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Preliminary experiments for the study of the absorption spectra of plasmas 1961

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PRELIMINARY EXPERIMENTS FOR THE STUDY OF THE ABSORPTION SPECTRA OF PLASMAS by SINCLAIR EDWARDS BUDD B . S c , U n i v e r s i t y o f B r i t i s h C o l u m b i a , i 9 6 0 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.Sc. i n t h e De p a r t m e n t o f PHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA O c t o b e r , 1961 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree tha t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives. It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. T — ' The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 3, Canada. Date ffij 1 IS Of A B S T R A C T A Flash Unit to supply a pulsed source of continuum radiation has been constructed to provide the l i g h t required for the study of absorption spectra of plasmas. The unit which contains the plasma has been designed to produce a gas of high purity. Several transitions i n the excited neon were seen i n absorption. At least two have not been reported previously. A preliminary determination of t r a n s i t i o n temper- atures has been made. TABLE OF CONTENTS Page INTRODUCTION 1 Chapter I THEORY 3 1. Introduction 3 2„ Transition Temperatures 7 3. Relative A Values 12 4. Correlation of Electron Temperature to Excited Level Populations 15 5o Neon Spectrum 18 II APPARATUS 20 1. Introduction 20 2. Flash Unit 20 3. Plasma Unit 36 h. Shutter Unit 38 5. Electronic Units 40 III RESULTS AND CONCLUSIONS ^3 1. Introduction *+3 2. Experiment *+3 3. Future Work 48 Appendix I TRANSFER EQUATION 50 1. Definitions and Fundamental Notions 50 2. Equation of Transfer 57 II DISCHARGE MODEL 58 BIBLIOGRAPHY 6 l FIGURES following page 61 1. Neon Spectrum 2. Apparatus 3. Flash Unit h. Window Geometries 5. Trigger Geometries 6. Waveforms 7. Plasma Unit 8. Shutter Unit 9. Trigger Unit i i i ACKNOWLEDGMENT I would l i k e to extend my thanks to Dr, R. Nodwell whose guidance and understanding have been of immeasurable assistance to me i n this work; to other members of the plasma physics group with whom discussions have been most informative; to John Turner for the time devoted to discussions of elect- ronics and whose a b i l i t y has made much of this experiment possible; to Johnny Lees for his excellent glass blowing, and to Alex Eraser and other members of the technical s t a f f for their cooperation. i v INTRODUCTION In the recent surge of i n t e r e s t i n plasma physics research one of the major d i f f i c u l t i e s connected with deter- mining the properties of the plasma has been the development of suitable diagnostic techniques. Four well-defined techniques are presently i n common use i n plasma physics laboratories. 1. R-E.technique using microwaves 2. D.C. probes 3 . Photographic techniques 4-. Spectroscopic techniques The f i r s t two of these, while providing much accurate, i n t e r e s t - ing and useful data have the major disadvantage that they introduce perturbations into the plasma, and the effect of these perturbations may mask or a l t e r the effect which i s being measured. Photographic techniques provide information about the l o c a t i o n of the plasmas and their approximate densities, but very l i t t l e detailed knowledge-. Spectroscopic techniques, used i n this laboratory for observations of both emission and absorption spectra, have a decided advantage over the f i r s t two techniques mentioned i n that the measurements have very l i t t l e effect on the plasma i t s e l f ; and over the photographic technique i n that much more information other than approximate density and position can be gathered. Besides these advantages spectroscopy i s capable of - 1 - giving information about the local properties of a plasma, and when combined with electronics, time resolution. In the interpretation of the data obtained by the study of emission spectra, i t i s often necessary to know the relative population densities of two levels and the probability of a transition between these levels. Unfortunately in many cases these transition probabilities are not well-known and the dis- tribution of electrons among the energy levels may depart significantly from the usually assumed Boltzmann distribution, due to presence of impurities, because of the particular exci- tation mechanism or because of insufficient time to reach thermal equilibrium. It i s therefore desirable that experimental investigations into transition probabilities and electron densities be undertaken. Ladenberg has shown that these quantities may be determined through measurement of anomalous dispersion and absorption spectra. It i s also foreseeable that, using an appropriate modern pulse technique to trigger a short duration continuum source, we might study the time evolution of the absorp- tion spectrum of a plasma. This thesis describes the preliminary experimental work which has been done in preparation of the study of absorption spectra of ionized gases. Namely, the construction of the back- ground source the design of which was inspired by the work of W.R.So Garton who has improved upon the many previous attempts to achieve a high brilliance discbarge with the continuum in the ultra violet. Chapter I THEORY 1. Introduction As was pointed out i n the introduction, considerable information about a plasma or a hot gas may be obtained by the study of i t s absorption spectrum. The absorption spectrum i s obtained by passing l i g h t from a source of continuum radiation through the gas under inve s t i g a t i o n . The source may be a carbon arc or, as i s used i n this experiment, a f l a s h discharge. Since th i s gas i s self-luminous the spectrum may exhibit bright l i n e s upon the darker continuum background or dark l i n e s upon the brighter continuum background. The result depends upon whether the background radiation i s respectively hotter or cooler than the gas. These observations can be deduced quantitatively by rearranging and solving equation Al*+. d's Now write the f i r s t term on the right. At t h i s point we should r e c a l l two important relationships between Einstein c o e f f i c i e n t s L L = Ub̂ L BUL. (2) - 3 - - h - where gj_ i s the m u l t i p l i c i t y of quantum state i . Using equation 2, equation 1 becomes NU„ t A« L hvuu = (NuVuuB^u -MutfuuBQ I h ^ L h U , , Tj £ C2- N<-v>m. b\-t<. _ ^ (4) I f the gas i s i n thermal equilibrium then 2 where T i s the temperature of the gas, N the t o t a l number of atoms present and £. the p a r t i t i o n function of the gas; hence From equation A6 and 3 we have K " L = e — • (5) Substituting equation 5 into equation 4, we get (6) The s p e c i f i c i n t e n s i t y inside a black body at a temperature T i s —1 = -D ( T) (7) Define Kviu. by K v . L = hv^( N ^ B _ - A / . v ^ B _ ) . (8) T h i s , from i t s appearance i n equation 9, o b v i o u s l y i s the a b s o r p t i o n c o e f f i c i e n t . S u b s t i t u t e equations 7 and 8 i n t o e q uation 6, and use the r e s u l t i n g e x p r e s s i o n to transform e q u a t i o n Alh i n t o We now s o l v e t h i s equation under circumstances a p p l i - c a b l e to the present experiment. In C a r t e s i a n c o o r d i n a t e s the e q u a t i o n of t r a n s f e r i s where (1, m, n) are the d i r e c t i o n cosines of the path of i n t e - g r a t i o n . ¥e choose to i n t e g r a t e along the y - a x i s , the equation becoming ; ; The g e n e r a l s o l u t i o n of t h i s equation i s J . ^ = Cs e J y + 3 , ( 1 ] . I f the a b s o r p t i o n c o e f f i c i e n t Kv> i s constant along the y - a x i s , t h at i s (slcci;^ a ^ d v>u.<_ are constant, the s o l u t i o n i s Let the plasma we are c o n s i d e r i n g s t a r t a t the y = 0 plane and extend i n the p o s i t i v e y d i r e c t i o n . I f there i s no e x t e r n a l source e m i t t i n g r a d i a t i o n i n the p o s i t i v e y d i r e c t i o n , the i n t e n s i t y at y = 0, Xco) , i n the p o s i t i v e d i r e c t i o n i s zero hence I . ( y ) = B J ; T ) ( I - e ' K v y j d o The expotential term represents self-absorption. I f there i s a black body of temperature radiating i n the positive y d i r e c t i o n from y = 0 then I(o) = B(T^) and the solution to the transfer equation i s = BXT)(i-e _ K^) +- BCr'le-"'* ( I D Equation 11 shows that 1^ at the point of observation w i l l equal B^CT1) for any frequency away from those corresponding to atomic t r a n s i t i o n s , for at these frequencies K v = 0. We thus see that i f J ^ B̂>. i~T^ t h e l i n e w i l 1 b e b r l § n t ? i f Xy '< Btf(T') t h e l i n e w 1 1 1 b e d a r k a n d l f ly = Bw(T'j t h e l i n e w i l l be merged with the background. I f the temperature of the background radiator i s greater than that of the plasma the l i n e w i l l be seen i n absorption. To show this we f i r s t note that from the monatomic behavior of B(T) B(f) > BCD T ' > T From equation 11 we have ( I v - B „ ( T > ) = [BJT'J - BJCDJ e'*'^ but i s r e s t r i c t e d to (0,1) because i s r e s t r i c t e d to ( o jcOO ) . Hence i f T'>T l v - j?v(T) > B j j ' j _ QUJ l v > B , ( T V S i m i l a r l y , we can show that i f the temperature of the black body i s lower than that of the plasma, the l i n e w i l l appear i n emission. - 7 - I f T = T1, i t follows immediately I = B d 1 ) , that i s , there w i l l be neither a bright l i n e nor a dark l i n e . I t w i l l have blended into the background. the assumption of thermal equilibrium i n the plasma since this was invoked i n the derivation of equation 5* However, the plasma temperature which we have been using to characterize the emission of the plasma at the frequency corresponding to a t r a n s i t i o n between a pair of l e v e l s 1 and u can be a trans- i t i o n temperature, T̂ , defined i n such a way that the ratio', of population between these two lev e l s i s given by This temperature i s d i f f e r e n t for each pair of l e v e l s and applies only to the t r a n s i t i o n occurring between those p a r t i c u l a r l e v e l s . .2. Transition Temperature Garton 2, because of uncertainty i n the temperature of his continuum source, was unable to obtain an exact value for BCT1) so he used a procedure which would at least indicate how wejl a common temperature could be ascribed to his plasmas. The t o t a l energy P f a l l i n g on the photographic plate per unit time i s given by I t might seem that these results were dependent on !L - cos 8 du> dv which for an emission l i n e becomes by equation 10 P = C (12) - 8 - where "BV(J) m a v b e t a k e n o u t o f the i n t e g r a l b e c a u s e i t i s a s l o w l y v a r y i n g f u n c t i o n o f v>5 and C i s a c o n s t a n t r e p r e s e n t i n g t h e i n t e g r a l o v e r an a p p r o p r i a t e s o l i d a n g l e . The v a l u e o f P, measured f o r d i f f e r e n t l i n e s , need o n l y be r e l a t i v e . The t o t a l a b s o r p t i o n ( o r e q u i v a l e n t b r e a d t h ) o f a l i n e f r o m a gas backed by a s o u r c e o f t e m p e r a t u r e T l i s now I v ^ BJl'J e"* v y i f H i s » T a n d J v o - Bvo(T'J s o V A / t h u s The -1 term r e p r e s e n t i n g f o r c e d e m i s s i o n i n t h e d e n o m i n a t o r o f th e P l a n c k f o r m u l a c a n be d r o p p e d s i n c e £ <T ^ 10 f o r = 7000 A Ox and T = 8000 °K, c o n d i t i o n s t y p i c a l o f t h e p l a s m a s we a r e s t u d y i n g . T h i s done ?we have f i n a l l y I f a p l o t o f L-n:'J^,g-i a g a i n s t V D r e s u l t s i n a s t r a i g h t l i n e , i t c a n be c o n c l u d e d t h a t t h e l e v e l s c o r r e s p o n d i n g t o t h e s e t r a n s - i t i o n s have a common t r a n s i t i o n t e m p e r a t u r e g i v e n by the r e c i p - r o c a l o f t h e s l o p e o f the l i n e . I n t h e p r e s e n t e x p e r i m e n t a d i f f e r e n t method i s u s e d . The p h o t o g r a p h i c p l a t e i s ex p o s e d t o t h e a b s o r p t i o n s p e c t r u m f o r a tim e t a , t h a t i s , f o r t h e d u r a t i o n o f the f l a s h , a f t e r w h i c h the e m i s s i o n s p e c t r u m i s s u p e r i m p o s e d f o r a time t e . I t i s - 9 - possible to adjust the time t e u n t i l neither an absorption nor an emission l i n e i s seen on the photographic plate. In an experiment one must take notice of the intermittency effect which w i l l be pronounced with such short exposures. This i s discussed more f u l l y i n Chapter I I I . This time, t e= td, i s called the disappearance time. E s s e n t i a l l y the emission l i n e f i l l s i n the absorption l i n e . I t i s d i f f i c u l t to expose the plate for the exact time td so two pictures are taken with d i f f e r e n t t e 5 s , allowing the disappearance time to be i n t e r - polated. The relationship between the disappearance time and the t r a n s i t i o n temperature T i s T T h >A L v (13) where T l i s the black body temperature. Interpreting the t r a n s i t i o n temperature as a parameter expression the r e l a t i v e population densities, we have »V<- 9L. t^+td These formulas are derived from the following consid- erations. Define P as the t o t a l energy entering the spectro- graph s l i t per unit area from one l i n e . P w i l l be manifest a;s a density on the photographic plate. The exposure P i s , by the d e f i n i t i o n of l v , given by P - J Xv COS 9 d^ 1 dv> cl"t (15) = c f ( l v dv) dt - 10 - where C allows for the geometrical i n t e g r a l . From equation 11 we have P a of the f l a s h exposure given by P*. - C t , B J T ) j l - e ^ y > H- c t . e y o r r ) f £ ~ ^ v , (16) The i n t e g r a l over t i n equation 15 i s obviously just the time exposure t a . As before, ~BJJ) and B^T) are removed from the i n t e g r a l and replaced by their values at the centre of the l i n e and BVi(T') respectively. P e incident from the emission spectrum of exposure time t e i s The t o t a l exposure i s then c ( - t ^ + t c J B y , ( T ; / ( i - c - K v V Y c t . BV6(j')[e'^c/v (17) I f the time t e i s equal to the disappearance time t^ then This equation combined with equation 17 results i n a relationship between the temperature and time t<j namely or Neglecting the term for forced emission i n the plasma and using Wein's law for the black body (a doubtful step), we have By taking logs we have equation 13« - l i - l t remains only to determine t<j. We measure on an ar b i t r a r y scale, the exposures P i and P 2 of a parti c u l a r l i n e (of f r e - quency VXAC ) i n the two d i f f e r e n t pictures mentioned above. Me know from equation 11 that and P i - C ( t ^ t S i ) B J T J / ( i - c - K ^ ) ^ t c t . S v o ( ^ ; e ~ M < / p where t e-j_ and t g 2 are the corresponding emission exposure times. These equations are arrived at i n a manner i d e n t i c a l to that used for equation 1 5 . With the above two equations we can solve for , C 6Vo(vf(i- e ' < ' > and C Ovlr') [e-^dy L i n t • enabling us to write an equation'; for the i n t e n s i t y as a function of the exposure time t e . I f we measure the background exposure P(j, we fi n d t ^ , by solving the general equation, to be Another determination of t r a n s i t i o n temperature may be made by exposing a plate separately to an absorption spectrum for a time t a and to an emission spectrum for a time t e . The exposure for the absorption l i n e i s The exposure for the emission l i n e i s The exposure for the continuum i s - 12 - The difference between P 0 and P a i s Po = [C * « . BUT') - C ( L V + t e , ) Six)] l? l - e - k " ^ v . The r a t i o of the difference to P e i s given as Po-a ± ^ f M L } _ Pc t e L Bvirj By establishing the exposures P Q, P a, P e on an arbit r a r y scale, from the observed densities on the photographic plate (remember- ing the intermittency effect) and knowing the exposure time t a t e and t e 1 _ , we can calculate the r a t i o of the continuum r a d i - ancy to the plasma radiancy. I f we know the continuum temperature we can fin d the t r a n s i t i o n temperature. Both these .methods are used i n the experiment to estimate the t r a n s i t i o n temperature. 3 . Relative A Values"' The measurement of the anomalous dispersion i n the neighbourhood of an absorption l i n e but outside the region of absorption combined with the measurement of the t r a n s i t i o n temp- erature allows us to calculate the r e l a t i v e t r a n s i t i o n probabil- i t i e s for l i n e s i which correspond to transitions to a common 3 l e v e l . The anomalous dispersion i s given by where (see Korff and B r e i t ) 1 + F M ; t - M A*cu wcl „ A - Since we know n ^ l j ^ ) - - corresponding to the l i n e s i , - 13 - we know F M I > J F S L Then _ ^ AU,L h U i L 9 ^ ^ . J i - e K I T that i s , we can fin d a l l the t r a n s i t i o n p r o b a b i l i t i e s with respect to that of l i n e 1. The absorption spectrum affords another method of determining the r e l a t i v e A values. From equation 1 1 we see that, i f the black body temperature i s much higher than the t r a n s i t i o n temperature and the absorption c o e f f i c i e n t i s small (conditions which certainly exist i n the present experiment) the in t e n s i t y i s given by thus ilu ' S K^ ^ • <18) But from equation 9 since S = Nu , J A U ^ - A/, 5 from their respective d e f i n i t i o n s . From equations 3> 5 and 18 we have J_ P y J L" ^ J ^ - M ^ f | - e ^ ) ( 1 9 ) QTTVJ- " e r r / which gives us the same information as does a measurement of anomalous dispersion. - 15 - gives us yet another advantage i n that i t i s not necessary to calculate the true i n t e n s i t y as Ladenberg had to, i n order to determine the r e l a t i v e A values for t r a n s i t i o n s with a common upper l e v e l . Supposing we have measured the anomalous dispersion for several of these l i n e s j (a measurement of the integrated absorption c o e f f i c i e n t would serve as well) we have r A ' ^v* h uw r A , s>^_ ((\)ULi y. l - g v*.Li i i - e Lj I i - t_ K T j but we know and so w. A/ That i s In summary, we gain two advantages which Ladenberg did not have when we know the t r a n s i t i o n temperature. F i r s t l y , we can calculate the r e l a t i v e A values for common lower l e v e l t r a n s i t i o n s when there i s a high t r a n s i t i o n temperature and secondly, we can calculate the r e l a t i v e A values for common upper l e v e l t r a n s i t i o n s without evaluating the i n t e g r a l of equation 1 9 . h. Correlation of Electron Temperatures to Excited Level Populations^'6 . The equilibrium d i s t r i b u t i o n i n the populations of the - 1 6 - l e v e l s of excited atoms i s dependent upon the electron d i s t r i - bution function;. This function i s governed by Boltzmann 1s transfer equation i£ -r v • Vr-F + e X 7 v f - -̂ V where the number of electrons n enclosed by the volume dx dy dz at the point xyz and with v e l o c i t y between v^^^+d^ , V/y , \J^+AVj and Vj , \Zj +- d i s given by d n . = n -f(% ^ J dx dy d v x dVj dV} n i s the density of electrons. I f the f i e l d i s i n x d i r e c t i o n only and i s a constant i n space the equation reduces to On the assumption that the plasma can be modelled after a Lorentz gas, that i s one where m the mass of an electron i s much less than the mass M of the molecules and the density of the electrons i s small as i n a weakly ionized gas, the v e l o c i t y d i s t r i b u t i o n i s nearly i s o t r o p i c except for small deviations due to e l e c t r i c f i e l d and d i f f u s i o n . The equation i s solved by expanding f i n spherical harmonics and 'equating corresponding terms. The answer depends on our approximation for ±A 2t / C o l l i s i o n s Margenau, considering only e l a s t i c c o l l i s i o n s and a constant electron mean free path, found that for small high frequency f i e l d s of amplitude x 0 and tngular frequency W i n which i o n i z a t i o n can be neglected 3the d i s t r i b u t i o n function i s Maxwellian with T e = +• M e* X „ y e K m l W S - 17 - Though the model used was only approximate we can expect to have a d i s t r i b u t i o n which i s n e a r l y Maxwellian. Under c e r t a i n g e n e r a l c o n d i t i o n s , t h e o r e t i c a l c o n s i d - e r a t i o n s show the e x i s t e n c e of a s t a t i s t i c a l e q u i l i b r i u m between e l e c t r o n s and e x c i t e d atoms and the v a l i d i t y of the Boltzmann law f o r the e x c i t e d atoms. To demonstrate t h i s , i t i s necessary only that the v e l o c i t i e s of the e l e c t r o n s i n the plasma have a near Maxwellian d i s t r i b u t i o n and that the c u r r e n t d e n s i t y be very h i g h so that c o l l i s i o n s of the second k i n d between the e l e c t r o n s and e x c i t e d atoms destroy per second approximately as many atoms as are e x c i t e d by e l e c t r o n i c c o l - l i s i o n s . That i s to say, these two processes of e x c i t a t i o n and d e - e x c i t a t i o n must predominate over those of c o l l i s i o n s with the w a l l s , c o l l i s i o n s with other atoms, spontaneous r a d i a t i o n and r a d i a n t e x c i t a t i o n . With these two c o n d i t i o n s i t i s shown that the r a t i o of the p o p u l a t i o n s of two atomic l e v e l s corresponds to a s t a t i s - t i c a l e q u i l i b r i u m at the e l e c t r o n temperature. At higher p r e s s u r e s t h i s s t a t i s t i c a l e q u i l i b r i u m w i l l be reached f o r lower c u r r e n t d e n s i t i e s . T h i s i s a n a t u r a l consequence of the decrease i n the r a t e of d i f f u s i o n to the w a l l s of the e x c i t e d atoms as the p ressure i s r a i s e d , and the i n c r e a s e i n the number of slow e l e c t r o n s r e s p o n s i b l e f o r c o l l i s i o n s of the second k i n d with the e x c i t e d atoms, with a r i s e of pressure at constant c u r r e n t . - 18 - 5. The Neon Spectrum The lowest s t a t e of neon i s the c o n f i g u r a t i o n 2p^, w^ich g i v e s r i s e to the s i n g l e s t a t e -'-SQ. T h i s c o n f i g u r a t i o n i s very s t a b l e and a l a r g e energy i s r e q u i r e d to b r i n g the.atom i n t o the f i r s t p o s s i b l e e x c i t e d s t a t e 2p5.3is which l i e s over 130,000 c m s - 1 h i g h e r . A l l the e x c i t e d s t a t e s l i e i n the r e g i o n betx^een 130,000 and 174,000 cms" 1 from the normal s t a t e . The lowest c o n f i g u r a t i o n of the neon i o n i s 2p5 which gi v e s r i s e to an i n v e r t e d 2 p s t a t e , with a doublet s e p a r a t i o n of 78O cms'l. Thus the e x c i t e d s t a t e s of n e u t r a l neon i n a f i r s t a pproximation can be considered to a r i s e from the a d d i t i o n of an e l e c t r o n to the core i n e i t h e r the o r 2p^ s t a t e . According to S h o r t l e y , the L S d e s i g n a t i o n can be assigned s i g n i f i c a n t l y to only the f o l l o w i n g c o n f i g u r a t i o n s , the 2p5.3p and the s e r i e s 2p5.ns. The three lowest l e v e l s of 2p5.3s, the f i r s t e x c i t e d c o n f i g u r a t i o n , form the i n v e r t e d 3p s t a t e , 3P££.$. The • • ' 1 P 1 s t a t e i s 1070 cms" 1 above 3pQ. The 3p2 and ^P Q l e v e l s are metastable while the and i P i l e v e l s com- bine with the normal s t a t e to give the u l t r a v i o l e t resonance l i n e s 74-3 and 736 A*. The l e v e l s ^P210 a 1 1 have approximately the same p o p u l a t i o n d e n s i t i e s , even though 3p^ ±s u n s t a b l e , s i n c e a t room temperature the mean energy of the neon atom i s of the same order as that o f the energy d i f f e r e n c e between these 1, l e v e l s , a l l o w i n g the p o p u l a t i o n of the ̂ p-^ term to be re p l e n i s h e d by c o l l i s i o n with the metastable s t a t e s 3p 2 and 3p Q „ The 2p^.3p c o n f i g u r a t i o n g i v e s r i s e to ten l e v e l s , 1 S 0 , 3s 1 ? 1 p Q ) 3p o l 2, - 19 - l ^ and D]_23* ^ n e "terms of the above configuration combine to give about t h i r t y spectral l i n e s . In figure 1, the l i n e s which were observed i n the experiment are indicated. Chapter I I APPARATUS 1. Introduction The general arrangement of the equipment used for the investigations described i n this thesis i s i l l u s t r a t e d i n figure 2. Light from a high temperature source of continuum radiation, the f l a s h u n i t , passes through a plasma generated i n the plasma un i t . In this experiment the plasma i s created by a Radio f r e - quency discharge but the plasma source could be replaced by other sources such as a shock wave. The l i g h t , having passed through the plasma, i s photographed with a spectrograph to record the resu l t i n g absorption spectra. In one phase of the experiment i t i s necessary to control the r e l a t i v e exposure times of the plasma and f l a s h u n i t s . This can only be accomplished with'rapid shuttering of the spectrograph since the plasma unit i s a con- tinuous radiator and the f l a s h unit a pulsed radiator. The f l a s h unit has to be synchronized with the shutter unite This i s achieved by f i r i n g the f l a s h unit with a pulse from the trigger unit which i s tripped by the output pulse of the delay unit. This delay unit pulse i s i n i t i a t e d by a signal from the shutter unit which occurs at a fixed time i n advance of the opening of the spectrograph shutter. 2. The Flash Unit The f l a s h u n i t , to f u l f i l l i t s function adequately, was constructed with many differ e n t operating c h a r a c t e r i s t i c s . - 20 - - 21 - F r o m a p r e l i m i n a r y e x p e r i m e n t u s i n g n e o n i n t h e p l a s m a u n i t a n d e m p l o y i n g t h e p o s i t i v e c r a t e r o f a c a r b o n a r c f o r t h e c o n t i n u u m r a d i a t i o n w i t h a s p e c t r a l s t e r a d i a n c y a p p r o x i m a t i n g t h a t o f a 5000°K b l a c k b o d y , i t b e c a m e o b v i o u s t h a t we w o u l d r e q u i r e e v e n h i g h e r s p e c t r a l s t e r a d i a n c y , , S i n c e i n t h e f u t u r e i t i s h o p e d t o a p p l y t h i s d i a g n o s t i c t e c h n i q u e t o o t h e r p l a s m a s a t t e m p e r a - t u r e s o f t e n s o f t h o u s a n d s d e g r e e s K e l v i n i t w a s d e c i d e d t o u s e a n i m p u l s i v e d i s c h a r g e f o r t h e s o u r c e o f r a d i a t i o n . B e s i d e s r e q u i r i n g t h e h i g h s p e c t r a l s t e r a d i a n c y f r o m o u r s o u r c e i t i s a l s o a d v a n t a g e o u s t o h a v e t h e s p e c t r u m f r e e o f l i n e s a n d b a n d s i n e i t h e r a b s o r p t i o n o r e m i s s i o n s o t h a t a b s o r p t i o n c o e f f i c i e n t i n t e g r a l s m a y b e e a s i l y e v a l u a t e d a n d t h e s p e c t r a l d i s t r i b u t i o n m a y b e c o m p a r e d c o n v e n i e n t l y t o t h a t o f a b l a c k b o d y . I n f u t u r e e x p e r i m e n t s i t i s h o p e d t o i n v e s t i g a t e w i t h t h i s t e c h n i q u e , t r a n s i e n t p l a s m a s d e c a y i n g i n t h e o r d e r o f m i l l i s e c o n d s . T o d o t h i s w i t h g o o d t i m e r e s o l u t i o n t h e p u l s e d i s c h a r g e s h o u l d h a v e a d u r a t i o n o f o n l y m i c r o s e c o n d s . H o w e v e r i n t h e s t e a d y s t a t e e x p e r i m e n t d e s c r i b e d i n t h i s t h e s i s t h e s h o r t d u r a t i o n o f t h e s o u r c e p r o v e d t o b e m o r e a n u i s a n c e t h a n a n a d v a n t a g e . I n o r d e r t o p r o d u c e a u s e f u l p h o t o g r a p h i c r e c o r d o f t h e a b s o r p t i o n s p e c t r u m r e s u l t i n g f r o m t h e p a s s i n g o f t h e d i s - c h a r g e l i g h t t h r o u g h t h e p l a s m a u n i t , i t r e q u i r e d t h e s u p e r - p o s i t i o n o f a t l e a s t f o u r e x p o s u r e s . Two p i c t u r e s , a n d p r e - f e r a b l y f o u r , a r e r e q u i r e d t o p r o v i d e s u f f i c i e n t d a t a f o r t h e d e t e r m i n a t i o n o f p o p u l a t i o n d e n s i t i e s a n d t r a n s i t i o n p r o b a b i l i t i e s . - 22 - We must thus have the f l a s h unit output i d e n t i c a l for at least eight discharges. As was pointed out i n the introduction to this chapter i t i s necessary to trigger the discharge at a precise moment. In the present experiment a j i t t e r time of the order of twenty microseconds between the triggering pulse and the discharge i n the f l a s h tube i s tolerable. However future experiments dealing with transient plasmas w i l l require much smaller j i t t e r times. Hence i t was decided to design the triggering system with as small a j i t t e r as possible. In the experimental evaluation of the f l a s h unit electronic measurements are made simultaneously with the discharge i n .'the f l a s h tube and for this reason i t i s desirable to choose a geometry for the e l e c t r i c a l leads which has a low radiating e f f i c i e n c y . The choice of construction materials and design of the f l a s h unit was made also with the purpose of assuring i t a long l i f e , of f a c i l i t a t i n g i t s alignment with the other units and making i t e a s i l y replaced or repaired. The design of the f l a s h u n i t i s i l l u s t r a t e d i n figure 3» This f i n a l choice was made i n an attempt to embody a l l the considerations mentioned above and to arrive at a compromise where c o n f l i c t s existed. In p r i n c i p l e , the operation of the unit i s very simple. The aluminum electrode cemented to the discharge tube 9 i s connected to the copper c o l l a r 4 . 8 cm. long, 2.7 cm. I.D.^, by means of eight r a d i a l screws. This copper c o l l a r i s connected - 23 - to the c e n t r e of the condenser through the plane l e a d L-j_. The aluminum e l e c t r o d e E 2 i s attached to the copper c o l l a r C 2 by a wire gauze so l d e r e d to the c o l l a r and necked down to the e l e c t r o d e where i t i s secured by a metal s t r a p . C o l l a r C 2 i s connected to the o u t s i d e of the condenser by the plane l e a d L 2 . Thus when the t r i g g e r pulse i s a p p l i e d to the t r i g g e r l e a d s TL, the condenser c u r r e n t r i s e s up through plane l e a d L 1 ? t r a v e l s down the o u t s i d e of the f l a s h tube through CQ_, i n through the e i g h t screws to the e l e c t r o d e E ^ , and then down the i n s i d e of the q u a r t z f l a s h tube, i n i t i a l l y under a vacuum of .1 microns to the e l e c t r o d e E 2 , where i t r e t u r n s to the condenser v i a the wire gau.ze to C 2 and L 2 . The i n s u l a t i n g p l a t e Ip, 1.5 mm. t h i c k , i s cemented to the i n s u l a t i n g c y l i n d e r I c , a l l o w i n g the p l a t e s Lj_ and L 2 to be placed c l o s e together. F i n a l l y the l i g h t from the discharge i s observed through the window W2, while through window W]_, the u n i t i s a l i g n e d . In the course of d e s i g n i n g the f l a s h u n i t , primary c o n s i d e r a t i o n was g i v e n to a c h i e v i n g a uniform continuum and h i g h temperatures. C o n t r i b u t i n g g r e a t l y to the u n i f o r m i t y of the d i s c h a r g e spectrum was the use of q u a r t z i n s t e a d of g l a s s f o r the d i s c h a r g e tube. With a g l a s s tube the d i s c h a r g e spectrum always showed the sodium D l i n e s s t r o n g l y i n a b s o r p t i o n . T h i s o c c u r r e d because sodium from decomposed g l a s s near the w a l l s was c o o l e r . The quartz tube showed no strong a b s o r p t i o n l i n e s . - 2h - As i s well-known from the work of Anderson'7, the par- ameter which determines to a large extent the uniformity of the. continuum i s the current density i n the discharge channel. From hi s investigations i t i s seen that a current of twenty or t h i r t y thousand amperes per square centimeter i s necessary. The current which flows during the discharge i s given by the expression As i s seen from this formula a low inductance i s important for high current densities. For t h i s reason coaxial geometry was i n i t i a l l y considered for the f l a s h u n i t . The low radiating e f f i c i e n c y of coaxial geometry added appeal for the choice of this form. I t i s fortunate that a uniform continuum and a high temperature are products of the same conditions. An equation expressing the conservation of energy for the discharge can be written where dE i s the rate of change of the t o t a l energy of the tube; dt i R i s the rate at which energy i s added to the discharge; E(tT) i s the energy of the discharge at a given time and given temper- ature. Since the plasma i s a gas, i t i s an increasing function of temperature; f(T) i s the f r a c t i o n of t o t a l energy l o s t per second by mechanisms other than radiation. I t i s most plausible h. that t h i s i s an increasing function of temperature; the term A <rT - 25 - represents the power loss by radiation. In a steady state i . e . dE _ 0 we see that we would have an increase i n temper-dt 5 ature with an increase i n current. From the foregoing consid- erations we conclude that to achieve a uniform continuum and high temperature large currents generated by the use of low inductance c i r c u i t s i n the leads and discharge tube, high voltages, and large capacitances are required. The condenser used was a 1.6 m,f.d. low inductance, 25 m^uh, high voltage, 25k.v.7. manufactured by Cornell-Dubilier, model NRG 323. The use of large currents creates a major problem. Since the currents are flowing i n opposite directions i n the two plates which are separated by only 1/16 inch of.perspex (to keep the self-inductance low) a strong repulsive force exists between them. The magnitude of this force can be e s t i - mated by using a very simple c a l c u l a t i o n . Supposing the.current i s damped out i n two periods we have approximately one-quarter of the stored energy dissipated i n a half period. I f a l l of thi s energy were converted into the k i n e t i c energy of the plates their f i n a l v e l o c i t y would be v = t where E i s the condenser voltage and m the mass of one plate. These plates acquire the v e l o c i t y ino.half period. Hence the force from F.AT = m.AV i s F - f i ^ (21) where P i s the period. - 26 - In s u b s t i t u t i n g values we have Th i s f o r c e would be a p p l i e d to the q u a r t z - e l e c t r o d e j u n c t i o n s i f the gauze c o l l a r which absorbs the shock were not used to j o i n the e l e c t r o d e E 2 to the p l a t e P 2. This made i t p o s s i b l e to use bla c k wax to cement the e l e c t r o d e E 2 to the quartz tube. The e l e c t r o d e E-j_ had to be cemented with epoxy because screws were used to connect the e l e c t r o d e to the copper c y l i n d e r , e n a b l i n g easy alignment. Even with the gauze a small f o r c e i s exerted on the tube. I f the tube i s g l a s s t h i s f o r c e tends to s h a t t e r i t a f t e r a few f i r i n g s s i n c e the s t r e n g t h of the g l a s s i s reduced by- c r a z i n g caused by the d i s c h a r g e . I t was found t h a t quartz d i d not craze as r e a d i l y as g l a s s a l l o w i n g the tube to withstand many more d i s c h a r g e s . T h i s i s another reason f o r the choice of quar t z over g l a s s i n the c o n s t r u c t i o n of the di s c h a r g e tube. The h i g h v o l t a g e s employed n e c e s s i t a t e s p e c i a l i n s u l - a t i o n p r e c a u t i o n s . F i g u r e ha shows the d e t a i l s o f the e l e c t r o d e s E-j_ and E 2 . The e l e c t r o d e s are grooved so that the q u a r t z - e l e c t r o d e j u n c t i o n s i n s i d e the vacuum of the di s c h a r g e tube occur recessed i n the e l e c t r o d e s , a r e g i o n of low e l e c t r i c Q f i e l d . T h i s i s i n accordance with the f i n d i n g s of Kofoid••. ' :•" The h o llow c y l i n d e r I c of perspex allows the discharge tube to be e a s i l y withdrawn and r e p l a c e d simply by undoing the gauze s t r a p and the screws. The c y l i n d e r extends 3 cms. on e i t h e r - 27 - s i d e of the i n s u l a t i n g p l a t e and by extending the e f f e c t i v e path i n a i r between the copper p l a t e s , breakdown i s prevented. The i n c r e a s e i n inductance from 3*6 myuh.with the r e t u r n conductor f l u s h with the d i s c h a r g e tube to 12 myah, with i t removed by . 8 cm. was considered worth the s a c r i f i c e f o r the s i m p l i f i c a t i o n of the removal and i n s u l a t i n g problems. In order to have the d i s c h a r g e spectrum r e p r o d u c i b l e to the demanded degree, f i v e d i f f e r e n t arrangements were t r i e d . The f i r s t t r i a l ( f i g u r e ha) had the windows placed f l u s h with the e l e c t r o d e . They became opaque a f t e r two shots because of d e p o s i t i o n r e s u l t i n g i n f o g g i n g and emulation r e s u l t i n g i n p i t t i n g . I t appeared that t h i s d e p o s i t was from the e l e c t r o d e s and w a l l s s i n c e one p a r t could be d i s s o l v e d from the windows with n i t r i c a c i d and another p a r t with h y d r o f l u r i c a c i d . The d e p o s i t i o n was examined by c o n s t r u c t i n g a p i n h o l e camera ( f i g u r e 4b) a t one end of the d i s c h a r g e tube. The m a t e r i a l was deposited l i g h t l y over the whole windoxi/ except f o r a dense r i n g centered on the a x i s of the tube. T h i s r i n g corresponded with the o p t i c a l image of the o p p o s i t e e l e c t r o d e . The e b u l a t i o n was c o n f i n e d to a c i r c l e i n the c e n t r e of the window. While the p i n h o l e camera was attached i t was decided to measure the d i r e c t i o n a l dependence of the l i g h t output of the d i s c h a r g e by u s i n g s e n s i t i z e d paper. I t was found to be e s s e n t i a l l y constant f o r at l e a s t 1 0 ° o f f the a x i s . These f i n d i n g s i n mind, a second t r y was made ( f i g u r e he) with a g l a s s b a f f l e of such s i z e t h at, placed near one - 28 - electrode, part of the nearby window could not see the far electrode. This f a i l e d because there was d i f f u s i o n and scat- tering of electrode material. In the next attempt a window was moved from the main discharge path by placing i t on the end of a branch of a wye (figure 4-d). After one shot, the window became contaminated due to the condensation of the discharge debris. From this observation a mechanism by which the main discharge tube keeps clean i s suggested. I t appears that the discharge evaporates the material condensed during the l a t t e r part of the previous discharge. At present experiments are being concluded to develop a window system which exploits this self-cleaning process. In the fourth design i t was hoped to make use of e l e c t r o s t a t i c d e f l e c t i o n . One window was moved away from the end of the discharge tube and electrode by adding a section of glass tubing (figure H-e). Two me t a l l i c deflection plates D, length L^, were placed diametrically opposite on the outside of the extension thus separating them by a distance S ~ l cm. They had a voltage placed across them equal to that of the condenser p o t e n t i a l . Assuming that a p a r t i c l e would convert a l l of i t s p o t e n t i a l energy to k i n e t i c energy, that i s where V i s condenser voltage. By the equation of motion, and assuming plane p a r a l l e l electrodes f - %& ~- It - m c ^ •S where E i s the e l e c t r o s t a t i c f i e l d inside the extension tube. - 29 - Hence the time required for a p a r t i c l e to t r a v e l from one side of the extension to the other i s The time to go from one end of the extension to the other, a distance L_ i s If these times were equal no p a r t i c l e would reach the window. That i s i f When such dimensions were used no improvement was noticed. Thus this suggested the discharge was i n the form of a neutral plasma since the particles could not have recombined to form neutral molecules i n the short t r a n s i t time. present experiment was a p a r t i a l success. As i n t r i a l four, extensions are used but this time, to keep the windows clean, a glass tube at one end of which there i s a c o n s t r i c t i o n i n the form of a s l i t , was placed inside each window extension with the s l i t towards the electrodes. This arrangement kept the windows clean for twelve discharges. The length of the ex- tension, 3 cms. i s determined by a compromise between two advan- tages. The further away the windows are from the discharge the cleaner they stay because they subtend a smaller s o l i d angle to the discharge? however the nearer the windows are to the s l i t the smaller the f number . they allow for the system. This design does not take advantage of the large diameter of the discharge L = 2S. The f i f t h design (figure 4-f) and the one used i n the - 30 - tube which could be used to present a source extended i n area f o r the experiment. In order to achieve s a t i s f a c t o r y t r i g g e r i n g two e n t i r e l y d i f f e r e n t methods were t r i e d . The f i r s t was an attempt to use u l t r a v i o l e t l i g h t r e c o g n i z i n g the f a c t t h a t i f i t worked, i t would be very safe as there would be no e l e c t r i c a l connections between the t r i g g e r i n g system and the h i g h v o l t a g e of the con- denser. L i g h t from a t r i g g e r e d spark passed through a quartz window and f e l l on the n e g a t i v e aluminum e l e c t r o d e E^ ( f i g u r e 5a). For t h i s to t r i g g e r the d i s c h a r g e the v o l t a g e of the condenser had to be set too near the breakdown v a l v e , causing s p u r i o u s d i s c h a r g e s . This method was then abandoned i n favour of i n t r o d u c i n g t r i g g e r e l e c t r o d e s d i r e c t l y i n t o the d i s c h a r g e tube as shown i n f i g u r e 5b. I n i t i a l l y one t r i g g e r e l e c t r o d e was used a l l o w i n g i t to a r c to the d i s c h a r g e e l e c t r o d e E]_. This would only t r i g g e r when E^ was n e g a t i v e with r e s p e c t to E2? r e g a r d l e s s of the p o l a r i t y of the 32 kv, . t r i g g e r p u l s e . Hence i t was concluded that the e l e c t r o n s emitted from the t r i g g e r d i s c h a r g e were necessary to i n i t i a t e the f l a s h d i s c h a r g e . ( I t was not the p h o t o - e l e c t r i c e l e c t r o n s from E j , s i n c e both p o l a r i t i e s of the t r i g g e r pulse do not work e q u a l l y w e l l ) . For more r e l i a b l e t r i g g e r i n g i t was necessary to i n t r o d u c e another t r i g g e r e l e c t r o d e running i t i n t o the space between E j and E 2 and to have the arc occur i n t h i s space where the e l e c t r i c f i e l d would a c c e l e r a t e the e l e c t r o n towards the f a r e l e c t r o d e . T h i s arrangement i s used i n - 31 - the f i n a l d e s i g n . I t i s necessary however to keep these t r i g g e r e l e c t r o d e s as near to the cathode Ej_ as p o s s i b l e so that when they are immersed i n the r e s u l t i n g d i s c h a r g e t h e i r p o t e n t i a l w i l l not r i s e too h i g h . Upon completion of the f l a s h u n i t determinations of s e v e r a l of i t s o p e r a t i n g c h a r a c t e r i s t i c s were made. The time d e r i v a t i v e of the c u r r e n t as a f u n c t i o n of time i s shown i n f i g u r e 6a. T h i s was photographed from an o s c i l l o s c o p e d i s p l a y at a sweep speed of one microsecond, per centimeter of the v o l t a g e induced i n a search c o i l placed near the d i s c h a r g e . This v o l t a g e i s given by V = M d i dt where M i s the mutual inductance between the c o i l and the d i s - charge c i r c u i t . The observed waveform corresponds a c c u r a t e l y to the c a l c u l a t e d one i n AV7. T h i s shows that the model used to d e r i v e equation Al5 i s q u i t e good. Using the method o u t l i n e d i n the appendix and the observed values of P = 19«6 - .09 x 1 0 " ^ seconds and LD = 1.52 - .07 we f i n d ^ = 3.3*+ x 1 0 6 i . i 5 seconds L = 56 - 5.6 x 1 0 - 9 h e n r i e s R = .087 t .007 ohms. The value of the p e r i o d i n the c a l c u l a t i o n must be taken from two s u c c e s s i v e zeros and not from the time zero and the f i r s t zero as h a l f a p e r i o d s i n c e there i s a phase angle (equation A 1 7 ) to be c o n s i d e r e d . Using the values of L and R the c u r r e n t i s -given to 30$ by - 32 - i = 8 2 , 7 0 0 x By o b s e r v a t i o n d i = 0 a t t = . 6 x 1 0 ° seconds. dt Hence the maximum c u r r e n t i s 48 , 7 0 0 amperes. From these values amps./ cm. . T h i s i s w e l l above the t h r e s h o l d f o r continuum r a d i a t i o n . condenser v o l t a g e was examined. At low v o l t a g e s or e q u i v a l e n t l y low c u r r e n t d e n s i t i e s there are l i n e s and bands, but as the v o l t a g e reaches 15 '-kv . the continuum becomes q u i t e uniform except f o r s e v e r a l bands most l i k e l y o r i g i n a t i n g from s i l i c o n . m u l t i p l i e r s e n s i t i v i t y curve was i n v e s t i g a t e d as a f u n c t i o n of time. This was c a r r i e d out with the i n t e n s i t y u n i t , the output of which was d i s p l a y e d on an o s c i l l o s c o p e with a sweep speed of one microsecond per centimeter and photographed ( f i g u r e 6 b ) . The appearance of the second higher peak i s e a s i l y e x p l a i n e d . One must f i r s t note that the time constant f o r the decay of the d i s c h a r g e i n t e n s i t y , a f t e r a l l the energy has been pumped i n t o i t , i s long compared to the p e r i o d of the d i s c h a r g e c u r r e n t . The t o t a l energy P pumped i n t o the system as a f u n c t i o n of time i s g i v e n by we see the c u r r e n t d e n s i t y i n the d i s c h a r g e i s 75 - 11 x K)3 The change i n output spectrum as a f u n c t i o n of the The s p e c t r a l s t e r a d i a n c y i n t e g r a t e d over a 931 photo- - 33 - where to a f i r s t approximation R i s assumed constant during the discharge. This i n t e g r a l i s evaluated graphically below -t Allowing for the expotential decay of the discharge energy at regions A and B i n the graph above we f i n d the energy of the discharge as a function of time i s shown i n the following graph -t - 3^ - I f the rate of radiation i s proportional to the energy content of the discharge, as i t most l i k e l y i s , this i d . l l be the observed l i g h t output s l i g h t l y distorted by the response curve of the photomultiplier. This d i s t o r t i o n r e s u l t s from change i n the d i s t r i b u t i o n of energy as the temperature of the discharge i s lowered. As Spitzer^ shows, the temperature of a plasma can be deduced from a measurement of i t s r e s i s t i v i t y . The r e s i s t i v i t y of a plasma i n which electron-electron c o l l i s i o n s are considered i s given by "I = 4^ (22) where y:. i s a function of the state of i o n i z a t i o n of the gas. 2 = 1 2 3 ^ = .582 .683 .785 and i s the theoret i c a l r e s i s t i v i t y of a Lorentz gas. ^*L_ i s given by -n3/z m e 2. c1- c i i A (23) 2 ( Z K T J H where e i s the electronic charge i n esu, K the Boltzmann constant, me the mass of the electron, and T the absolute temperature. >. i s given by 2- B e3 \ rr r\& J where n Q i s the electron density. A table of Ln 7A for dif f e r e n t values of T and n g i s given by Spitzer. Substituting the numerical values for the constants i n equations 22 and 23 for a singly ionized gas we f i n d T = 3.4-9 / LnX \ i (24) - 35 - A more convenient variable than Ln X i s K = Ln X /T ^. The table below gives this for d i f f e r e n t values of T and n e. T°K ELECTRON DENSITY electrons /cc. 1 10^ IO* 2 1 0 1 ? 1 0 1 8 10 10 2 1.6xlO- 2 9.4-3xl0 3 IO 3 6.21x10"^ 4.04xlO~ l f 1.88x10"^ 1<A 2.32x10"^ 1 .63x10-? 9.4-3x10 ~ 6 5.57x10" 6 10? 8.41x10-7 6.21x10-7 4.04x10-7 2.97x10-7 1.87x10-7 IO 6 2.97x10~ 8 2.28xlO" 8 1 .59x10" 8 1.24x10-8 8 . 9 6 x 1 0 " ^ 5.54x10-9 The temperature i s best found by p l o t t i n g log]_QT against log-j^K for the value of nQ during the discharge- n e can be found by n e = 3.22 x 10 1? P 2 where P i s the f i n a l pressure of the discharge i n mm., of Hg. and H i s the degree of i o n i z a t i o n . K i s given by K = 1 .53 x 10 - I + RA/L (see equation 24) where R is- resistance of the discharge; A i s cross section.df. discharge; L i s length of discharge. This equation i s based on the assumption that the discharge has uniform cross section. 15 For the present f l a s h tube n g has the value n e 10 y and K has the value K = 3=9 x 10^. This results i n an estimate of the temperature at 40 - 10 x 10 3 °K. I t should be noted that t h i s result depends upon a the o r e t i c a l expression for which i s good only for low densities and high temperatures. Furthermore the theory requires - 36 - that the energy gained between c o l l i s i o n s from the e l e c t r i c f i e l d be much l e s s than the average k i n e t i c energy. A quick check shows that the c o n d i t i o n s of the discharge are i n the domain of a p p l i c a b i l i t y of the theory. T h i s estimate was made i n an attempt to e s t a b l i s h the s p e c t r a l d i s t r i b u t i o n curve f o r the d i s c h a r g e . At present a more d i r e c t approach to the problem i s being used. The s p e c t r a l s t e r a d i a n c y of the d i s c h a r g e i s compared to that of a standard carbon arc u s i n g the i n t e n s i t y u n i t attached to a mon- ochromator. 3 . Plasma U n i t The plasma u n i t was designed to generate a uniform plasma i n a gas of any d e s i r e d p u r i t y and composition. The a b s o r p t i o n tube i n which the plasma i s formed i s a g l a s s tube two centimeters i n diameter and f i f t y centimeters i n l e n g t h , as shown i n f i g u r e 7 a . Glass windows through which the f l a s h u n i t l i g h t i s passed are welded to each end of the a b s o r p t i o n tube. The d i s c h a r g e which produces the plasma takes p l a c e between two e l e c t r o d e s P and N, set in, s i d e arms A and B r e s p e c t i v e l y . With the e l e c t r o d e s i n the s i d e arms, only the plasma i n the D.C. d i s c h a r g e of the p o s i t i v e column w i l l be present i n the a b s o r p t i o n tube. The r e s t of the d i s c h a r g e w i l l be i n the s i d e arms, and furthermore the e l e c t r o d e s w i l l not o b s t r u c t the o p t i c a l path. Because the e l e c t r o d e s are watercooled i t i s p o s s i b l e to s e a l them to the g l a s s with De Khotinsky Wax, i n s p i t e of the l a r g e amount of heat generated i n the order of - 37 - 400 watts at the cathode for a D.C. discharge and of 10 watts for each electrode i n an A.C. discharge. Attaining a discharge of s u f f i c i e n t purity presented a d i f f i c u l t problem. During a D.C. discharge a metal f i l m i s sputtered onto the wall of side arm B. Gases w i l l occlude on this f i l m and when the next discharge i s run the heating of the wall b o i l s them o f f , releasing them to the discharge. This source of impurities i s eliminated by making side arm B U-shaped and immersing i t i n a bath of l i q u i d nitrogen. This procedure also freezes out a large amount of oxygen. When there i s an A.C. discharge this problem occurs at both side arms A and B. How- ever there was not s u f f i c i e n t time to modify side arm A. To remove the remaining active gases, a chamber to contain f i n e l y divided uranium was appended to the absorption tube. This follows the method of G. H. D i e k e 1 0 ' 1 1 . Two grams of uranium turnings, cleaned i n n i t r i c acid shortly before, are introduced into the chamber and baked for two hours at a high temperature under vacuum.. Hydrogen gas i s then allowed to f i l l the system to a pressure of about one atmosphere. The reaction of the uranium with the hydrogen was started by an i n i t i a l hard heating of the turnings after which the temperature i s maintained at about 250°C. In about one-half hour the effect of the reaction can be seen - whiskers form on the turnings. After several hours the reaction goes to com- ple t i o n leaving uranium hydride powder. The hydrogen i s then pumped off and the uranium hydride i s heated to 4-00°C to reduce - 38 - i t to a f i n e l y d i v i d e d uranium. This powder i s prevented from e n t e r i n g the a b s o r p t i o n tube by p l a c i n g a wad of g l a s s wool between the chamber and the tube. I t should be noted that the uranium powder can i g n i t e spontaneously i f exposed to a i r . A three l i t r e g l a s s r e s e v o i r guarantees a ready supply of the major c o n s t i t u e n t under study. I t i s l o c a t e d near the anode where c a t a p h o r e s i s may be e x p l o i t e d , G. H. Dieke . Gataphoresis i s the c o n c e n t r a t i o n at the cathode of the minor c o n s t i t u e n t of a mixture of gases. This works whether the minor c o n s t i t u e n t i s an i n e r t gas or a monatomic molecule. The d e s i r e d gas i n the r e s e v o i r w i l l have the i m p u r i t i e s i n i t swept toward the cathode and powdered uranium where they are removed, i f a c t i v e , and concentrated i n the s i d e arm B, i f i n e r t . I f the s i d e arm f i l l s , the r e s e v o i r i s shut o f f , the a b s o r p t i o n tube pumped out, the r e s e v o i r reopened and the process s t a r t e d a g a i n . T h i s i s repeated u n t i l the d e s i r e d p u r i t y i s reached. In summary, two main processes are used i n p u r i f y i n g the gas, c a t a p h o r e s i s f o r the i n e r t gases and g e t t e r i n g by uranium f o r the a c t i v e gases. Once the gas i s p u r i f i e d the d e s i r e d i m p u r i t i e s can be i n t r o d u c e d through the arrangement shown i n f i g u r e 7b. 4. S h u t t e r U n i t The s h u t t e r u n i t ( f i g u r e 8) as mentioned i n the i n t r o - d u c t i o n of t h i s chapter, i s used to c o n t r o l the exposure of the plasma and to time the t r i g g e r i n g of the f l a s h u n i t . There are - 3 9 - two diametrically opposite slots A and B i n the rotating d i s c ; Slot A, near the rim, to control the exposure by adjustment of i t s width, and Slot B, near the a x i s , to control the timing. The minimum exposure i s three milleseconds, this being determined by the f - 20 of the spectrograph, the speed of the disc r.p.s. = 1 7 2 5 , and the distance s = 3 cm. between the spectrograph s l i t and the disc. The minimum exposure i s given by *min ~ l s  f 2 TTR x r.p.s. where R = 3«7 cm. i s the mean distance from the axis to Slot A. Since Slot A w i l l expose the spectrograph about twenty- eight times per second, a compur shutter, which i s open for just under the time of one revolution of the disc, i s placed i n front of the disc, thus l i m i t i n g the number of exposures to one. This exposure w i l l occur when the shutter i s open. The f l a s h unit f i r i n g i s timed by a pulse from the photomultiplier PT_ produced by a burst of l i g h t from the lamp L, as Slot B passes i n front of the photomultiplier. This event i s arranged to take place i n advance of the coincidence of Slot A with the spectrograph s l i t by placing the photo- m u l t i p l i e r off the diameter formed by the spectrograph s l i t and the disc axis. The photomultiplier pulse i s delayed by the Tektronix 5*+5-A oscilloscope u n t i l the spectrograph s l i t opens. This pulse gets through to the trigger unit only i f the compur shutter i s open. - hO - Low j i t t e r i n the order of ten microseconds i s assured by having a large slope to the photomultiplier pulse. This slope of .2 v o l t s per microsecond i s achieved by imaging lamp B i n the pl a i n of the disc with lens L and placing stops on both sides of the image. The synchronization of the f l a s h f i r i n g and the spectrograph opening i s accomplished by the f o l - lowing procedure. The pulse from the photomultiplier, Pj triggers the display sweep of the oscilloscope. Input A i s connected to another photomultiplier P 2 located at the plate po s i t i o n of the spectrograph. A carbon arc used to simulate the plasma produces a pulse (displayed on the oscilloscope) when the spectrograph s l i t i s open. The delayed output pulse of the oscilloscope i s fed to input B and displayed. Synchroni- zation takes place when these two pulses coincide, as the delayed pulse f i r e s the discharge tube. 5. Electronic Units The two remaining units of the six used i n the experi- ment, namely the trigger unit and the in t e n s i t y unit are electronic i n nature. The triggering unit was designed after the work of G.A. Theophanis-*-30 Two three-meter long, type R.G. 58U coaxial cables, i n p a r a l l e l , are charged to 16 kv. with a high frequency and high voltage supply of the type used i n t e l e v i s i o n receivers. The far end of the cables i s terminated with a 50 /^yK farads 20 kv. condenser i n series with ten one-megohm r e s i s t o r s , i n p a r a l l e l , arranged about the condenser. This i s es s e n t i a l l y an i n f i n i t e termination. The sheaths of the coaxial - 4-1 - c a b l e s are grounded while the i n n e r conductors a t 16 k v " . are connected to the anode of a hydrogen f i l l e d t h y a t r o n . When a s i g n a l i s a p p l i e d to the g r i d of the th y a t r o n i t shor t s the end of the attached c a b l e . Since the cables are at 16 fcv' . t h i s sends a - 16 kv • pul s e down the cable which i s r e f l e c t e d with a c o e f f i c i e n t of +1. In order that the v o l t a g e across the condensor remains constant, e.g. l 6 k v " . , the f a r s i d e must f a l l to -32 kv' . This pulse i s then taken o f f across the r e s i s t o r s . The hydrogen t h y a t r o n i s f i r e d with a 2D21 which i s f i r e d i n t u r n from a delay p u l s e . The compur s h u t t e r i s con- nected to the g r i d c i r c u i t of the 2D21 so that c o n t r o l i s e x e r c i s e d over the f i r i n g of t h i s tube. The turn on time of the 2D21 i s longer than the d u r a t i o n of the delayed p u l s e from the o s c i l l o s c o p e , so a u n i v i b r a t o r was i n t r o d u c e d i n t o the c i r c u i t with an output pulse of 50 microseconds d u r a t i o n . T h i s i n t r o d u c e d a d e l a y o f 35 microseconds with a j i t t e r time of f i v e microseconds. With t h i s j i t t e r , the t o t a l j i t t e r time of the system mounts to about 25 microseconds. The i n t e n s i t y u n i t i s used to determine the i n t e g r a t e d l i g h t output f o r the f l a s h u n i t , and w i l l be used to determine the s p e c t r a l d i s t r i b u t i o n of the output as compared with that of a carbon a r c . T h i s u n i t c o n s i s t i n g of a p h o t o m u l t i p l i e r 9 3 1 A and a t r a n s i s t o r (type 2N1177, 144 mc. alpha cut o f f frequency) i s completely enclosed, with i t s power s u p p l i e s , i n a brass box. I t i s necessary to use t h i s p a r t i c u l a r design i n - k2 - order to avoid pickup of the e l e c t r i c a l n o i s e from the di s c h a r g e . The t r a n s i s t o r i s i n the common c o l l e c t o r c o n f i g u r a t i o n , so matching the h i g h generator impedence of the p h o t o m u l t i p l i e r 931^ with the 52 ohm c h a r a c t e r i s t i c impedence of the ca b l e s connecting i t to the o s c i l l o s c o p e i s made p o s s i b l e . By ar r a n g i n g an imped- ence match at the o s c i l l o s c o p e end a l s o , there i s very loxtf n o i s e pickup from the c a b l e . This u n i t works very s a t i s f a c t o r i l y . Besides the u n i t s designed and co n s t r u c t e d f o r the experiment, s e v e r a l other pieces of a v a i l a b l e equipment are used. They a r e : a T e k t r o n i x o s c i l l o s c o p e type 54-5A, a tuned g r i d "28 megacycle o s c i l l a t o r , a J a r r e l l - A s h microphotometer, H i l g e r automatic g l a s s - q u a r t z spectrograph and two h i g h v o l t a g e s u p p l i e s , one f o r the plasma u n i t capable of d e l i v e r i n g two amperes at 1200 v o l t s , the other f o r the f l a s h u n i t capable of 30,000 v o l t s a t 30 m i l l i a m p e r e s . Chapter I I I RESULTS AND CONCLUSIONS 1. Introduction Upon completion of the construction of the present apparatus, a preliminary experiment was run to demonstrate the effectiveness of the theory and apparatus. There follo\tfs i n t h i s chapter an account of the experiment with i t s results and conclusions suggesting e f f i c i e n t operating conditions and possible improvements i n the equipment. In addition, experiments i n which the f l a s h unit could e f f e c t i v e l y be used are proposed. 2. Experiment Neon was chosen as the gas i n which the discharge occurs, since i n future experiments i t s use w i l l enable the result s to be compared with the investigations of Kopfermann and Ladenberg. The discharge, taking place i n the neon at a pressure of 2.2 millimeters, was excited by the radio frequency o s c i l l a t o r generating about 20 watts, an unknown fraction being dissipated i n the discharge. This energy was introduced through the two electrodes P and N. The neon was not free of impurities i n spite of the aids employed since the metal com- ponents of the absorption tube outgassed too rapidly. I t should be noted that the apparatus was c a r e f u l l y arranged so that a l l portions of i t would flood the spectroscope prism. The data obtained i s derived from one plate containing four spectrograms. One consisted of an emission spectrum only. Two consisted of six shots each of the spectrum resu l t i n g from - 4-3 - - 44 - the passage of the continuum l i g h t through the neon plasma. These twelve shots were taken through the same discharge tube window. These two spectrograms differed by having an exposure time t e , equal to . 4 5 milliseconds for one and . 7 6 milliseconds for the other. The fourth spectrogram consisted of a twenty-five shot exposure of the continuum source only through a seven step graded f i l t e r (platinum on glass, e s s e n t i a l l y a neutral f i l t e r for the wave length range studied). Uniform i l l u m i n a t i o n of the plate was assured by forming an image of the discharge on the collimator lens of the spectrograph with a lens i n close proximity to the step f i l t e r and spectrograph s l i t . The f l a s h continuum, rather than other sources, was used to establish the character- i s t i c curve by exposure of the plate through the step xvedge since this exposure must be made under the same conditions as were the spectrograms to which the curve would be applied. The pertinent data and results for the di f f e r e n t l i n e s examined are given i n the table below. Line 6163 S143 6334 6074 6096 Trans- From i t i o n To 3 P ( 3 P I ) 3 s ( 3 p c ) 3s(3P 2) 3 P ( 3 D 2 ) 3 S ( 3 P 2 ) 3 P ( 3 P 0 ) 3 S ( 3 P I ) 3 P ( 3 P 2 ) 3 s ( 3 p x ) t e i .45xlO""3 sec. tep . 7 6 x l O ~ 3 s e c . td .45xlO _ bsec. 5 4 x 1 0 ~ bsec. .65x10-6 . 5 7 x 1 0 " 6 . 5 8 x 1 0 ^ s B(T)/B(T 1) .0044 . 0 0 3 6 . 0 0 3 0 . 0 0 3 4 . 0 0 3 4 R P 1 . 0 2 1 T 4730 4240 4000 4220 - 4200 - 45 - For the two p a i r s of t r a n s i t i o n s with d i f f e r e n t common lower l e v e l s 3p 1 and 3p 2 ? the r a t i o r p of the values B(T)/B(T 1) gives the r e l a t i v e p o p ulation of the upper s t a t e s of each p a i r . The temperature T i s c a l c u l a t e d on the assumption that the discharge i s a 40,000 °K black body. The t r a n s i t i o n temperatures appear to be q u i t e reasonable, since when a carbon arc at a temperature of about 5000 °K was used as a continuum source, the l i n e s were seen f a i n t l y i n absorption. During the c o n s t r u c t i o n of the apparatus'many p l a t e s were taken upon i^hich no c a l i b r a t i o n exposures were made but which did show i n t e r e s t i n g r e s u l t s . One p l a t e revealed s i x t e e n t r a n s i t i o n s i n abso r p t i o n between the 3p5»3p and 3p5»3s con- f i g u r a t i o n ^ while another p l a t e showed two t r a n s i t i o n s which, to the best of our knox^ledge, have never been reported as seen i n a b s o r p t i o n . These t r a n s i t i o n s occurred betv>een the states 3p1(2p?.3p) - 3P2(2p5.5s) and 3p 0( 2 p53p) . 3p1(2p55s). The values of BCD/BCT 1) are i n er r o r by at most 30$ estimated by t r a c i n g the maximum e r r o r s i n measurements through the c a l c u l a t i o n s i n v o l v e d . There are three important sources of random e r r o r ; a r i s i n g from measurements of time, density and i n t e n s i t y . The greatest d i f f i c u l t y i n the measurement of the time t e , r e s u l t i n g i n an er r o r of 5$, i s caused by the f i n i t e mechanical opening time of the s l i t . In the determination of the percentage transmission of the p l a t e an e r r o r of about 2% a r i s e s , not from the J a r r e l l - A s h microdensitometer which i s used f o r the measurement, but rather from the general noise l e v e l of the p l a t e . - 4-6 - The absorption l i n e appears as only a h% v a r i a t i o n of the continuum, and since the difference between the absorption and background exposures i s used i n these calculations, a large source of error i s introduced. This error could be diminished considerably by shortening the exposure time t e l . T n e third error arises from the graphical evaluation of the exposure from the transmission of the photographic plate. The twenty-five shots used to establish the ch a r a c t e r i s t i c curve resulted i n over-exposure, allowing only the lower portion of the curve to be well established. However, only an approximate curve i s needed, since small variations i n exposure are measured. Unfortunately, this inaccurate curve did not allow the second method, mentioned i n Chapter I and requiring a measurement of both emission and absorption spectra, to be used since large variations i n exposure are involved. Besides the above random errors, several systematic ones were present. A l l the formulas developed i n Chapter I were dependent upon an i n t e g r a l over l i n e width, but since the l i n e s are so s l i g h t l y i n absorption or emission, the maximum depth or height of the l i n e s was taken as a measure of their i n t e g r a l s , that i s , i t was assumed that they a l l have the same l i n e shape. Another error i s introduced by the progressive darkening of the window from the discharge debris. This was allowed for i n a f i r s t approximation by assuming that the two sets of exposures were taken with black bodies of differ e n t temperatures, necessitating the use of the s l i g h t l y modified formula - 47 - td = ( P n b - p i ) ( t e 2 + t a ) - (P2 b - P 2 ) ( t e i + t a ) _ ta (P2 - r P i ) instead of equation 17a where r = P2 b/P]_ b and P i b and P 2 b are background intensities of the exposures 1 and 2. The other symbols are the same as those i n Chapter I. I f i t i s assumed that a fixed quantity of material i s deposited on the window after each discharge, then the exposure of the plate from the n^h discharge i s given by P m = cT111"1 where T i s the transmission. By measuring the above plate we fi n d T = .9938. I t has been e x p l i c i t l y assumed i n calculating the temperature of the plasma that the plasma column examined was uniform and at a common temperature. The diameter of the absorption tube, 2 cms., may make this assumption i n v a l i d . Another error which i s as yet undetermined results from the time behavior of the temperature of the f l a s h discharge. Since the source peaks at a very high temperature this error would be r e l a t i v e l y small. Other errors which may be important result from an intermittancy effect and the f a i l u r e of the Reciprocity Law. The intermittancy effect w i l l arise from the superposition of the s i x shots, with a time i n t e r v a l of about one minute, to form a single spectrogram. The Reciprocity Law may f a i l because of the d i f f e r e n t exposure times of the continuum and plasma; and of the step wedge and spectrograms. I t i s believed however . 1+8 - that t h i s error will be s l i g h t because of the short times and high i n t e n s i t i e s involved. 3. Future Work After running the experiment, areas which are open to improvement became evident. To observe transitions at higher temperatures i t w i l l be necessary to construct a shuttering mechanism with an open time approaching that of the duration of the f l a s h . This short time w i l l p a r t i a l l y eliminate the d i f f i c u l t i e s caused by the intermittancy effect since the ex- posures of the plasmas which at present are for time t e , w i l l be composed of a series of exposures each of duration t a but which w i l l t o t a l to time t e . To avoid d i f f i c u l t i e s encountered with the purity of the neon, i t i s suggested that an absorption tube be b u i l t which w i l l be e n t i r e l y free of electrodes but s t i l l incorporates uranium as a getter. In this tube the plasma would be generated by an electrodeless R.F. discharge. From a detailed study of the time behavior of the discharge spectrum a better estimate of time t a \rould be a v a i l - able. I t i s also recommended that the spectral radiancy of the source be compared to that of a standard black body so that t r a n s i t i o n temperatures may be determined with a degree of certainty. Further investigations of the discharge may suggest changes i n the design of the f l a s h unit to improve on the uni- formity of the continuum. I t i s hoped that i n the future several i n t e r e s t i n g and important experiments w i l l be conducted with this f l a s h unit. - 4-9 - T h e a d a p t a t i o n o f t h i s t e c h n i q u e t o t h e s t u d y o f t r a n s i e n t p l a s m a s i s o f c o n s i d e r a b l e i n t e r e s t t o w o r k i n t h i s l a b o r a t o r y s i n c e i t m a y b e u s e d t o c h e c k a s s u m p t i o n s m a d e i n d e t e r m i n i n g t e m p e r a t u r e s o f s h o c k g e n e r a t e d p l a s m a s . A n o t h e r p r o j e c t e d e x p e r i m e n t w i l l d e t e r m i n e t h e e f f e c t o f i m p u r i t i e s o n t h e r e l a t i v e p o p u l a t i o n d e n s i t i e s o f a s t e a d y s t a t e p l a s m a , a w o r k o f c u r r e n t i n t e r e s t i n t h e d e v e l o p m e n t o f o p t i c a l m a s e r s « A b s o r t i o n s t u d i e s o f p l a s m a s a r e v e r y l i k e l y t o b e c o m e a v e r y i m p o r t a n t d i a g n o s t i c t e c h n i q u e n o w t h a t h i g h t e m p e r a t u r e c o n - t i n u u m s o u r c e s a r e a v a i l a b l e . Appendix I THE EQUATION OF TRANSFER 1. Definitions and Fundamental Notions, (a) The specific intensity of radiation at a point P and in a given direction: Consider a point in a f i e l d of radiation. Through this point construct a small elemental surface d cr ; in a specific direction s construct cones of solid angle d UJ , with apex on ds at every point of do- , Then during the time interval dt, the energy traversing the area do- and from the semi-infinite volume so defined can be xvritten as dE = I cos 8 dco do~ dt. (Al) where 9 i s the angle between s and the normal to der . -S I obviously depends upon the point P and the direction s. It is called the specific intensity or steradiancy at the point P̂  and in the direction s. In an isotropic radiation f i e l d I i s inde- pendent of s. (b) Monochromatic Specific Intensity. The monochromatic specific intensity i s so defined that I v cos0 d r dco dt d^ (A2) is the total energy in the frequency interval ( \) , V + dV ) which crossed the elemental area d <X in the direction Q , in a solid angle d cj and in time dt. From the definition - 50 - - 51 - i t f o l l o w s t h a t I v d V = I . Vie c a l l I the i n t e g r a t e d i n t e n s i t y , (c) Amount o f R a d i a n t Energy F l o w i n g Through One Element o f S u r f a c e to Another. ^ A/, L e t I be the s p e c i f i c i n t e n s i t y a t P-^, i n the d i r e c t i o n of P 1^2* T l l e e n e r g y which t r a v e r s e s dcr-^ i n u n i t time and which a l s o t r a v e r s e d d (T , i s from E q u a t i o n ( A l ) dE = I cos 6 2 d o " d UJ dt where d co i s the s o l i d a n g l e t h a t d 0~ 2 makes a t P-j_. d 6J 2_ = cos 0 2 do~p That i s , so dE I cos 6A cos Q 2 do~i dQ~2 dt (A3) (d) Energy D e n s i t y o f R a d i a t i o n a t a P o i n t . The energy d e n s i t y , u , o f the i n t e g r a t e d r a d i a t i o n a t a g i v e n p o i n t , i s the amount o f r a d i a n t energy per u n i t volume which i s i n cou r s e o f t r a n s i t , per u n i t t i m e , i n the neighborhood o f the p o i n t con- s i d e r e d . C o n s i d e r a p o i n t P surrounded by a s m a l l volume V o f convex bounding s u r f a c e 0~ . Surround the volume w i t h - 52 - a n o t h e r convex s u r f a c e S such t h a t the l i n e a r d i mensions o f 2 a r e l a r g e compared to those o f cr , but s m a l l enough t h a t the i n t e n s i t y i n a g i v e n d i r e c t i o n i s c o n s t a n t f o r a l l p o i n t s i n s i d e 2. A l l r a d i a t i o n c r o s s i n g V must have c r o s s e d 2. C o n s i d e r dZ an element t h r o u g h which some of the r a d i a t i o n has passed. The energy f l o w i n g a c r o s s d2 and der , an element o f cr , i s from E q u a t i o n (A3) dE = I cos 9 cos 6 do- d 2 r 2 L e t 1 be the d i s t a n c e t r a v e r s e d by t h i s r a d i a t i o n t h r o u g h ¥. The time o f t r a v e l i s 1/c where c i s the v e l o c i t y o f l i g h t . Hence the amount o f r a d i a n t energy due to t h i s p e n c i l o f l i g h t i s I cos (9 cosQ do~ d 2 1 , 2 r ^ c But the element o f volume dv o f V i n t e r c e p t e d by t h i s ray i s d V = d o - cos d 1. The s o l i d a n g l e subtended by d E a t P i s d U) = cos Q d 2 r 2 Hence the t o t a l energy E i n t r a n s i t through the volume V i s E = 1 J J I d V d u» = V J l aco, c c The energy d e n s i t y u = E = 1 I I d c J . (A4-) V If the r a d i a t i o n i s i s o t r o p i c u = h IT I. c T h i s f o l l o w s i d e n t i c a l l y f o r I v ,and u v a l s o . - 5 3 - (e) The E m i s s i o n C o e f f i c i e n t : C o n s i d e r an element of mass m. The amount of energy e m i t t e d by t h i s element i n t o a s o l i d a n g l e d CO i n time dt i n a f r e q u e n c y i n t e r v a l ( V , V* +d x> ) i s g i v e n by jv Bi du dt dV, (A5) j v i s c a l l e d the e m i s s i o n c o e f f i c i e n t . To get a p h y s i c a l i n t e r p r e t a t i o n o f t h i s we d i s c u s s the d e t a i l s o f the atomic p r o c e s s e s i n v o l v e d . I f t h e r e a r e t r a n s i t i o n s o f atoms o f the medium from quantum s t a t e u to L then the f r e q u e n c y o f r a d i a t i o n i s g i v e n by h ~V u L = E u - E L ( A 6 ) where E u and E^ are the e n e r g i e s o f the two c o r r e s p o n d i n g s t a t e s . T h i s e m i s s i o n p r o c e s s i s d e s c r i b e d by the E i n s t e i n c o e f f i c i e n t s A U J j and B U L . They a r e d e f i n e d as f o l l o w s . The p r o b a b i l i t y t h a t i n an i n t e r v a l o f time d t an atom i n the e x c i t e d s t a t e u emits a quantum o f energy h V u ^ i n the d i r e c t i o n c o n f i n e d to an element o f s o l i d a n g l e d U) , and i n the absence o f an e x t e r n a l r a d i a t i o n f i e l d i s A U L d u) d t . ( A 7 ) T h i s spontaneous e m i s s i o n i s u n i f o r m i n a l l d i r e c t i o n s . I f the atom i s exposed to a r a d i a t i o n f i e l d the p r o b a b i l i t y o f a t r a n s i t i o n i n c r e a s e s . T h i s i s taken c a r e o f by i n t r o d u c i n g B U L d e f i n e d i n such a way t h a t the p r o b a b i l i t y t h a t an e x c i t e d atom i n s t a t e u i s s t i m u l a t e d by an e x t e r n a l r a d i a t i o n f i e l d to emit a quantum h V u L i n the d i r e c t i o n s p e c i f i e d by doJ, i n time d t i s B u L d U d t - ( A 8 ) - 54 - where I V ) ( t L i s i n the d i r e c t i o n d e f i n e d by d C J . That i s , the e m i s s i o n takes p l a c e i n e x a c t l y the same d i r e c t i o n as the i n c i d e n t r a d i a t i o n . The t o t a l energy emitted by a s i n g l e atom per u n i t time, by Equations (A7) and (A8) i s h ^uL ( \ L + B u L 1 V u L } = H V « L ( 4 - T T A U L + B U L J l y u L dw) I f there are N U y u ^ atoms per u n i t volume i n the s t a t e u which can r a d i a t e at frequency V u J j , from Equation (A5) we see t h a t J V u L = ( A u L + B U L I l ^ u L ) h ^uL M*iVuL (A9) d where d i s the d e n s i t y . E i n s t e i n ' s c o e f f i c i e n t s are a l s o d e f i n e d f o r emission and a b s o r p t i o n i n i s o t r o p i c energy d e n s i t i e s and i n t e n s i t i e s . The r e l a t i o n s h i p between these c o e f f i c i e n t s i s shown below. The t o t a l number of t r a n s i t i o n s per u n i t time per atom must be the s a m e Tunder any system. Hence a u L + \ L U V U L = ^ A n L + B u L J 1 V uL d ^ where a u ^ and b u j j are de f i n e d f o r i s o t r o p i c energy d e n s i t i e s but u u L = 1 J I v U L d ^ c u so a u L = 4 TT A U L and b u L = C B U L A l s o a u L + b u L J V U L =  h A u L + B u L j  1V U L d ^ where a ^ and b ^ are d e f i n e d f o r i s o t r o p i c i n t e n s i t i e s . - 55 F o r i s o t r o p i c i n t e n s i t i e s I dcj I ^ u L 4 TT . H e n c e 4-TTA. u L a n d b u L = 4 T T B u L , ( f ) T h e A b s o r p t i o n C o e f f i c i e n t . A p e n c i l o f r a d i a t i o n t r a v e r - s i n g a m e d i u m w i l l b e w e a k e n e d b y a b s o r p t i o n , , I f t h e s p e c i f i c i n t e n s i t y I v o f r a d i a t i o n a t f r e q u e n c y b e c o m e s I v + d l y a f t e r i t h a s t r a v e r s e d a m e d i u m o f t h i c k n e s s d s , we c a n w r i t e I t s h o u l d b e r e m a r k e d t h a t I v + d l v i s t h e i n t e n s i t y o f t h e e m e r g e n t r a d i a t i o n w h i c h i s i n p h a s e w i t h t h e i n c i d e n t r a d i a t i o n . T h e q u a n t i t y k v s o i n t r o d u c e d i s d e f i n e d a s t h e " m a s s a b s o r p t i o n c o e f f i c i e n t ' 4 f o r r a d i a t i o n o f f r e q u e n c y Vs, I f we c o n s i d e r t h e c a s e o f a b s o r p t i o n b e t w e e n t w o s t a t i o n a r y s t a t e s u a n d L , t h e n t h e a b s o r p t i o n o f r a d i a t i o n o f f r e q u e n c y \J u ^ a r i s e s f r o m t h e e x c i t a t i o n o f t h e a t o m s f r o m t h e l o w e r s t a t e L t o t h e h i g h e r s t a t e u . We e x p r e s s t h i s q u a n t i t a t i v e l y i n t e r m s o f t h e E i n s t e i n c o e f f i c i e n t o f a b s o r p t i o n B ^ , d e f i n e d i n s u c h a w a y t h a t t h e p r o b a b i l i t y o f a n a t o m i n t h e s t a t e L , e x p o s e d t o r a d i a t i o n o f f r e q u e n c y V U L , a b s o r b i n g a q u a n t u m h V U L i n t i m e d t i s g i v e n b y dl •v - k I v d s (A10) B ' L u ( A l l ) w h e r e t h e i n t e g r a l i s e x t e n d e d o v e r t h e c o m p l e t e s p h e r e . - 56 - (g) T o t a l A b s o r p t i o n . Consider an element of mass m exposed to a r a d i a t i o n f i e l d . To c a l c u l a t e the amount of r a d i a t i o n energy absorbed i n frequency i n t e r v a l d V per u n i t time, en c l o s e the mass i n a l a r g e s u r f a c e X chosen such that the bounding s u r f a c e cr of m has l i n e a r dimensions smaller than 22 * The energy passing an element d Z of Z and i n c i d e n t upon der , an element of o - , i s from Equation ( A 3 ) dE = I v cos Q cos B dcr d S d v r2 of t h i s energy the amount absorbed from the p e n c i l when t r a v e r s i n g l e n g t h l o f the mass: k v 1 , dE that i s *v cos <9 cos 9 do~ d,£ d v> k v 1 2 r = I v k dm d V d c J where dm = 1 cos 6 .d ; d> i s an element of mass of m and dco= d S cos 9 . the s o l i d angle subtended at the mass p o i n t by dS . The t o t a l energy absorbed i s dv JJ I v k y dm 6 00 = d v k u m J l y d L t J l . I f the number of atoms i n s t a t e L present per u n i t volume which can absorb energy at t h i s frequency, V a L are the t o t a l amount absorbed by them by Eq u a t i o n ( A l l ) Is hence k v U L_ = h N ^ , B-^ ( A 1 2 ) d - 57 - 2. T h e e q u a t i o n o f t r a n s f e r . C o n s i d e r a s m a l l c y l i n d e r o f c r o s s e c t i o n d e r a n d l e n g t h d s n o r m a l t o d cr , L e t I v b e t h e i n t e n s i t y o f t h e r a d i a t i o n o f f r e q u e n c y i n c i d e n t o n o n e f a c e o f t h e c y l i n d e r i n t h e s d i r e c t i o n . T h e i n t e n s i t y e m e r g e n t f r o m t h e s e c o n d f a c e i n t h e s a m e d i r e c t i o n i s Iv + d l y . T h e a m o u n t o f r a d i a n t e n e r g y c r o s s i n g i n t i m e d t a n d i n t h e d i r e c t i o n o f t h e s o l i d a n g l e d w a b o u t s i s I v d v do d cr dt, o f t h i s k ^ d d s I v d V d e j d e r - d t i s a b s o r b e d b y t h e c y l i n d e r ; t h e a m o u n t r a d i a t e d i s d d s d e r j v d CJ d e r d t h e n c e i n t h e s t e a d y s t a t e d I v> d v 6u) d o - d t = d( j v - k \> I ^ ) <r d v d t d s i . e . d l ^ _ = d s " T h i s i s t h e e q u a t i o n o f T r a n s f e r . We c a n w r i t e t h i s e q u a t i o n i n t e r m s o f E i n s t e i n ' s c o e f f i c i e n t s u s i n g e q u a t i o n s (A9) a n d (A12) . d I ^ u L = N ^ u L ^ L + S u L I v u L ) h V u L - N L U L B L u h ^ u L I y u L (A14) o A p p e n d i x I I DISCHARGE MODEL A m o d e l f o r t h e e l e c t r i c c i r c u i t o f t h e f l a s h u n i t i s shown b e l o w . J B -4JL8JL R B R f B R d I t i s d e r i v e d f r o m an o b v i o u s c o r r e s p o n d e n c e between p h y s i c a l e l e m e n t s o f the u n i t and common c i r c u i t e l e m e n t s . C i s a c a p a c i t o r o f 1.6 m i c r o f a r a d s o r t h a t o f t h e f l a s h u n i t c a p a c i t o r . The i n d u c t a n c e Lf r e p r e s e n t s t h e i n d u c t a n c e o f the u n i t c o n d e n s e r and l e a d s , a b o u t 37 m i l l ! m i c r o h e n r i e s . The r e s i s t a n c e s R f and R^ assume t h e v a l u e s o f t h e l e a d and d i s c h a r g e r e s i s t a n c e s r e s p e c t i v e l y . The B a t t e r y B r e p r e s e n t s the c h a r g i n g u n i t w i t h Rg t h e c h a r g i n g r e s i s t a n c e 200 K ohms and L g the c h a r g i n g i n d u c t a n c e . When t h e d i s c h a r g e i s t r i g g e r e d t h e c h a r g i n g u n i t r e s i s t o r Rg and i n d u c t a n c e L g e s s e n t i a l l y d i s c o n n e c t t h e b a t t e r y B f r o m t h e c o n d e n s e r as RgC ~ 3 « 2 seconds w h i l e t h e d i s c h a r g e p e r i o d i s a b o u t t h r e e m i c r o s e c o n d s . Thus we s i m p l i f y t h e c i r c u i t t o t h a t shown b e l o w - 58 - - 5 9 a. i H'l-B-'! <R < f i The equation f o r t h i s c i r c u i t i s R t d 2 i + R t d i + i d t 2 "dt c 0 where R^ = R^+R^. The appropriate s o l u t i o n when the switch s i s moved from contact a to contact b at time t = 0 i s - _ - D - RT 1 ~ e VT, s i n ^ t rr\ L where 1 ./R! 2 ? V (ic™ \2L) j i ; 'Z (Ai5) (A16) The sw i t c h i n g corresponds to t r i g g e r i n g the discharge. From equation (Al) the time d e r i v a t i v e of the current i s di - B -Rt dt ~^TL e 2L ( ̂ \ c o s ^ t - IL. s i n ^ t ) or R t co s where @ = ar c t a n __R_ 2L/>] (Al?) - 5 9 - a. O r> o ~> .3* '•'rRd " i""! ' !—B~""" , /»— ' The e q u a t i o n f o r t h i s c i r c u i t i s R t f i d t 2 + R t di d t + i c = 0 where R^ = R^+R^. The a p p r o p r i a t e s o l u t i o n when t h e s w i t c h s i s moved f r o m c o n t a c t a t o c o n t a c t b a t t i m e t = 0 i s . : _ - D - RT x ~~r e T T s i r i / > i t ^ L where 1 L c ? 1 $ i R j V (A15) (A16) The s w i t c h i n g c o r r e s p o n d s to t r i g g e r i n g t h e d i s c h a r g e . From e q u a t i o n ( A l ) t h e t i m e d e r i v a t i v e o f t h e c u r r e n t i s d i — B —Ht d t ~/iVL e 2L ( ^ c o s ^ t - R__ s i n ^ t ) I 2L o r -Rt •|- 2 c e c o s ( ^ t + © ) where 0 = a r c t a n R (A17) - 60 - The l o g a r i t h a m i c d e c r i m e n t LD d e f i n e d by (LD)= l o g e d t / 1/  u 7 T + 2 T i s g i v e n by (LD) = 2 J I - sty 2 L f ( A 1 8 ) W i t h t h e e x p r e s s i o n A3 and A*f i t i s p o s s i b l e to c a l c u l a t e b;-. . R f and L„ f o r a d i s c h a r g e by o b s e r v i n g d i . M e a s u r i n g 2 d t LD and P t h e p e r i o d we have L = P 1 and R = L(LD) c 1+TT2 + ( L D ) 2 p BIBLIOGRAPHY 1. G a r t o n , W.R.S., P r o c e e d i n g s o f t h e 4th I n t e r n a t i o n a l C o n f e r e n c e o f I o n i z a t i o n Phenomena i n Gases, I 9 6 0 , IID 518. 2. G a r t o n , W.R.S., and R a j a r a t n a m a , A., 1957 > P r o c e e d i n g s o f t h e R o y a l S o c i e t y , A 7 0 8l5. 3. L a d e n b e r g , R „ , 1934, R e v i e w s o f Modern P h y s i c s , 5 243, 4. K o r f f , S.A., and B r e i t , G., 1932, R e v i e w s o f Modern P h y s i c s , 4 4-71. 5. L a d e n b e r g , R „ , and L e v y , S „ , 1930, Z e i t s c h r i f t F u r P h y s i k , 65 189. 6. F r a n c i s , G., I o n i z a t i o n Phenomena i n Gases, Page 90. 7. A n d e r s o n , J.A., 1932, A s t r o p h y s i c s , J 75 394. 8. K o f o i d , J.M., i960, Power A p p a r a t u s and S y s t e m s , 51 999= 9. S p i t z e r , L „ , P h y s i c s o f F u l l y I o n i z e d Gases, P. 81. 10. D i e k e , G.H., and C r o s s w h i t e , H.M., 1954, J o u r n a l o f A p p l i e d P h y s i c s , 25, 196. 11. D i e k e , G.H., and Cunningham, S.P., 1952, J o u r n a l o f t h e O p t i c a l S o c i e t y o f A m e r i c a , 42 187. 12. R i e s z , R., and D i e k e , G.H., 1954, J o u r n a l o f A p p l i e d P h y s i c s , 25, 196. 13. T h e o p h a n i s , G.A., i960, Review o f S c i e n t i f i c I n s t r u m e n t s , 31, 4. - 61 - FIGURE 1 - NEON LEVELS < FIGURE 2 - APPARATUS Kl \A////// r \ \ \ \ x v \ v r^^^Insulating Plate iP Copper Collar C 0 Wire Gauge /////// \\\\\\z Quartz Flash Tube , Insulating Cylinder I r •///////////////////// Window Wo Plane Lead L_ S t Insulating Plate I ( I VT777~777 <7- Windows Electrode Tube / / / / /~i •S3 2. 5 cm 4 cm- \ \ \ \ Y Tube 1 mm_ 3 3: 171 Z_Z V/J///A / / / / / / / / r z / I 1 PI / / / / / / / / KV V / * / Deflection Plate D IS S S N N I Z 2 Z Z Z W Z 3 Reflection Plate D _ Extension Tube F I G U R E 4 - WINDOW G E O M E T R I E S Negative Electrode - Trigger Electrodes F I G U R E 5 - T R I G G E R I N G G E O M E T R I E S FIGURE 6 - UAVI3 FORMS Electrode - P Electrode - N Sidearm A Resevoir a - Absorbtion Tube > Absorption Tube Pirani Gauge McLeod Ga Impurity Gas Supply^ \ , \ , ^ ) 1 Pump Needle Valve Flash Tube b - Flow Scheme FIGURE 7 - PLASMA UNIT Input B Oscilloscope b - Synchronization FIGURE 8 - SHUTTER UNIT FIGURE 9 -HIGH VOLTAGE PULSE GENERATOR

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