F o r Runs 1, 2 and 3 53 F i g u r e (5-1) S t a r k W i d t h s Vs E l e c t r o n D e n s i t y 61 F i g u r e (5-2) M e a s u r e d P r o f i l e s 63 vi Acknowledgements Without the help of many of the other members of the plasma physics group t h i s project might not have been completed and i t would be ingracious not to give s p e c i f i c thanks where due. F i r s t and foremost, I g r a t e f u l l y acknowledge the di r e c t i o n and support received from my supervisor, Dr. A. J . Barnard, throughout the project. He o r i g i n a l l y steered me into the plasma physics f o l d , provided me with research grants, conceived the experiment, cleared t h e o r e t i c a l obstacles from my path and used his battery of computer programs to my advantage. I am also indebted to Al Cheuck who designed and b u i l t the electronic gating system, helped me f i x inumerable equipment f a i l u r e s and, with extensive use of c h i l d pyschcology, prevented me from destroying the del i c a t e , expensive apparatus. John Barnard provided the computer programs used to transform the raw data from the OMA to finished plots and answered a lot of questions and Dr. F. L. Curzon acted as my supervisor while Dr. Barnard was on sabatical leave. Many, in fact most, of the other members of the group had a hand in the f i n a l product but s h a l l remain anonymous, unless they complain. 1 CHAPTER 1 INTRODUCTION When an e l e c t r i c f i e l d i s applied to, an atom, i t s eigenstates and energy l e v e l s are perturbed. In a plasma each atom experiences a time varying e l e c t r i c f i e l d from the rest of medium and the combined perturbations cause a broadening of the emitted spectral l i n e s . The perturbing f i e l d produced at an atom by another p a r t i c l e , the perturber, can be described by a multipole expansion of the perturber's charge d i s t r i b u t i o n . Stark broadening i s the widening of the spectral l i n e by the monopole term (or charge) of the perturber's multipole expansion, averaged over the ensemble of perturbers. Since the monopole f i e l d has the longest range, neutral interactions can often be ignored in a hot dense plasma and Stark broadening i s the dominant broadening mechanism. The broadening of a l i n e w i l l depend on the plasma temperature, electron density, composition, opacity and homogeneity and the states involved in the t r a n s i t i o n . By matching theory to experiment, l i n e broadening provides a powerful diagnostic tool to study both the thermodynamic state of the plasma and the basic atomic parameters of the emitter. Due to the complexity of the phenomenom a un i f i e d theory i s not possible. However, semiempirical formulae have been developed, v a l i d over li m i t e d regimes. Though these formulae are in f a i r l y good agreement with experiments for 2 neutral and singly ionized l i g h t e r elements (see H.R.Griem (1974)) and allow us to use some hydrogen and helium l i n e s as spectroscopic standards, t h i s i s not true for l i n e s from multiply charged, heavier ions. More experiments are needed to help elucidate further which components of the theory apply in which density-temperature regimes. For example, present theory predicts that for the Stark broadening of many nonhydrogenic l i n e s the linewidth at half maximum scales approximately l i n e a r l y with free electron density, N e, (H.R.Griem (1974) page 2) and i s only weakly dependent on temperature. Thus the linewidth i s an excellent means of measuring N e, one of the most important plasma parameters. In a recent study on N II and N III l i n e broadening by E.Kallne, L.A.Jones and A.J.Barnard (1979), the authors suggest that simple linear scaling i s inappropriate at higher N e. They measured linewidths in a plasma with N e = 1.4 x 10 1 8 cm"3 and compared them with e a r l i e r measurements made at lower N e. The twofold aim of th i s experiment was to make extensive measurements at electron densities between that of E.Kallne, e t . a l . , and most of the e a r l i e r measurements (see review a r t i c l e by N. Konjevic and W.L.wiese (1976)) to check linear scaling and to provide a broader base of experimental data for comparison to the o r e t i c a l predictions. To minimize the eff e c t of inhomogeneities, measurements were made at three d i f f e r e n t electron d e n s i t i e s . Linewidths measured at d i f f e r e n t N e's, from the same plasma source, could then be compared to study linear scaling. If the 3 diagnostics were not exact the error would at least affect a l l measurements s i m i l a r l y . The thesis i s divided into fi v e chapters. In chapter two we outline the theory of l i n e broadening, p a r a l l e l i n g semiclassical and quantum mechanical interpretations. A general result for the predicted width of an isolated l i n e , showing the linear dependence on electron density, is presented. In chapter three we describe the experimental apparatus and technique and data c o l l e c t i o n procedures. In chapter four we discuss the thermodynamic state of the plasma, various diagnostics and the temperature and electron density measurements. Included i s a lengthy discussion on o p t i c a l depths made necessary by the p a r t i a l opacity of our plasma. In chapter f i v e we present the Stark widths of twenty-seven N II and N III li n e s measured at three d i f f e r e n t electron densities along with' their estimated errors. Following t h i s i s a discussion of the r e s u l t s . Also in t h i s chapter we give suggestion for improvements and future work. 4 CHAPTER 2 THEORY OF T.TNE BROADENING An ideal spectrometer acts as a fourier analyser of electromagnetic radi a t i o n . Its output i s proportional to the power spectrum of the incident radiation. To study the energy l e v e l system of an atom or ion, we examine the spectrum of l i g h t emitted from atomic t r a n s i t i o n s and use the r e l a t i o n E = -fiu. If the radiation from an ensemble of emitters undergoing the same t r a n s i t i o n were pe r f e c t l y monochromatic, or equivalently i f a l l the photons had exactly the same energy, the spectrum would be a delta function peaked at u. However, the f i e l d i s never p e r f e c t l y monochromatic and the emitted photons always have a f i n i t e spread in possible energies so the spectrum peaks have f i n i t e widths. This widening of the ideal spectra i s c a l l e d l i n e broadening. The parameter most accessible to measurement in l i n e broadening studies i s the ful l w i d t h of the l i n e at half maximum, 2w, so we w i l l give i t ca r e f u l consideration throughout. An adequate description of l i n e broadening i s an extremely complex quantum mechanical problem. As the formulation of quantum mechanics was i n i t i a l l y modelled on c l a s s i c a l arguments, i t i s ins t r u c t i v e to discuss l i n e broadening by p a r a l l e l i n g the quantum picture with semiclassical models. F i r s t consider an isolated , excited atom emitting dipole radiation as i t undergoes a t r a n s i t i o n between two 5 states. C l a s s i c a l l y we picture the atom as a l i g h t l y damped, o s c i l l a t i n g dipole with angular frequency u = AE/n. AE i s the energy i n i t i a l l y stored in the o s c i l l a t o r ( t r a n s i t i o n energy). An o s c i l l a t i n g dipole emits electromagnetic radiation at i t s c h a r a c t e r i s t i c frequency of o s c i l l a t i o n . The lineshape of t h i s radiation ( e s s e n t i a l l y the frequency dependence of the power spectrum) can be shown to be (M.Born and E.Wolf (1975)) : L U ) = l i m d / T ) | f f (t)exp(-iot)dt | 2 (2-1) f(t) i s the complex generalization of the time dependence of the o s c i l l a t o r , or equivalently the f i e l d i t produces ( e . g . f(t) = e x p ( i o 0 t ) ) . From J.Cooper (1969) t h i s can be more conveniently written as : L(u) = ( l / j r j R e J *(s)exp(-ios)ds (2-2) +(s) i s the autocorrelation function given by : *(s) = <Cf*(0)f(sj> (2-3) The average i s over an ensemble of emitters. We can use an ensemble average rather than a time average by invoking the ergodic hypothesis. Because a dipole o s c i l l a t o r emits radiation at a rate proportional to i t s physical amplitude, i t s amplitude decays exponentially in time. This i s c a l l e d radiation damping (H .R.Griem (1964) pgs.8-10)). Hence i t has a time dependence given by f(t) = exp(-yt+io 0t). This gives L(o) (normalized) 6 from (2-1) or (2-2) and (2-3) as : LU) = U/r) (2-4) (U-u 0) 2 + r 2) L(u) i s a Lorentzian with halfwidth r (r i s defined as 1/lifetime of the o s c i l l a t o r ) . C l a s s i c a l l y for v i s i b l e l i g h t y ~ 108 sec" 1 and o 0 ~ 2 x 101 * sec" 1, so natural l i n e broadening produces a very narrow peak. Another effect that broadens the atomic l i n e s i s the motion of atoms r e l a t i v e to the spectrometer which Doppler s h i f t s the emitted ra d i a t i o n . For a Maxwellian v e l o c i t y d i s t r i b u t i o n the l i n e s are Gaussian with 1/e halfwidth given by : wd = 4.6 x lO"U 0(T e (ev) / M(amu)) 1 / 2 (2-5) T e i s the ion temperature and M the atomic mass of the emitters. For nitrogen and helium at 3 ev, which i s approximately the temperature of the plasmas we studied, t h i s gives wd ~ .1 A and .2 A respectively, in wavelength units. This width affected only the narrowest l i n e s measured in t h i s experiment (see section (3-4)). Broadening also occurs because nearby p a r t i c l e s interact with and perturb the o s c i l l a t o r s . In Stark broadening the perturbers' e f f e c t s depend on t h e i r charges, impact parameters and r e l a t i v e v e l o c i t i e s and pos i t i o n s . The o s c i l l a t o r ' s energy (and hence frequency) i s s h i f t e d by V = -£(t)«d(t) where £(t) i s the time dependent f i e l d at the emitter from the perturbers and d(t) i s the dipole moment of the emitter. 7 From the properties of the Fourier transform, the time a signal must be observed to give a p r o f i l e accurately at a frequency separation Au from the l i n e center i s At ~ 1/Au. Experimentally we measure the halfwidth (w) so we need At ~ 1/w. Note w ~ 1/lifetime ~ v where v i s the average c o l l i s i o n frequency. C l a s s i c a l l y the perturbers are point p a r t i c l e s following c l a s s i c a l paths. Since the closer the p a r t i c l e approaches the stronger the perturbation i t causes, we may say the o s c i l l a t o r i s perturbed only during a c o l l i s i o n time t ~ f>/v. p i s the distance of closest approach (impact parameter) and v i s the ve l o c i t y at closest approach (thermal v e l o c i t y for neutrals). The c a l c u l a t i o n can be greatly s i m p l i f i e d for two special l i m i t s of the average c o l l i s i o n time r = <t>. For perturbers that move r e l a t i v e l y slowly we may calculate their effect as i f they are stationary. This is appropriate i f T >> 1/Au or i f Ao = w the perturbers must move l i t t l e during the l i f e t i m e of the dipole. The p r o f i l e i s then found by ca l c u l a t i n g the frequency s h i f t as a function of applied e l e c t r i c f i e l d , then averaging over the s t a t i s t i c a l d i s t r i b u t i o n of f i e l d strengths to find * ( s ) . This i s c a l l e d the quasis t a t i c approximation and i s often v a l i d for the r e l a t i v e l y slow moving ions of the plasma. It w i l l hold for the l i n e wings to a smallest frequency separation from l i n e center depending on T . Finding the f i e l d d i s t r i b u t i o n (called the Holt'smark f i e l d ) i s the d i f f i c u l t part and the references are H.R.Griem (1974) and 8 C .F.Hooper, J r . (1966) and ( 1 9 6 8 ) . The H o l t s m a r k f i e l d , w h i c h d epends on t h e i o n i c c h a r g e d e n s i t y , g i v e s t h e number of a p a r t i c u l a r e m i t t e r s p e c i e s f e e l i n g a c e r t a i n s t r e n g t h f i e l d a s a f u n c t i o n o f f i e l d s t r e n g t h . The s e c o n d l i m i t a p p l i e s f o r T « 1/Au. These p e r t u r b e r s p a s s t h e e m i t t e r q u i c k l y , a b r u p t l y d i s t u r b i n g t h e p hase o f t h e o s c i l l a t o r . O n l y t h e n e t e f f e c t o f a c o l l i s i o n , n o t t h e a c t u a l t i m e d e p e n d e n c e o f t h e i n t e r a c t i o n , need be c o n s i d e r e d . T h i s i s c a l l e d t h e i m p a c t a p p r o x i m a t i o n and i s o f t e n v a l i d f o r e l e c t r o n s o v e r much of t h e l i n e . The s i m p l e s t t h e o r y assumes t h e s e c o l l i s i o n s c o m p l e t e l y d e s t r o y t h e w a v e t r a i n . Then f ( t ) = exp( i o t - i / t ) . The F o u r i e r t r a n s f o r m i s a L o r e n t z i a n w i t h h a l f w i d t h v. The L i n d h o l m t h e o r y i s a more c a r e f u l d e r i v a t i o n i n w h i c h t h e c o l l i s i o n s d i s t u r b t h e phase s l i g h t l y b ut a b r u p t l y , a r e a d i a b a t i c and a r e i n d e p e n d e n t i n t i m e . I t a l s o g i v e s a L o r e n t z i a n p r o f i l e b u t w i t h h a l f w i d t h w = N e < v > « r and f r e q u e n c y s h i f t d = N e<v>tfj . tfr and * j a r e t h e r e a l and i m a g i n a r y p a r t s of t h e t o t a l o p t i c a l c r o s s - s e c t i o n s . The i m p a c t a p p r o x i m a t i o n i s v a l i d i n t h e c e n t r a l p a r t o f t h e p r o f i l e t o a f r e q u e n c y s e p a r a t i o n d e t e r m i n e d by T . In t h e i n t e r m e d i a t e r a n g e ( T ~" 1/Au) t h e t h e o r y i s more complex b e c a u s e t h e t i m e d e p e n d e n c e of t h e p e r t u r b a t i o n s must be a n a l y s e d i n d e t a i l . F o r t u n a t e l y , t h e r a n g e s o f a p p l i c a b i l i t y o f t h e q u a s i s t a t i c a p p r o x i m a t i o n f o r i o n s and t h e i m p a c t a p p r o x i m a t i o n f o r e l e c t r o n s o f t e n o v e r l a p f o r much o f t h e l i n e p r o f i l e . T h a t i s , we have T ( i o n s ) >> 1/w >> T ( e l e c t r o n s ) . A c c u r a t e p r e d i c t i o n of t h e 9 linewidth i s often possible using these two approximations. Now we formulate the above ideas in the language of quantum mechanics. The lineshape for an atom emitting spontaneous dipole radiation when an electron decays from state m to n, summing over a l l the states i s (J.Cooper (1969),H.R.Griem(1964)) : LU) - 2 n 8 ( » - » m n ) | < m | d | n > | ^ m (2-6) where ^ u m n =energy difference between states m and n d =dipole operator pm =probability state m i s occupied (given by the Saha Boltzmann equation when the plasma i s in equilibrium) This may be written using the quantum autocorrelation function in the same form as (2-2) and (2-3). The e s s e n t i a l difference between the c l a s s i c a l and quantum descriptions i s that we replace the c l a s s i c a l dipole o s c i l l a t o r with the matrix element of d between states m and n. The excited states of isolated atoms have a constant t r a n s i t i o n p r o b a b i l i t y , r, which leads to the exponential decay law for an ensemble of emitters. This i s quantum analog of c l a s s i c a l radiation damping. The energy l e v e l s are not discrete but have a f i n i t e width because of the uncertainty p r i n c i p l e and the nonstationarity of excited states. The l i n e p r o f i l e for spontaneous emission i s again a Lorentzian with width r . r i s n e g l i g i b l e except for very low density, cold plasmas or special t r a n s i t i o n s . Interactions also broaden the l i n e by adding a time 10 varying potential to the emitter's Hamiltonian. The state vectors of (2-6) are no longer eigenfunctions of the unperturbed Hamiltonian but are eigenfunctions of an emitter and surrounding perturber system. To find the lineshape we must set up and solve the time dependent Shrodinger equation with t h i s more complicated Hamiltonian (H.R.Griem (1964) and (1974), J.Cooper (1969)). The t o t a l wavefunction ty obeys : i*a^ = ( H . + H p + V ) ^ (2-7) dt where H A = the unperturbed emitter Hamiltonian Hp = the perturbers' Hamiltonian and V = the interaction term The problem can be greatly s i m p l i f i e d by using the c l a s s i c a l path assumption that almost a l l calculations are based upon. The assumption i s that the perturbers are c l a s s i c a l p a r t i c l e s moving along c l a s s i c a l t r a j e c t o r i e s dependent only on the emitter's charge and not i t s state ( i . e . charge d i s t r i b u t i o n ) . This w i l l be v a l i d i f the perturbers' average de Broglie wavelength i s small compared to the impact parameters of a l l c o l l i s i o n s that contribute s i g n i f i c a n t l y to the broadening. Also the c o l l i s i o n s are considered independent of changes caused in the emitter by the perturber (no back reaction). The back reaction can be ignored i f the average change in kinetic energy of the perturbers in a c o l l i s i o n (~'n'w) i s small compared to the average perturber kinetic energy (kT). This implies that 11 broadening c o l l i s i o n s are much more frequent than exciting or de-exciting c o l l i s i o n s . This i s almost always true for li n e s in the op t i c a l range. Using the c l a s s i c a l path assumption the problem s i m p l i f i e s to solving : itfaX = (HA+Vr. ( t ) ) X (2-8) X describes the state of the emitting system and V c (_(t) i s the potential the emitter feels from a perturber with a c l a s s i c a l path. To find the lineshape we must solve (2-8) and substitute the solutions . into (2-6). Though general solutions for (2-8) do not exist from which actual widths have been calculated, solutions can be obtained for the quasist a t i c ( T >> 1/w) and impact ( T << 1/w) approximations. For the quasistatic case V C L(t)=-£«d. £ i s the time independent monopole f i e l d from the perturber at the emitter. We obtain the p r o f i l e by ca l c u l a t i n g the s t a t i c Stark s h i f t s of the energy l e v e l s of the upper and lower states as a function of applied f i e l d (E.Merzbacher (1970)), then average over the f i e l d d i s t r i b u t i o n W(£). We get : L Q S U ) = J w < £ > d £ 2 |<m|d[n> | 2 / 5 mS(u-u m n-(AE f n(£)-AE n(e))/K) (2-9) where AE m(£), AE n(£) are the energy s h i f t s of the upper and lower states respectively. Standard perturbation theory provides an expansion technique to determine the l e v e l s h i f t s in terms of the 12 perturbation potential's matrix elements between unperturbed states ( V m n ' s ) . Note that V i s an odd operator. For hydrogenic emitters the f i r s t term of the expansion gives the strong linear Stark ef f e c t (energy s h i f t « | V n n | 2 ) . Most states of nonhydrogenic ions have d e f i n i t e parity because they are nondegenerate in the o r b i t a l quantum number. This means V n n i s zero because V i s odd. The energy s h i f t of these states is thus approximated by the second term in the expansion (^^| V m n| 2 ) . This s h i f t i s c a l l e d the quadratic m*n Stark e f f e c t (E.Merzbacher (1970)). In the impact approximation the average interaction i s assumed weak so that to f i r s t order each c o l l i s i o n may be considered s t a t i s t i c a l l y independent. Since in general i t takes many of these weak c o l l i s i o n s to disturb the atom i t is only the average effect of c o l l i s i o n s that matters and V C L ( t ) in (2-8) can be considered as a time independent perturbation to H A < As in the c l a s s i c a l picture, the det a i l e d time dependence of a c o l l i s i o n can be ignored for small T . Only the net ef f e c t of a c o l l i s i o n need be considered. Thus V"CL can be expressed in terms of S-matrices for the scattering of perturbers off the upper and lower l e v e l s . The p r o f i l e i s found by averaging the perturbation over possible impact parameters, v e l o c i t i e s and times of approach. 1 3 Cooper (1969) gives an expression for L(o) v a l i d for tran s i t i o n s between two well separated l e v e l s , a and b as : L T U ) = 1 Re 2 d m n<fmn| (iu-i(H -H. ) . )" 1 | m' n ' ^ d*,, I r mm'-mn N S 1 v - a b ab 1 / / -mn' (2-10) where d = dipole matrix element — mn c H g j H j j = the emitter Hamiltonians that act on the substates m and n respectively 4>Qb = the interaction operator written in terms of scattering matrices In plasmas the ions can usually be treated q u a s i s t a t i c a l l y and the electrons in the impact approximation. To obtain the f i n a l p r o f i l e we f i r s t c alculate the impact broadening by electrons of the states of the Hamiltonian H Q ( £ ) , which now depends on the s t a t i c f i e l d strength produced by the ion perturbers, £. Then we average over the ion e l e c t r i c f i e l d d i s t r i b u t i o n . The f i n a l p r o f i l e i s given by : L U ) - l j w ( £ ) d £ R e ^ d m n ^ d * v (2-11) (2-11) w i l l be v a l i d i f the uncertainty introduced by neglecting the ion motion i s small compared to the electron impact width or distance from l i n e center, whichever i s greater. For isolated l i n e s from nonhydrogenic emitters, such as nitrogen, q u a s i s t a t i c ion broadening w i l l cause s h i f t s due to the quadratic Stark e f f e c t . Often t h i s f i e l d dependence 1 4 i s a r e l a t i v e l y weak eff e c t and the p r o f i l e can be calculated d i r e c t l y from (2-10). To f i r s t order (2-10) gives a Lorentzian p r o f i l e with width and frequency s h i f t determined by # a b. The electron impact width i s (J.Cooper (1969)) : W = N e < ( v / 2 ) ( f f m + < r n + J d n | f m ( n ) - f n ( o ) | 2 ) > v e | (2-12) <rm and <rn are the t o t a l i n e l a s t i c o p t i c a l crossections in the upper and lower states respectively and f m ( n ) and f n ( n ) are the e l a s t i c scattering amplitudes. Crossections are usually evaluated by imposing large and small cutoffs for the impact parameters. The large cutoff i s introduced because the Debye sphere shields distant perturbers. The low cutoff i s introduced because the scattering matrices breakdown for small impact parameters. The small cutoff w i l l be v a l i d i f strong co-llisions do not occur frequently enough to a f f e c t the p r o f i l e . It i s important to note that the width i s proportional to N e and only weakly dependent on T e (from the v e l o c i t y average). We hope to support the linear scaling of width with free electron density in t h i s experiment by taking measurements at d i f f e r e n t electron densities but fixed temperature. 1 5 CHAPTER I I I EXPERIMENTAL APPARATUS AND TECHNIQUE The e x p e r i m e n t a l a p p a r a t u s c o n s i s t s of a p u l s e d p l a s m a s o u r c e , an o p t i c a l s p e c t r o s c o p i c s y s t e m , a t i m i n g s y s t e m and c a l i b r a t i o n e q u i p m e n t . The o v e r a l l l a y o u t o f t h e e x p e r i m e n t minus t h e t i m i n g s y s t e m i s shown i n f i g u r e ( 3 - 1 ) . 3-1 The Plasma S o u r c e The p l a s m a s t u d i e d was a w a l l s t a b i l i z e d d i s c h a r g e s i m i l a r t o t h a t u s e d by H.James (1970) and R . N e l s o n ( 1 9 7 0 ) . The p l a s m a was formed by d i s c h a r g i n g a l a r g e c u r r e n t f r o m a c a p a c i t o r bank t h r o u g h a vacuum s e a l e d , 1/2 i n c h b o r e , 4.5 i n c h l o n g q u a r t z t u b e w i t h f l a r e d ends as shown i n f i g u r e ( 3 - 2 ) . T h i s shape was c h o s e n b e c a u s e t h e c o n s t r i c t e d c e n t e r p o r t i o n p r o d u c e s a h o t , d e n s e p l a s m a . The e l e c t r o d e s , p l a c e d a t e i t h e r end of t h e t u b e , were h o l l o w w i t h .78 i n c h b o r e a l l o w i n g us t o o b s e r v e t h e p l a s m a a l o n g i t s main a x i s . By e x t e n d i n g t h e p o s i t i o n o f t h e q u a r t z windows away f r o m t h e h o t t e s t p a r t o f t h e p l a s m a t h e y s u f f e r e d l e s s c o n t a m i n a t i o n f r o m e l e c t r o d e m a t e r i a l s . The t u b e was f i l l e d w i t h 50% h e l i u m a n d 50% n i t r o g e n o f r e s e a r c h g r a d e a t p r e s s u r e s o f 3, 6 and 9.5 t o r r . The s i m p l e RC d i s c h a r g e c i r c u i t w i t h C = 20.4 uF and R ~ 1 n i s shown i n f i g u r e ( 3 - 1 ) . When t h e bank was dumped i t p r o d u c e d a damped o s c i l l a t i n g c u r r e n t w i t h 30 usee f i r s t h a l f c y c l e . The p l a s m a was o b s e r v e d f o r a 1 usee t i m e i n t e r v a l by e l e c t r o n i c a l l y s w i t c h i n g t h e d e t e c t o r s y s t e m a t 16 20.4 fiF ALIGNMENT LASER OMR SPARK SWITCH D 1 DISCHARGE TUBE A M -in IM SPECTROMETER < 19 MM 3 M 0 M 1205 D GATE POWER SUPPLY SCOPE CHART RECORDER I205A OMA C O N S O L E COMPUTER MINI .» TO MAIN TERMINAL COMPUTER COMPUTER F i g u r e (3-1) : L a y o u t o f e x p e r i m e n t w i t h o u t t i m i n g s y s t e m . 17 # OPTICAL CONE m m F L A T Figure (3-2) : Quartz discharge tube. 18 t h e f i r s t c u r r e n t maximum. The e l e c t r o n d e n s i t y o f t h e p l a s m a was v a r i e d by c h a n g i n g t h e f i l l i n g p r e s s u r e and bank c h a r g i n g v o l t a g e . The t e m p e r a t u r e v a r i e d o n l y a l i t t l e . T h r e e c o n d i t i o n s were u s e d i n t h e e x p e r i m e n t and t h e y a r e t a b u l a t e d i n t a b l e ( 3 - 1 ) . TABLE (3-1) E x p e r i m e n t a l C o n d i t i o n s TUBE CHARGING I MAX FIRING N e T e RUN PRESSURE VOLTAGE ENERGY X 1 0 " 1 7 t o r r kv kamps k j cm" 3 ev 1 3 . 0 6 7 .36 1 3 .1 2 6 . 0 1 0 1 1 1 2.2 3 .1 3 9.5 10 1 1 1 2.9 3 .1 The d l / d t t r a c e , a s measured w i t h a Rowgowski c o i l , i s shown i n f i g u r e (3-3) w i t h t h e s i g n a l f r o m a p i n d i o d e p l a c e d a l o n g t h e o p t i c a l p a t h . The d i o d e a p p r o x i m a t e l y m e a s u r e s t h e t o t a l l i g h t i n t e n s i t y f r o m t h e p l a s m a as a f u n c t i o n of t i m e . The d i s c h a r g e c u r r e n t was a p p r o x i m a t e l y p r o p o r t i o n a l t o t h e l i g h t s i g n a l f o r a b o u t t h e f i r s t 1/3 c y c l e , p e a k i n g a t a l m o s t t h e same t i m e . The g a t e s i g n a l i n f i g u r e (3-3) shows when t h e d e t e c t o r was a c t i v a t e d ( a t d l / d t = 0 ) . B e c a u s e t h e c u r r e n t v a r i e s s l o w l y a t t h a t t i m e , t h e p l a s m a c o n d i t i o n s were r e l a t i v e l y c o n s t a n t a l l o w i n g us t o assume N e and T e t i m e i n d e p e n d e n t ( s e e s e c t i o n ( 4 - 4 ) ) . The t r a c e s f o r d l / d t and l i g h t i n t e n s i t y f o r r u n s 2 and 3 had t h e same t i m e dependence as r u n 1 but h i g h e r a m p l i t u d e s . 19 6KV CHARGING VOLTAGE 3TORR TUBE PRESSURE 2 MSEC DIV Figure (3-3) : Arc current trace and timing. 3-2 The Optical Spectroscopic System The o p t i c a l system is shown in figure (3-1) and the o p t i c a l cone or observed plasma region in figure (3-2). The plasma was observed along i t s main axis for almost a l l of the measurements. This was done to allow the c o l l e c t i o n of a s u f f i c i e n t amount of l i g h t to study weak as well as strong l i n e s . As a consistency check N II 4614 and 4643 were studied side-on as well. For the end-on measurements, the central axis of the tube was accurately aligned with the entrance s l i t of a SPEX 1 meter spectrometer by using a He-Ne laser. The two lenses shown in figure (3-1), along with a 19 mm diameter stop between them, defined the o p t i c a l cone. At the point just before the vessel widens, the o p t i c a l cone had a diameter — 1/4 the diameter of the vessel. The dispersion of the spectrometer i s 8.0 A/mm with resolution — .1 A. Because li n e s of varying strengths were 20 s t u d i e d , a s t e p f i l t e r was p o s i t i o n e d a t t h e e n t r a n c e of t h e s p e c t r o m e t e r t o a l l o w c o n t r o l l e d amounts of l i g h t t h r o u g h t h e s l i t . The d e v i c e u s e d t o r e c o r d t h e l i n e p r o f i l e s was an O p t i c a l M u l t i c h a n n e l A n a l y s e r (OMA). I t c o n s i s t s o f t h e 1205D v i d i c o n d e t e c t o r u n i t and 1205A memory s t o r a g e c o n s o l e . T h i s d e v i c e r e c o r d s an i n d i v i d u a l p r o f i l e i n a s i n g l e s h o t . The OMA works as f o l l o w s . A s e l e c t e d p o r t i o n of t h e s p e c t r u m i s i n c i d e n t upon t h e 1205D's l i g h t s e n s i t i v e s u r f a c e . T h i s s u r f a c e i s a 12.5 mm wide by 10 mm h i g h r e c t a n g l e d i v i d e d i n t o 500 v e r t i c a l s t r i p s , e a c h a 25 m i c r o n w i d e , s e p a r a t e p h o t o d e t e c t o r . The c u r r e n t p r o d u c e d by t h e p h o t o d e t a c h e d e l e c t r o n s i s a m p l i f i e d by t h e a m p l i f y i n g s t a g e o f t h e 1205D and f o c u s e d upon a l i n e a r a r r a y o f 500 c h a r g e d d e t e c t o r s . The c u r r e n t s t r i k i n g e a c h of t h e s e d e t e c t o r s r e d u c e s t h e s t o r e d c h a r g e p r o p o r t i o n a l t o t h e l i g h t i n c i d e n t upon t h e c o r r e s p o n d i n g p h o t o d e t e c t o r . The 1205D r e a d s t h e s p e c t r u m by m e a s u r i n g t h e c u r r e n t i n an e l e c t r o n beam as i t sweeps a c r o s s t h e a r r a y o f d e t e c t o r s . T h i s d a t a i s t h e n t r a n s m i t t e d t o t h e 1205A c o n s o l e and s t o r e d d i g i t a l l y i n a 500 c h a n n e l memory. The b a n d w i d t h o f t h e s p e c t r u m r e c o r d e d d e p e n d s on t h e d i s p e r s i o n a c r o s s t h e 12.5 mm wide p h o t o s e n s i t i v e s u r f a c e o f t h e 1205D. The OMA c o u l d be u s e d i n e i t h e r c o n t i n u o u s ( = r e a l t i m e ) o r g a t e d modes w h i c h g i v e t i m e i n t e g r a t e d o r t i m e r e s o l v e d s p e c t r a r e s p e c t i v e l y . In g a t e d mode t h e d e t e c t o r ' s a m p l i f y i n g s t a g e i s f i r s t d e f o c u s e d by o p e r a t i n g i t a t a 21 reduced voltage. Then at the desired time i t i s turned on by applying a large voltage for 1 ^sec. In t h i s mode the OMA has a machine width of — 7 channels. During the experiment we observed N II and N III l i n e s which had widths of ~ 1 A as well as HE I 5876 and 6678 which had widths ~ 10 A. To observe nitrogen l i n e s much wider then the machine width yet small compared to the width of the detector surface, i t was necessary to place a magnifying lens at the e x i t hole of the spectrometer. This enlarged the image — 6.5 times giving linewidths of 20-40 channels (cal - ,03A/ch). The helium l i n e s were recorded without the lens (cal - .2A/ch). The OMA vidicon unit was placed on a mount which allowed careful rotational and v e r t i c a l alignment. The OMA console could produce plots on a chart recorder or o scilloscope. After each shot the data was transferred to a minicomputer and then to a f i l e in the university's main computer for later manipulation. 3-3 The Timing System The timing system for gated mode operation i s shown in figure (3-4). After the discharge tube has been f i l l e d to the desired pressure and the capacitor bank charged to the desired voltage, a manual switch i s triggered which ini a t e s the discharge procedure. To know how to time our discharge we must understand the i n t e r n a l timing of the OMA. The OMA reads the signal from the channels sequentially in 38.4 msec as the electron beam sweeps across the detectors (the read c y c l e ) . It then 22 r e s e t s i n .6 msec ( t h e d e a d t i m e ) and t h e r e a d c y c l e r e p e a t s . To t i m e r e s o l v e o u r p l a s m a we must f i r e t h e d i s c h a r g e and r e c o r d t h e s p e c t r u m d u r i n g t h e d e a d t i m e . T h i s i s done by d i s a b l i n g t h e a m p l i f i e r o f t h e p h o t o d e t e c t o r s u n t i l a s e t t i m e ( a t t h e d i s c h a r g e c u r r e n t maximum) when i t i s t u r n e d on by a p p l y i n g a -1300 v o l t , 1 usee d u r a t i o n p u l s e . The a c t u a l f i r i n g s t a r t s w i t h t h e manual s w i t c h w h i c h a l l o w s t h e t i m i n g u n i t t o s e n d a s i g n a l t o t h e OMA c o n s o l e . The c o n s o l e t h e n w a i t s u n t i l t h e v i d i c o n r e a c h e s i t s dead t i m e , t h e n s e n ds a s i g n a l back t o t h e t i m i n g u n i t . The t i m i n g u n i t t h e n s e n d s a s i g n a l t o a SCR u n i t w h i c h p r o d u c e s a s h o r t 100 v o l t p u l s e . T h i s p u l s e i s b o o s t e d t o 20 kv by a t r a n s f o r m e r and i s t h e n a p p l i e d t o t h e c e n t e r p i n o f a p r e s s u r i z e d a i r s p a r k s w i t c h . The s p a r k i t p r o d u c e s i o n i z e s t h e a i r between t h e main e l e c t r o d e s o f t h e a i r s p a r k t r i g g e r a l l o w i n g t h e d i s c h a r g e of t h e c a p a c i t o r bank t o commence. The g a t e i s t i m e d f r om t h e f a s t r i s i n g , l e a d i n g edge of t h e DI/Dt s i g n a l as m e asured by a Rowgowski c o i l . The c o i l ' s s i g n a l i s r e c e i v e d by a t r i g g e r u n i t w h i c h s w i t c h e s when t h e s i g n a l r e a c h e s a p r e s e t l e v e l ( o r t i m e ) . The t r i g g e r u n i t , a f t e r a v a r i a b l e d e l a y , s e n d s a s i g n a l t o a k r y t r o n s w i t c h . T h i s i m m e d i a t e l y f i r e s a l l o w i n g t h e g a t e power s u p p l y t o p r o v i d e t h e -1300 v o l t 1 »»sec l o n g p u l s e t o t h e 1205D and h e n c e measurement o f t h e s p e c t r u m . By o b s e r v i n g t h e DI/Dt t r a c e ( o r I a f t e r i n t e g r a t i o n ) a n d t h e g a t e t r a c e on an o s c i l l o s c o p e , t h e t i m i n g o f t h e g a t e c o u l d be a d j u s t e d u s i n g t h e v a r i a b l e d e l a y of t h e t r i g g e r u n i t t o any t i m e d u r i n g 23 I205A OMA CONSOLE TIMING UNIT mm — f A I205D ^ I V:>DETECTORyy SCR UNIT GATE POWER SUPPLY KRYTRON SWITCH T R I G G E R UNIT I^NAIR S P A R K \J T R I G G E R -> vcr ROGOWSKL COIL F i g u r e (3-4) : T i m i n g s y s t e m 24 the discharge. Timing j i t t e r from shot to shot was less then .1 (isec by the above method. 3-4 Cal i b r a t i o n To measure the Stark widths of the l i n e p r o f i l e s we f i r s t had to ca l i b r a t e the wavelength accurately. The recorded p r o f i l e s are the convolution of the actual emitted p r o f i l e with the broadening function of our measurement system. To determine the Stark widths from the t o t a l widths we had to determine the machine broadening function. This was measured by recording the p r o f i l e of a helium neon laser at 6328.2 A. The laser l i g h t has a negl i g i b l e width compared to the machine width. The machine width was — 7 channels at halfmaximum and — 14 channels wide at 1/10 maximum. To find the Stark widths one usually assumes the machine p r o f i l e to be a Voigt p r o f i l e (the convolution of a Gaussian and Lorentzian). Then, using the machine widths at 1/2 maximum and 1/10 maximum the Stark widths can eas i l y be found from the measured p r o f i l e s by using the deconvolution tables provided in a paper by H. van de Hulst and J.Reesnick (1947). Analysis by t h i s method gave the machine broadening correction to be usually ~ 10% and at most 20% for some of the narrowest l i n e s . Unfortunately the width at 1/10 maximum i s d i f f i c u l t to measure because the apparatus provides such few points on the machine p r o f i l e and because noise i s s i g n i f i c a n t at that l e v e l s i g n a l . Also the appreciable asymetry of the machine p r o f i l e makes the analysis questionable. Thus instead of 25 u s i n g t h e d e c o n v o l u t i o n t a b l e s , we e x p e r i m e n t a l l y d e t e r m i n e d t h e m achine b r o a d e n i n g by r e c o r d i n g N I I 3919 and 3995 a t Run 2 c o n d i t i o n s and He I 5876 a t Run 1 c o n d i t i o n s , a t two d i f f e r e n t d i s p e r s i o n s a c r o s s t h e OMA d e t e c t o r s u r f a c e . The two d i f f e r e n t d i s p e r s i o n s were p o s s i b l e by m e a s u r i n g t h e l i n e s w i t h and w i t h o u t t h e e x i t l e n s . W i t h t h e l e n s i n p l a c e t h e l i n e w i d t h s were 1.0, 1.8 and 4.3 A (150 c h a n n e l s ) and w i t h o u t , 2.2, 3.0 and 5.4 A (29 c h a n n e l s ) f o r N II 3919, N II 3995 and He I 5876 r e s p e c t i v e l y . T h e s e a r e c o n s i s t e n t i f t h e machine b r o a d e n s l i k e a L o r e n t z i a n . T h a t i s , we s i m p l y s u b t r a c t t h e m a c h i n e w i d t h of 7 c h a n n e l s from t h e m e a s u r e d w i d t h s t o o b t a i n t h e S t a r k w i d t h s . T h i s s h o u l d be c h e c k e d more c a r e f u l l y b e f o r e l o w e r i n g t h e e r r o r f o r t h e m a c h i n e b r o a d e n i n g below ± 1 0 % . A l s o , t o d e t e r m i n e whether t h e m a c h i n e b r o a d e n i n g v a r i e d w i t h c h a n n e l number, t h e He-Ne l a s e r p r o f i l e was m e a s u r e d a t i n t e r v a l s o f 50 c h a n n e l s a c r o s s t h e f u l l 500 c h a n n e l s . Though i t was s l i g h t l y w i d e r a t t h e l o w e r c h a n n e l s (FWHM ~ 8 c h a n n e l s a t c h a n n e l 150) t h i s d i d n o t a f f e c t t h e m e a s u r e d p r o f i l e s . To c a l i b r a t e t h e OMA c h a n n e l s t o w a v e l e n g t h we u s e d an i r o n a r c p l a c e d i n f r o n t of t h e e n t r a n c e s l i t o f t h e s p e c t r o m e t e r . The i r o n a r c has many w e l l - i d e n t i f i e d narrow s t r o n g l i n e s i n t h e o p t i c a l r a n g e (C.Hodgman ( 1 9 5 7 ) ) p e r m i t t i n g a c c u r a t e c a l i b r a t i o n t o t h r e e s i g n i f i c a n t f i g u r e s o v e r t h e whole w a v e l e n g t h r a n g e of i n t e r e s t (3800-6800 A ) . The c a l i b r a t i o n was f o u n d t o d i f f e r by ~ 3% o v e r t h i s r a n g e (due t o t h e s p e c t r o m e t e r ) . S i n c e t h i s was much l e s s t h e n 26 o t h e r e r r o r s t h e c a l i b r a t i o n a t 4500 A was u s e d . The c a l i b r a t i o n was a l s o f o u n d t o be l i n e a r a c r o s s t h e 500 c h a n n e l s t o w i t h i n a few %. One add e d c o m p l i c a t i o n was t h a t t h e i r o n a r c l i n e s were t o o weak t o be o b s e r v e d i n g a t e d mode and c o u l d o n l y be u s e d t o c a l i b r a t e t h e OMA i n r e a l t i m e . The r a p i d f o c u s i n g and d e f o c u s i n g o f t h e 1205D's a m p l i f i e r i n g a t e d mode c a u s e s a w i d e n i n g o f t h e w a v e l e n g t h s c a l e o r s h i f t i n c h a n n e l number o f t h e l i g h t s i g n a l . The g a t e d t o r e a l t i m e s h i f t a s a f u n c t i o n o f r e a l t i m e c h a n n e l number was o b t a i n e d by p o s i t i o n i n g t h e He-Ne l a s e r l i n e on a s p e c i f i c c h a n n e l i n r e a l t i m e , t h e n s w i t c h i n g t o g a t e d mode and r e c h e c k i n g t h e c h a n n e l number. By d o i n g t h i s a c r o s s t h e 500 c h a n n e l s an a l m o s t s t r a i g h t l i n e g r a p h f o r s h i f t v s c h a n n e l number was o b t a i n e d . Though i n d i v i d u a l c h a n n e l s g i v e a l i n e a r r e s p o n s e t o t h e l i g h t s i g n a l t h e y r e c e i v e , up t o a c e r t a i n l i m i t , t h e r e l a t i v e s e n s i t i v i t y of d i f f e r e n t c h a n n e l s i s n o t t h e same, e s p e c i a l l y i n g a t e d mode. The r e s p o n s e i s f a i r l y c o n s t a n t f r o m c h a n n e l 150 t o 450 but i s weaker above and below t h a t r a n g e . To measure t h e r e l a t i v e r e s p o n s e we needed a l i g h t s o u r c e c o n t i n u o u s a c r o s s t h e 500 c h a n n e l s . To p r o d u c e t h e c o n t i n u u m we f i r e d t h e d i s c h a r g e w i t h p u r e h e l i u m and o b s e r v e d t h e s p e c t r u m a t 5300 A where h e l i u m h a s a s t r o n g c o n t i n u u m and no s p e c t r a l l i n e s . B e c a u s e t h e a l i g n m e n t o f t h e d e t e c t o r a f f e c t e d t h i s c o n t i n u u m r e s p o n s e , i t was me a s u r e d a f t e r e a c h r e a l i g n m e n t o f t h e o p t i c s , w i t h and w i t h o u t t h e e x i t l e n s i n p l a c e . The measured r e s p o n s e f u n c t i o n v s c h a n n e l number was l a t e r u s e d t o c o r r e c t t h e 27 m e a s u r e d s p e c t r a . I t t u r n e d o u t t h a t a l l measured l i n e s had f u l l w i d t h s l e s s t h a n t h e s p r e a d of t h e l i n e a r r e g i o n of t h e OMA and t h u s c o u l d be p o s i t i o n e d t o m i n i m i z e t h e e f f e c t s o f t h e r e s p o n s e f u n c t i o n . However, t h e p l o t s l o o k a l o t b e t t e r when c o r r e c t e d . U s u a l l y a c a l i b r a t i o n of t h e r e s p o n s e o f t h e OMA v s w a v e l e n g t h o f i n c i d e n t l i g h t w o u l d be n e c e s s a r y . T h i s has t o be done when t h e m a g n i t u d e s o f two l i n e s a r e compared f o r t e m p e r a t u r e measurements. However t h e l i n e s we u s e d were s e p a r a t e d by 2-30 A. The OMA r e s p o n s e does not v a r y a p p r e c i a b l y o v e r t h i s r a n g e . We t e s t e d t h i s w i t h a t u n g s t e n lamp j u s t t o be s u r e . 3-5 F i r i n g P r o c e d u r e B e c a u s e t h e a l i g n m e n t a f f e c t e d t h e c a l i b r a t i o n s and b e c a u s e measurements had t o be made w i t h and w i t h o u t t h e e x i t l e n s e , we had t o f o l l o w a r a t h e r c o m p l i c a t e d p r o c e d u r e when t a k i n g d a t a . The s t e p s were : (1) Mix h e l i u m and n i t r o g e n i n m i x i n g chamber. (2) A l i g n o p t i c a l s y s t e m w i t h e x i t l e n s i n p l a c e . (3) Measure g a t e d t o r e a l t i m e c h a n n e l number c o r r e c t i o n and machine w i d t h u s i n g he ne l a s e r . D e t e r m i n e w a v e l e n g t h s c a l e o f OMA u s i n g i r o n a r c . (4) Measure c o n t i n u u m r e s p o n s e by f i r i n g d i s c h a r g e i n t o p u r e h e l i u m . (5) R e c o r d N II and N I I I s p e c t r a a s w e l l as n e a r b y c o n t i n u u m s f o r e a c h l i n e . The p r o f i l e s were p l o t t e d on g r a p h p a p e r and s t o r e d d i g i t a l l y i n t h e main computer 28 a f t e r e a c h s h o t . The d i s c h a r g e was pumped o u t and r e f i l l e d w i t h c l e a n gas b e f o r e e a c h s h o t . (6) Remove e x i t l e n s and r e a l i g n OMA d i r e c t l y on s p e c t r o m e t e r . (7) Redo s t e p ( 4 ) . (8) F i r e d i s c h a r g e and r e c o r d He I 5876 and 6678. T h i s p r o c e d u r e was p e r f o r m e d f o r a l l t h r e e r u n s . 3-6 D a t a H a n d l i n g E a c h p r o f i l e was s t o r e d i n a computer f i l e a s a 500 e l e m e n t a r r a y o f 6 d i g i t numbers t h a t r e p r e s e n t e d t h e l i g h t i n t e n s i t i e s t h a t f e l l upon t h e 500 p h o t o d e t e c t o r s . The computer programs of J o hn B e r n a r d , d e v e l o p e d f o r a s i m i l a r p r o j e c t (Msc. t h e s i s ( 1 9 7 9 ) ) , were u s e d t o t r a n s f o r m t h i s raw d a t a i n t o f i n i s h e d p l o t s . The p r o g r a m s c o r r e c t e d f o r t h e c o n t i n u u m r e s p o n s e of t h e OMA, s l i g h t l y smoothed t h e p r o f i l e s , s u b t r a c t e d t h e d e t e r m i n e d b a c k g r o u n d c o n t i n u u m s , n o r m a l i z e d t h e l i n e c e n t e r i n t e n s i t i e s t o one, c a l i b r a t e d t h e w a v e l e n g t h s c a l e and p r o d u c e d f i n i s h e d p l o t s on f i n e r u l e d g r a p h p a p e r . From t h e s e f i n a l p l o t s t h e f u l l w i d t h s were measured w i t h a r u l e r . 29 CHAPTER IV PLASMA DIAGNOSTICS In C h a p t e r I we g i v e an e x p r e s s i o n f o r t h e e l e c t r o n i m p a c t h a l f w i d t h t h a t depends l i n e a r l y on N e and w e a k l y on T e t h r o u g h t h e v e l o c i t y a v e r a g e ( s e e ( 2 - 1 2 ) ) . T h e r e f o r e t o t e s t our w i d t h measurements a g a i n s t t h e o r y we had t o d e t e r m i n e b o t h N e and T e . The e l e c t r o n d e n s i t y was e s t i m a t e d f r o m t h e w i d t h o f He I 5876 and t h e t e m p e r a t u r e from t h e r a t i o s o f s e v e r a l N I I l i n e i n t e n s i t i e s t o N I I I l i n e i n t e n s i t i e s . T h e s e d i a g n o s t i c methods depended on the p l a s m a b e i n g i n l o c a l thermodynamic e q u i l i b r i u m as w e l l as p l a s m a h o m o g e n e i t y , r e p r o d u c i b i l i t y , t i m e d ependence and o p a c i t y . We d i s c u s s e a c h i n d e t a i l b e f o r e g i v i n g t h e t e m p e r a t u r e and e l e c t r o n d e n s i t y measurements. 4-1 L o c a l Thermodynamic E q u i l i b r i u m (H.Griem (1964) ch.6) In a h o t d ense p l a s m a e x c i t a t i o n , d e - e x c i t a t i o n , i o n i z a t i o n and r e c o m b i n a t i o n a r e c o n t r o l l e d p r i m a r i l y by e l e c t r o n c o l l i s i o n s . The c o l l i s i o n s c a n c r e a t e an e q u i l i b r i u m c o n d i t i o n between a t o m i c s t a t e s and s p e c i e s a t t h e e l e c t r o n t e m p e r a t u r e c a l l e d l o c a l t h ermodynamic e q u i l i b r i u m ( L T E ) . A p l a s m a i n L T E has d e n s i t i e s i n v a r i o u s quantum s t a t e s of an i o n g i v e n by t h e B o l t z m a n n e q u a t i o n and d e n s i t i e s i n d i f f e r e n t i o n i z a t i o n s t a g e s g i v e n by t h e Saha e q u a t i o n . 30 The Boltzmann equation for the density of ions in the excited state n i s : N i n = N, g l n exp(-E i n /kTfi ) (4-1) where N ) n = the density in the excited state E j n = the excitation energy Nj = the t o t a l density of the ion Z,(T e) = the p a r t i t i o n function and g j n = the degeneracy of the excited state. The Saha equation for the r a t i o of t o t a l densities in two consecutive ionization stages i s : Ne Nj = 6 x 10- 2 1Z j ( T e ) ( k T P ) 3 / 2 e x p ( - E ; r o / k T e ) (4-2) Nj Z j (T e) The higher ionization stage i s l a b e l l e d by i and the lower by j . m i s the electron mass. We ignore the small lowering of the ionization potential by the Debye sphere which i s .1 ev in thi s experiment. To solve for the ionic densities at a p a r t i c u l a r N e and T e we use (4-2) and the equation of macroscopic charge n e u t r a l i t y . The l a t t e r i s : N e = ZzjNj (4-3) i Zj i s the charge number of the i t h ion stage. The sum i s over a l l ions present in the plasma. Using (4-2) with (4-3) gives us an equal number of equations and unknowns. Table (4-1) shows the ionic densities calculated from (4-2) and (4-3) by Dr.A.J.Barnard's computer programs, at the 31 e s t i m a t e d t e m p e r a t u r e and e l e c t r o n d e n s i t i e s o f t h e p l a s m a s s t u d i e d ( s e e s e c t i o n s (4-7) and ( 4 - 8 ) ) . The h e l i u m i s ~ 99% s i n g l y i o n i s e d and t h e n i t r o g e n ~ 7-20% s i n g l y i o n i s e d and ~ 90-80% d o u b l y i o n i s e d . See s e c t i o n (4-5) f o r a d e s c r i p t i o n o f t h e p r o g r a m s u s e d t o c a l c u l a t e t h e v a l u e s i n T a b l e ( 4 - 1 ) . TABLE (4-1) I o n i c D e n s i t i e s At T e = 3.1 ev N e cm" 3 0.9 X 1 0 1 7 2 . 2 X 1 0 1 7 2.9 X 1 0 1 7 Ion L o g , 0 ( N . c m " 3 ) ) He I 1 4.06 14.85 15.09 He II 16.48 16.88 17 . 0 1 He I I I 14.26 14.28 14.28 N I 1 1 .38 12.52 12.87 N I I 1 5.26 1 6 . 0 2 16.25 N I I I 1 6.45 16.82 16.93 N IV 14.59 14.57 14.44 The e l e c t r o n s w i l l have a d e f i n a b l e t e m p e r a t u r e i f t h e e l e c t r o n v e l o c i t y d i s t r i b u t i o n i s M a x w e l l i a n . The t i m e r e q u i r e d t o e s t a b l i s h a M a x w e l l i a n v e l o c i t y d i s t r i b u t i o n i s g i v e n by ( s e e H.Griem ( 1 9 6 4 ) ) : t e e ~ 1 0 5 ( k T e / e v ) 3 / 2 N e ' c m " 3 s e c (4-4) U s i n g T e = 3 ev and N e = 2 x 1 0 1 7 cm" 3, (4-4) g i v e s t e e ~ 3 x 10" 1 2 s e c . F o r i o n s o f mass m. t h e t i m e i s t j j ~ ( m j / m e ) 1 / 2 t e e and t h e t i m e f o r b o t h i o n s and e l e c t r o n s t o e q u a l i s e t h e i r t e m p e r a t u r e s i s t | e ~ ( m \ / m e ^ t e e * F o r n i t r o g e n we g e t t j j " 1.3 x 1 0 " 1 0 sec and t j e ~ .1 »isec and f o r h e l i u m t j j ~ .7 x 1 0 " 1 0 s e c and t j ~ .025 >.sec. S i n c e o u r p l a s m a s v a r i e d l i t t l e i n .1 usee ( s e e s e c t i o n ( 4 - 4 ) ) i t i s s a f e t o assume t h a t b o t h e l e c t r o n s and i o n s have 32 Maxwellian v e l o c i t y d i s t r i b u t i o n s at the same temperature. For a Boltzmann d i s t r i b u t i o n to exist at T e, the electron density must be high enough so c o l l i s i o n a l excitations completely dominate over radiative de-excitations. Estimates of the minimum neccessary electron density are often made by requiring the average c o l l i s i o n a l e x citation rate of a l e v e l to be 10 times greater than the average radiative de-excitation rate. The densities in the various states w i l l then follow (4-1) to within 10%. In general t h i s i s more e a s i l y s a t i s f i e d by the higher states because they have larger c o l l i s i o n a l cross-sections and lower radiative decay rates due to smaller energy separations between l e v e l s . Thus the ratios of densities in the higher excited states are often governed by (4-1) even i f the lower states are r e l a t i v e l y overpopulated by radiative decay ( p a r t i a l LTE). A process which often helps the plasma r e a l i z e f u l l LTE is reabsorption of resonance l i n e radiation (radiation emitted during t r a n s i t i o n s to the ground state) . This e f f e c t i v e l y reduces the radiative decay rate to the ground state and hence the minimum neccessary N e for a Boltzmann d i s t r i b u t i o n . In a paper on the thermal equilibrium c r i t e r i a for a N II and N III plasma at 3 ev, W.A.Cilliers, e t . a l . (1975), consider c o l l i s i o n a l processes and resonance absorption. They give the minimum neccessary N e for f u l l LTE as 3 x 10 1 6 cm"3. Since t h i s i s well below the estimated electron densities found in thi s experiment (~ 2 x 10 1 7 cm"3) equations (4-1) and (4-2) should be accurate to within 33 a few % f o r t h e n i t r o g e n I I and I I I i o n s . P a p e r s by R.Mewe (1967) and H.W.Drawin (1964) show t h a t we c a n e x p e c t f u l l L T E f o r He I I but n o t f o r He I . In t h e s e p a p e r s t h e a u t h o r s c a l c u l a t e t h e r a t i o o f s t a t e d e n s i t i e s f r o m (4-1) t o d e n s i t i e s c a l c u l a t e d by c o n s i d e r i n g r e s o n a n c e a b s o r p t i o n , c o l l i s i o n a l e x c i t a t i o n and r a d i a t i v e d e c a y r a t e s . We c o n c l u d e f u l l L T E f o r He I I by i n t e r p o l a t i n g T a b l e I I o f Mewe f o r t h e c a s e o f a plas m a t h a t s t r o n g l y r e a b s o r b s ( o p t i c a l l y t h i c k ) t h e 304 A r e s o n a n c e l i n e . Our p l a s m a s were o p t i c a l l y t h i c k t o t h e 304 A l i n e b e c a u s e t h e y were p r e d o m i n a n t l y i n t h e He I I s t a g e ( s e e t a b l e ( 4 - 1 ) ) . I n t e r p o l a t i n g from t a b l e s 1 and 2 o f D r a w i n we see t h a t t h e g r o u n d s t a t e of He I i s ~ 10 t i m e s o v e r p o p u l a t e d f o r an o p t i c a l l y t h i n r e s o n a n c e l i n e b u t by t h e s e c o n d p r i n c i p a l quantum number t h e l e v e l s a r e c l o s e t o L T E . The h i g h e r s t a t e s of t h e He I w i l l a l s o be i n LTE w i t h t h e g r o u n d s t a t e of He I I b e c a u s e of t h e s m a l l e n e r g y d i f f e r e n c e . B e c a u s e our pl a s m a i s p r e d o m i n a n t l y i n t h e He I I s t a g e , t h e o v e r p o p u l a t i o n of t h e He I g r o u n d s t a t e w i l l n o t d e c r e a s e t h e d e n s i t y o f t h e He I I a p p r e c i a b l y and t h e e l e c t r o n d e n s i t y e v e n l e s s (~ 2/3 o f f r e e e l e c t r o n s come from n i t r o g e n i o n i z a t i o n ) . Thus t h e d e n s i t i e s of t h e He I l e v e l s o t h e r t h a n t h e g r o u n d s t a t e may be p r e d i c t e d w i t h (4-1) and (4-2) u s i n g t h e p o p u l a t i o n o f t h e g r o u n d s t a t e o f He I I . T h i s i s i m p o r t a n t f o r t h e l o w e r s t a t e o f t h e He I 5876 t r a n s i t i o n ( t r i p l e t 2 3 P ° ) when we c a l c u l a t e t h e o p t i c a l d e p t h s ( s e e s e c t i o n ( 4 - 5 ) ) . B e s i d e s a minimum N e r e q u i r e m e n t , t h e v a r i o u s i o n s must 34 t a k e s u f f i c i e n t l y s h o r t t i m e s t o r e a c h e q u i l i b r i u m . The plasma must respond r a p i d l y t o changes i n the e x t e r n a l p arameters which i n t h i s experiment v a r i e d by the o r d e r of s e v e r a l «sec. The e q u i l i b r i u m time may be e s t i m a t e d by the s l o w e s t of t h e p r o c e s s e s t h r o u g h which e q u i l i b r i u m i s r e a c h e d . T h i s i s the c o l l i s i o n a l e x c i t a t i o n of the ground s t a t e because of the l a r g e energy d i f f e r e n c e s between the ground s t a t e and l o w e s t e x c i t e d s t a t e s . H.Griem ( ( 1 9 6 4 ) , e q u a t i o n 6-65) g i v e s an e x p r e s s i o n f o r the c o l l i s i o n a l e x c i t a t i o n t i m e which we use t o c a l c u l a t e the e q u i l i b r a t i o n t i m e s f o r N I-111 and He I and I I . They a r e t a b u l a t e d i n T a b l e (4-2) f o r N e = 2 X 1 0 1 7 . The l o n g e s t i s f o r He I I a t .2 y<sec which i s s t i l l s i g n i f i c a n t l y s h o r t e r than the plasma v a r i a t i o n t i m e . T a b l e (4-1) E q u i l i b r a t i o n Times From Resonance E x c i t a t i o n Rates N e = 2 x 1 0 1 7 cm* 3 T e = 3.1 ev I on He I He I I N I N I I N I I I Resonance L i n e (A) 584 304 1 135 1 084 990 E q u i l i b r a t i o n Times ( s e c ) 1x10- 6 2 x 1 0" 6 2 x 1 0 " 1 2 4X10" 9 5 x 1 0 " 1 1 4-2 Plasma Homogeneity To i n t e r p r e t our measured p r o f i l e s we must be c e r t a i n t h a t c o n t r i b u t i o n s t o t h e l i n e i n t e n s i t i e s were not r e c e i v e d from r e g i o n s of d i f f e r i n g N e and T e. In our plasma regime inhomogeneity a r i s e s because uneven Ohmic h e a t i n g and heat 35 transport to cooler regions creates temperature, density and pressure gradients. By the Saha equation, lower temperature regions have lower electron density because of less i o n i z a t i o n . In several previous studies performed on similar plasma sources, the r a d i a l and a x i a l dependence of the plasma was studied. R.Nelson (1970) established that a uniform plasma was formed in the constricted section of the vessel when a 9 kamps current was discharged into a 10 torr helium gas. He showed that N e was uniform r a d i a l l y to within .05 i n . of the tube walls (10% of the t o t a l diameter). This i s well outside the o p t i c a l cone for the end-on measurements (see figure (3-2)). Though the r a d i a l temperature d i s t r i b u t i o n was not measured, the uniformity of N e suggests that T e is also uniform, at least to well outside the o p t i c a l cone. Nelson also showed that the temperature was very constant along the main tube axis in the constricted section of the vessel. Past the point where the tube f l a r e s , the temperature drops rapidly. As a rough estimate from his data the temperature approximately halves in half the distance from the widening point to the electrodes. By assuming a l i n e a r temperature gradient and that N e drops by 2/3 we can estimate the amount of l i n e radiation coming from the cooler region. We use N e at 1/3 for the cold region because with any s i g n i f i c a n t temperature gradient the plasma i s solely in the He I and N II stages instead of the He II and N III stages that predominate in the constricted section of the tube. Using tables from Dr.Barnard's programs based on equation (4-11) 36 f o r l i n e i n t e n s i t i e s , we e s t i m a t e t h a t ~ 5% o f He I 5876, ~ 3% N I I l i n e i n t e n s i t i e s and n e g l i g i b l e amounts o f He I I and N I I I l i n e i n t e n s i t i e s come from t h e c o o l e r r e g i o n s . T h e s e a r e o f c o u r s e v e r y i n a c c u r a t e e s t i m a t e s s i n c e we d o n ' t know t h e d e t a i l e d t e m p e r a t u r e and e l e c t r o n d e n s i t y p r o f i l e s . F i n a l l y N e l s o n showed t h e a x i a l e l e c t r o n d e n s i t y was u n i f o r m by c o m p a r i n g s i d e - o n and end-on p r o f i l e m e asurements. He f o u n d t h a t t h e w i d t h of He I 3889 o b s e r v e d s i d e - o n was w i t h i n 5% o f t h e w i d t h o b s e r v e d end-on. Thus our w i d t h s s h o u l d not be s e r i o u s l y a f f e c t e d by i n h o m o g e n e i t i e s . 4-3 R e p r o d u c i b i l i t y The p l a s m a c o n d i t i o n s were v e r y r e p r o d u c i b l e from s h o t t o s h o t i f a b o u t t e n warmup s h o t s were t a k e n and i f t h e measurements were t a k e n i n f a i r l y r a p i d s u c c e s s i o n (~ one m i n u t e i n t e r v a l s ) . M easurements of l i n e w i d t h s and hence N e v a r i e d by "~ 5%. The l i n e i n t e n s i t i e s v a r i e d by ~ 15% and hence T e by "~ 1%. However a t l o n g e r i n t e r v a l s between f i r i n g s t h e r e p r o d u c i b i l i t y was n o t as good. A l s o t h e s y s t e m t e n d e d t o d r i f t o v e r s e v e r a l h o u r s o f o p e r a t i o n a s a l i g n m e n t s c h a n g e d , q u a r t z windows s t a i n e d , e l e c t r o d e s p i t t e d , t i m i n g s v a r i e d , e t c . S i n c e t h e d a t a t a k i n g was f a i r l y i n v o l v e d i t t o o k a t l e a s t f i v e m i n u t e s between s h o t s and a b o u t s i x h o u r s f o r a f u l l d a t a r u n . B e c a u s e of t h i s we s h o u l d r a i s e our e s t i m a t e s o f p l a s m a i r r e p r o d u c i b i l i t y somewhat. The e f f e c t o f r e p r o d u c i b i l i t y c o u l d have been r e d u c e d i f we had a v e r a g e d s e v e r a l s h o t s o f e a c h p r o f i l e but b e c a u s e o f t h e l a r g e number of l i n e s s t u d i e d t h i s was n o t 37 done. 4-4 Time Dependence A s t u d y o f t h e w i d t h and i n t e n s i t y of He I 5876 vs g a t e t i m i n g showed them t o v a r y ~ 5% o v e r t h e 1 usee we o b s e r v e d t h e p l a s m a a t t h e f i n a l c h o s e n t i m i n g . T h i s means our e l e c t r o n d e n s i t y v a r i e s by ~ 5% d u r i n g our o b s e r v a t i o n t i m e and t h e t e m p e r a t u r e n e g l i g i b l y . T h i s i s s m a l l compared t o t h e o t h e r u n c e r t a i n t i e s and t h e p l a s m a c a n c o n s i d e r e d q u a s i s t a t i o n a r y . 4-5 O p t i c a l D e p t h P h o t o n s e m i t t e d f r o m a t o m i c t r a n s i t i o n s w i t h i n a f i n i t e p l a s m a may be r e a b s o r b e d by t h o s e atoms o f t h e p l a s m a a l r e a d y i n t h e l o w e r s t a t e o f t h e t r a n s i t i o n . B e c a u s e t h e a b s o r p t i o n p r o f i l e i s t h e same a s t h e e m i s s i o n p r o f i l e i n a c o l l i s i o n d o m i n a t e d p l a s m a , p h o t o n s n e a r t h e l i n e c e n t e r a r e p r e f e r e n t i a l l y r e a b s o r b e d . S t r o n g r e a b s o r p t i o n f l a t t e n s t h e e m i t t e d p r o f i l e s and t h e p l a s m a i s t h e n c a l l e d o p t i c a l l y t h i c k . P r o f i l e h a l f w i d t h s o f t h e r e a b s o r b e d l i n e s , d e t e r m i n e d f r o m t h e h e i g h t a t l i n e c e n t e r , w i l l o v e r e s t i m a t e t h e S t a r k w i d t h . To c a l c u l a t e t h e o p t i c a l t h i c k n e s s , T , c o n s i d e r t h e l i g h t i n t e n s i t y e m i t t e d by a homogeneous, s t a t i o n a r y , LTE p l a s m a o f l e n g t h 1 and c o n s t a n t a b s o r p t i o n c o e f f i c i e n t p e r u n i t l e n g t h K ( o ) . The c o n t r i b u t i o n t o t h e i n t e n s i t y measured a t t h e edge of t h e p l a s m a , I m ( o ) , from an i n f i n i t e s i m a l volume e l e m e n t w i t h i n t h e p l a s m a a t x, w i t h e m i s s i v i t y 38 I e ( o ) / l ( e m i t t e d power p e r u n i t l e n g t h ) c a n be w r i t t e n as : d l m ( u ) = d x ( I e ( o ) / l ) e x p ( - K ( o ) x ) I n t e g r a t i n g a l o n g t h e l i n e o f s i g h t f r o m 0 t o 1 g i v e s : I m U ) = I e U) ( 1 - e x p ( - K ( u ) l ) ) = IpU) ( l-exp(-rU) ) (4-5) K ( o ) l T T O ) where T ( u ) = K ( o ) 1 An e x p r e s s i o n f o r T f o r a s p e c t r a l l i n e e m i t t e d d u r i n g a t r a n s i t i o n f r o m s t a t e m t o n i s g i v e n by H.Griem ( ( 1 9 6 4 ) pg 173). I t i s : T ( U ) = 2 n 2 r 0 c f n m N n ( l / e x p ( - W k T e ) ) L ( o ) l (4-6) where r 0 = t h e c l a s s i c a l e l e c t r o n r a d i u s f n m = t h e a b s o r p t i o n o s c i l l a t o r s t r e n g t h N n = t h e i o n d e n s i t y i n t h e l o w e r s t a t e L ( o ) = t h e n o r m a l i z e d l i n e shape We r e w r i t e (4-6) i n t h e more p r a c t i c a l w a v e l e n g t h u n i t s . A s s u m i n g t h e e m i t t e d p r o f i l e s a r e L o r e n t z i a n w i t h h a l f w i d t h w t h e n L(X. 0) = 1/irw where X.0 i s t h e l i n e c e n t e r . U s i n g (4-1) f o r N n we g e t f o r T a t l i n e c e n t e r : T 0 = 2.82 x 1 0 - 2 1 f n m N 0 g n ( e x p ( - E n / k T B ) - e x p ( - E m / k T e ) ) X 0 2 l / w Z ( T e ) (4-7) W i t h T 0 below 1 t h e t o t a l e m i t t e d i n t e n s i t y i s r e d u c e d by ~ T 0 / 4 x 100%. U s u a l l y one a t t e m p t s t o keep t h e o p t i c a l d e p t h below .4 by c o n s i d e r i n g t h e p a r a m e t e r s i n ( 4 - 7 ) . I n i t i a l c a l c u l a t i o n s on s e v e r a l N II and N I I I l i n e s and 39 He I 5876 showed o p t i c a l d e p t h s i n t h e .5 t o 3 r a n g e so we were f o r c e d t o r e a s s e s s t h e e x p e r i m e n t . T h e r e were t h r e e ways open t o us t o r e d u c e t h e o p t i c a l d e p t h s . (1) O b s e r v e t h e p l a s m a s i d e - o n t h u s r e d u c i n g 1. U n f o r t u n a t e l y we o n l y r e a l i z e d r e a b s o r p t i o n was a p r o b l e m f a i r l y l a t e i n t h e e x p e r i m e n t so c h a n g i n g t h e a p p a r a t u s was u n d e s i r a b l e . B e s i d e s r e s t r u c t u r i n g t h e e q uipment we would have had t o r e c h e c k a l l t h e l i n e s a t v a r i o u s p r e s s u r e s and v o l t a g e s t o see i f t h e y were s t i l l o b s e r v a b l e w i t h t h e r e d u c e d o p t i c a l p a t h l e n g t h . A l s o t h e p l a s m a v e s s e l g e t s d i r t y and s t a i n e d f r o m r e p e a t e d f i r i n g s making o b s e r v a t i o n s t h r o u g h i t d i f f i c u l t e s p e c i a l l y s i n c e we w i s h e d t o c o l l e c t a l a r g e amount of d a t a . At t h e v e r y end of t h e e x p e r i m e n t we d i d however c l e a n t h e t u b e w i t h h y d r o f l u o r i c a c i d and t o o k s i d e - o n measurements o f N I I 4614 and 4643 f o r t h e t h r e e f i r i n g c o n d i t i o n s . (2) Reduce t h e number d e n s i t y i n t h e l o w e r s t a t e by v a r y i n g t h e f i l l i n g p r e s s u r e o r gas m i x t u r e . R e d u c i n g t h e t o t a l f i l l i n g p r e s s u r e would r e d u c e t h e e l e c t r o n d e n s i t y and hence t h e i n t e r e s t o f t h i s e x p e r i m e n t . I t i s a l s o known t h a t p l a s m a h o m o g e n e i t y i s a p r o b l e m a t l o w e r f i l l i n g p r e s s u r e s ( C . R . N e u f e l d ( 1 9 6 6 ) ) . We c a n n o t r e d u c e t h e o p t i c a l d e p t h p r o b l e m by j u s t c h a n g i n g t h e r a t i o o f h e l i u m t o n i t r o g e n b e c a u s e b o t h s u f f e r f r o m r e a b s o r p t i o n a t t h e 50:50 r a t i o . We c o u l d have d i l u t e d t h e n i t r o g e n - h e l i u m m i x t u r e w i t h a n o t h e r gas s u c h as a r g o n . T h i s w o u l d have f o r c e d us t o r e d o our s u r v e y of n i t r o g e n l i n e s t o s e e w h i c h were o b s c u r e d by a r g o n l i n e s b e s i d e s c o m p l i c a t i n g a l l t h e LTE c o n s i d e r a t i o n s . Thus we p a s s e d on t h i s o p t i o n . 40 (3) C hoose r e l a t i v e l y weak l i n e s w i t h low o s c i l l a t o r s t r e n g t h s . U n f o r t u n a t e l y most o f t h e weaker l i n e s a r e g e n e r a l l y more d i f f i c u l t t o measure and of l e s s i n t e r e s t b e c a u s e t h e y have been i n f r e q u e n t l y s t u d i e d , e x p e r i m e n t a l l y or t h e o r e t i c a l l y . However, one t h i n g i n our f a v o r i s t h a t l i n e s i n t h e same m u l t i p l e t have t h e same S t a r k w i d t h , t o a c l o s e a p p r o x i m a t i o n , e x c e p t i n u n u s u a l c a s e s ( N . K o n j e v i c and M . S . D i m i t r i j e v i c ( 1 9 8 1 ) ) . Thus by m e a s u r i n g t h e weaker l i n e s i n a m u l t i p l e t we c a n g e t a c l o s e a p p r o x i m a t i o n t o t h e s t r o n g e r , more i n t e r e s t i n g l i n e s . The p r o b l e m i s t o c h o o s e l i n e s s t r o n g enough t o be o b s e r v e d y e t n o t a b s o r b e d . F o r t h e f i n a l s e l e c t i o n of l i n e s we p i c k e d t h o s e w i t h low o p t i c a l d e p t h s and a mix o f p r e v i o u s l y m e a s u r e d and new l i n e s . As a c h e c k on o p t i c a l d e p t h we a l s o t r i e d t o measure two l i n e s o f d i f f e r i n g s t r e n g t h from t h e same m u l t i p l e t . As w e l l as r e d u c i n g t h e o p t i c a l d e p t h , i n p r i n c i p l e we c a n c o r r e c t t h e p r o f i l e s i f t h e o p t i c a l d e p t h i s known. U s i n g (4-5) and ( 4 - 7 ) , we g e t f o r t h e S t a r k w i d t h w s v s t h e m e a s u r e d w i d t h w m : w s = w „ (4-8) ( r 0 / l n ( l / ( l + e x p ( - T 0 ) ) ) - 1 ) 1 w s/w m i s p l o t t e d i n f i g u r e (4-1) f o r r0 from 0 t o 4. S i n c e T 0 d e p e n d s on ws, (4-8) must be s o l v e d i t e r a t i v e l y . The p r o b l e m w i t h u s i n g (4-8) i s t h a t T 0 i s h a r d t o d e t e r m i n e a c c u r a t e l y . The u n c e r t a i n t i e s i n 1, f n m , T e , N e and ws c a u s e c o n s i d e r a b l e e r r o r s i n T 0 . We t a b u l a t e t h e e r r o r s i n T 0 i n t a b l e ( 4 - 3 ) . The u n c e r t a i n t i e s i n 1 a r e l e s s t h a n 10% f o r He I a n d N I I and l e s s t h a n 5% f o r N I I I i f we a c c e p t t h e 41 F i g u r e (4-1) : C o r r e c t e d S t a r k w i d t h t o measured w i d t h r a t i o ( w s / w m ) v s o p t i c a l d e p t h . r o u g h e s t i m a t e s o f s e c t i o n ( 4 - 3 ) . The u n c e r t a i n t i e s i n t h e o s c i l l a t o r s t r e n g t h s a r e g i v e n by W.L.Wiese, e t . a l . ( 1 9 6 6 ) . The t e m p e r a t u r e measurement i s e s t i m a t e d i n s e c t i o n (4-7) t o w i t h i n 7% and t h e N e measurements t o w i t h i n ~ 30% i n s e c t i o n ( 4 - 8 ) . The c o r r e s p o n d i n g e r r o r s t h e s e c a u s e i n T 0 can be e s t i m a t e d f r o m (4-2) a n d ( 4 - 7 ) . We u s e d an a v e r a g e e r r o r f r o m c h a p t e r 5 f o r w s. 42 T a b l e (4-3) E r r o r In T 0 SOURCE OF ERROR IN T 0 (±%) w s/w m ERROR FROM T 0 ION 1 T e N e W s TOTAL T 0 = • 5 1 1 .5 He I 5 1 10 25 7 50 5 10 15 N I I 5 10 1 2 25 15 65 7 14 21 N I I I 2 12 32 16 15 70 7 15 22 The v a l u e s i n t a b l e (4-3) show t h a t t h o u g h t h e e r r o r s i n T 0 a r e l a r g e , t h e u n c e r t a i n t i e s i n w s/w m a r e not e x c e s s i v e . A l s o ~ 2/3 o f t h e s e e r r o r s a r e s y s t e m a t i c t o t h e t h r e e s e t s o f d a t a , a nd t h u s s h o u l d n ot a f f e c t t h e N e s e a l i n g . A n o t h e r method o f d e t e r m i n i n g T 0 i s p o s s i b l e by c o m p a r i n g t h e i n t e n s i t i e s o f l i n e s w i t h i n t h e same m u l t i p l e t . C o n s i d e r two l i n e s f r o m t h e same m u l t i p l e t , w i t h o p t i c a l d e p t h s T 0 and T 0 ' . The l i n e s w i l l have a p p r o x i m a t e l y e q u a l t r a n s i t i o n e n e r g i e s , S t a r k w i d t h s and o p t i c a l p a t h s . Thus from (4-7) we g e t : T_o_= 9rifnm = BC (4-9) T o' 9p fpq where B = g n / g p and C = fnm/fpq • From e q u a t i o n (4-4) t h e r a t i o o f measured i n t e n s i t i e s a t l i n e c e n t e r i s : D = I m U o ) = I e U n ) ( 1 - e x p ( - T 0 ) ) / T N I m U o ) I e U o ) ( 1 - e x p ( - T 0 ' ) ) / T 0 ' (4-10) 43 From H.Griem ( 1 9 6 4 ) , page 1 75 , the emitted intensity at l i n e center i s : I eUo) = 4 i r 2hc 2rog nf nmN mL()\ 0) ( 4 - 1 1 ) and therefore using ( 4 - 2 ) the r a t i o of emitted i n t e n s i t i e s i s : I e U p ) = gnfnm = BC ( 4 - 1 2 ) iIUo) 9pfpq Substituting ( 4 - 9 ) and ( 4 - 1 2 ) in ( 4 - 1 0 ) we get : T 0 = -ln(D(exp(-T 0/BC ) - 1 ) + 1 ) ( 4 - 1 3 ) Equation ( 4 - 1 3 ) i s e a s i l y solved numerically for T 0 which then can be used to f i n d T 0 ' from ( 4 - 9 ) . To use t h i s method we must measure the r e l a t i v e i n t e n s i t i e s of at least two li n e s from the same multiplet. Equation ( 4 - 1 3 ) can give s i g n i f i c a n t improvement over ( 4 - 7 ) because i t does not depend on the accuracy of 1, T e, N e, ws, or the absolute o s c i l l a t o r strengths. The accuracy is governed by C and D. In t h i s experiment D was measured to within 30% but b y measuring the two l i n e s simultaneously or averaging several shots, i t could e a s i l y be determined to within a few percent. The o s c i l l a t o r strengths given by W.L.Wiese, e t . a l ( 1 9 6 6 ) , were measured in emission experiments using ( 4 - 1 1 ) integrated over the wavelength scale. The given absolute f n t T / s are inaccurate because absolute l i n e i n t e n s i t i e s and number densities in excited states are d i f f i c u l t to measure. However, re l a t i v e o s c i l l a t o r strengths for l i n e s within the 44 same multiplet w i l l obey (4-12). The accuracy of the given C's w i l l depend only on the r e l a t i v e i n t e n s i t i e s of two nearby l i n e s . This i s very easy to measure because there are no c a l i b r a t i o n problems. Thus the C's calculated from the tables of Wiese are probably accurate to within a few percent. The a p p l i c a b i l i t y of (4-13) w i l l depend on whether the two l i n e s d i f f e r s u f f i c i e n t l y in strength so that one i s p r e f e r e n t i a l l y absorbed. That i s D/BC < .8 say. If such a condition i s not met (4-13) i s extremely susceptible to errors in D, v i r t u a l l y r u l i n g out the use of t h i s method. Unfortunately in this experiment we did not measure the r e l a t i v e l i n e i n t e n s i t i e s to the degree of accuracy possible because we had not worked out t h i s theory before the data was c o l l e c t e d . We must be s a t i s f i e d with D's good to within ±15%. This t y p i c a l l y gives an error of ~ 100 % or more in T 0 so we used (4-7) instead, though we note (4-13) for possible future use. In chapter 5 we present values for T 0 computed with (4-13) for comparison with (4-7). From such a comparison we could in p r i n c i p l e check our LTE assumptions since (4-7) depends on LTE and (4-13) does not. An important point to note i s that though the o p t i c a l depths of many li n e s were large enough to a f f e c t end-on measurements, only the resonance l i n e s were strong enough to a f f e c t population densities in their t r a n s i t i o n states. This i s because the p r o b a b i l i t y that a l i n e i s absorbed in a l l directions depends on the radius of the cylinder and not the length of the major axis. 45 4-6 L T E C o m p u t a t i o n s E x t e n s i v e use was made o f an i n t e g r a t e d s e t of computer p r o g r a m s d e v e l o p e d by D r . A . J . B a r n a r d w h i c h c a l c u l a t e d v a r i o u s q u a n t i t i e s a s a f u n c t i o n o f N e and T e a s s u m i n g L T E . The p r o g r a m s f i r s t computed , f o r g i v e n N e and T e , t h e d e n s i t i e s o f a l l t h e i o n s p e c i e s i n t h e p l a s m a u s i n g t h e Saha e q u a t i o n ( 4 - 2 ) , t h e g i v e n r a t i o o f h e l i u m t o n i t r o g e n (50:50) and t h e m a c r o s c o p i c c h a r g e n e u t r a l i t y e q u a t i o n ( 4 - 3 ) . The p a r t i t i o n f u n c t i o n s , n e e ded f o r ( 4 - 2 ) , were e s t i m a t e d from t h e t a b l e s o f C.Moore (1959) and t h e g n ' s and i o n i z a t i o n e n e r g i e s were o b t a i n e d from W.L.Wiese, e t . a l . ( 1 9 6 6 ) . U s i n g t h e i o n d e n s i t i e s , t h e p r o g r a m s n e x t c a l c u l a t e d t h e t o t a l d e n s i t y of a l l t h e i o n s (N) from t h e c o n s e r v a t i o n of mass e q u a t i o n , t h e p l a s m a p r e s s u r e (P) from t h e i d e a l gas law and Q eff d e f i n e d by ( 4 - 1 8 ) . Then, u s i n g (4-11) i n t e g r a t e d o v e r w a v e l e n g t h , t h e t o t a l i n t e n s i t i e s of s p e c i f i e d He I, N I I and N I I I l i n e s were c a l c u l a t e d from t h e N e ' s and t h e B o l t z m a n n e q u a t i o n ( 4 - 1 ) . The e n e r g y l e v e l s and o s c i l l a t o r s t r e n g t h s u s e d i n (4-1) came f r o m Wiese e x c e p t f o r N I I I 4634 an d 4641.. The o s c i l l a t o r s t r e n g t h s f o r t h o s e two l i n e s were c a l c u l a t e d by a n o t h e r o f D r . B a r n a r d ' s p r o g r a m s t h a t assumed t h e Coulomb a p p r o x i m a t i o n (D.R.Bates and A.Damgaard, ( 1 9 4 9 ) ) . F i n a l l y t h e programs c a l c u l a t e d t h e o p t i c a l d e p t h s of e a c h l i n e u s i n g (4-7) and ( 4 - 1 ) . F o r s p e c i f i e d r a n g e s and s p a c i n g s o f N e and T e v a l u e s , t h e p r o g r a m s o u t p u t l o g ( N e ) f o r e a c h i o n , l o g ( N ) , l o g ( P ) , Q eff , and, f o r e a c h l i n e , l o g ( r e l a t i v e i n t e n s i t y ) and l o g ( T 0 / L U 0 ) l ) • 46 It i s worth noting that the programs did not assume a constant density given by the i n i t i a l f i l l i n g pressure and thus allowance made for the d r i f t of p a r t i c l e s from the hot central region of the plasma to lower temperature regions. In table (4-3) we give the t o t a l density calculated assuming no p a r t i c l e d r i f t and the densities given by the programs. Table (4-4) Plasma Densities Total density without d r i f t Total density with d r i f t % Drop Run 1 1.1 x 10 1 7 .63 x 10 1 7 40 Run 2 2.3 x 10 1 7 1.6 x 10 1 7 30 Run 3 3.6 x 10 1 7 2.0 x 10 1 7 40 4-7 Temperature Measurements The temperature was determined by measuring the ratios of the t o t a l l i n e i n t e n s i t i e s of N II 4601, 4607, 4614, and 4641 to the intensity of N III 4643 and the r a t i o of N II 4552 to N III 4515. These rat i o s are strongly dependent on the electron temperature and weakly dependent on the free electron density. Using (4-1), (4-2) and (4-11) integrated over the wavelength scale, the r a t i o of t o t a l l i n e i n t e n s i t i e s of l i n e s from subsequent ionization stages i s : I j =_§_ = 2fnmqnX' 3 A n k T \ 3/2exy(-Em+E/00-En\ (4-14) If a' N e f ^ q g p X 3 \2vh2] \ kT e J The primes label the lower stage l i n e . I T and If are the t o t a l i n t e n s i t i e s and a and a' are the t o t a l areas under the p r o f i l e s . For Lorentzian p r o f i l e s a/a' = wh/w'h' where w and w' are the Stark widths and h and h' are the heights at l i n e 47 c e n t e r . To use (4-14) we must f i r s t have an e s t i m a t e f o r N e . T h i s i s o f t e n done from t h e w i d t h o f He I 5876 w h i c h i n an o p t i c a l l y t h i n p l a s m a i s a l m o s t i n d e p e n d e n t o f T e . However t h i s l i n e i s w i d e n e d somewhat by r e a b s o r p t i o n w h i c h i s s t r o n g l y t e m p e r a t u r e d e p e n d e n t . Thus f o r t h e f i r s t N e e s t i m a t e s t o use i n (4-14) we compared our w i d t h measurements of o p t i c a l l y t h i n N I I and N I I I l i n e s w i t h p r e v i o u s e x p e r i m e n t s a s s u m i n g l i n e a r s c a l i n g o f S t a r k w i d t h w i t h e l e c t r o n d e n s i t y . The N e ' s , (1.2, 2.5, and 3) x 1 0 1 7 cm" 3 f o r r u n s 1, 2 and 3 r e s p e c t i v e l y , were s u b s t i t u t e d i n (4-14) t o c a l c u l a t e t h e T e ' s . The t e m p e r a t u r e i s o n l y w e a k l y d e p e n d e n t on N e so t h a t t h e T e ' s d e t e r m i n e d a t t h e above N e ' s were not a p p r e c i a b l y d i f f e r e n t f r o m t h e v a l u e s a t our f i n a l N e e s t i m a t e s . The a/a' r a t i o s f o r t h e l i n e s m e n t i o n e d were measured f o r e a c h run and t h e c o r r e s p o n d i n g t e m p e r a t u r e s d e t e r m i n e d f r o m ( 4 - 1 4 ) . U s i n g t h e s e l i n e s had s e v e r a l i m p o r t a n t a d v a n t a g e s . F i r s t , s i n c e t h e y a r e so c l o s e i n w a v e l e n g t h , no r e l a t i v e i n t e n s i t y c a l i b r a t i o n s were n e c e s s a r y . S e c o n d l y t h e N I I I l i n e s had a b o u t t h e same i n t e n s i t i e s a s t h e N II l i n e s . T h i s meant t h e same n e u t r a l d e n s i t y f i l t e r s c o u l d be u s e d a t t h e e n t r a n c e t o t h e s p e c t r o m e t e r and need n o t be c a l i b r a t e d . A l s o r e a b s o r p t i o n w o u l d a f f e c t a l l t h e l i n e s s i m i l a r l y and n o t change a/a' much. F i g u r e (4-2) shows p l o t s of I j / I f v s T e as g i v e n by L T E . The p l o t t e d p o i n t s a r e t h e measured r a t i o s . From t h i s f i g u r e t h e t e m p e r a t u r e s were 3.06 ± .04 ev, 3.09 ± .03 ev 48 RUN 3 < tr. >- II H CO Ul I-3.0 3.1 T,(ev) 3.2 CURVES FROM SAHA-BOLTZMANN EQUATION 1 N2 4643/N3 464I 2 N2 4601/N 3 4641 3N2 4607/N3 4641 4N2 4621/N3 4641 5 N2 46I4/N3 4641 PLOTTED POINTS ARE MEASURED RATIOS Figure (4-2) : N II / N III intensity r a t i o s from the Saha Equation 49 and 3.07 ± .02 ev f o r r u n s 1, 2 and 3 r e s p e c t i v e l y . The e r r o r s q u o t e d a r e t h e s t a n d a r d d e v i a t i o n s . They r e p r e s e n t t h e e r r o r c a u s e d by t h e s h o t - t o - s h o t i r r e p r o d u c i b i l i t y and t o some e x t e n t t h e t h e v a r i e d r e a b s o r b t i o n o f d i f f e r e n t N I I l i n e s . The N I I 4552 t o N I I I 4515 r a t i o gave t e m p e r a t u r e s o f 3.08, 3.12 and 3.06 ev f o r r u n s 1, 2 and 3 r e s p e c t i v e l y . Added t o t h e s t a n d a r d d e v i a t i o n i s t h e s y s t e m a t i c e r r o r i n (4-14) from a 30% e r r o r i n N e and 50% e r r o r i n fnm/^pq • However, t h e s e e r r o r s o n l y a dd a n o t h e r 4% e r r o r t o t h e t e m p e r a t u r e measurements. Thus we a r r i v e a t a t e m p e r a t u r e o f 3.1 ± .1 ev f o r a l l 3 r u n s . I t may seem odd t h a t t h e t e m p e r a t u r e i s t h e same f o r t h e t h r e e r u n s when s u c h d i f f e r e n t f i r i n g v o l t a g e s and f i l l i n g p r e s s u r e s were u s e d b u t t h e e x t r a e n e r g y i s a b s o r b e d by i o n i z a t i o n p r o c e s s e s . We d i d n o t measure t h e t e m p e r a t u r e by f i n d i n g t h e r a t i o o f He I 5876 t o He I I 4686 as i s more commonly done b e c a u s e He I I 4686 was o b s c u r e d by s e v e r a l N I I l i n e s . 4-8 E l e c t r o n D e n s i t y Measurements As m e n t i o n e d i n t h e i n t r o d u c t i o n , good agreement e x i s t s between t h e o r y and e x p e r i m e n t f o r t h e S t a r k b r o a d e n i n g o f n e u t r a l and s i n g l y i o n i z e d , l i g h t e r e l e m e n t s . The s t r o n g d e p e n d e n c e on e l e c t r o n d e n s i t y and weak d e p e n d e n c e on t e m p e r a t u r e o f t h e w i d t h s o f many o f t h e s e l i n e s , make them s e n s i t i v e p r o b e s f o r N e . I n t h i s e x p e r i m e n t t h e p l a s m a was f o r m e d i n a m i x t u r e o f 50% n i t r o g e n and 50% h e l i u m so N e c o u l d be measured from t h e w i d t h o f t h e He I 5876 l i n e . As a f u r t h e r c h e c k He I 6678 was m e a s u r e d f o r r u n s 1 and 2 as 50 w e l l , t h o u g h not f o r run 3 b e c a u s e i t was t o o b r o a d f o r t h e OMA. I s o l a t e d l i n e s s u c h as He I 5876 a r e b r o a d e n e d p r i m a r i l y by e l e c t r o n i m p a c t s and r e l a t i v e l y c r u d e a p p r o x i m a t i o n s a r e s u f f i c i e n t t o a l l o w f o r i o n e f f e c t s . H.Griem ( ( 1 9 7 4 ) , e q u a t i o n ( 2 2 6 ) ) , g i v e s an e x p r e s s i o n f o r t h e f u l l S t a r k h a l f w i d t h , ws, o f t h e s e a p p r o x i m a t e l y L o r e n t z i a n l i n e s as : w s = W + 1.75 A (1-.75 R) W (4-15) W i s t h e e l e c t r o n impact w i d t h d e t e r m i n e d by ( 2 - 1 2 ) , A i s a d i m e n s i o n l e s s p a r a m e t e r t h a t m e asures t h e r e l a t i v e i m p o r t a n c e o f s t a t i c i o n b r o a d e n i n g and R i s a n o t h e r d i m e n s i o n l e s s p a r a m e t e r t h a t m e asures t h e r e l a t i v e i m p o r t a n c e o f Debye s h i e l d i n g and i o n - i o n c o r r e l a t i o n s . The s e c o n d t e r m i s 20% o f t h e t o t a l h a l f w i d t h f o r He I 5876 i n t h i s e x p e r i m e n t . W s c a l e s l i n e a r l y w i t h N e and A w i t h H^". R i s g i v e n by : R = 8.34 x 1 0 - * ( T e ( e v ) ) - 1 / 2 N e 1 / s (4-16) G r i e m g i v e s t a b l e s f o r W and A f o r He I atoms immersed i n a p l a s m a w i t h o n l y s i n g l y i o n i z e d p e r t u r e r s , a t N e = 1 0 1 6 cm" 3 and T e ~ 10,000-40,000 °K. A i s p r o p o r t i o n a l t o t h e n o r m a l H o l t s m a r k f i e l d s t r e n g t h g i v e n by : F 0 = 2.61 Zq,N?/ 3 (4-17) q f i s t h e c h a r g e and Nj t h e d e n s i t y o f an i o n s p e c i e s . To c o n v e r t t h e v a l u e s o f A g i v e n by G r i e m t o v a l u e s a p p r o p r i a t e 51 f o r a p l a s m a c o n t a i n i n g m u l t i p l y c h a r g e d i o n s , we must use (4-17) and ( 4 - 3 ) . A f t e r some s i m p l e a l g e b r a we f i n d we must m u l t i p l y G r i e m ' s v a l u e s by Q e f f . Q e f f i s g i v e n by : Qeff = l i Q i N K 3 , (4-18) T h i s i s c a l c u l a t e d by D r . B a r n a r d ' s programs as m e n t i o n e d i n s e c t i o n ( 4 - 6 ) . I t t u r n s o u t t h a t Q e f f ~ 1.5 f o r t h e N e - T e r a n g e o f t h i s e x p e r i m e n t . The e l e c t r o n d e n s i t y c a n now be d e t e r m i n e d f r o m (4-15) knowing how W, A and R s c a l e w i t h N e . U n f o r t u n a t e l y , s i n c e He I 5876 i s w i d e n e d by r e a b s o r b t i o n , we c o u l d n o t s u b s t i t u t e t h e m e a s u r e d w i d t h s d i r e c t l y i n t o (4-15) t o o b t a i n N e a c c u r a t e l y . We had t o use an i t e r a t i v e p r o c e d u r e o f f i r s t c a l c u l a t i n g N e from (4-15) a s s u m i n g no r e a b s o r p t i o n , t h e n c a l c u l a t i n g t h e o p t i c a l d e p t h w i t h t h i s N e and t h e m e asured w i d t h ; c o r r e c t t h e w i d t h u s i n g (4-8) and r e p e a t . T h i s c o n v e r g e d w i t h i n t h r e e i t e r a t i o n s . The l a r g e s t c o n t r i b u t i o n t o t h e e r r o r i n N e comes f r o m t h e o p t i c a l d e p t h s whose e r r o r s a r e t a b u l a t e d i n t a b l e (4-1) a l o n g w i t h t h e e r r o r s t h e y c a u s e i n t h e S t a r k w i d t h d e t e r m i n a t i o n . Added t o t h e s e e r r o r s a r e t h e e s t i m a t e d a c c u r a c y o f t h e t h e o r y s a i d t o be ""10% by G r i e m and c a l i b r a t i o n , h o m o g e n e i t y and r e p r o d u c i b i l i t y e r r o r s t h a t a r e ~ 10%. A b o u t ~ 2/3 o f t h e s e e r r o r s a r e s y s t e m a t i c . Our f i n a l e s t i m a t e d d e n s i t y measurements a r e (.9 ± .1) x 1 0 1 7 , (2.2 ± .3) x 1 0 1 7 and (2.9 ± .4) x 1 0 1 7 a l l i n c u r 3 f o r r u n s 1, 2 and 3 r e s p e c t i v e l y . T a b l e (4-4) shows t h e measured f u l l w i d t h s w s, t h e w i d t h s a f t e r m achine c o r r e c t i o n w', t h e 52 o p t i c a l d e p t h s T 0 , t h e f i n a l S t a r k w i d t h s we and t h e e l e c t r o n d e n s i t i e s p r e d i c t e d by t h e S t a r k w i d t h s f o r He I 5876 and 6678. T a b l e (4-5) W i d t h s Of He I L i n e s And C o r r e s p o n d i n g N e ' s Run w _ m w' T 0 w s N e e n r 3 He I 5876 1 5.4 4.1 .2 4.0 (0.9 ± . 1 ) x 1 0 1 7 2 12.3 1 1 .5 9.7 (2.2 ± . 3 ) X 1 0 1 7 3 16.3 15 .6 12.6 (2.9 t ^ J x l O 1 7 He I 6678 1 10.3 9.0 .05 9.0 1.0 x 1 0 1 7 2 21.8 20.5 . 1 20 2.3 x 1 0 1 7 He I 6678 i s n o t as good a p r o b e f o r N e as He I 5876 b e c a u s e i t i s q u i t e weak and i t s w i d t h h a r d t o measure. A l s o i t i s n o t as w e l l documented. In i t s f a v o r i s t h a t i t has a l m o s t n e g l i g i b l e o p t i c a l d e p t h . The f a c t t h a t t h e N e ' s we c a l c u l a t e from t h e w i d t h s o f He I 6678 a r e c l o s e t o t h o s e from He I 5876 g i v e s us g r e a t e r c o n f i d e n c e i n t h o s e v a l u e s . In f i g u r e (4-3) we show t h e p l o t s o f He I 5876 f o r t h e t h r e e r u n s w i t h b a c k g r o u n d c o n t i n u u m s s u b t r a c t e d , c h a n n e l i n t e n s i t y r e s p o n s e c o r r e c t e d , w a v e l e n g t h c a l i b r a t i o n a p p l i e d and a l i t t l e s m o o t h i n g f o r c o s m e t i c p u r p o s e s o n l y . 53 WAVELENGTH IN ANGSTOMS F i g u r e (4-3) : He I 5876 f o r Runs 1, 2 and 3 54 CHAPTER V LINEWIDTH MEASUREMENTS AND CONCLUSIONS In t h i s c h a p t e r we p r e s e n t t h e e x p e r i m e n t a l l y m e asured l i n e w i d t h s o f t w e n t y - s e v e n N I I and N I I I l i n e s , e m i t t e d by p l a s m a s o f t h r e e d i f f e r e n t e l e c t r o n d e n s i t i e s . 5-1 P r e l i m i n a r y Work B e f o r e t h e f i n a l s e t s o f c a l i b r a t e d d a t a were c o l l e c t e d , a l o t o f p r e l i m i n a r y o b s e r v a t i o n s had t o be made t o f i n d s u i t a b l e f i r i n g c o n d i t i o n s and m e a s u r a b l e l i n e s . O r i g i n a l l y we w i s h e d t o r e c o r d l i n e s a t N e i n t h e (1-5) x 1 0 1 7 c m - 3 r a n g e . T h i s would p r o v i d e d a t a i n t e r m e d i a t e t o most measurements l i s t e d i n t h e r e v i e w by N . K o n j e v i c , e t . a l . (1976) and t h o s e o f E . K a l l n e , e t . a l . ( 1 9 7 9 ) . P r e v i o u s s t u d i e s on s i m i l a r d e v i c e s showed t h i s c o u l d be o b t a i n e d a t f i l l i n g p r e s s u r e s of 2-10 t o r r and bank c h a r g i n g v o l t a g e s o f 10 kv ( s e e H.James, (1965) e . g . ) . Our e a r l y measurements of some He I , N I I and N I I I l i n e s showed t h e p l a s m a t e m p e r a t u r e t o be 3 ev and t h e f r e e e l e c t r o n d e n s i t y t o be 2 x l O 1 7 cm" 3 f o r run 2 c o n d i t i o n s . We f o u n d we c o u l d , v a r y N e by a b o u t a f a c t o r o f t h r e e . A t h i g h e r N e , a c h i e v e d by h i g h e r f i l l i n g p r e s s u r e s and c h a r g i n g v o l t a g e s , r e a b s o r b t i o n was t o o s t r o n g f o r end-on measurements. At l o w e r N e most n i t r o g e n l i n e s were- t o o nar r o w t o measure a c c u r a t e l y w i t h t h e o p t i c a l s y s t e m we had c h o s e n and D o p p l e r b r o a d e n i n g becomes i m p o r t a n t . To make t h e f i n a l s e l e c t i o n o f l i n e s t o be s t u d i e d , we 55 f i r s t made a l i t e r a t u r e search to find a l l the theoreti c a l linewidth predictions and experimental linewidth measurements. Next, rough p r o f i l e measurements were taken of a l l the N II and N III li n e s between 3500 A and 6500 A l i s t e d in the tables of W.L.Wiese, e t . a l . (1966). We used run 2 conditions for t h i s study. The li n e s were recorded without the exit lens, allowing measurement of many li n e s in a single shot. The Stark widths could not be determined from these spectra because most of the nitrogen l i n e s were narrower than the machine p r o f i l e . This quick survey showed us which l i n e s were s u f f i c i e n t l y strong and isolated to permit accurate recording of their p r o f i l e s . Also i t showed where to measure the background continuums for each l i n e . Then, we calculated the o p t i c a l depths for the li n e s not excluded by the preliminary survey, using the programs of Dr.Barnard (see section (4-6)). For these calculations we used our rough estimates of N e, T e, and linewidths from the quick survey and e a r l i e r measurements. The l i n e s were rated on the basis of s u f f i c i e n t strength, i s o l a t i o n and low o p t i c a l depths. F i n a l l y , we chose a l i s t of l i n e s to be measured accurately from the highest rated l i n e s . The l i s t represented an appropriate mix of previously measured and new l i n e s . Where possible we t r i e d to include two li n e s from the same multiplet so we could compare their widths and try the second method of determining o p t i c a l depths (see section (4-5)). 56 Table (5-1) : Stark Widths For Run 1 N e = (.9 ± .1) x 10 1 7 cm"3 T e - 3.1 ev ION LINE MLT wm w d w s ±% R N II 571 1 (3) 0.58 0.34 0.12 0.44 18 1 .0 N II 5045 (4) 0.47 0.62 0.11 0.31 23 1 .0 N II 3919 (17) 0.36 0.36 0.08 0.26 23 1 .0 N II 4601 (5) 0.47 0.40 0.10 0.35 20 1.0 N II 4607 (5) 0.42 0.34 0.10 0.30 20 1 .0 N II 4614 (5) 0.43 0.19 0.10 0.33 18 1 .0 N II 4621 (5) 0.43 0.29 0.10 0.32 19 1 .0 N II 4630 (5) 0.53 1 .45 0.10 0.29 36 1 .0 N II 4643 (5) 0.40 0.52 0.10 0.26. 27 1 .0 N II 5952 (28) 0.78 0.12 0.13 0.69 17 1 .0 N II 5942 (28) 0.94 0.61 0.13 0.75 27 1 .0 N II 5496 (29) 0.64 0.24 0.12 0.53 1 4 1 .0 N 11 5351 (69) 0.65 0.03 0.12 0.59 1 4 1 .0 N II 5321 (69) 0.70 0.01 0.11 0.64 21 1 .0 N II 3830 (30) 0.88 0.03 0.08 0.87 1 2 1.0 N II 4552 (58) 1 .80 0.10 0.10 1 .76 12 1 .0 N II 3995 (12) 0.55 1 .69 0.09 0.30 39 1 .0 N III 4097 (1) 0.43 1.41 0.09 . 0.22 36 1.0 N III 41 03 (1 ) 0.35 0.74 0.09 0.20 28 1 .0 N III 4515 (3) 0.36 0.18 0.10 0.25 18 1 .0 N III 451 1 (3) 0.33 0.14 0.10 0.22 18 1 .0 N III 3771 (4) 0.33 0.04 0.08 0.26 18 1 .0 N III 3755 (4) 0.28 0.03 0.08 0.20 20 1 .0 N III 4867 (9) 0.42 0.10 0.11 0.32 18 1 .0 N III 4874 (9) 0.41 0.01 0.11 0.32 20 1 .0 N III 4634 (2) 0.40 0.50 0.10 0.26 23 1 .0 N III 4641 (2) 0.48 0.79 0.10 0.31 29 1 .0 5-2 Stark Widths And Conclusions In tables (5-1), (5-2) and (5-3) we present the ca l i b r a t e d f u l l linewidth measurements in angstroms. In the tables MLT i s the multiplet number given by C.Moore, (1959). w m i s the uncorrected width from the OMA. T 0 i s the o p t i c a l depth. wd is the Doppler width . ws i s the Stark width corrected for machine broadening (-.2 A), o p t i c a l depth and Doppler broadening. ±% i s the estimated error from a l l sources for the Stark widths. R i s the r a t i o of ws to the Stark width of the same l i n e measured in Run 1. 57 T a b l e (5-2) : S t a r k W i d t h s F o r Run 2 N e = (2.2 ± .4) x 1 0 1 7 cm" 3 T e = = 3.1 ev ION LINE MLT w m w d w s ±% R N I I 571 1 (3) 1 .30 1 .02 0.12 1.01 25 2.3 N I I . 5045 (4) 1.11 1 .60 0.11 0.71 34 2.3 N I I 391 9 (17) 0.80 1.12 0.08 0.57 26 2.2 N I I 4601 (5) 1 .00 1 .38 0.10 0.68 29 1 .9 N I I 4607 (5) 0.87 1.14 0.10 0.62 28 2.1 N I I 461 4 (5) 0.83 0.60 0.10 0.67 20 2.0 N I I 4621 (5) 0.86 0.99 0.10 0.63 25 2.0 N I I 4630 (5) 1 .90 3.30 0.10 0.95 52 3.3 N I I 4643 (5) 1 .00 1 .52 0.10 0.65 33 2.5 N I I 5952 (28) 1 .36 0.41 0.13 1 .23 20 1.8 N I I 5942 N I I 5496 (29) 1 .32 0.77 0.12 1 .09 23 2.1 N I I 5351 (69) 1.13 0.10 0.12 1.10 15 1 .9 N I I 5321 N I I 3830 (30) 1 .90 0.08 0.08 1 .86 22 2.1 N I I 4552 (58) 3.40 0.31 0.10 3.15 1 9 1.8 N I I 3995 (12) 1 .60 6.49 0.09 0.51 64 1 .7 N I I I 4097 (1 ) 0.80 2.02 0.09 0.46 41 2.1 N I I I 4103 (1 ) 0.66 0.98 0.09 0.48 28 2.4 N I I I 4515 (3) 0.66 0.23 0.10 0.58 1 7 2.3 N I I I 451 1 (3) 0.63 0.18 0.10 0.56 19 2.5 N I I I 3771 (4) 0.50 0.07 0.08 0.45 1 7 1 .7 N I I I 3755 (4) 0.50 0.05 0.08 0.46 25 2.3 N I I I 4867 (9) 0.85 0.12 0. 1 1 0.83 1 4 2.6 N I I I 4874 (9) 0.85 0.01 0.11 0.85 22 2.6 N I I I 4634 (2) 0.80 1 .24 0.10 0.54 36 2. 1 N I I I 4641 (2) 0.80 0.60 0.10 0.65 37 2.1 The e r r o r s i n ws come m a i n l y f r om t h e u n c e r t a i n t y i n t h e o p t i c a l d e p t h w h i c h i s ' t a b u l a t e d i n t a b l e ( 4 - 2 ) . The e r r o r s due t o i n h o m o g e n e i t y , c a l i b r a t i o n s , r e p r o d u c i b i l i t y and t i m e v a r i a t i o n s t o t a l a b o u t ± 5 % . The e r r o r i n m a c h i n e w i d t h c o r r e c t i o n o f ± 10% a f f e c t s t h e n a r r o w e s t l i n e s o f run 1 e s p e c i a l l y . F o r some o f t h e weaker l i n e s and t h o s e n o t so w e l l i s o l a t e d (N I I 4641 and N I I I 4643 f o r example) we a l s o e s t i m a t e h i g h e r e r r o r s b a s e d on how a c c u r a t e we c o u l d measure t h e halfmaximum h e i g h t . The e f f e c t i s somewhat m i n i m i z e d b e c a u s e t h e h a l f w i d t h o c c u r s a t t h e s t e e p e s t p a r t 58 T a b l e (5-3) : S t a r k W i d t h s F o r Run 3 N e = (2.9 ± .4) x 1 0 1 7 c n r 3 T e • = 3.1 ev ION LINE MLT w m w d w s ±% R N I I 571 1 (3) 1 .70 1 .76 0.12 1.12 35 2.6 N I I 5045 (4) 1 .45 3.26 0.11 0.68 51 2.2 N I I 3919 N I I 4601 (5) 1 .40 2.25 0.10 0.84 46 2.4 N I I 4607 (5) 1 .20 1 .90 0.10 0.77 41 2.6 N I I 4614 (5) 1 .05 1 .03 0.10 0.82 25 2.5 N I I 4621 (5) 1 .20 1 .53 0.10 0.83 30 2.6 N I I 4630 (5) 2.40 8.12 0.10 0.69 83 2.4 N I I 4643 (5) 1 .40 2.55 0.10 0.79 54 3.0 N I I 5952 (28) 1 .60 0.72 0.13 1 .34 23 1 .9 N I I 5942 N I I 5496 (29) 1 .60 1 .40 0.12 1.14 32 2.2 N I I 5351 (69) 1 .40 0.16 0.12 1 .35 16 2.3 N I I 5321 N I I 3830 (30) 2.20 0.13 0.08 2.13 23 2.4 N I I 4552 (58) 4.60 0.45 0.10- 4.12 1 7 2.3 N I I 3995 (12) 2.60 9.22 0.09 0.74 83 2.5 N I I I 4097 (1 ) 0.78 3.75 0.09 0.29 53 1 .3 N I I I 41 03 (1 ) 0.70 1 .40 0.09 0.46 29 2.3 N I I I 4515 (3) 0.80 0.26 0.10 0.75 20 3.0 N I I I 451 1 (3) 0.75 0.21 0.10 0.67 20 3.1 N I I I 3771 (4) 0.66 0.07 0.08 0.65 19 2.5 N. I l l 3755 (4) 0.54 0.06 0.08 0.50 19 2.5 N I I I 4867 (9) 0.83 0.16 0.11 0.76 14 2.4 N I I I 4874 N I I I 4634 (2) 0.90 0.74 0.10 0.71 29 2.7 N I I I 4641 (2) 0.95 1 .54 0.10 0.61 41 2.0 of t h e p r o f i l e ( d 2 L / d o 2 = 0 ) . W i t h t h e s e p o i n t s i n mind we worked o u t t h e e r r o r f o r e a c h l i n e i n d i v i d u a l l y . We n o t e t h a t ~ 1/2 o f t h e s e e r r o r s a f f e c t a l l t h r e e r u n s t h e same and s h o u l d n o t change t h e R's. As e x p e c t e d , t h e w s's f o r l i n e s w i t h i n t h e same m u l t i p l e t and run a r e g e n e r a l l y v e r y c l o s e . However, t h i s amounts t o l i t t l e more t h a n a c o n s i s t e n c y c h e c k b e c a u s e most a l l e r r o r s a f f e c t i n g s u c h a s e t of l i n e s a r e s y s t e m a t i c ( e x c e p t f o r s h o t t o s h o t r e p r o d u c i b i l t y and u n d e r o r o v e r c o r r e c t i o n f o r r e a b s o r p t i o n ) . 59 We see from t h e t a b l e s t h a t t h e R's a r e n o t as u n i f o r m as we had hoped, p a r t i c u l a r l y f o r run 3, but n o t e t h e y a r e v e r y s u s c e p t i b l e t o e r r o r s i n t h e r u n 1 w i d t h s . The s i d e - o n and end-on measurements o f N II 4614 and 4643 compare v e r y f a v o r a b l y . The s i d e - o n m e asured S t a r k w i d t h s o f b o t h l i n e s were .30 A, .61 A and .90 A f o r r u n s 1, 2 and 3 r e s p e c t i v e l y . T h e s e measurements a r e n o t a f f e c t e d by o p t i c a l d e p t h ( T 0 < . 0 5 ) . I f t h e y were, N I I 4643 would have been w i d e r b e c a u s e i t i s 2.4 t i m e s a s s t r o n g a s N I I 4614. B e c a u s e o f t h e c l o s e a g r e e m e n t between s i d e - o n and end-on measurements we s u s p e c t our e r r o r e s t i m a t e s a r e o v e r l y p e s s i m i s t i c . To c h e c k l i n e a r s c a l i n g o f N e w i t h w s we compare t h e r a t i o s o f t h e e l e c t r o n d e n s i t i e s f r o m t h e t h r e e r u n s t o t h e a v e r a g e r a t i o s of t h e S t a r k w i d t h s . F o r N e we g e t 1 : 2.45 ± .2 : 3.2 ± .3 and f o r w s we g e t 1 : 2.2 ± .4 : 2.5 ± .3 f r o m t h e a v e r a g e R o f l i n e s w i t h l e s s t h e n 30% e r r o r i n t a b l e s ( 5 - 1 ) , (5-2) and ( 5 - 3 ) . The e r r o r s we g i v e i n t h e N e r a t i o a r e computed by s u b t r a c t i n g t h e ~ 2/3 s y s t e m a t i c e r r o r from t h e e s t i m a t e d 30% e r r o r i n t h e N e measurement. The e r r o r s i n t h e ws r a t i o a r e t h e s t a n d a r d d e v i a t i o n s . L i n e a r s c a l i n g i s a l m o s t o b e y e d w i t h i n o u r e r r o r b a r s . B e c a u s e t h e u n c e r t a i n t i e s a r e so l a r g e we c a n n o t c o n c l u d e whether w s i s o r i s not p r o p o r t i o n a l t o N e . We need t o i n c r e a s e t h e r a n g e o f N e and r e d u c e t h e e r r o r . We g i v e s u g g e s t i o n s f o r t h i s i n s e c t i o n ( 5 - 3 ) . F i g u r e (5-1) shows t h e f u l l S t a r k w i d t h s o f N-II 4614, 5496 and 4552 p l o t t e d a g a i n s t N e . T h e s e a r e t h r e e o f our 60 more a c c u r a t e l y m easured l i n e s . The p o i n t s w i t h e r r o r b a r s were drawn s u b t r a c t i n g t h e s y s t e m a t i c e r r o r . T h o s e p o i n t s w i t h o u t e r r o r b a r s r e p r e s e n t e x p e r i m e n t a l measurements an d t h e o r e t i c a l p r e d i c t i o n s o f o t h e r a u t h o r s . As we c a n see f r o m t h e f i g u r e , f a i r l y good a g r e e m e n t w i t h l i n e a r s c a l i n g i s o b e y e d . The o n l y w i d t h s we can compare w i t h E . K a l l n e e t . a l . , a r e N I I 3995, N I I I 4097 and N I I I 4103. T h e i r w i d t h s a r e a p p r o x i a m a t e l y d o u b l e what l i n e a r s c a l i n g w ould g i v e w i t h our r u n 1 d a t a . Though t h e a u t h o r s c a l c u l a t e t h e o p t i c a l d e p t h s a s n e g l i g i b l e , we n o t e t h a t t h e w i d t h s o f t h e s t r o n g e r l i n e s w i t h i n t h e same m u l t i p l e t a r e w i d e r t h r e e o u t o f f o u r t i m e s . T h i s would be c o n s i s t e n t w i t h o p t i c a l l y t h i c k l i n e s and may e x p l a i n t h e d i s c r e p a n c y . In t a b l e (5-4) we g i v e t h e o p t i c a l d e p t h s c a l c u l a t e d w i t h e q u a t i o n (4-13) when f e a s i b l e . Agreement w i t h t h e T 0 ' S g i v e n i n t a b l e s ( 5 - 1 ) , (5-2) and (5-3) i s n o t good, but a r e w i t h i n e r r o r e s t i m a t e s . The T 0 ' S f o r t h e N I I 4601, 4607, 4614, 4621, 4630 and 4643 m u l t i p l e t were f o u n d by a v e r a g i n g t h e v a l u e s o f N I I 4614 t o e a c h o f t h e o t h e r l i n e s , t h e n u s i n g ( 4 - 9 ) . T h i s gave us f i v e v a l u e s f o r T 0 o f N I I 4614 (and hence f o r e a c h o f t h e o t h e r l i n e s t h r o u g h ( 4 - 9 ) ) . FIG (5-1) STARK WIDTHS VS ELECTRON DENSITY ro tr O 1.5. Q _l < X CVJ Q o Z> u. Id T h3l X 3d 3e »c T h2H J- 2a la lb 2d Id I-3H 1 r-2-l 1 1 N 2 4614 2 N 2 5496 3 N 2 4552 i T f I i a b BARRED POINTS FROM REF. (10) REF. (9) REF. (6) THIS EXPERIMENT d REF. (21) e REF. (16) I N . X I Q 17 cm -3 62 T a b l e (5-4) : O p t i c a l D e p t h s From I n t e n s i t y R a t i o s ION LINE RUN 1 RUN 2 RUN 3 N I I 4601 1.5 2.3 2.8 N I I 4607 1 .3 1 .9 2.4 N I I 4614 .68 1.0 1.2 N I I 4621 1.0 1 .6 1.9 N I I 4630 4.9 7.2 8.9 N I I 4643 1 .6 2.4 3.0 N I I 5952 .12 N I I 5942 .67 N I I I 4097 1 . 1 2.4 2.8 N I I I 4103 .54 1 .2 1 .4 N I I I 4634 .49 1 . 1 N I I I 4641 .87 1 .9 N I I I 451 5 0.0 .83 .8 N I I I 451 1 0.0 .61 .6 I n f i g u r e (5-2) we p r e s e n t s e v e r a l o f t h e measured p r o f i l e s w i t h b a c k g r o u n d c o n t i n u u m s s u b t r a c t e d . 5-3 Improvements And F u r t h e r Work The b i g g e s t e r r o r came from t h e o p t i c a l d e p t h w h i c h s h o u l d be e l i m i n a t e d o r c i r c u m v e n t e d . The b e s t way would have been t o o b s e r v e t h e p l a s m a b o t h s i d e and end-on. E x p e r i e n c e w i t h N I I 4614 and 4643 showed t h a t s i d e on measurements of t h e s t r o n g l i n e s a r e f e a s i b l e w h i l e t h e weak l i n e s c o u l d s t i l l be measured a l o n g t h e t u b e a x i s . We f e e l a l o t more work i s n e c e s s e s a r y on t h e d i a g n o s t i c s o f t h e p l a s m a c o l u m n . A b e l i n v e r s i o n s and N e measurements a t t h e t u b e c e n t e r and j u s t p a s t t h e w i d e n i n g p o i n t s h o u l d be done. T h i s would t e l l us how t h e p l a s m a t e m p e r a t u r e and e l e c t r o n d e n s i t y d e c r e a s e w i t h d i s t a n c e from t h e c o n s t r i c t e d p o r t i o n o f t h e v e s s e l , and h ence i f l a r g e amounts o f N I I and He I come f r o m t h e c o o l e r , l o w e r N e £9 64 r e g i o n s . The p r o b l e m w i t h t h e narrow s e c t i o n s t a i n i n g r a p i d l y , making s i d e - o n measurements d i f f i c u l t , c o u l d be e l i m i n a t e d by making a s e c t i o n o f i t r e m o v a b l e . T h i s p o r t i o n c o u l d be t a k e n o u t and c l e a n e d o r r e p l a c e d e a s i l y . The w i d e r s e c t i o n s do n o t s t a i n r a p i d l y . The e r r o r c a u s e d i n t h e n a r r o w e r l i n e s ' w i d t h s by machine b r o a d e n i n g c o u l d be r e d u c e d by two methods. F i r s t a m e c h a n i c a l s h u t t e r s y e t e m c o u l d be i n s t a l l e d i n f r o n t o f t h e s p e c t r o m e t e r ' s e n t r a n c e ' s l i t t o r e p l a c e t h e e l e c t r o n i c g a t i n g o f t h e OMA. The OMA c o u l d t h e n be u s e d i n r e a l t i m e mode w h i c h h a s l e s s t h a n 1/2 t h e m a c h i n e w i d t h of g a t e d mode. A l s o i n t h i s mode t h e OMA has a much more l i n e a r r e s p o n s e a c r o s s t h e 500 c h a n n e l s . T h i s would d o u b l e th e w a v e l e n g t h band o f t h e s p e c t r u m we c o u l d o b s e r v e i n e a c h s h o t . In s e v e r a l c a s e s t h i s would a l l o w t h e measurement o f a N II and N I I I l i n e , and hence T , i n a s i n g l e s h o t . U s i n g r e a l t i m e has two added a d v a n t a g e s . The r e a l t i m e t o g a t e d mode c h a n n e l c a l i b r a t i o n i s u n n e c e s s e s a r y and t h e c o n t i n u u m r e s p o n s e a c r o s s t h e 500 c h a n n e l s i s e a s i l y m e a s u r e d . The s e c o n d method o f e l i m i n a t i n g t h e machine b r o a d e n i n g i s t o d e t e r m i n e p r e c i s e l y how i t a f f e c t s t h e n a r r o w e s t l i n e s . T h i s c o u l d be a c c o m p l i s h e d by p l a c i n g a more a d j u s t a b l e l e n s a t t h e e x i t s l i t o f t h e s p e c t r o m e t e r . W i t h s u c h a l e n s we c o u l d o b s e r v e t h e same l i n e a t d i f f e r e n t d i s p e r s i o n s a c r o s s t h e OMA a n d t h u s d e t e r m i n e p r e c i s e l y how th e m a c h i n e p r o f i l e b r o a d e n s L o r e n t z i a n l i n e s o f v a r y i n g w i d t h s . The s h o t t o s h o t j i t t e r i n e l e c t r o n d e n s i t y c o u l d be 65 b y p a s s e d by o b s e r v i n g t h e He I 5876 l i n e w i t h a s e p a r a t e s p e c t r o m e t e r OMA s y s t e m as was done by J . B e r n a r d ( 1 9 7 8 ) . T h i s w o u l d g i v e e l e c t r o n d e n s i t y measurements w i t h e a c h l i n e and e l i m i n a t e any f e a r s t h a t t h e s y s t e m c h a n g e s d u r i n g a l o n g d a t a r u n . W i t h t h e above improvements t h e e r r o r on most l i n e s c o u l d be below 10% and t h e r e l a t i v e e r r o r even l e s s . We w i s h t o e x t e n d t h e N e r a n g e w h i l e s t i l l u s i n g t h e same p l a s m a s o u r c e . N e c a n be l o w e r e d q u i t e e a s i l y by r e d u c i n g t h e f i l l i n g p r e s s u r e a n d o r f i r i n g v o l t a g e . A l s o we c o u l d o b s e r v e t h e p l a s m a l a t e r i n t h e d i s c h a r g e , when t h e c u r r e n t h as d e c r e a s e d . However, s i n c e t h e t e m p e r a t u r e i s r e l a t i v e l y f i x e d , many o f t h e l i n e s a r e D o p p l e r b r o a d e n e d i f N e i s l o w e r e d s i g n i f i c a n t l y . O n l y two l i n e s f r o m our t a b l e s w ould f i t t h e c r i t e r i o n t h a t t h e S t a r k w i d t h be a t l e a s t f o u r t i m e s t h e D o p p l e r w i d t h a t N e = .5 x 1 0 1 6 c m - 3 . To r a i s e N e we would i n c r e a s e t h e f i l l i n g p r e s s u r e and f i r i n g v o l t a g e . To a v o i d t h e a c c o m p a n y i n g p r o b l e m w i t h o p t i c a l d e p t h we c o u l d o b s e r v e a l i n e end-on u n t i l t h e i n c r e a s e d d e n s i t y c a u s e s r e a b s o r b t i o n . Then we would s w i t c h t o s i d e - o n measurements f o r t h a t l i n e . We m i g h t i n c r e a s e N e t o a b o u t 5 x I 0 1 7 c m - 3 by t h i s method and he n c e t h e ra n g e t o an o r d e r o f m a g n i t u d e f o r some l i n e s . I t w o u l d be i n t e r e s t i n g t o t e s t e q u a t i o n ( 4 - 1 3 ) . W i t h t h e s u g g e s t e d c h a n g e s t o t h e OMA g a t i n g s y s t e m many l i n e s w i t h i n a m u l t i p l e t c o u l d be o b s e r v e d i n a s i n g l e s h o t ( b a n d w i d t h ~ 15 A ) . The r a t i o o f t h e i r l i n e c e n t e r i n t e n s i t i e s would be me a s u r e d v e r y a c c u r a t e l y . To t e s t 66 (4-13) we would choose plasma conditions such that two or more l i n e s of varying strength were reabsorbed end-on but not side-on. Then using (4-13), we would cal c u l a t e their o p t i c a l depths, correct t h e i r measured widths from (4-8) and compare with side-on measurements. Also we could compare these o p t i c a l depths to those from (4-7) to see i f our LTE assumptions were incorrect. 67 BIBLIOGRAPHY (1) B a t e s , D.R. a n d Damgaard, A., P h i l o s o p h i c a l T r a n s a c t i o n s o f t h e R o y a l S o c i e t y o f London, A242, 101 ( 1 9 4 9 ) . (2) B e r n a r d , J . , Msc. T h e s i s , 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 , ( 1 9 7 9 ) . (3) B o r n , M., and W o l f , E . , P r i n c i p l e s of O p t i c s , Pergamon P r e s s , O x f o r d ( 1 9 7 5 ) , s e c t i o n 10.2. (4) C i l l i e r s , W.A., Hey, J.D., and Rash, J.P.S., J o u r n a l of Q u a n t i t a t i v e S p e c t r o s c o p y and R a d i a t i v e T r a n s f e r , 15, 963 ( 1 9 7 5 ) . ~ (5) C o o p e r , J . , L e c t u r e s i n T h e o r e t i c a l P h y s i c s , V o l XIC, Gordon and B r e a c h , New York ( 1 9 6 9 ) . (6) C o o p e r , J . , O e r t e l , G.K., P h y s i c s Review L e t t e r s , 18, 985 ( 1 9 6 7 ) . (7) D r a w i n , H.W., Z e i t s c h r i f t F u r N a t u r f o r s c h u n g , 19A, 1451 ( 1 9 6 4 ) . . (8) G r i e m , H.R. , P h y s i c s Review, J_3j_, 1170 ( 1973). (9) G r i e m , H.R., P h y s i c s Review, 165, 258 ( 1 9 6 8 ) . (10) G r i e m , H.R., P h y s i c s Review L e t t e r s , _T7, 509 ( 1 9 6 6 ) . (11) G r i e m , 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 Book Co., New Y o r k , ( 1 9 6 4 ) . (12) G r i e m , H.R., S p e c t r a l L i n e B r o a d e n i n g by P l a s m a s , A c a d e m i c P r e s s , New Y o r k , ( 1 9 7 4 ) . (13) Hodgman, C., e d . , Handbook o f C h e m i s t r y and P h y s i c s , E d i t i o n 39, C h e m i c a l Rubber Company, C l e v e l a n d ( 1 9 5 7 - 5 8 ) . (14) H o o p e r , C.F., J r . , P h y s i c s Review, 149, 7 ( 1 9 6 6 ) . (15) H o o p e r , C.F., J r . , P h y s i c s Review, 165, 215 ( 1 9 6 8 ) . (16) Hey, J.D., J o u r n a l o f Q u a n t i t a t i v e S p e c t r o s c o p y and R a d i a t i v e T r a n s f e r , 20, 557 ( 1 9 7 8 ) . (17) J a l u f k a , N.W. and C r a i g , J . P . , P h y s i c s Review A, 1, 221 ( 1 9 7 0 ) . (18) James, H.G., Phd. 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,c (1968). c (19) K a l l n e , E., J o n e s , L.A. and B a r n a r d , A . J . , J o u r n a l o f Q u a n t i t a t i v e S p e c t r o s c o p y a n d R a d i a t i v e T r a n s f e r , 22, 589 ( 1 9 7 9 ) . 68 (20) K o n j e v i c , N. and D i m i t r i j e v i c , M.S., P r o c e e d i n g s of t h e  F i f t h C o n f e r e n c e on S p e c t r a l L i n e S hapes , W a l t e r de G r u y t e r , B e r l i n ( 1 9 8 1 ) . (21) K o n j e v i c , N., and W i e s e , W.L., J o u r n a l o f P h y s i c a l and C h e m i c a l R e f e r e n c e D a t a , 5, 259 ( 1 9 7 6 ) . (22) Marganeau, H. and L e w i s , M., Review o f Modern P h y s i c s , 3 1 , 569 ( 1 9 5 9 ) . (23) M e r z b a c h e r , E., Quantum M e c h a n i c s , S e c o n d E d i t i o n , J o h n W i l e y and Sons, I n c . , New Y o r k , ( 1 9 7 0 ) . (24) Mewe, R. , B r i t i s h J o u r n a l o f A p p l i e d P h y s i c s , J_8, 107 ( 1 9 6 7 ) . (25) Moore, C , M u l t i p l e t T a b l e o f A s t r o p h y s i c a l I n t e r e s t , N a t i o n a l B u r e a u o f S t a n d a r d s , ( 1 9 5 9 ) . (26) N e l s o n , R.H., Phd. T h e s i s , 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 , ( 1 9 7 0 ) . (27) N e u f e l d , C R . , Phd. T h e s i s , 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 , ( 1 9 6 6 ) . (28) S t e v e n s o n , D., Msc. T h e s i s , 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 , ( 1 9 7 3 ) . (29) van de H u l s t , H.C. and R e e s i n c k , J . , A s t r o p h y s i c s J o u r n a l , 106, 121, ( 1 9 4 7 ) . (30) W i e s e , W.L., S m i t h , B.W., and G l e n n o n , B.M., A t o m i c T r a n s i t i o n P r o b a b i l i t i e s , N a t i o n a l B u r e a u of S t a n d a r d s , W a s h i n g t o n , D.C. ( 1 9 6 6 ) . 

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