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Absolute intensity measurements in a helium plasma 1966

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ABSOLUTE INTENSITY MEASUREMENTS IN A HELIUM PLASMA by CYRUS SHANTZ MACLATCHY B.Sc, Acadia University, 1964 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1966 In presenting this thesis in par t i a l fulfi lment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shal l make i t f reely available for reference and study, 1 further agree that permission-for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives„ It is understood that copying or publication of xhis thesis for f inancia l gain shal l not be allowed without my written permission. Department of The University of Br i t i sh Columbia Vancouver 8, Canada - i i - ABSTRACT The temperature of a Helium plasma produced i n a shock tube has been determined from absolute i n t e n s i t y measurements. The plasma was considered to be homogeneous, transparent and i n l o c a l thermodynamic equilibrium. The emissivity of the plasma has been measured by comparing the plasma ra d i a t i o n to the radiation from a carbon arc through a simple o p t i c a l system. The influence of errors i n measured parameters and the presence of impurities i s discussed. Temperatures which depend on large exponential terms are r e l a t i v e l y i n s e n s i t i v e to both errors i n measurement and the impurity content of -the plasma. The accuracy of absolute i n t e n s i t y measurements i s at best comparable to r e l a t i v e i n t e n s i t y measurements. - i i i - TABLE OF CONTENTS Page ABSTRACT i i LIST OF FIGURES v LIST OF TABLES v ACKNOWLEDGEMENTS v i CHAPTER I INTRODUCTION CHAPTER II EQUATIONS OF THE PLASMA (a) Introduction 5 (b) Local Thermodynamic Equilibrium 5 (c) Emissivity and Excited State Populations 7 (d) Line Broadening and Electron Densities 10 (e) Equilibrium Equations of the Plasma 12 (f) S e n s i t i v i t y of the Temperature Measuring Techniques 21 CHAPTER III THE ABSOLUTE INTENSITY CALIBRATION' (a) Introduction 24 (b) Light Gathering of the Monochromator 24 (c) Standard Sources 28" (d) Shock Tube Absorption 33 (e) Comparison of Light Sources 36 CHAPTER IV APPARATUS AND TECHNIQUE (a) Introduction 44 (b) Shock Tube 44 (c) Optical Equiment and Measuring Techniques 46 (d) Carbon Arc 46* - i v - Page CHAPTER V RESULTS AND CONCLUDING REMARKS (a) Introduction 50 (b) Results 51 (c) Discussion 52 BIBLIOGRAPHY 58" -v- LIST OF FIGURES Figure Page 1. qkT as a function of L 15 2. Light gathering of a monochromator with a large condensing lens 25 3. Light gathering of a monochromator with a small condensing lens 27 4. Measuring the shock tube absorption 35 5. Radiance and l i g h t f l u x 37 6. Comparison of l i g h t sources 3$ 7. Schematic diagram of apparatus 45 S. Line sampling techniques 47 9. Impurity electrons as a function of kT 53 10. H e l l population as a function of kT 54 LIST OF TABLES Table 1. S e n s i t i v i t y factors 2. Fi n a l r e s u l t s Page 23 55 - v i - ACKNOWLEDGEMENTS I am grateful to Dr. A.J. Barnard for h i s guidance and patience during the preparation of t h i s t h e s i s . I also wish to express my appreciation to fellow students and members of the teaching and techn i c a l s t a f f for h e l p f u l discussions during the course of the work. CHAPTER I INTRODUCTION This thesis i s concerned primarily with the evaluation of the measurement of absolute i n t e n s i t i e s of spectral l i n e s as a diagnostic technique i n the study of plasmas. Although measuring the absolute value of the emissivity of the plasma i s b a s i c a l l y a simple procedure, the inference of physical properties of the plasma from the measurement of a spectral l i n e depends c r i t i c a l l y on the degree of equilibrium which i s attained i n the plasma. As a source of plasma, a shock tube was used. There has been considerable discussion i n the l i t e r a t u r e concerning the actual state of equilibrium i n shock tube plasmas generally. For example, McLean et a l . (I960) claim to have measured the temperature with errors of 2% i n a shock heated plasma. More recently, I s l e r and Kerr (1965) and Eckerle and McWhirter (1966) have suggested deviations from thermal equilibrium. Assuming that one can produce a plasma which i s i n equilibrium, a knowledge of the absolute i n t e n s i t y of a spectral l i n e can y i e l d useful information concerning the plasma. In p r i n c i p l e , i t should be the simplest spectroscopic method of measuring the k i n e t i c temperature since i t requires the study of only one l i n e p r o f i l e . In addition, i f one can evaluate a r e l i a b l e temperature by t h i s or other means, an absolute value of the emissivity of the plasma for a spectral l i n e w i l l allow one to calculate the absolute value of the t r a n s i t i o n -2- p r o b a b i l i t y . In recent years there have-appeared only a few measure- ments of absolute i n t e n s i t i e s , for the most part, experimenters have r e l i e d on r e l a t i v e i n t e n s i t y measurements for evaluating the temperature. This technique i s generally assumed f a i r l y r e l i a b l e because of the consistent r e s u l t s one achieves by using i t . However, as w i l l be pointed out, large variations i n measured parameters are required before noticeable changes in the calculated values of temperature occur. This property tends to n u l l i f y the e f f e c t of r e l a t i v e l y poor measurements of the electron density sometimes achieved. The absolute i n t e n s i t y technique has been studied i n the hope of removing t h i s d i f f i - culty and of c a l c u l a t i n g a more r e l i a b l e temperature. In the chapters which follow, the absolute i n t e n s i t y technique i s described and compared to r e l a t i v e i n t e n s i t y measurements i n terms of both accuracy and s e n s i t i v i t y to errors i n measurement. Chapter Ilcontains a review of the equilibrium equations of the plasma and indicates how these equations might be used to calculate electron densities, excited state populations, and k i n e t i c temperatures from spectral observations. The sections on l o c a l thermodynamic equilibrium (LTB"), plasma ( s e n s i t i v i t y and Stark broadening are b r i e f descriptions of widely used techniques. The fourth section i s based on the Saha and Boltzmann equations which describe the plasma and i s e s s e n t i a l l y a manipulation of these equations to f i n d the temperature of a pure plasma and an impurity contaminated plasma. F i n a l l y , an attempt has been made to compare the -3- s e n s i t i v i t y of absolute and r e l a t i v e i n t e n s i t y measurements to errors i n measuring techniques. The t h i r d chapter i s mainly concerned with the geometrical optics"of"making the absolute i n t e n s i t y c a l i b r a - t i o n . A general rule for simplifying the c a l c u l a t i o n of the l i g h t gathering e f f i c i e n c y i s set for t h i n the f i r s t section, while a review of standard sources i s contained i n the second. The absorption of radiation by the shock tube i s discussed i n the t h i r d section with special emphasis to problems peculiar to the p a r t i c u l a r apparatus used. The f i n a l section of Chapter III describes i n considerable d e t a i l the comparison of the plasma to the standard source. Chapter IV Is a short description of the apparatus and experimental technique. A standard shock tube with a "coplanar d r i v e r " has been used as a plasma l i g h t source. Hel 5S76, 667S and H e l l 1+686 l i n e p r o f i l e s have been time resolved using a Jarrell-Ash monochromator. Absolute inten- s i t y c a l i b r a t i o n s were carried out using a carbon arc as a standard source. In Chapter ¥, an i n d i c a t i o n of the impurity content of the plasma i s included along with a comparison of temper- atures calculated from absolute and r e l a t i v e i n t e n s i t i e s . It i s pointed out that corrections for impurities have l i t t l e e f f e c t for r e l a t i v e and absolute i n t e n s i t i e s , as long as the exponential terms i n the equations have large arguments. Temperatures calculated from absolute i n t e n s i t i e s are at best no more reliable' than those calculated from r e l a t i v e i n t e n s i t i e s . -4- and i n some instances are much worse. Only under certain r e s t r i c t i v e conditions i s the use of the more tedious-absolute i n t e n s i t y technique warranted. CHAPTER II EQUATIONS OF THE PLASMA (a) Introduction By measuring the electron density of a plasma, some conclusions can be drawn concerning i t s state of equilibrium. Assuming that LTE exists, one can deduce both the electron density and excited state populations from the measurement of l i n e p r o f i l e s and integrated absolute i n t e n s i t i e s . In t h i s chapter, equations are introduced from which the equilibrium temperature of the plasma can be calculated from both r e l a t i v e and absolute i n t e n s i t i e s . F i n a l l y , a t h e o r e t i c a l comparison of the s e n s i t i v i t i e s of these measuring techniques i s made. (bD Local Thermodynamic Equilibrium In practice i t i s extremely d i f f i c u l t to'produce a plasma whose entire volume i s i n thermodynamic equilibrium. Since the absolute i n t e n s i t y measurement depends heavily on the preponderance of equilibrium, i t i s necessary to be able to locate a region i n the plasma which simulates s t r i c t equi- l i b r i u m or LTE. In the most r e s t r i c t i v e sense, an LTE region i s one i n which the quantum states of the ionized gas are populated i d e n t i c a l l y to those of an equal volume of gas which i s i n thermodynamic equilibrium and has the same t o t a l density, temperature and chemical composition as the system. However, the laboratory plasma seldom approaches t h i s i d e a l , so that a l e s s stringent condition, that of p a r t i a l LTE, i s generally -6- sought. In p a r t i a l LTE, only a r e s t r i c t e d number of quantum states need be populated according to equilibrium conditions. The v a l i d i t y of the r e s u l t s of any set of measurements depending on the assumption of equilibrium i n the plasma cannot be e f f e c t i v e l y discussed unless certain c r i t e r i a f o r LTE are established and evaluated f o r the p a r t i c u l a r plasma i n question. One assumes a p r i o r i that both the temperature and p a r t i c l e gradients are n e g l i g i b l e i n the region of observation. Griem (1964) has been able to suggest order-of-magnitude conditions which should hold i n order that LTE calculations be j u s t i f i e d . Because of the importance df the LTE assumption, a b r i e f des- c r i p t i o n follows. I f the plasma i s to be considered i n LTE, i t i s e s s e n t i a l that c o l l i s i o n a l processes dominate. For a p a r t i c u l a r l e v e l m with population n m one writes: ott XctL cL± t r a c t . The radi a t i v e rate of decay can be found from the E i n s t e i n r e l a t i o n to be introduced i n the next section. The c o l l i s i o n a l term i s found from quantum mechanical considerations. The plasma i s considered to be o p t i c a l l y t h i n . For a l i n e whose upper l e v e l i s 1m the electron population i n a homogeneous, time independent plasma should be such that -7- E^ i s the ion i z a t i o n energy f o r Hydrogen and ^ i s the frequency of the radiation f o r a t r a n s i t i o n from l e v e l m to l e v e l n. The shock tube plasma i s a transient plasma. This si t u a t i o n puts l i m i t a t i o n s on the duration of the period of observation i n such a way that a measurement must be made over a period of time much greater than the e q u i l i b r a t i o n time of the l e v e l s and much l e s s than the period i n which gross changes i n the plasma occur. The second of these con- d i t i o n s i s i n general e a s i l y accomodated, but the f i r s t condition must be dealt with cautiously since i t depends on the e q u i l i b r a t i o n time of the l e v e l s . ' E s s e n t i a l l y , i t i s necessary that the quantum l e v e l s of the plasma are i n a state of "near equilibrium! 1 at a l l times of change of the plasma. Of the e q u i l i b r a t i o n times within the plasma, that of the bound states i s the greatest. For t h i s reason, i t i s wise to check the e q u i l i b r a t i o n times of these l e v e l s i n l i g h t of the physical parameters of the experimental plasma. Griem(1964) has suggested order of magnitude calculations which allow one to form some conclusion concerning t h i s time. However, there often remains some doubt as to the LTE nature of the plasma. (c) Emissivity .and Excited State Populations The populations of excited states may be related to the integrated absolute- i n t e n s i t y of speirtral l i n e s . To i l l u s t r a t e the-assumptions-made i n r e l a t i n g these properties, the problem-of" l i g h t transmission through the plasma w i l l be examined i n the general case and then s i m p l i f i e d to meet the conditions presumed present i n the author's laboratory plasma. F i r s t l y , notice that the s p a t i a l gradient of the radiant i n t e n s i t y I(V, xi> x 2, X 3) along the l i n e o f sight can be represented by where v i s the frequency of the radiation, x-̂ , x 2 and x^ represent s p a t i a l co-ordinates with X]_ oriented along the l i n e of sight, and £ ( V > *!> x 2, X 3 ) i s the emissivity due to spontaneous t r a n s i t i o n s of electrons between states i n the plasma. k ( V , x-p X g , x^) i s a c o e f f i c i e n t which represents both absorption and induced emission processes. I f i t i s assumed that the plasma i s homogeneous, the s p a t i a l dependence of dl/dx^ may be dispensed with. Also, i f only non resonance radiat i o n i n the plasma i s considered, the r e l a t i v e l y low population of the excited states usually warrants the neglection of absorption and induced• trans- mission processes, both of which are proportional to the number density of the excited states which give r i s e to the radiat i o n involved. Under these conditions, The emissivityE ( V m n ) i s defined by -9- where m and n represent the upper and lower excited states Q£ a t r a n s i t i o n , n m i s the population of the upper l e v e l , and i s the E i n s t e i n c o e f f i c i e n t giving the p r o b a b i l i t y of an electron making a spontaneous t r a n s i t i o n from l e v e l m to l e v e l no The E i n s t e i n c o e f f i c i e n t must be evaluated from quantum mechanical considerations. It i s defined by where r Q i s the c l a s s i c a l electron radius, c i s the v e l o c i t y of l i g h t , g n and g m are s t a t i s t i c a l weights of the two states involved, f i s the absorption o s c i l l a t o r strength whose determination requires the evaluation of matrix elements describing the exchange between states m and n. where x^ represents the co-ordinates of the electron making the t r a n s i t i o n . The evaluation of f i s imprecise both nm ^ a n a l y t i c a l l y and experimentally and may be a substantial source of error i n experimental procedure of t h i s t h e s i s . Because of various l i n e broadening mechanisms i n the plasma, the predominant one i n t h i s case being Stark broadening, i t i s necessary to integrate the emissivity £(V) over the complete l i n e shape. Further, one assumes that the percentage var i a t i o n i n V-™ i s small throughout the t o t a l l i n e . Thus, -10- £ < 0 =• j^COWv) 2:8- i.e. Vw W ' 1 kv\ VA <S * 7 Hence the excited state population may be calculated from where etfu must be evaluated from considerations of the optical system and comparison with a standard source. (d) Line Broadening and Electron densities The shape of a spectral line i s normally influenced by a number of broadening mechanisms. To the plasma physicist, the two most important of these mechanisms are the Doppler broadening and Stark broadening. The f i r s t of these i s caused by the thermal motion of the particles and the second by the electric f i e l d of the electrons and ions in the neighbourhood of the emitting particle. In low density plasmas, Doppler broadening dominates and i s a function of the temperature of the emitting species o n l y . At high particle densities, the Stark b T o a d e n i i r g --dominates. Stark broadening- i s found to be only slightly dependent on the temperature and strongly -In- dependent on the electron density. There are i n essence three approaches to using the Stark e f f e c t to measure the electron density. These are, i n order of increasing accuracy, the l i n e s h i f t , the l i n e h a l f width and the l i n e p r o f i l e technique. Line s h i f t s cannot generally be measured accurately i n dense plasmas because of the excessive l i n e broadening. Of the other techniques, a study of the l i n e shape of w i l l y i e l d about 5% accuracy i n the calculated electron density; while h a l f widths of other H l i n e s and of He l i n e s are known to about 10$. (Griem, 1964) The h a l f width, the width of the l i n e at h a l f the peak i n t e n s i t y , i s a function of the electron density, n e, and the electron temperature, TLq. For non-hydrogenic atoms i t i s given by ^ W x = C ( T e ) - ^ «» 2 = 11 where Wi. i s the measured h a l f width and WQ i s one-half the h a l f width at a spe c i f i e d electron density, n 6 > o * Since the h a l f width i s a slowly varying function of temperature, one can choose an approximate temperature and assume H e = C t " 0 ^ ° 2 : 1 2 Griem (1964) has l i s t e d tables of values f o r C(T e) from which -12- n i s e a s i l y calculated. Once n i s found, a f i r s t approxima- t i o n to the temperature i s calculated. Successive values of n and T are found by using i t e r a t i v e techniques. (e) Equilibrium Equations of the Plasma The laboratory plasma i s seldom derived from a pure gas. For t h i s reason, two approaches to the treatment of the plasma w i l l be discussed. I n i t i a l l y , i t w i l l be assumed that there are two components of the plasma; that derived from the p r i n c i p a l gas, and that derived from impurities which inadvertently contaminate the plasma. These two elements of the plasma w i l l be designated by the subscripts prin. and imp. respectively. The standard spectroscopic! notation for i n d i c a t i n g i o n i c species w i l l be used such that (n* ^ )„_.•_ i s the number density of the i t n ions of prxn. the p r i n c i p a l component of the plasma. Thus, the t o t a l electron density n can be written 2:13 where a i s the atomic number of the component gas. Each species of ion i n the plasma i s i n equilibrium with the electrons. i . L-M n 7 n - h e 2:14 -13- For t h i s reason, the Saha equation can be written i n the general form 2 :15 where i t i s understood that t h i s equation can be used to describe the r e l a t i v e population of a l l adjacent i o n i c specie i n the plasma. In the Saha equation, k represents the Boltzmann constant, T, the temperature of the plasma, and I s the i o n i z a t i o n potential of the i t n stage ion. Yi+^" and Y* are the p a r t i t i o n functions of the ionic species i+1 and i respectively and are defined by T = Z 5^ — j 2:16 1 th where g m i s the s t a t i s t i c a l weight of the m excited l e v e l and E J J J 1 i s the ex c i t a t i o n energy of that l e v e l . The second term i n the square brackets i s usually much l e s s than unity and w i l l be neglected for the most part i n t h i s treatment. The equilibrium populations of excited states i n the plasma,n^, are given by -14- In subsequent parts of t h i s section, i t w i l l be assumed that both n e and n m * for any species can be measured and the temperature,T, w i l l be treated as an unknown parameter. The two approaches to c a l c u l a t i n g the temperature within the l i m i t s of the preceding information are; (a) Assume that the impurities i n the plasma are n e g l i g i b l e and calculate a s e l f consistent set of values from equations 2:13, 2:15 and 2:17, neglecting the second term i n 2:13. (b) Find an approximate value of temperature using method (a). Using t h i s value of T, f i n d a consistent set of values from equations 2:12,2:15 and 2:17 assuming that the impurities i n the plasma are not n e g l i g i b l e . Turning to the f i r s t solution, and assuming that only singly and doubly ionized species contribute to the electron density, one has from equation 2:13 H e ^ ^ l A 3 3 1 2:15 For the time being, neglect the subscripts for the p r i n c i p a l component gas since no ambiguity w i l l arise from doing so. Keeping i n mind that the Saha equation can be used to f i n d the r a t i o of n to n , one has n - 2:19 The evaluation of the temperature i s s l i g h t l y d i f f e r e n t for n m * and n m** values. Singly ionized species w i l l be examined f i r s t . Solving equations 2:15 and -2:19 and -taking natural logarithms, an i m p l i c i t expression f o r the temperature r e s u l t s . -15- kT 2:20 i— * i/S ft** Y m4 JLA Using a scaling factor s i m i l a r to that used by Neufeld(1964), the equation may be transformed into Q.KT a. ' - 2:21 - L -f- A L where has been chosen such that 2-22 and ^L^ i s understood to be the correction term In [ 1 + 2 ( 1 ? / ^ ) ] . Equation 2:21 may be plotted f o r L=f(o^kT) as has been done i n F i g u r e ( 1 ) . When n m x and n e are known, a f i r s t approximation to the temperature may be found by neglecting In Ql+2(n'^'Vn"''^0 • Subsequent i t e r a t i o n s may then be carried out using the value of n^*/n** calculated from the Saha equation. Thus, the measurement of the population of an excited state of a i neutral species, nffl leads to an estimate of the temperature.  -17- Equation 2:19 may be solved with equation 2:17, written for a singly ionized species, as well. In t h i s case one has This equation i s also solved using an i t e r a t i v e technique i n conjunction with the Saha equation. Suppose that there are impurities present in' the plasma and that the impurities are dominated by a p a r t i c u l a r i o n i c species n a + \ Then ' \ / \ 2:24 L— J. \ i-.o / l m P As before, assume that the p r i n c i p a l gas i s predominantly composed of only the f i r s t two ion i c stages. Then f\e - ( „ D ) + ( z * 0 1 ) . 2:25 With the help of the Saha equation, t h i s expression can be rearranged to become -It- imp. ^ o u n d &y measuring the excited state pop- a+1 \ u l a t i o n ( n m ) i m D . Then, 2:27 From equation 2:17, \ V 1 * - cx" \ K~ / Equations 2:26 and 2:2^ are most e a s i l y solved by p l o t t i n g p r i n a s a ^ u n c - t i ° n °f T i n t n e region of solution for the pure plasma and f i n d i n g the point of i n t e r s e c t i o n of the two curves defined by 2:26 and 2:28>. For the excited states of neutrals, i t i s possible to write an equation of the form 2:29 x n. / -+-Z (-) -19- Th e introduction of a scaling parameter q s i m p l i f i e s the solution of the equation. = L -f- * L, - A Figure 1 can be used to f i n d solutions o f equation 2:30 and i t e r a t i v e techniques must be used to get a temperature which i s consistent with a l l of the measured parameters. In equation 2:30 AL^ i s defined by 2:31 In evaluating the absolute i n t e n s i t y measurement procedure, i t w i l l be advantageous to compare the r e s u l t s with those of r e l a t i v e i n t e n s i t y measurements made on the same apparatus. So that t h i s might be e a s i l y accomplished, the derivation o f the appropriate equation w i l l be outlined and c i t e d f o r future reference. I f the i n t e g r a l i n equation 2:5 i s replaced by 1 ^ , then i L - <~\»L 2 : 3 2 - 20- Th e r a t i o of the t o t a l i n t e n s i t y of two l i n e s of two adjacent species i s then given by The excited state populations can be eliminated by using the Holtzmann equation 2:17 and eliminating the r a t i o nVni+^ by using the Saha equation 2:15. The r e s u l t i n g equation contains only constants of known value, and the measurable r a t i o I m ^ / l m n ^ " as a function of kT. This equation may be written i n the form P + - E 2. 2:35 The solution of equation 2:35 i s best ca r r i e d out by using a scaling parameter and a graphical technique s i m i l a r to that already demonstrated i n t h i s discussion. -21- (f) S e n s i t i v i t y of the Temperature Measuring Techniques Both the absolute and r e l a t i v e i n t e n s i t y measure- ments require the measurement of two parameters of the plasma. I t i s i n s t r u c t i v e to calculate the d i f f e r e n t i a l v a r i a t i o n i n the calculated temperature as a function of percentage variations i n the measured parameters. For example, consider equation 2:20 f o r a neutral species of a pure plasma rewritten i n exponential form. 2:36 I f the dependence o f the Saha t e n t m / n on temperature i s considered n e g l i g i b l e for small changes i n the temper- ature, then a r e l a t i v e l y simple expression r e l a t i n g A(kT)/kT to A ( n m I ) / n m I can be - f otrath by "d-i"f*erentiating equation 2:36 with respect to kT, assuming n ^ i s the only variable which depends on the temperature. -22- 2:37 Dividing equation 2:37 by equation 2:36 and rearranging, one has 1*1) kT 2:3S J 2. where the d i f f e r e n t i a l s have been written as A(kT) and A(n^)to indicate small macroscopic changes i n the v a r i a b l e s . Similar expressions can be found for other species i n the plasma written f o r changes i n other measurable parameters. The general expression may be written as ^ / Percentage change\ ^ k J= V J i n the measurable 1 2:39 k T [ p a r a o e t e r J where X represents the f a c t o r which gives the dependence of (kT)/kT on -the percentage change of the measured parameter. Table 1 l i s t s values f o r X derived from the various equations i n t h i s t h e s i s . A c V V c H S 0 -0 1J L m s a) +> X H + I + ! i »- M + I + is 0 c UJ •iJ + o o •J <0 to -J CHAPTER II I THE ABSOLUTE INTENSITY CALIBRATION (a) Introduction The measurement of absolute i n t e n s i t i e s requires the comparison of the unknown r a d i a t o r to a standard source. In the simplest experimental arrangement, both sources have the same geometrical configuration and each i s observed through an i d e n t i c a l o p t i c a l system. However, i n measuring the absolute value of plasma emissivity,the experimenter i s often confronted with comparing a plane, homogeneous standard source to a vdumetric, inhomogeneous source. For simple geometries, i t i s possible to make certain assumptions which greatly reduce the complexity of measuring the absolute value of the emissivity. This chapter deals with only one aspect of t h i s problem, that of measuring the emissivity of a homogeneousj, c y l i n d r i c a l l y shaped plasma. Corrections for the shock tube absorption have also been included* (b) Light Gathering of the Monochromator In t h i s discussion, i t w i l l be demonstrated that the proper choice of condensing lens w i l l considerably simplify the geometrical optics. An examination of Figure (2) reveals three d i s t i n c t regions i n the image space of the s l i t * These regions are d i f f e r e n t from one another because of the s o l i d angles into which l i g h t from each i s radiated. In region 1, the s o l i d angle i s subtended by the SiDg VIEW t 2 encode. ^ono/ecii/ 'n^ Lews, FIGURE 2.1 LL<jk* of^tkerc C o w o(e CM*? (.ins. or -fck -26- projection of the collimator on the condensing lens; i n region 2, by the s l i t image; and i n region 3, by the s l i t image and the projection of the collimator on the condensing lens. A volumetric source occupying the region of the s l i t image would thus have parts which are not equally e f f i c i e n t i n producing a f i n a l image i n the monochroraater. For t h i s reason, integration must be carried out i n each of the emitting regions separately, taking into account the transmission properties peculiar to each region. Niel«swi (1930) has analyzed the problem-geometrically for both plane and volumetri-c sources, both with and without a condensing lens. A rule-of-thumb which allows one to know i f a thorough approach i s necessary can -be -formulated. I f the f-value of the condensing lens i s greater than the f-value of the collimator, then a simpli- f i c a t i o n of the cal c u l a t i o n of the useful flux passing through the o p t i c a l system can be made. Figure 3 shows the sit u a t i o n i n which the condensing lens, having the larger f-value, l i m i t s the l i g h t f l u x i n the o p t i c a l system. A l l points emitting useful radi a t i o n are contained i n the l i g h t cone subtended by the condensing lens and the s l i t image, and the e f f e c t i v e s o l i d angle i s defined by the condensing lens. A l l radiat i o n from points f u l f i l l i n g these conditions, which i s not scattered out of the system and which passes through the condensing l e n s , i s focused on the f i n a l image of the system.  -26- It should be noted that t h i s technique i s p a r t i c - u l a r l y i n e f f i c i e n t and cannot be used where low i n t e n s i t y sources are to be studied. On the other hand, the sub- s t a n t i a l gain i n s i m p l i f i c a t i o n by using a smaller condenser lens often warrants the use of t h i s technique i n observing bright plasma sources. (c) Standard Sources i n t e n s i t y measurement and i t i s the accuracy of these standards which ultimately l i m i t s the v a l i d i t y of data involving absolute i n t e n s i t i e s . Standard sources may be divided into two main categories: primary sources which are used i n standard laboratories, and secondary sources which are calibrated i n the standard lab and f i n d applica- t i o n i n other laboratory experiments. The primary standard i s i d e a l l y a black body whose radiant i n t e n s i t y obeys Plank's law, namely where W(̂ .,T) i s the t o t a l power per unit area radiated into- a s o l i d angle 27f . 7L arrd T have the usual meaning of wavelength and temperature, and c-̂  and c 2 depend on atomic constants only. The major d i f f i c u l t y with a primary source-is defining i t s temperature. Griem (1964) has described Standard sources are ess e n t i a l to the absolute -29- some of the problems associated with accurate temper- ature determinations. Molten gold or platinum i s often used as a primary standard. An additional primary standard which has been used i n the standardization of tungsten lamps i s the cavity radiator. Larrabee (1959) for example, compared the radiation from a c y l i n d r i c a l filament of tungsten to the radiation from a small hole i n the cylinder i n order to measure the emissivity of the surface. The most commonly used secondary standard source i s the tungsten ribbon lamp. The standard laboratory quotes the brightness temperature, T D, f o r the lamp when a s p e c i f i e d current i s flowing through the filament. T, i s defined such that a black body with b temperature T^ would have the same radiant i n t e n s i t y as the tungsten filament at a given wavelength, usually . o 6500 A. I f Wien's law i s considered to be a good approx- imation of the radiation, then where "feĈ O i s the transmission of the glass envelope and £(3.<jr) i s the emissivity of the tungsten surface at the calibrated wavelength XC . B[7.T) * s defined by -30- = W t P j T ) , 3:3 where WT and WB.B. a^e the power radiated fro* the tungsten ribbon and a black body respectively for the same temperature and wavelength. A solution of equation 3:2 gives the relationship between the true temperature and the brightness temperature. JL =_!..+. i X [ { ( ^ U C J T ) l 3:4 Once T i s found, the radiant intensity can be found at other wavelengths. W T G T ) =-|; ™p(~)i (2) fiUj) 3=5 DeVos (1954) has elaborated on the relationship between true temperature and brightness temperature, and has also plotted values for^(^.,T) as a function of Ti for various values of T. There i s some degree of controversy concerning the precise values of £(/?.,T} and the exper- -31- imenter should be aware of t h i s before using a p a r t i c u l a r set of values. The transmission of the envelope must be considered f o r i n d i v i d u a l cases. When a l l sources of error are considered, the tungsten ribbon lamp should give a respectable degree of accuracy. I f the tungsten ribbon lamp i s calib r a t e d at only one point, measurements for wavelengths widely divergent from the c a l i b r a t i o n wavelength should be highly suspect. Errors may vary from about 3% i n the red end of the spectrum to about 12% i n the blue. More c a l i b r a t i o n points w i l l reduce t h i s high l e v e l of error. The power requirements for the lamp are small and the l i g h t i s both very steady and reproducible. However, the i n t e n s i t y of the lamp may be too low f o r some applications, and the range i s l i m i t e d to the v i s i b l e portion of the spectrum. A much more intense source of standard r a d i a t i o n i s the carbon arc. The colour temperature i s generally quoted f o r the operation of the arc. The colour temper- ature of a radiator i s that temperature of a black body which has the same spectral d i s t r i b u t i o n of energy i n the v i s i b l e region as the secondary source. According to de Vos, the emissivity must be of the form 3:6 where K i s some constant l e s s than or equal to one, and k i s the Boltzmann constant. Using Wien's Law, 3:7 Thus, the true temperature i s related to the colour temperature There i s some discussion i n the l i t e r a t u r e as to the actual value of T. Euler (1954) has suggested a temperature of 3'995°K with an emissivity of about 0.75, while l a t e r authors, Null and Lozier (1962) have suggested a value of 36*00°K with (3.,T)£0.95 depending on the value of "X. In the v i s i b l e region i t appears that one can make the assumption Tc=T=3$00 K with |S> U-,T)=1. In regions beyond 6000 A, the emissivity f a l l s below orre. In the region below 2500 A, the arc plasma radiatio n comprises the major portion of the spectrum. In addition, there are -various radiat i o n bands which can cause trouble" i n the v i s i b l e r e g i o n . The-molecular radiati o n bands in the pyrometric arc spectrum, as they appear i n Null and Lozier (1962) are: by T -33- Source CN CN CN 35*5 3350, 3390 4150, 4225, 4500, 45$0 4700, 4730 5163 5633 These bands of radiation should of course be avoided. The operation of the arc requires some consistency of technique. In theory, one observes the anode spot whose temperature i s the sublimation temperature of carbon. However, i n practice, onefinds that the anode spot may not be uniformly bright, nor does i t remain f i x e d and stable. The method of operation used i n the course of t h i s experiment follows c l o s e l y that prescribed by Null and Lozier and w i l l be described l a t e r i n connection with the experimental techniques. (d) Shock Tube Absorption tube changes i t s transmission c h a r a c t e r i s t i c s during a series of shots. It i s suspected that impurities are evaporated from the material i n the spark gap region, and i t i s these impurities condensing on the inside of the tube which cause the change i n transmission. Suppose t h i s to be the case and consider that a layer of constant thickness i s deposited a f t e r each shot. Let the layer thickness be AX. and l e t the number of shots be n. I f k i s a constant which depends on the deposited material and L i s the absorption of the glass wall, then Because of the method used i n construction, the shock I 3:9 -34- yvhere I Q i s the in t e n s i t y of rad i a t i o n f a l l i n g on the tube and I i s the transmitted i n t e n s i t y . Setting k'^^c =k , one has I = I . L e^p (- 3:10 The t o t a l l i g h t energy, A, transmitted i n a series of shots n^ w i l l be - J A H o r I - e jo (- k ) 3:11 Define a mean transmission c o e f f i c i e n t by 0 = L I G 3:12 and write the f i n a l i n t e n s i t y as U lo = L I 0 e.*p(-Wv\+) 3:13 Then 3:14 Combining equations 3:11, 3:12 and 3:13 one has -35- Figure 4: Measuring the shock tube absorption In figure 4 the shock tube i s shown placed i n front of the monochromator so that L can be measured for a p a r t i c u l a r wavelength. The P.M. voltage with the tube i n place i s Vy{/L) and without the tube i t i s . I f the incident i n t e n s i t y 2 i s I„ and the transmitted i n t e n s i t y i s L I . then o * o 3 s 16 -36- S i m i l a r l y , at the end of a run Vr(2) 3:17 In order to make t h i s measurement, i t i s esse n t i a l to keep the distance d great so that most of the l i g h t s t r i k e s the tube at nearly normal incidence; otherwise, the scattering properties w i l l be much di f f e r e n t from those encountered when l i g h t i s emitted from the i n t e r i o r of the tube. A shot to shot value of the e f f e c t i v e transmission can be calculated by fin d i n g k from equation 3:9 and estimates of L and L~. A plot of i / l versus n i o y i e l d s the e f f e c t i v e transmission f o r each shot. During the course of a run of 40 shots, the e f f e c t i v e trans- mission has changed by as much as 15% depending on the spectral region under observation. (e) Comparison of Light Sources In order to calculate the population of an excited state i n the plasma, i t i s necessary to measure the emissivity ZfSX) of the plasma at a c a r e f u l l y defined wavelength ?., The technique involved requires the comparison of the energy radiated from a well defined volume of the ionized gas to the energy radiated from a sp e c i f i e d area of a standard source. There are two related quantities associated with r a d i a t i n g surfaces which are indispensable to t h i s technique. The f i r s t of these i s the radiance B0U) tfhich i s the amount of energy - 37- radiated normally from the surface per second per unit area per steriadian.. The second quantity i s the t o t a l power radiated into the h a l f sphere and i s denoted by W(2.). From figure 5, B(©-)=3Q cose and 3:13 where integration i s carried out over the h a l f sphere. Integration of equation 3:13 y i e l d s W(*)-1TB W. The t o t a l power radiated into the h a l f sphere f o r a black body i s given by Plank's Law, equation 3:1» One of the p r i n c i p a l equations of photometry rel a t e s the power, dP(/0, i n t e r - cepted by an area, dA 2, which i s radiated from a surface,dA^, of brightness B Q(/0. See figure 5 for d e t a i l s . The area elements are separated by a distance R, and the normals of dA^ and dA g make angles of and # 2 with the l i n e j o i n i n g the area elements. 3:19 (a) (b) Figure 5: Radiance and l i g h t f l u x  -39- Suppose now that an o p t i c a l system composed of a condenser lens and a monochromator can be arranged i n such a way that the condenser, focuses the s l i t of the monochromator either on the standard source or i n the i n t e r i o r of the plasma. It i s assumed that the e f f e c t i v e f-number of the condenser i s much larger than the f-number of the monochromator. Figure 6 shows the schematic diagram of the apparatus. Since the f-number of the condenser i s much larger than that of the monochromator, any l i g h t emitted from the image of the s l i t and passing through the condenser lens, which i s not absorbed or scattered by the system, w i l l eventually reach the exit s l i t of the monochromator. Let P {/L)&X be the power radiated s from the standard source at wavelength 7- i n the wavelength i n t e r v a l where i s li m i t e d by the s l i t width and dispersion of the monochromator. From equation 3;19 where t i s the transmission" c o e f f i c i e n t of the-system. Since the areas i r e p a r a l l e l , c o s ^ =cos -cos©. The area of the image of the s l i t i s very small and i s repre- -40- sented by dAj. An area element on the c i r c u l a r lens of radius a i s given by 2Tfrdr. Integration y i e l d s where -&0 i s the angle subtended by the condenser lens. Assume that the response of the photomultiplier i s l i n e a r . Then the voltage output of the photomultiplier c i r c u i t i s given by V_(3-)^2_ -SPB[Xi » where S i s the c o e f f i c i e n t of response for the system. Equation 3:20 becomes \/sM±l= Z-tJ(P<T7r %U) S u i ' ^ X 3:21 In performing the same ca l c u l a t i o n for the plasma source, i t w i l l be necessary to integrate over the volume of the emitting plasma. The c a l c u l a t i o n i s s i m p l i f i e d considerably i f one notes that the e f f e c t i v e radiation originates only from plasma i n the region bounded by the cone, whose base i s defined by the collimator lens, and whose apex i s the image of the s l i t . Note that the mirror image of t h i s cone, r e f l e c t e d i n the plane which passes through the apex normal to the axis of symmetry, also emits l i g h t into the o p t i c a l system. Further, only l i g h t rays which pass through the s l i t image or which, when projected backwards, would pass through the s l i t image w i l l enter the monochromator. Equation 3:19 must be revised to f u l f i l l these conditions. Consider the emissivity of the plasma i n the wavelength i n t e r v a l 4 7L to be EpCl)^ The t o t a l power radiated from a small element of volume 27T/odpdz i s given by 27pdpdz £p{3.) -41- where (̂ o, z,&) are the c y l i n d r i c a l co-ordinates of a co-ordinate system oriented with the z-axis coincident with the o p t i c a l axis of the apparatus. Figure (6) demonstrates t h i s s i t u a t i o n . It i s further assumed that the emissivity i s not a function of position i n the region of observation. As well, there i s no absorption i n the part of the spectrum under consider- ation. Under these circumstances, the amount of useful f l u x radiated by t h i s volume element depends on the s o l i d angle which the area of the s l i t image dAj sub- tends at a distance r from the volume element. Thus, the radiated power which passes through the exit s l i t w i l l be P fUW = i f T^Hf ̂  W ^ — ^ 3:22 The 47)'appears i n the denominator since £p(/L) i s the energy radiated i n a l l d i r e c t i o n s and t i s , as before, the transmission c o e f f i c i e n t of the system. The integration of equation 3:22 requires the simple change of variable P=%fcan-&-. On reduction £U)*7.- ^ ' ^ ^ f l i f s i V J e f c l * 3:23 where 0Q i s the angle subtended by the lens and d i s the depth of the plasma. Integration yields, P̂ CO** = - f c f . U ) ^ ( / - c o s g , ) ^ 3:24 - 4 2 - The output voltage of the photomultiplier, \Zp[/L), i s then given by V p U ) A , l r (\-c-o$%)<Jlfi* 3:25 Combining equations 3 : 2 1 and 3:25 y i e l d s the emissivity of the plasma ZpiX) at a p a r t i c u l a r wavelength i n terms of known and measurable quantities. S P U ) 3 ' W(X) 3:26 In practice, the plasma i s confined i n a c y l i n - d r i c a l tube, so that side-on observations do not s t r i c t l y adhere to the conditions of observing an i n f i n i t e slab of depth d as assumed i n the above discussion. However, i f &Q i s r e l a t i v e l y small, the error i n assuming a plane surface i s not great. Secondly, the glass or quartz cylinder walls absorb and r e f l e c t r a d i a t i o n . For t h i s reason, Vp(T-) must be corrected f o r loss of ra d i a t i o n . As has been suggested, n 1 depends on the i n t e g r a l of over the l i n e shape. Thus, i t i s esse n t i a l to correct a l l points i n a plot of Vp(T-) versus X . When a corrected l i n e p r o f i l e has been drawn, equation 3:26 i s used to fi n d the absolute value of the peak radia t i o n . Graphical methods may then be used to f i n d oJt> found i n -43- quation 2:10. The excited state population can then alculated from CHAPTER IV APPARATUS AND TECHNIQUE (a) Introduction The experiment was arranged to measure absolute i n t e n s i t i e s . Relative i n t e n s i t i e s were then calculated from the same set of data. Temperatures calculated from each set of measurements were compared. Helium was used as a working gas i n a shock tube with a coplanar d r i v e r . Side-on observations were taken through a simple o p t i c a l system designed to f u l f i l l the conditions of the preceding chapter. A l l measurements were time resolved by using e l e c t r o n i c devices, and a carbon arc was used f o r the absolute i n t e n s i t y c a l i b r a t i o n . The shock tube, o p t i c a l arrangement, detection devices, and the carbon arc are described i n t h i s chapter. (b) Shock Tube The shock tube used i n t h i s experiment has been amply described i n other reports o r i g i n a t i n g from t h i s laboratory. For t h i s reason, only a short description i s given here and the interested reader i s referred to Sirapkinson (196^) or Neufeld (1963). The shock tube consists of a one inch diameter quartz or glass tube with a two centimeter spark gap at one end. Three 5/<-f capacitors are connected i n p a r a l l e l across the spark gap with a maximum charging voltage of 20 KV. The discharge i s i n i t i a t e d through an open a i r spark gap switch. In t h i s p a r t i c u l a r application, only one of the three capacitors was  -46- used at a charging voltage of 12 KV. The gas used was He at an i n i t i a l pressure of 300 Hg. Under these conditions, James (1965) has suggested that He plasmas produced i n t h i s shock tube exhibit equilibrium c h a r a c t e r i s t i c s . (c) Optical Eqipment and Measuring Techniques The plasma was observed ,at right angles to the tube at a point 17 centimeters from the spark gap. A Jarr e l l - A s h (62-010) monochromator with a 50 centimeter f o c a l length was arranged as shown i n figure 7. The rotating mirror acts both to give a 90° d e f l e c t i o n of the l i g h t when observing the He plasma, and to function as a shutter when observing the standard source. In t h i s way, both the plasma and the carbon arc l i g h t signals were received at the PM as a.c. signals. The stationary 90° d e f l e c t i o n mirror allows either the plasma or the standard source to be observed through i d e n t i c a l lenses. Note that distances d-̂  and dg are equal so that the o p t i c a l paths are equivalent. The lenses L are focused on the anode spot and the center of the shock tube. The photomultipliers used were an RCA 1P26 i n the range 3000 A to 6000 I and a P h i l i p s CVP 150 i n the region 5000 1 to 7000 A. The photomultiplier signals were amplified on a cathode follower amplifier and displayed on a Tektronix 545A oscilloscope. The displays were photographed, and the averages of three or more readings were taken i n order to smooth out the shot to shot fluctuations i n l i g h t i n t e n s i t y . Before p l o t t i n g on graph paper, these readings were adjusted f o r tube absorption according to the technique outlined i n -47- e a r l i e r sections. s (c) Figure S: Line Sampling Techniques There are three techniques for measuring the integrated l i n e i n t e n s i t y . These are demonstrated i n figure 3 and explained beldw. (a) Choose a s l i t width which covers the entire l i n e and the output signal w i l l be proportional to the t o t a l l i n e strength. Griem (1964) discusses t h i s technique i n d e t a i l . Note that i t i s necessary to correct for both the continuum radiati o n and the wings of the l i n e . (b) Choose a s l i t width which covers a known f r a c t i o n of the t o t a l l i n e width and then take voltage readings at wavelengths i n such a way that the i n t e r v a l s just touch. The sum of the voltages w i l l be proportional to the t o t a l l i n e i n t e n s i t y . It -43- i s again necessary to subtract the continuum radiation but the wings of the l i n e can be accounted f o r . There i s also some uncertainty as to the actual f r a c t i o n of the l i n e sampled. (c) Choose a narrow s l i t and measure the l i n e p r o f i l e . In t h i s case the t o t a l i n t e n s i t y w i l l be proportional to the area under the curve. In addition, the electron density i s e a s i l y calculated from l i n e shape or l i n e half-widths. As before, the continuum radiation must be subtracted. In t h i s experiment a l l three techniques were con- sidered but since n e was to be calculated , the l i n e p r o f i l e method was chosen because t h i s technique allows the ca l c u l a t i o n of both the excited state population and the electron density. (d) Carbon Arc Both the tungsten ribbon lamp and the carbon arc were considered as possible standard sources. Considerable exper- imentation indicated that the r e l a t i v e l y low i n t e n s i t y of the tungsten lamp made i t unacceptable with the elec t r o n i c tech- niques which were r e a d i l y a v a i l a b l e . The carbon arc, on the other hand, proved very suitable because of i t s r e l a t i v e l y high temperature of 3300°K. A 150 v o l t , 15 amp, regulated dire c t current power supply (Sorensen Nobatron DCR 150-15) was used. A high current, variable carbon r e s i s t o r was placed i n series so that the arc could be operated with an ov e r a l l p o s i t i v e resistance i n the c i r c u i t . This of course f a c i l i t a t e d stable operation of the arc. The current was adjusted to about 10 amps depending on the electrode separation. As prescribed i n Null and Lozier (1962), the electrodes were oriented at 90*. - 49- Th e arc was operated just below the "hissing point" as described i n the l i t e r a t u r e . The arc i t s e l f was a standard commercial model, made by Leybold, with the projection lens removed. Ringsdorff spectroscopic carbons RW 202 and RW 401 were used for the anode and cathode respectively. The diameter of the anode spot image on the monochromator was adjusted to be considerably larger than the s l i t height. This ensured that the image area was small as required by the theory and reduced fluctuations i n the standard source i n t e n s i t y over the s l i t . CHAPTER V RESULTS AND CONCLUDING REMARKS (a) Introduction Electron densities were measured using the half-widths of HEI l i n e s , and excited state populations were calculated using techniques described i n Chapters II and I I I . In the course of the work, an attempt was made to check on various important parameters such as the electron density, absorption, and impurity consent of the plasma. The electron densities were checked against Griem's ( 1 9 6 4 ) c r i t e r i a f o r LTE and the absorption calculated using t h e o r e t i c a l expressions found i n 1 many texts on spectroscopy. The plasma appeared to f u l f i l l the conditions of LTE and transparency required by the theory. The impurity content was estimated using the absolute i n t e n s i t y of impurity l i n e s . The excited state populations could thus be calculated and the number of electrons supplied by the ionized species of the impurities estimated. In order to a r r i v e at a f i n a l estimate of the temper-- ature, an i t e r a t i v e technique was employed. I n i t i a l l y i t was assumed that the H e l l supplied a l l the electrons. A few calculations and comparison with tables indicated that the number of doubly ionized species present was substantial at the temperature calculated. Graphical representations of both the impurity content and the degree of i o n i z a t i o n of He as a function of temperature were used to calculate a f i n a l temperature which would be consistent with a l l of the available data. -51- (b) Results determined to be 7X10 cm with an error of 20%. The 20$ error has been assumed from research into accumulated data from the same apparatus for identical conditions collected both by Simkinson (1964) and James (196$) and i s attributable largely to the reproducibility of the plasma. Shot to shot fluctuations of the plasma were found to be about 20%. For this reason, averages of several measurements were used. Lines were time- resolved, and a l l readings were taken at the time of maximum intensity of Hel lines. Although measurements are very insensitive to variations in measured parameters, wide deviations from LTE are required before they would appear here. temperature of the He plasma. The purpose of each method was to determine with some degree of certainty the actual number of Hell particles in the plasma. The f i r s t method assumes a pure plasma as presumed in equation 2:19, while the second considers that there are a large percentage of impurity electrons assumed in equation 2:26. In order to estimate the actual impurity content, CII 3919 and S i l l $056 were measured. Two approaches have been used in determining the Impurity line watts cm ster 3 X 10 6 1.6X 10 6 Intensity -1 CII 3919 1.6 X 10 10 10 S i l l 5056 3.4 X10 The number of electrons supplied by these species i s -52- 13 -3 2*10 cm . However, a c a l c u l a t i o n with the Saha equation indicated that the S i l l l population i s comparable to n Q f o r temperatures' i n the 3 ev. range. Hence, using the S i l l l 5056 upper state population value, along with the Saha equation, a plot of S i l l l as a function of kT was drawn as i n figure 9. The r a t i o of Hell/Hel was plotted from the Saha equation so that equations 2:19 and a revised form of 2:26 could be plotted as i n figure 10. The absolute i n t e n s i t y of Hel 6676, 5675 and H e l l 4666 were measured and excited state populations calculated. The r e s u l t s of these calculations along with the respective temperatures are to be found i n Table 2. The agreement between H e l l absolute i n t e n s i t i e s and r e l a t i v e i n t e n s i t i e s appears to be within experimental error, the difference i n the r e s u l t s of each method being about 6%, The absolute i n t e n s i t y of neutral helium l i n e s on the other hand, y i e l d a s u b s t a n t i a l l y higher temperature which varies about 15$ from the others. The ef f e c t of including the impurities does not appear to be s i g n i f i c a n t , having l i t t l e or no e f f e c t on the calculated -temperatures. (c) Discussion The impurity content of the plasma has been estimated from the measurements of CII and S i l l l i n e i n t e n s i t i e s as pointed out above. This technique has considerable weakness i n that i t required the use of a second equilibrium equation, the Saha equation, as well as the Boitmnann equation -. However-, t h i s estimate of the impurity electron content indicates that  Figure 10: H e l l population as a function of kT TABLE 2 FINAL RESULTS OF RELATIVE AND ABSOLUTE INTENSITY MEASUREMENTS Line n*(-25$) Relative I n t e n s i t i e s Pure Plasma Impurities Considered Hel 667# 5376 H e l l 4636 3.2x 10 3X 10 1.3 X10 11 11. 11 3.2 ev. 3.2 ev. 3.7 ev. 3.̂  ev. 3.4 ev. 3.5 ev. 3.7 ev. 3.4 ev. n = 7 X 1 0 — 20$ -56- 17% of the t o t a l electrons supplied by S i l l l and that approximately 9% of the t o t a l ions are S i l l l ions. Using the r e s u l t s of Table 1, the s e n s i t i v i t y of the temperature c a l c u l a t i o n to changes i n measured parameters i s almost i d e n t i c a l f o r both H e l l absolute i n t e n s i t i e s and Hell-Hel r e l a t i v e i n t e n s i t i e s . In each case, the percentage change i n the temperature i s about l/20 the percentage change i n the measured parameters. Thus, the temperatures calculated from these techniques are of about equal r e l i a b i l i t y . The Hel cal c u l a t i o n , on the other hand, i s extremely sensitive to variations i n n e and n m*. Since errors of about 20% are expected i n these measurements,.alone, no significance can be placed on the higher temperature calculated from the Hel l i n e s . Although the plasma has been found to more than f u l f i l l Griem's (1964) c r i t e r i a f or equilibrium, for the above reasons, the r e s u l t s of t h i s experiment cannot be used to support the LTE assumption. The necessity of including the impurity content of the plasma i n the calculations appears to depend on the l i n e under study. The i n s e n s i t i v i t y of the H e l l technique to changes i n the measured n e density would indicate that impurities can be neglected i n t h i s approach. On the other hand, i f Hel l i n e s are under study, impurities must be considered. These conclusions can be carr i e d into a general statement. For l e v e l s whose populations depend -57- o n a l a r g e e x p o n e n t i a l t e r m , t h e i m p u r i t i e s may b e n e g l e c t e d . T h e a b s o l u t e i n t e n s i t y t e c h n i q u e h a s t h e a d v a n t a g e o f p r o d u c i n g a d i r e c t e s t i m a t e o f e x c i t e d s t a t e p o p u l a t i o n s . A l s o , i n some s i t u a t i o n s i t may n o t b e p o s s i b l e t o c o m p a r e t w o l i n e i n t e n s i t i e s . I n t h i s i n s t a n c e , t h e a b s o l u t e i n t e n s i t y m e a s u r e m e n t c a n b e u s e d w i t h g o o d r e l i a b i l i t y i f a p p r o p r i a t e l i n e s a r e c h o s e n . H o w e v e r , t h e r e s e e m s t o b e n o i n c r e a s e i n a c c u r a c y b y u s i n g a b s o l u t e i n t e n s i t y m e a s u r e - m e n t s , s o t h a t t h e i n c r e a s e d d i f f i c u l t y i n m e a s u r i n g t h e a b s o l u t e i n t e n s i t y d o e s n o t w a r r a n t i t s u s e i n t e m p e r a t u r e c a l c u l a t i o n s i f r e l a t i v e i n t e n s i t i e s c a n b e m e a s u r e d . -53- BIBLIOGRAPHY de Vos, J.C., (1954) Physica 20, 690. de Vos, J.C.and Rutgers, G.A.W., (1954) Physica 20, 715. Eckerle, K.L. and McWhirter, R.W.P., (1966) Phys. Fluids 2, 31. Euler, J., (1954) Ann. Physik 14., 145. Griem, H.G., (1964) Plasma Spectroscopy, McGraw-Hill. i B l e r , Ralph C. and Kerr, Donald E., (1965) Phys. Fluids 3, 1176. James, H.G., (1965) M.Sc. Thesis, University of British Columbia Johnson, F.S., (1956) J-OptSoc. Am. £6, 101. Larrabee, R.D., (1959)J.Opt. Soc. Am. /£, 619. McLean, E.A., Faneuff, C.E., Kolb, A.C., and Griem, H.R., (I960) Phys. Fluids 1, 343. Neufeld, C.R. (1963) M.Sc. Thesis, University of British Columbia Nielson, J. Rud, (1930) J. Opt. Soc. Am. 20, 701. Null, M.R. and Lozier, W.W., (1962) J. Opt. Soc. Am. £2, 1156. Simpkinson, W.V., (1964) Ph.D. Thesis, University of British Columbia.

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