"Science, Faculty of"@en . "Physics and Astronomy, Department of"@en . "DSpace"@en . "UBCV"@en . "Simpkinson, William Vaughan"@en . "2011-12-02T20:06:02Z"@en . "1961"@en . "Master of Applied Science - MASc"@en . "University of British Columbia"@en . "Photographic and Photoelectric measurements were made on the shock excited spectra of Argon and Helium. The plasma temperature and electron density in the region behind the shock wave were calculated from the spectroscopic measurements.\r\nThese quantities were compared with the values obtained from the Rankine Hugoniot shock theory including the effect of ionization. Considerable disagreement was found between experimental results and theoretical predictions."@en . "https://circle.library.ubc.ca/rest/handle/2429/39451?expand=metadata"@en . "SPECTROSCOPIC DIAGNOSTIC TECHNIQUES FOR SHOCK HEATED PLASMAS by WILLIAM VAUGHAN SIMPKINSON B.A.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1957 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.A.Sc. i n the Department of PHYSICS W.e accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 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 that 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. Department of Physics The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date September 29. 1960 ABSTRACT Photographic and P h o t o e l e c t r i c measurements were made on the shock e x c i t e d spectra of Argon and Helium. The plasma temperature and e l e c t r o n d e n s i t y i n the r e g i o n behind the shock wave were c a l c u l a t e d from the spectroscopic measure-ments. These q u a n t i t i e s were compared wi t h the values obtained from the Rankine Hugoniot shock theory i n c l u d i n g the e f f e c t o f i o n i z a t i o n . Considerable disagreement was found between experimental r e s u l t s and t h e o r e t i c a l p r e d i c t i o n s . ( i i ) TABLE OF CONTENTS Chapter Page I INTRODUCTION 1 I I THEORY h Spectroscopic Theory !+ (a) Stark Broadening of Hydrogen Lines k (b) S p e c t r a l Line S h i f t i n g 7 (c) Temperature Determination from S p e c t r a l I n t e n s i t i e s 8 Shock Theory 12 I I I APPARATUS 17 Shock Tube 17 Spectroscopic Equipment 18 E l e c t r o n i c A n c i l l i a r y Equipment 19 Arrangement of the Equipment and Miscellaneous D e t a i l s 20 IV EXPERIMENTAL 22 P r e l i m i n a r y I n v e s t i g a t i o n 22 Measurements 2*+ Data Reduction of Time Integrated Spectra 25 Data Reduction of Time Resolved S p e c t r a l I n t e n s i t i e s 27 V RESULTS 29 (A) ARGON Pr e l i m i n a r y 29 Time Integrated Measurements 30 (a) Ne Determination from H^ Broadening and Line S h i f t i n g 30 (b) Observed Line I n t e n s i t i e s 31 (c) Temperatures from Observed Line I n t e n s i t i e s 32 Time Resolved Measurements 33 T h e o r e t i c a l Temperatures and D e n s i t i e s 35 (B) HELIUM P r e l i m i n a r y 36 Time Integrated Measurements 37 Time Resolved Measurements 37 (a) Hydrogen and Helium Line I n t e n s i t i e s 37 (b) N and kT Behind Shock 39 T h e o r e t i c a l Temperatures and D e n s i t i e s kO ( i i i ) TABLE OF CONTENTS (cont'd) Chapter Page VI CONCLUSIONS hi Appendix I THEORETICAL LINE STRENGTHS hh Argon Line Strengths hh Helium Line Strengths h6 BIBLIOGRAPHY hQ ILLUSTRATIONS Page lo pkT versus L 12 2. One Dimensional Shock Wave 13 3. Shock Tube 17 h. Arrangement of Apparatus 20 5. E l e c t r o d e l e s s Discharge C i r c u i t 21 6. Trace Photograph 25 7. F i l t e r e d P r o f i l e s 27 8. versus Log I n t e n s i t y 27 9. Spectrophotometer S e n s i t i v i t y 28 10. I ( t ) f o r A l l 329^ A\u00C2\u00B0 33 11. I ( t ) f o r AIII 3285 A 0 33 12. I ( t ) at hQ55 AO 38 13. K t ) at U-835 A 0 38 Ih. I ( t ) f o r Hel 5876 38 15. K t ) f o r H e l l h686 38 16. kT and N e versus t 39 TABLES Page I 30 I I 31 I I I Plasma Temperature (ev) 32 IV Line I n t e n s i t i e s f o r Various Shock V e l o c i t i e s v s ( i n cm/microsecond) 3*+ V Plasma Temperature kT (ev) 35 VI 36 VII hO ( i v ) ACKNOtfLEDGEMEM TS I am very g r a t e f u l to Dr. A. J . Barnard for the invaluable d i r e c t i o n and assistance given throughout the course o f this work. Special thanks are extended to Mr. G.D. Cormack who designed and constructed most of the apparatus used i n this i n v e s t i g a t i o n while working for his MSc degree. I am also indebted to Dr. A.M. Crooker for the generous loan of spectro-scopic equipment. (v) I INTRODUCTION In the g r e a t l y expanding f i e l d of high temperature or plasma physics much e f f o r t i s going i n t o the development of d i a g n o s t i c techniques. The development of plasma d i s g n o s t i c s i s rendered d i f f i c u l t by the t r a n s i e n t nature of the la b o r a t o r y plasmas produced, l i f e t i m e s of the order of microseconds being t y p i c a l . Broadly speaking, plasma d i a g n o s t i c techniques can be d i v i d e d i n t o two c a t e g o r i e s , the f i r s t being those techniques which perturb the plasma and then measure the e f f e c t of the p e r t u r b a t i o n , the second being those which do not perturb the plasma. P e r t u r b i n g techniques as a r u l e introduce some uncer-t a i n t y i n that the p e r t u r b a t i o n may change the e f f e c t being measured. Spectroscopic techniques, which do not i n v o l v e plasma p e r t u r b a t i o n s , are a u s e f u l and powerful means of i n v e s t i g a t i o n . Study of the emission spectra from a plasma can lead to i d e n t i -f i c a t i o n of the elements present and y i e l d a q u a n t i t a t i v e estimate of the e l e c t r o n d e n s i t y , e l e c t r o n temperature, and degree of i o n i z a t i o n . In a d d i t i o n to the above, the i o n k i n e t i c temperature can be obtained f o r plasmas at very h i g h tempera-tures (T ~ - 1 0 6 \u00C2\u00B0K). The approach employed i n t h i s experiment was to d r i v e a strong shock wave down a quartz tube and observe the emission spectra from the heated region behind the shock. The values of - 1 -- 2 -e l e c t r o n d e n s i t y , e l e c t r o n temperature, and the degree of i o n i -z a t i o n obtained from spectroscopic observations were compared with those expected from theory f o r the shock v e l o c i t i e s observed. From the above comparison some inf e r e n c e may be made of c o n d i t i o n s i n the plasma being s t u d i e d . The most important question i s whether or not the plasma i s i n thermal e q u i l i b r i u m . Here e q u i l i b r i u m i m p l i e s the existence o f : (1) a Maxwellian v e l o c i t y d i s t r i b u t i o n f o r e l e c t r o n s , i . e . , a unique e l e c t r o n temperature, and (2) a d i s t r i b u t i o n of atoms and/or ions i n various energy s t a t e s , E n , the population of each d e s c r i b a b l e by a term containing a Boltzmann f a c t o r , exp(-E n/kT), i n which the temperature, T, equals the e l e c t r o n temperature (k i s the Boltzmann co n s t a n t ) . Spectroscopy i s extremely w e l l - s u i t e d to i n v e s t i g a t i o n s of energy l e v e l populations. The spectroscopic measurements to be made are of l i n e broadening, l i n e s h i f t i n g , and of the r e l a t i v e i n t e n s i t i e s of l i n e s of various adjacent atomic and i o n i c s p e c t r a * . I t w i l l be seen that i n t h i s experiment the temperature and d e n s i t i e s are such that measurable l i n e broadening and s h i f t i n g are due only to. the e l e c t r i c m i c r o f i e l d s w i t h i n the plasma, so that measurement of these observables permits determination of e l e c t r o n and i o n d e n s i t i e s . The measurement of r e l a t i v e l i n e i n t e n s i t i e s \"\u00E2\u0080\u00A2Adjacent spectra are the spectra of an atom and an i o n Cor of two ions) each possessing the same nucleus but whose complements of e l e c t r o n s d i f f e r by one. - 3 -from adjacent s p e c t r a , i n an e q u i l i b r i u m plasma of known e l e c t r o n d e n s i t y , y i e l d s the plasma temperature. Other workers (McLean et a l , i960) have done the above type of experiment with a helium plasma produced by a ma g n e t i c a l l y d r i v e n shock wave. In the present experiment both helium and argon plasmas have been i n v e s t i g a t e d . The work on helium allows some comparison with that of McLean as the c o n d i t i o n s are roughly s i m i l a r though the a n a l y s i s d i f f e r s somewhat. Nothing was found i n the l i t e r a t u r e on stud i e s of argon spectra e x c i t e d by magnetically d r i v e n shock waves. I I THEORY Spectroscopic Theory (a) Stark Broadening: of Hydrogen Lines In an assembly of e m i t t i n g atoms and ions the p r i n c i p a l s p e c t r a l l i n e broadening mechanisms a re: ( 1 ) p e r t u r b a t i o n of one or both of the associated energy l e v e l s of the atom or i o n * by the e l e c t r i c m i c r o f i e l d s due to surrounding ions and e l e c t r o n s (Stark e f f e c t ) , (2) Doppler e f f e c t on emission frequencies due to random thermal motion of the r a d i a t i n g atom or i o n , and (3) p e r t u r b a t i o n of energy l e v e l s by van der Waals forces between atoms and/or ions (Pressure e f f e c t ) . The above mechanisms have been discussed i n many a r t i c l e s , the most u s e f u l of which was found to be a review a r t i c l e by R.G. Breene J r . ( 1 9 5 7 ) * I t can be shown, that at the temperatures and d e n s i t i e s a t t a i n e d i n t h i s experiment, the Doppler and pressure broadening are l e s s than a few tenths of an angstrom. This leaves only the Stark e f f e c t as s i g n i f i c a n t ; I t should be pointed out here that the Stark e f f e c t has two ma n i f e s t a t i o n s , l i n e broadening and l i n e s h i f t i n g . Line broadening without s h i f t i n g r e s u l t s from the energy l e v e l p e r t u r bations changing sign with the f l u c t u a t i n g m i c r o f i e l d ( l i n e a r Stark e f f e c t ) . \u00E2\u0080\u00A2The associated energy l e v e l s , E^ and E^, are r e l a t e d to the s p e c t r a l frequency, V m n , by the well-known r e l a t i o n : hV=Ei-E* where h i s Planck's constant (6.6 x 1 0 ^ 7 e r g - s e c ) . - k -- 5 -The most pronounced l i n e a r Stark e f f e c t i s seen i n the spectrum of hydrogen which i s present as an i m p u r i t y i n almost a l l plasmas. In t h i s experiment broadening measurements were made only on hydrogen l i n e s . A theory f o r the l i n e a r Stark broadening of hydrogen l i n e s was f i r s t developed by Holtsmark (1919). He assumed that the p e r t u r b a t i o n s of the energy l e v e l s were due e n t i r e l y to the q u a s i - s t a t i o n a r y f i e l d s of the i o n s , the frequency of perturba-t i o n by the e l e c t r o n f i e l d s being too high to cause the energy l e v e l s to respond. Holtsmark c a l c u l a t e d the p r o b a b i l i t y f o r a given f i e l d at an e m i t t i n g atom due to surrounding, s t a t i o n a r y , s i n g l y charged ions of number d e n s i t y , N j . I f the f i e l d was expressed i n u n i t s of F Q , where F 0 i s given by: (1) F Q = 2.6leNj J (where e i s the e l e c t r o n i c charge, h.8 x 10\"10 coulombs), the p r o b a b i l i t y d i s t r i b u t i o n s coincided f o r a l l N j . F 0 i s u s u a l l y r e f e r r e d to as the Holtsmark normal f i e l d . S i m i l a r i l y , the p r o f i l e s of a hydrogen l i n e f o r d i f f e r e n t N j can be represented on a s i n g l e curve by p l o t t i n g the s p e c t r a l i n t e n s i t y versus the parameter f to a f i r s t approximation. The accurate expression for the electron density i s : ( 3 ) N e = N-_ + 2N 2 + 3N3 + = ^ L i r L i = l Recent work was done by Griem, Kolb, and Shen (1959) on hydrogen l i n e broadening due to electronic and i o n i c f i e l d s i n a plasma of atoms, electrons, and singly charged ions. An elaborate numerical analysis was made and the theore t i c a l l i n e p r o f i l e s obtained have shown better agreement with experiment than the previous Holtsmark theory. The t h e o r e t i c a l p r o f i l e s of Griem, Kolb, and Shen 2/3 (where F Q = 2.6leN e ) are moderate corrections to the Holtsmark theory. Therefore, i t w i l l be assumed that for the purposes of this experiment the theory of Griem et a l may be extended to include multiply charged ions by substituting NQff (given by Equation (2)) for N e. In this work, values of F Q were determined by f i t t i n g the experimental l i n e p r o f i l e s with the theoretical p r o f i l e s for temperature and density nearest that estimated to occur. The constant by which P C i s multiplied to get the best f i t i s F which y i e l d s N e f f . A simple method of making the above f i t i s to replot the p r o f i l e s on log-log scale with for the theore t i c a l p r o f i l e - 7 -on the same scale as A X f o r the experimental p r o f i l e a b s c i s s a e ) . The h o r i z o n t a l s h i f t required to a l i g n the p r o f i l e s i s F Q ( v e r t i c a l s h i f t i s unimportant). (b) S p e c t r a l Line S h i f t i n g Considering again the Stark e f f e c t , l i n e s h i f t i n g as w e l l as broadening occurs when the energy l e v e l p e r t u r b a t i o n i s a f u n c t i o n only of the magnitude of the f l u c t u a t i n g m i c r o f i e l d (quadratic Stark e f f e c t ) . The f u n c t i o n a l r e l a t i o n s h i p between f i e l d strength and s h i f t of the s p e c t r a l l i n e wavelength or frequency i s known from experiments i n x^hich a gaseous discharge i s maintained i n a steady^: uniform e l e c t r i c f i e l d . In the spectra of argon the stark s h i f t i s r e a d i l y measured. The s h i f t s of many argon l i n e s have been i n v e s t i g a t e d by Minnhagen (19^ 8) and M a i s s e l (1958) and been found more or l e s s p r o p o r t i o n a l to the square of the f i e l d s t r ength. In helium the Stark e f f e c t i s more complicated than i n argon and as a r e s u l t i t i s d i f f i c u l t to o b t a i n u s e f u l i n f o r m a t i o n from helium l i n e s h i f t i n g . In t h i s experiment l i n e s h i f t data w i l l be used only i n the work on argon. I t remains to r e l a t e the l i n e s h i f t observed i n the shock spectra to the e l e c t r o n (ion) density i n the plasma. The frequency s h i f t , A V , of a given l i n e w i l l be assumed to be r e l a t e d to the f i e l d strength F by: (-+) A N = CF 2 where C i s a constant known from Stark e f f e c t experiments. The l i n e i n t e n s i t y d i s t r i b u t i o n f u n c t i o n I ( /\~~)) ) i s r e l a t e d to the normalized Holtsmark* p r o b a b i l i t y d i s t r i b u t i o n W(F/F0) by: (5) K A V )d(A\> ) = ^ ' w ( F / F 0 ) d F where I Q i s the t o t a l s p e c t r a l i n t e n s i t y of the l i n e under d i s c u s s i o n , /-yt-\u00C2\u00A9o I (A\) )d(ZaV)) -oo The Holtsmark f u n c t i o n W ( ^ ) i s obtained from Chandrasekhar (19^ 3). WC/3 ) vanishes at p- 0,\u00C2\u00A9O^ peaks at = 1.6 and has a h a l f width of /\p<^2,25<, From Equations (h) and (5) \u00E2\u0080\u00A2 (6) I(A\V ) = I D W(F/FG) T2~ 2CFg -*/F o s as Thus the i n t e n s i t y d i s t r i b u t i o n f u n c t i o n K^^V ) peak W(P ) . When p l o t t e d from the curve f o r W ( ) the peak of W(P) i s found to be at For a given l i n e , the frequency s h i f t of the i n t e n s i t y d i s t r i b u t i o n maximum i s measured spectro-s c o p i c a l l y . The corresponding f i e l d strength, F f f l a x, c a l c u l a t e d from Equation (^ f), and d i v i d i n g F m a x by 1.05 y i e l d s F D. N e f f can then be found from Equation (1) (with N e f f r e p l a c i n g Nj_ ). (\u00C2\u00B0) Temperature Determination from S p e c t r a l I n t e n s i t i e s Assuming e q u i l i b r i u m between e l e c t r o n and i o n i c temp-*W(y3) i s normalized by the requirement that the p r o b a b i l i t y f o r w( j 3 ) d p = 1). - 9 -e r a t u r e s , the temperature of a plasma can be determined from i n t e n s i t i e s of l i n e s w i t h i n a given spectrum or from l i n e s of adjacent s p e c t r a . However, because of the l a r g e d i f f e r e n c e between energies of i o n i z a t i o n f o r successive i o n species com-pared with the small d i f f e r e n c e s between energy s t a t e s w i t h i n a spec i e s , the temperature i s most s e n s i t i v e l y determined from comparison of measurements from adjacent spectra. The absolute i n t e n s i t y of a s p e c t r a l l i n e r e s u l t i n g from a t r a n s i t i o n between the energy l e v e l s W~ and of an i - t h stage i o n i s given by (see f o r example Condon and S h o r t l e y ) : ( n , T i _ N 1 (m) ; f f l r TT^c i , v (7) I x = \u00E2\u0080\u0094 - \u00E2\u0080\u0094r - r r S (m,n; g 1 3 A % , n ) gm \" ' \" l where N^(m) i s the d e n s i t y of i - t h stage ions of energy E*, g^ i s the degeneracy of the energy s t a t e E^, ~\(m,n,)\u00C2\u00B1s the wavelength of the l i n e , c i s the speed of l i g h t , and S1(m,n) i s the t h e o r e t i c a l l i n e strength of the t r a n s i t i o n E^-E?: (Ei; w i l l m n m always be taken as the upper l e v e l ) . F ollowing Condon and \u00E2\u0080\u00A2Shortley the term l i n e strength i s taken to be the sum of the squares of the e l e c t r i c d i p o l e matrix elements. The l i n e strengths f o r the helium and argon l i n e s studied i n t h i s experiment are tabulated i n Appendix I . Now i n thermal e q u i l i b r i u m , at temperature T, the N 1(m) can be expressed as the product of the s t a t i s t i c a l weight., g^, f o r the energy l e v e l and the Boltzmann f a c t o r , exp(-E^/kT) (k i s the Boltzmann constant). Therefore - 1 0 (8) fe=^ N i(in)=^ ,g iexp(-2m)= ^S^l fe g iexp(-=fra) = ^ i - f P l Z 1 m m m k T g i fe m kT g 1 o o where Z 1 i s the p a r t i t i o n f u n c t i o n f o r i - t h stage i o n s , and N 1 ( 0 ) and g^ are the density and s t a t i s t i c a l weight r e s p e c t i v e l y , f o r i - t h stage ions i n the ground s t a t e (E^ = 0 ) . From Equation ( 8 ) (9) s i M = NiLoj. ( _ % = r \u00C2\u00A3 ( _ ^ P i e i kT 2 i * kT gm g o and Equation (7) becomes on s u b s t i t u t i n g I ^ C f e / g 1 : rn ( 1 0) i i ,6i^ tosi ( . ^ } m ' n 3X1^,11) Z 1 kT A second r e l a t i o n i n v o l v i n g the N 1 i s obtained by i n t r o d u c i n g Saha's equation which gives the r a t i o of the. numbers of ions i n the various stages of i o n i z a t i o n : ( 1 1 ) NV+I _ 2 ( 2 m e ^ k T } 3 / 2 _ E i ) N i + l z i N e h 2 \"kT where M i s the e l e c t r o n mass and E 1 i s the i o n i z a t i o n energy of the i - t h stage i o n (the energy required to remove the ( i + l ) - t h e l e c t r o n ) . Combining Equation ( 1 1 ) with Equation ( 1 0 ) taken f o r i - t h and ( i + l ) - t h stage i o n s : h , i \u00E2\u0080\u009E\"u \u00E2\u0080\u009E ^2mJTkTtiv \ E i + E i + 1 - E i l 2 n f e n 1 Ai(m,n) ( 1 2 ) Tm.n = A j + l ^ V 1 ) ^ \" s'cm>i) i \u00C2\u00B1 + 1 -ZTh \" 2 1 fe ; h \u00C2\u00A7 Ei E x xo f e ..*\ ^ kT - 11 -Taking l \u00C2\u00B0 g 1 0 \u00C2\u00B0? Equation (12) : (13) M = (1/2-TOD ( E~ * Em + 1 - K) t 3/21og 1 0kI + 3/21og 1 0(S2 | a ) + l O g 1 0 ( \u00C2\u00A3 i l ^ L _ where S 1(m,n) and /\. (m,n) have been r e w r i t t e n and /\. \u00E2\u0080\u00A2 .Inserting numerical values i n Equation (13) g i v e s : d^) k T = .(I/2.303) ( > J|2 3/21og 1 0kT + 21.8 + l o g 1 0 ( where kT i s i n e l e c t r o n v o l t s . (15) kT = I t i s seen that Equation (1*+) has the form: A ._ 3/2 log 1 0kT~+ B and thus lends i t s e l f e a s i l y to g r a p h i c a l s o l u t i o n . This i s best accomplished by i n t r o d u c i n g a s c a l i n g parameter p, such that pA i s constant. For convenience pA w i l l be set equal to 10, and Equation (15) then becomes: ( l 6 ) J k f \u00E2\u0080\u00A2 3 / 2 1 O g 1 0 p k T = ( B + 3 / 2 l 0 g 1 0 TV ) = L F i g u r e 1 i s a graph of L versus pkT from which kT can be obtained f o r -given B and A. \u00E2\u0080\u00A2*> 12 \u00E2\u0080\u0094 Figure 1 - pkT vs. L pkT It should be added here that an exact value of H e for insertion i n Equation (Ik) w i l l not always be available from line broadening and shifting measurements. If these measurements give only e^ff as defined by Equation (2), a f i r s t approximation to kT can be obtained ,by inserting N e f f for TS& i n Equation (Ik). N^, N 2 etc. are found from Sana's equation using these approximations to kT and N . Equation (3) then yields a better value for N which in turn w i l l improve the approximation for kT. Shock Theory We w i l l consider here a strong, one dimensional shock - 1 3 -wave propagating w i t h v e l o c i t y v g i n t o a gas at r e s t . F o l l o w i n g the n o t a t i o n on Figu r e 2, the s u b s c r i p t Q w i l l denote q u a n t i t i e s before the shock. The symbols p, T, U, N, v, denote r e s p e c t i v e l y pressure, temperature, i n t e r n a l energy per p a r t i c l e , number den s i t y of ions and/or atoms combined, and f l o w v e l o c i t y . F i g u r e 2 - One Dimensional Shock Wave p,T,U,N Vo = 0 Po> To> Uo> No As i t i s assumed that the shock i s strong: PDC^ denotes the f r a c t i o n of i times ionized atoms ( oC = N V N ) . Assuming thermal equilibrium between ions and electrons, ( i . e . T. = T ) Equations (17) (a), (b) and (18) can be supple-mented with the equation of state and the equation for the i n t e r n a l energy of an i d e a l gas: (a) p = (N+NQ)kT = (l+oC)NkT (20) (b) U = 3/2 (1+oOkT + U i e where U^ e i s the i o n i z a t i o n and the excitation energy per ion. Solving Equations (17) (a), (b), (18) and (20) for N Q and v 2, s and introducing numerical values: {1+cC), (a) N = N e ( i f d + c O + 2 U i e / k T (21) (b) v2 _ 1 9 2 / (,2XT(l+<\u00C2\u00A3) + UlQ,). 2 (cm./microsec.) 2 s J - ^ M 3/2 kT ( l+\u00C2\u00ABC) + U i e ^ c m \u00C2\u00AB / m i c r o s e c - ' where kT and U^ e are i n electron v o l t s and M i s the atomic weight of the rest gas. For comparison with values of kT and N g obtained from spectroscopic measurements i t i s necessary to express kT and N e - 15 -i n terms of the observables, v s and N . I t should be noted that and U. are themselves f u n c t i o n s of kT and N Q. In t h i s l i e e experiment the temperature i s of the order of a few e l e c t r o n v o l t s and so the e x c i t a t i o n energy of an i o n , given by: e , g \u00C2\u00AB*- & ^ E 1 V g J exp(- _n) i s small compared with the i o n i z a t i o n energy. Thus, n e g l e c t i n g the e x c i t a t i o n energies, U. can be expressed i n terms of the xP^ (22) U. = X,E\u00C2\u00B0 + o4(E\u00C2\u00B0+ E 1) + + c/T(E\u00C2\u00B0+...+Er-l) + ... i e 1 2 r Assuming thermal e q u i l i b r i u m , the \u00C2\u00A9\u00C2\u00A3 are given by the Saha equations: (23) - B r + 1 - 2 z ^ l 2 - ekT 3/2 \u00E2\u0080\u00A2 E r and by: (2h) \u00C2\u00A3e\u00C2\u00A3 = 1 To solve Equations (21) ( a ) , (b), ( 2 2 ) , (23) and (2k) f o r kT, N g and the c?\u00C2\u00A3 a method of successive approximations was adopted. We w i l l f i n d i t convenient to r e w r i t e Equation (21) i n form: = -b+-VMvs/l.92'1/7 (a) kT 8(1+^0 (25) - 16 -where b and c are given by: b = (IfU, -3/2MV2, ) l e J / s/i.92 y c = (^U. + 9 A M v 2 7 ) i e + 7 / s/i.92 I n s e r t i n g estimated values f o r the i n Equations (22) and (25) gives a f i r s t approximation to kT- and N^ *. S u b s t i t u t i o n of these f i r s t approximations i n Saha's equation y i e l d s b e t t e r values f o r the oC. This process i s continued u n t i l s e l f c o n s i s t e n t values of o\u00C2\u00A3 are obtained. The above method of s o l u t i o n s i m p l i f i e s i n p r a c t i c e f o r values of kT such t h a t : , , T r r + l 15.1? kT ^ = minimum ( a \u00E2\u0080\u0094 ~ S \u00E2\u0080\u0094 ) At such temperatures only the f o r which need be considered. This i s a t once apparent from Saha's equation. Thus, i n most cases o n l y two of the need be used i n the approximating precedure. However, i f or \u00C2\u00AB ^ + 2 are s i g n i f i c a n t as c a l c u l a t e d from Saha's equation using the approximate values of kT and N then the approximating procedure must be c a r r i e d one step f u r t h e r . I n s e r t i n g i n Equation (2*+) whichever of \u00C2\u00A9\u00C2\u00A3. -. or o \u00C2\u00A3 i s s i g n i f i c a n t , the above procedure 1 \u00E2\u0080\u0094J- i+2 i s repeated g i v i n g b e t t e r values f o r and <^\+i> This whole process i s continued u n t i l a c o n s i s t e n t value of or \u00C2\u00B0^+2 i s found. I l l APPARATUS Shock Tube The shock tube used f o r t h i s work consisted of a quartz tube of 2 .5 cm i n s i d e diameter, approximately 100 cm long, and f i t t e d w ith an electromagnetic d r i v e r . The general d e t a i l s of the d r i v e r , energy storage c i r c u i t and v e l o c i t y measuring apparatus are shown i n f i g u r e 3 (not to s c a l e ) . F i g u r e 3 - Shock Tube RCA Type 931 The spark switch, when t r i g g e r e d , feeds current to the d r i v e r from the ca p a c i t o r bank which i s rated at four mfd. at 15 KV. I t can be seen from the d r i v e r geometry that the arc current i s t i g h t l y coupled to the current i n the bac&strap and i s thus given a strong magnetic r e p u l s i o n which i n a d d i t i o n - 17 -- 18 -to sudden expansion by heating causes a shock wave to be pro-pagated down the tube. The shock v e l o c i t y i s c a l c u l a t e d from the time i n t e r v a l between the p h o t o m u l t i p l i e r responses to the l i g h t from the luminous f r o n t f o l l o w i n g the shock. The design, c o n s t r u c t i o n , and operation of t h i s shock tube are f u l l y described by Cormack (i960). Spectroscopic Equipment Time i n t e g r a t e d spectra were obtained using a H i l g e r E l spectrograph. This spectrograph could be f i t t e d w ith a seven step n e u t r a l d e n s i t y f i l t e r f o r determination of the emulsion d e n s i t y versus l i g h t i n t e n s i t y r e l a t i o n f o r any p l a t e r e q u i r e d . To study time v a r i a t i o n of s p e c t r a l i n t e n s i t i e s a H i l g e r constant d e v i a t i o n spectrograph was modified by the a d d i t i o n of an ad j u s t a b l e s l i t i n the focus plane, followed by a p h o t o m u l t i p l i e r . The r e s u l t i n g spectrophotometer could only be used i n the v i s i b l e s p e c t r a l r e g i o n . This spectrograph was l a t e r replaced by a Bausch and Lomb g r a t i n g monochromator when one became a v a i l a b l e . For time i n t e g r a t e d s t u d i e s , the wavelength range 2000-7200 A 0 could be covered by the H i l g e r E l spectrograph. By u s i n g an RCA IP 28 p h o t o m u l t i p l i e r i n the spectrophotometer, time resolved measurements could be made i n the range 2500-6000A 0 . The d i s p e r s i o n of the E l spectrograph ranges from approximately 1.2A\u00C2\u00B0/mm at 2000A0 to i+SAO/mm at 66OOA0 while - 19 -that of the g r a t i n g spectrophotometer i s l6A\u00C2\u00B0/mm throughout the spectrum. The s l i t width used on the E l instrument and the average g r a i n s i z e of p l a t e emulsion allowed r e s o l u t i o n of l i n e s on the p l a t e separated by approximately .1 mm. The g r a t i n g spectrophotometer with the s l i t widths used (entrance s l i t \u00E2\u0080\u00A2^ s-.0i+ mm, e x i t s l i t '\"%-s09 mm) was capable of r e s o l v i n g o two l i n e s of h a l f width 1.5A\u00C2\u00B0 separated by h to 5A\u00C2\u00B0. E l e c t r o n i c A n c i l l i a r y Equipment The standard e l e c t r o n i c s used consisted of a p l a t e voltage supply, a v a r i a b l e , c a l i b r a t e d 0-1.5 KV. supply f o r the p h o t o m u l t i p l i e r s and a Tektronix type 551 dual beam o s c i l -loscope f i t t e d with a s i n g l e input p r e a m p l i f i e r , a d i f f e r e n c e p r e a m p l i f i e r , and a Dumont trace recording camera. The photo-m u l t i p l i e r c i r c u i t s were made up i n the l a b o r a t o r y . The output of the v e l o c i t y measuring p h o t o m u l t i p l i e r s was fed through shielded cable to the d i f f e r e n c e a m p l i f i e r on the o s c i l l o s c o p e . The output of the p h o t o m u l t i p l i e r on the mono-chromator was fed i n t o a cathode f o l l o w e r of standard design. The output of the cathode f o l l o w e r was fed through shielded cable to the s i n g l e i n p u t p r e a m p l i f i e r . The r i s e time of the p h o t o m u l t i p l i e r , cathode f o l l o w e r and p r e a m p l i f i e r c i r c u i t was of the order of .1 microsecond. The o s c i l l o s c o p e was t r i g g e r e d by a pick-up c o i l coupled to the current i n the shock tube d i s -charge. The v a r i a b l e high voltage power supply to the photo-m u l t i p l i e r s allowed adjustment of spectrophotometer s e n s i t i v i t y - 20 -to accommodate a great range of spectral i n t e n s i t i e s without changing the spectrophotometer entrance s l i t . Arrangement of the Equipment and Miscellaneous Details The apparatus was arranged as i n figure h (not to scal e ) . : Figure k - Arrangement of Apparatus Quartz objective lens Velocity measurin pho tomulti p l i e r s Shock_ driver RCA IP28 / T h o tomul t i p l i er Cathode ^/\"follower n T o ^ / o s c i l l o s c o p e Electrodeless discharge tube K ^ h i eld with s l i t to define object region 110 volts d.c. Removable mirror for use with electrodeless discharge source Displacement of observation point from shock tube discharge (variable) The i r o n arc and electrodeless discharge tube y i e l d comparison spectra which can be superimposed by use of a Hartmann - 2 1 -diaphragm on the time i n t e g r a t e d shock spectra obtained by the H i l g e r E l instrument. The e l e c t r o d e l e s s discharge tube was connected to the shock tube vacuum system so that the pressure of the gas being e x c i t e d could be regulated by the same valves as c o n t r o l l e d the pressure i n the shock tube. The c i r c u i t diagram f o r the e l e c t r o d e l e s s discharge i s given i n f i g u r e 5 \u00C2\u00BB F i g u r e 5 - E l e c t r o d e l e s s Discharge C i r c u i t Spark gap Discharge tube 2 2 0 v o l t s a.c: 50KV X-ray transformer Capacitors . 0 0 2 5 to . 0 ' IV EXPERIMENTAL P r e l i m i n a r y I n v e s t i g a t i o n Several time i n t e g r a t e d shock spectra were taken on I l f o r d HP3 p l a t e s of the i l l u m i n a t i o n of a s t a t i o n 10 cm from the d r i v i n g e l e c t r o d e s . Each spectra was taken at a d i f f e r e n t shock v e l o c i t y . The shock v e l o c i t y could be changed r e a d i l y by a d j u s t i n g the i n i t i a l voltage on the capac i t o r bank. A f t e r f i f t e e n to twenty f i r i n g s the i n s i d e of the shock tube became blackened and i t was necessary to remove the d r i v e r and clean the tube (see f i g u r e 3). F i f t e e n f i r i n g s of the tube were found ample f o r a good exposure. The photographic p l a t e so obtained was analyzed using the i r o n arc spectrum as a reference. R e l a t i v e i n t e n s i t i e s of the l i n e s were estimated from the emulsion d e n s i t i e s . From the s p e c t r a l l i n e s i d e n t i f i e d on the p l a t e some were chosen f o r f u r t h e r study. The c r i t e r i a f o r the s e l e c t i o n were freedom from i m p u r i t y i n t e r f e r e n c e , p r o x i -mity to other l i n e s of the same and adjacent spectra and a v a i l a b i l i t y i n the l i t e r a t u r e of Stark s h i f t c o e f f i c i e n t s . The second c r i t e r i o n was d e s i r a b l e as no ready means was a v a i l a b l e f o r checking the manufacturers' s p e c t r a l s e n s i t i v i t y versus wavelength r e l a t i o n f o r the spectrophotometer. I t may be added that s p e c t r a l l i n e s which were expected and not found on the p l a t e s were looked f o r with the spectrophotometer. This was t r i e d because i n the region 2500 - 5000A0 the spectrophoto-meter gave a strong response to s p e c t r a l l i n e s which were very weak on the p l a t e . - 22 -- 2 3 -As the Stark broadening of the and l i n e s were to be used f o r the determination of e l e c t r o n density i t was d e s i r a b l e to know t h e i r time h i s t o r i e s . Their a r r i v a l times at the 1 0 cm s t a t i o n and pulse shape were observed using the spectrophotometer and compared with h i s t o r i e s of the l i n e i n t e n s i t i e s of the r e s t gas being used. A f t e r the e x p l o r a t o r y work above had been completed the spectrophotometer was adjusted and c a l i b r a t e d f o r the l i n e s to be s t u d i e d . The p h o t o m u l t i p l i e r supply voltage was set to 1 2 0 0 v o l t s and the entrance s l i t width was set f o r \"on scale'\"' responses from the weakest l i n e to be i n v e s t i g a t e d . Then the e x i t s l i t was adjusted by s e t t i n g the spectrophotometer on the widest l i n e and narrowing the e x i t s l i t by small increments u n t i l the response showed a sudden decrease. Next, the r e l a t i o n between spectrophotometer s e n s i t i v i t y and p h o t o m u l t i p l i e r supply voltage was determined by s e t t i n g the instrument on a s p e c t r a l l i n e whose response was eleven to t h i r t e e n v o l t s and then de-creasing the supply voltage by one hundred v o l t s and taking the response again. In t h i s manner i n t e n s i t i e s taken at 1 2 0 0 , 1 1 0 0 , 1 0 0 0 v o l t s e t c e t e r a could be r e l a t e d . I t was assumed that the p h o t o m u l t i p l i e r - c a t h o d e f o l l o w e r c i r c u i t gave l i n e a r response w i t h s p e c t r a l i n t e n s i t y below the s a t u r a t i o n point (output \" ^ - 1 6 v o l t s ) . F i n a l l y , the e l e c t r o d e l e s s discharge was adjusted to give the best p o s s i b l e reference spectrum f o r the gas being s t u d i e d , i . e . narrow u n s h i f t e d s p e c t r a l l i n e s of the same spectra - 2k -as were observed i n the shock tube. The best c o n d i t i o n s were chosen by comparing s e v e r a l exposures taken with various capacitances and spark gaps i n the discharge c i r c u i t ( f i g u r e 5) and with the gas pressure at a low value (p ^ 2 0 microns). Measurements The observations were a l l made at the 10 cm s t a t i o n and at three values of shock v e l o c i t y corresponding to d r i v i n g voltages of 10 KV, 11.25 KV and 12.5 KV. As the seven step n e u t r a l d e n s i t y f i l t e r was not a v a i l a b l e u n t i l the work was almost completed, only one exposure was made through the f i l t e r , at a d r i v i n g voltage of 12.5 KV with argon. Some of the time i n t e g r a t e d spectra were exposed i n j u x t a p o s i t i o n w i t h e l e c t r o d e -l e s s discharge spectra i n order to measure Stark s h i f t s . Whenever p o s s i b l e , time i n t e g r a t e d and time resolved data were obtained from the same f i r i n g s . Quadruple P o l a r o i d exposures were taken of the o s c i l l o s c o p e t r a c i n g s to average out random f l u c t u a t i o n s i n i n t e n s i t y and v e l o c i t y . In t h i s manner the average shock v e l o c i t y was recorded f o r each time i n t e g r a t e d spectrum and any abnormal d e v i a t i o n f o r a s i n g l e shot could e a s i l y be seen. A t y p i c a l o s c i l l o s c o p e trace photo i s p i c t u r e d i n Fi g u r e 6. R e f e r r i n g to Figure 6, the upper traces are the responses of the spectrophotometer to r a d i a t i o n i n the v i c i n i t y of the l i n e . A f t e r four exposures had been made of the spectrophotometer response to a given s p e c t r a l l i n e the background continua was recorded. The spectro-- 2 5 -photometer was turned to a nearby wavelength region f r e e from s p e c t r a l l i n e s and four more exposures were taken (with the lower trace removed). The lower trace i s the response of the two v e l o c i t y measuring p h o t o m u l t i p l i e r s taken through the d i f f e r -ence p r e a m p l i f i e r . The shock v e l o c i t y i s obtained from the lower t r a c e , the separation of the d i s c o n t i n u i t i e s i n the trace marking the time f o r shock passage through 5 cm. Figu r e 6 - Trace Photograph v o l t s ^ \ \ / \ / i V \ 3*\" time Where p o s s i b l e time resolved p r o f i l e s were obtained of the and l i n e s . This was done by recording average time h i s t o r i e s at 5A\u00C2\u00B0 i n t e r v a l s ranging from the l i n e centre to a poin t where only the background s i g n a l was observed. Data Reduction of Time Integrated Spectra A J a r r e l - A s h microphotometer coupled with a B r i s t o l pen recorder was used to scan the l i n e s of i n t e r e s t on the time i n t e g r a t e d spectra f o r s p e c t r a l i n t e n s i t y and the broadening of the and ELg l i n e s . These pen recorder traces were made f o r the exposure transmitted through each segment of the seven step f i l t e r . The maximum emulsion d e n s i t i e s read from the above traces (excepting those f o r hydrogen l i n e s ) were p l o t t e d f o r each s p e c t r a l l i n e a gainst the logarithm of the i n t e n s i t y ( t a k i n g the u n f i l t e r e d i n t e n s i t y as u n i t y and the logarithms of f i l t e r e d i n t e n s i t i e s as the negative of the f i l t e r d e n s i t i e s ) . A l l the curves so obtained were f i t t e d to a s i n g l e curve by s h i f t i n g p a r a l l e l to the l o g i n t e n s i t y a x i s . From t h i s curve the r e l a t i v e i n t e n s i t y versus emulsion density was read. The procedure f o r determination of hydrogen l i n e broadening d i f f e r e d from the above. In t h i s case the emulsion d e n s i t y , f o r each f i l t e r step was p l o t t e d versus wavelength (on the same scale) as sketched i n Figure 7\u00C2\u00BB Next, p l o t s of wave-le n g t h versus l o g i n t e n s i t y were made f o r s e v e r a l values of constant P, the f i l t e r d e nsity d i f f e r e n c e and hence Z \ ( l o g i n -t e n s i t y ) being known between each two steps. As the p l o t s of I versus ~\ swere symmetrical, only a h a l f p r o f i l e was used as i s seen i n F i g u r e 8. The p r o f i l e of l o g i n t e n s i t y versus / \ i s ob-tained by v e r t i c a l l y s h i f t i n g the curves of F i g u r e 8 to a best f i t s i n g l e curve. - 27 -Figure 7 - F i l t e r e d P r o f i l e s Figure 8 - Avs Log Intensity Data Reduction of Time Resolved Spectral I n t e n s i t i e s The spectrophotometer traces were plotted on a larger scale with their respective backgrounds. The backgrounds were subtracted leaving the net in t e n s i t y of each spectral l i n e . The i n t e n s i t y scale was a r b i t r a r i l y chosen so that the responses i n volts for the highest photomultiplier supply voltage could be plotted without change. Traces for which the supply voltage was reduced to avoid saturation of the electronics were corrected using the s e n s i t i v i t y versus supply voltage r e l a t i o n previously determined. Corrections for va r i a t i o n i n spectrophotometer sensi-t i v i t y with wavelength were required for comparison of two l i n e s separated by more than 100-200\u00C2\u00B0A. A spectrophotometer s e n s i t i -v i t y curve (Figure 9) was drawn from the grating e f f i c i e n c y curve for the Bausch and Lomb monochromator combined with the - 28 -s p e c t r a l s e n s i t i v i t y curve f o r the IP 28 p h o t o m u l t i p l i e r taken from RCA tube data. F i g u r e 9 - Spectrophotometer S e n s i t i v i t y R e l a t i v e S e n s i t i v i t y Time resolved hydrogen l i n e p r o f i l e s were obtained d i r e c t l y from the P o l a r o i d trace photographs by p l o t t i n g the response at a given time from each averaged trace against the wavelength at which the trace was taken ( a f t e r s u b t r a c t i n g the background s i g n a l f o r the given time from each response). V RESULTS This chapter w i l l be d i v i d e d i n t o two parts (A) Argon and (B) Helium. (A) Argon P r e l i m i n a r y The p r e l i m i n a r y p l a t e s of the argon shock spectra contained a generous number of strong A l l and A I I I l i n e s . Impurity l i n e s present were H^ , Hg, , many C I I , S i l l , Cul l i n e s , the stronger C a l l l i n e s and only the strongest C I I I l i n e s , * + 6 5 0 . l 6 and l+-65l\u00C2\u00AB35A\u00C2\u00B0 ( u n r e s o l v a b l e ) . The l i n e s chosen f o r i n t e n s i t y measurement were: A l l A I I I 3 2 9 3 . 9 5 A \u00C2\u00B0 3 2 8 5 . 8 5 A \u00C2\u00B0 3307.2*+A\u00C2\u00B0 3301.88A\u00C2\u00B0 3 3 5 0 . 9 ^ A \u00C2\u00B0 33H. 2 5 A \u00C2\u00B0 3 3 7 6 A 6 A \u00C2\u00B0 3 3 3 6 . 1 3 A \u00C2\u00B0 3 3 8 8 . 1 7 A 0 3 3 M f . 7 2 A \u00C2\u00B0 3 3 5 8 A 1 A 0 while those f o r measurement of Stark s h i f t were: A l l 3 5 5 9 . 5 3 A \u00C2\u00B0 3 5 6 l . O * r A \u00C2\u00B0 3 5 7 6 . 6 2 A \u00C2\u00B0 3 5 8 8 . M + A O The HP3 p l a t e cut o f f i n s e n s i t i v i t y at about 6 5 7 0 A 0 so that measurement of the H^ p r o f i l e n e c e s s i t a t e d an exposure with a Kodak type F p l a t e which has r e l a t i v e l y constant s e n s i t i ' v i t y i n t h i s region. - 2 9 -- 30 -Time resolved a n a l y s i s could not be made of the Hg l i n e because many A l l l i n e s overlap i t s p r o f i l e and the H^ 1 l a y o u t s i d e the s e n s i t i v e region of the spectrophotometer. The e l e c t r o d e l e s s discharge tube was found to y i e l d strong A l l and A I I I l i n e s with C = .0075 mfd. and a spark gap of one i n c h . Time Integrated Measurements (a) Ne Determination from H^ Broadening and Line S h i f t i n g The H^ p r o f i l e as obtained by the procedure o u t l i n e d i n Chapter IV (Figures 7 and 8) was f i t t e d best i n the wings by the t h e o r e t i c a l p r o f i l e f o r T=20,000\u00C2\u00B0K and We=1017Cm~3. The r a t i o =Fn f o r best f i t was (212\u00C2\u00B12*f) s t a t volts/cm which y i e l d e d , from F Q=2.6leN 2/3, N( N' e f f = (.7-.D101 7 cm\"3, The A l l l i n e s h i f t i n g gave F values tabulated below; Table I Line (A\u00C2\u00B0) Weighted* F ( s t a t volts/cm) Average F 7h7 3588.tf 1001 3576.6 llk7 833stv/cm 3561.0 1900 3559.5 977 Taking average F=833 s t a t v/cm, F = =793 s t a t v/cm and 0 1.05 Ne?iN e f f=(5\u00C2\u00B1l)10 17 cm-3. \u00E2\u0080\u00A2Average i s weighted i n favour of A l l k]+7)+.8Au which showed best agreement with <\u00C2\u00A3>V= CF 2 and against A l l 356lA\u00C2\u00B0 which showed worst agreement. - 31 -I t i s seen that the two estimates of N e d i f f e r by a f a c t o r of seven, though both w i l l be lowered a f t e r o b t a i n i n g an approximation f o r kT and the oC^ and then s o l v i n g equations (2) and (3) f o r a second approximation to N . (a) Observed Line I n t e n s i t i e s The A l l and A l l time i n t e g r a t e d t o t a l l i n e i n t e n s i t i e s were taken as the product of the i n t e n s i t y corresponding to the peak of the l i n e emulsion d e n s i t y p r o f i l e as taken from the pen recorder t r a c i n g and the width of the p r o f i l e taken at a density reading corresponding to one-half peak i n t e n s i t y . These i n t e n -s i t i e s observed at Vs=1.92 cm/microsecond, are tabulated below with upper energy l e v e l s , E * v and i o n i z a t i o n energys, E 1 , as taken from Moore (19*+9) \u00E2\u0080\u00A2 Table I I A l l El=2?.5ev A I I I E 2 = H - 0 . 7 e v M u l t i p l e t Line (A\u00C2\u00B0) I n t e n s i t y y , E * ( e v ) , Mu^.tiplet Line (AO) I n t e n s i t y E|(ev) 83 3293.9 kk 23.53 1 3285.8 25.28 83 3307.2 52.5 23. k5 1 3301.9 ko 25.26 109 3350.9 ko 2k.72 1 3 3 H . 2 23 25.25 109 3376.5 k5 2k ,71 3 3336.1 25 27.98 96 3388.1 50 23.53 3 3 3 ^ . 7 19 27.96 3 3358. \u00C2\u00BBf 12 27.9^ - 32 -(c) Temperatures from Observed Line I n t e n s i t i e s S o l u t i o n s to equation (1*+) using l i n e strengths, S^, from Appendix I , energy l e v e l s , i o n i z a t i o n energies, and p a i r s of l i n e i n t e n s i t i e s from (b) above and f o r each value of Ne i n (a) above are tabulated belox-/. The lower numbers are values of kT f o r Ne=5xl0 1' 7cm\"3, the upper numbers values f o r Ne=.7x-101'c Table I I I - Plasma Temperature (ev) \AIII LINES A l l ( A O ^ 3285 . 8 3301 . 9 . 3311.2: 3336.I 33M+.7 3358 A 3293.9 2.06 2.36 2.10 2 A 2 2.10 2 A l 2.11 2.39 2.13 2 A 2 2.13 2 A 1 3307.2 1.93 2.19 1.97 2.2k 1.97 2.2k 1.97 2.22 1.99 2.25 1.97 2.2^ 3350.9 1.39 1.61 1.3^ 1.58 3376.5 l A 1.62 1.3^ 1.61 3388 . 1 2.11 2 A 1 2.16 2 A 9 2.15 2 A 8 2.15 2 A 5 2.18 ' 2 A 6 2.17 2 A 6 Only a few temperature c a l c u l a t i o n s were made using A l l 3350.9A\u00C2\u00B0 and 3376.5A\u00C2\u00B0 as the l i n e strength theory seemed to break down f o r these l i n e s and give i n c o n s i s t a n t r e s u l t s (see Appendix I ) . A b e t t e r approximation to the higher estimate of N e was made using the average value of kT from Table I I I ( d i s -counting c a l c u l a t i o n s i n v o l v i n g A l l 3350.9 and 3376.5A\u00C2\u00B0), - 33 -s o l v i n g f o r c ? ^ , (assuming c/C^ + &0> = 1) and then sub-s t i t u t i n g J^i\") \u00C2\u00A32 i n equations (2) and ( 3 ) . This c a l c u l a t i o n y i e l d e d N e = 3\u00C2\u00BB 9xl0-*-'7cm\"\"3 which i n turn caused the second approximation to kT to be reduced. - .O'+ev (a 2% r e d u c t i o n ) . Time Resolved Measurements In the work with argon time resolved h i s t o r i e s could not be obtained from the and l i n e s . The A l l and A I I I i n t e n s i t y h i s t o r i e s could, however, be used to check the t o t a l i n t e n s i t y values obtained from the time i n t e g r a t e d s p e c t r a . T y p i c a l averages of A l l and A I I I i n t e n s i t y h i s t o r i e s are r e p l o t t e d i n Figures 10 and 11. F i g u r e 10 - I ( t ) f o r Figure 11 - I ( t ) f o r A l l 329>+A0 A I I I 3285A 0 K t ) I ( t ) t (microseconds, from discharge) The second peak, which i s q u i t e apparent i n A l l 3291*-, i s caused by a second shock which occurs due to r i n g i n g i n the discharge c i r c u i t (see Cormack, i 9 6 0 ). For comparison with time i n t e g r a t e d - 3h -i n t e n s i t i e s the i n t e g r a l J l(t)dt was c a l c u l a t e d f o r each i n t e n s i t y versus time curve. The i n t e g r a t e d i n t e n s i t i e s are tabulated below f o r the three d r i v ing voltages ( i . e . f o r shock v e l o c i t i e s v s ) . Table IV - Line i n t e n s i t i e s f o r various shock v e l o c i t i e s v s ( i n cm/microsecond) A l l A I I I Line (A\u00C2\u00B0) I n t e n s i t y Line (AO) I n t e n s i t y 10KV v s = 1 . 5 1 1 . 2 5 K V v s = 1 . 7 2 1 2 . 5 K V v s = 1 . 9 2 10KV v s = 1 . 5 11.25KV v s = 1 . 7 2 1 2 . 5 K V v s = 1 . 9 2 329-+ 2k.1 3 6 . 5 \u00C2\u00BBf 5.0 3 2 8 6 k.6 2 5 . 6 If2.5 3 3 0 7 2 0 . 1 2 9 . 9 3 3 . 6 3 3 0 2 5 . 9 1 1 . 9 2 2 . 3 3 3 5 1 2 1 2 2 . 7 k2.7 3 3 3 6 8 . 7 1 2 . 1 3 3 8 8 no readj ngs taken kl.2 3 3 ^ 5 8 . 2 8 . 6 3 3 5 8 8 . 7 'From Tables I I and IV i t can be seen that the two methods of measuring t o t a l l i n e i n t e n s i t y show only rough agree-ment. However, when the temperature c a l c u l a t i o n i s made using the i n t e n s i t i e s of Table IV the values of kT obtained cover the same range as those i n Table I I I . C a l c u l a t i o n s were made of average temperatures, kT, at v = 1 . 5 and 1 . 7 2 cm/microsecond using i n t e n s i t i e s of A l l 329*f, 3307AO and A I I I 3 2 8 6 , 3 3 0 2 , 3 3 3 6 , and 3 3 ^ A \u00C2\u00B0 from Table IV. These values are seen i n Table V. The average e l e c t r o n d e n s i t i e s used i n the above c a l c u l a t i o n s were estimated from shock theory, - 35 -as time did not permit Stark s h i f t measurements at these shock v e l o c i t i e s . At vs=1.92 cm/microsecond the e l e c t r o n d e n s i t i e s as c a l c u l a t e d from the shock theory and from the Stark s h i f t s d i f f e r e d s i g n i f i c a n t l y , and ther e f o r e the e l e c t r o n d e n s i t i e s c a l c u l a t e d from shock theory were scaled down i n pr o p o r t i o n f o r the lower shock speeds. In Table V the upper e n t r i e s are kT values f o r v =1.72 cm/microsecond, N =3\u00C2\u00BB!+x lO-^^cm\"^ while the lower ones are f o r v =1.5 cm/microsecond, N =2.95xl0^^cm~^. Table V - Plasma Temperature kT(ev) \ A I I I Lines (A\u00C2\u00B0) A l l :C\ 3285.8 s 3301.9 3336.1 33^.7 3293.9 2.25 2.05 2.19 2.12 2.21 2.25 3307.2 2.15 ^ 1.96 2.09 2.0M-2 0 1 -L 2.15 T h e o r e t i c a l Temperatures and D e n s i t i e s The values of the plasma temperature, kT, and e l e c t r o n d e n s i t y , N e, c a l c u l a t e d from the shock theory f o r v =1.5j 1.72, and 1.92 cm/microsecond and i n i t i a l r e s t gas de n s i t y , N Q=2.12X10 l 6cm _3 (from p0=.6 mm Hg at 68\u00C2\u00B0F) are d i s -played i n Table VI, Also shown i n Table VI are the average values of s p e c t r o s c o p i c a l l y determined temperatures and d e n s i t i e s . - 36 -Table VI \u00E2\u0080\u00A2vs (cm/microseconds) Spectroscopic Values Shock Theory Values kT(ev) N e(10 1 7cra-3) kT(ev) Ne(10 1^cm-3) 1.92 2.32 3 . 9 C - . 8 ) 3.33 6.32 1.72 2.18 - 2.88 5.55 1.50 2.0h - 2.38 *f.75 (B) Helium P r e l i m i n a r y On the p l a t e s taken of the helium shock spectra only two He l i n e s were obviously present- these were Hel 5876 and H e l l l+686. A very f a i n t l i n e was seen at 3888A 0 which may have been Hel 3888 (though there i s a weak CII l i n e at 3889A 0). This l i n e was c l e a r l y observed with the spectrophotometer as was the l i n e H e l l 3203. No other He l i n e s could be found. Impurity l i n e s present i n a d d i t i o n to and Hg were many CI I , C I I I , O i l , S i l l l i n e s and the stronger C u l , C a l l , and S i l l l l i n e s . The i d e n t i f i c a t i o n of these l i n e s was v e r i f i e d by n o t i n g that the i n t e n s i t i e s of l i n e s of the t h i r d spectra showed a more r a p i d i n c r e a s e w i t h shock v e l o c i t y than i n the case of the second s p e c t r a . Hel 5876, H e l l -^686 and 3203 were f a r enough from i m p u r i t y l i n e s (5A\u00C2\u00B0) to be resolved by the Bausch and Lomb monochromator. An estimate of the i n t e n s i t y of Hel 3888A 0 - 37 -could be made by c o r r e c t i n g f o r the response at 3888A0 due to CII 3889. The i n t e n s i t y of CII 3889 was i n turn estimated from the response of other CII l i n e s of strength. Both the H^ - and Ep, l i n e s were f r e e from i n t e r f e r e n c e by other l i n e s . Time Integrated Measurements No q u a n t i t a t i v e measurements were made on helium spectra as the n e u t r a l density f i l t e r was not a v a i l a b l e while t h i s work was i n progress. Time Resolved Measurements Usable measurements on helium were made only at a d r i v i n g voltage of 1 2 . 5 KV. Much e x p l o r a t o r y work i n the v i s i b l e s p e c t r a l region was done with the modified H i l g e r constant d e v i a t i o n spectrograph but no s p e c i f i c r e s u l t s came from t h i s work as the s p e c t r a l s e n s i t i v i t y of the instrument could not r e a d i l y be determined. A f t e r the a r r i v a l of the Bausch and Lomb monochromator only a l i m i t e d amount of work was done on helium. (a) Hydrogen and Helium Line I n t e n s i t i e s Time resolved observations of s p e c t r a l i n t e n s i t y i n the v i c i n i t y of the E^ l i n e y i e l d e d Hg p r o f i l e s f o r d i f -f e r e n t times. T y p i c a l Ej^ i n t e n s i t y h i s t o r i e s are shown i n Figu r e s 12 and 13 f o r wavelengths near the l i n e centre (H-861A\u00C2\u00B0) and i n the wings. - 38 -F i g u r e 12 - I ( t ) a t H-855A0 F i g u r e H - I ( t ) a t W 5 A \u00C2\u00B0 I ( t ) I ( t ) I t i s r e a d i l y seen from Figures 12 and 13 that i f a time i n t e g r a t e d i n t e n s i t y i s measured f o r the H^ l i n e ( i . e . from a photographic exposure) such a measurement w i l l be h e a v i l y weighted by the second pulse (caused by the second current surge i n the r i n g i n g of the di s c h a r g e ) . The time i n t e g r a t e d measurement would give a much narrower p r o f i l e than i s a c t u a l l y the case immediately behind the shock. T y p i c a l i n t e n s i t y h i s t o r i e s of Hel and H e l l l i n e s are shown i n Figures 1*+ and 15. From these curves i t can be seen that the i o n i c l i n e s peak and decay sooner than do the atomic l i n e s . F i g u r e l n - K t ) f o r Hel 5876 F i g u r e 15- I ( t ) f o r H e l l ^686 (microseconds, from discharge) - 39 -(b) N p and kT Behind Shock Approximations to N e ( i . e . N e f f ) were determined from the H p r o f i l e s at various times a f t e r the passing of the shock; these d e n s i t i e s are p l o t t e d i n F i g u r e 16. Having time resolved values of e l e c t r o n d e n s i t i e s , the plasma temperature could be c a l c u l a t e d using the Hel and H e l l l i n e i n t e n s i t y h i s t o r i e s . The temperatures so obtained are a l s o p l o t t e d i n Fi g u r e 16. The o r i g i n of the time a x i s i n F i g u r e 16 i s taken to be the p o i n t where the l u m i n o s i t y f i r s t begins to r i s e as seen i n F i g u r e s 12 -15., The temperatures and d e n s i t i e s shown are such that <^<$C 1 and thus \u00C2\u00AEQf\u00C2\u00A3 = ^ e to the accuracy of t h i s experiment. F i g u r e 16 - kT and N e versus t X - N e N ( c m ^ x l O - ^ ) 0 _ k T kT(ev) .5 i . o 1.5 time (microseconds) - ko -T h e o r e t i c a l Temperatures and D e n s i t i e s The plasma temperature and e l e c t r o n d e n s i t y c a l c u -l a t e d from the shock theory f o r v g = l f . 8 cm/microsecond and N 0=1.17xlO l 6 cm-3 (from p Q =.33 mm Hg at 68\u00C2\u00B0F) are shown i n Table VII with the spectroscopic values f o r comparison. Table V I I Spectroscopic Values Shock Theory Values kT(ev) N o (10 1 7cm-3) kT(ev) R e d O ^ c m ^ ) 3.73 5 . 3(-D 3.83 1.52 VI CONCLUSIONS For the gases used i n t h i s experiment, the tempera-ture, measured s p e c t r o s c o p i c a l l y was i n a l l cases equal to or l e s s than that expected from the shock theory. However, the e l e c t r o n d e n s i t i e s determined from spectroscopic measurements were greater f o r helium and l e s s f o r argon than the shock theory p r e d i c t e d . The above r e s u l t s are at variance with those observed by McLean et a l ( i 9 6 0 ) , t h e i r spectroscopic temperatures being higher than expected. A p o s s i b l e f a c t o r i n volved here i s the dis t a n c e from the discharge to the s t a t i o n at which the obser-v a t i o n s were made. McLean's observations were made at 6 cm, those here at 10 cm. With the l i m i t e d amount of data a v a i l a b l e from the work done to date no s p e c i f i c conclusions can be drawn as to q u a n t i t a t i v e departure from the shock theory. Much more i n v e s t i g a t i o n i s required of shock behavior at d i f f e r e n t speeds and s t a t i o n s i n order to determine i f the observed d i s c r e p a n c i e s are f u n c t i o n s of the apparatus or are due to i n v a l i d i t y of the theory. A l s o , the e f f e c t of i m p u r i t i e s , which has not been considered i n t h i s work, re q u i r e s some study. For reasons o u t l i n e d i n the r e s u l t s , time i n t e g r a t e d or average values of N e (or N e f f ) can best be determined from s h i f t or broadening measurements made on the spectra of the - kl -- 1+2 -p a r t i c u l a r rest gas being used. Determination of electron densities from observation of impurity spectra such as that of hydrogen must be made from time resolved spectra. The use of the spectrophotometer i n obtaining hydrogen l i n e p r o f i l e s and hence electron densities appears to be a very promising technique. While the techniques of measuring l i n e i n t e n s i t i e s are adequate f o r rough (- 10%) determination of temperatures they require much refinement i n order to check the equilibrium assumption on which the spectroscopic theory i s based. To make such a check, i n t e n s i t i e s of far separated l i n e s of many d i f f e r -ent multiplets must be accurately determined and then compared. Such a comparison would require c a l i b r a t i o n of the spectroscopic apparatus for absolute in t e n s i t y versus wavelength. Having absolute i n t e n s i t i e s for the spectral l i n e s , Equations (3), (10) and (11) can be solved for kT and N e, A separate deter-mination of N e which i s independent of the equilibrium assumption can be made from measurements such as hydrogen l i n e broadening. Agreement between the two values of N g would substantiate the o r i g i n a l assumption of equilibrium. Future investigations could be directed toxrards plasma properties and behaviors which are sensitive to the existence or non-existence of equilibrium. Attempts could be made to determine the time required to establish equilibrium conditions. In summary, the conclusions to be drawn from this experiment are that while spectroscopy i s a very useful tool - ^3 -f o r a i d i n g i n the determination of c o n d i t i o n s w i t h i n a plasma, i t r e q u i r e s refinement i n both theory and experimental technique. However, to f u r t h e r develop these techniques r e q u i r e s a more thorough understanding of the processes w i t h i n a plasma. APPENDIX I THEORETICAL LINE STRENGTHS The t h e o r e t i c a l l i n e strengths to be used i n c a l c u -l a t i o n s f o r argon and helium w i l l be taken d i r e c t l y from published values where a v a i l a b l e . As no values are a v a i l a b l e f o r the strengths of argon l i n e s used, these must be c a l c u l a t e d , Argon Line Strengths Fo l l o w i n g Condon and S h o r t l e y the l i n e strength, S, can be expressed as f o l l o w s : \"> s = ^ Z f e where T ^ f i s a f a c t o r depending on the m u l t i p l e t * , ^ i s a f a c t o r depending on the p a r t i c u l a r l i n e i n the m u l t i p l e t , and where S* 2 i s r e l a t e d to the i n i t i a l e l e c t r o n angular momentum quantum number, J^, and to the r a d i a l wave fu n c t i o n s R^ and Rf of the i n i t i a l and f i n a l s t a t e s by: poo ( 2 ) ^ 2 = I f l t l , R i R f r d r * The products 7?fJ^ are e a s i l y found from the e l e c t r o n c o n f i g -u r a t i o n s of the associated energy l e v e l s (Moore, 1 9 ^ 9 and 1 9 5 9 ) and from formulae and t a b l e s i n Chapter 9, Condon and S h o r t l e y . *A m u l t i p l e t i s a group of l i n e s emitted by t r a n s i t i o n s from upper energy st a t e s of common p r i n c i p a l and o r b i t a l angular momentum quantum numbers, (n,-#), but d i f f e r i n g t o t a l angular momentum quantum numbers, ( j ; , to lower energy st a t e s having the same r e l a t i o n s h i p to one another. - M f -- if5 -Bates and Damgaard (1950) have integrated (2) using wave functions which are solutions i n the Coulomb approximation* to the Schroedinger equation. Bates and Damgaard use the expression: where C i s the excess electronic charge on the nucleus (one for neutral atom, two for singly ionized atom, etc.), and ^ cP are = 2/3 C/n* R(n\u00C2\u00A3 _ 1,^-l,C)R(n^ , i ?,C) r dr, The quantity n^ i s the ef f e c t i v e p r i n c i p a l quantum number corresponding to the state with electron o r b i t a l angular momentum Jl. The n* and nJ^_]_ a r e given by the simple r e l a t i o n : = C Y (g,)*\u00C2\u00BB n ^ - i l&j) where ^ is the energy of a l e v e l below the i o n i z a t i o n l i m i t for the pa r t i c u l a r atom or ion. In the above work the j^n*,^) and C^(n*\u00C2\u00A3^r^ ,A) are tabulated for given n* , ^ L i > a n ( 3 ^ . The calculated l i n e strengths for the argon l i n e s of i n t e r e s t are shown i n the table below. Values of /-.were **In the Coulomb approximation the electron i s assumed to move i n a Coulomb potential (Potential energy = C where C i s ex-cess electronic charges on nucleus). r - h6 -taken from Moore (19!+9). A l l AIII Line (A\u00C2\u00B0) S 3293.6 5.26 3307.2 2.10 3350,9 .018 3376.5 .025 3388.5 9.2 Line ( A 0 ) s 3285.8 25.2 3301.9 18.0 3311.2 10.8 3336.1 33^.7 29.6 3358.5 20.0 The l i n e strengths f o r A l l 3350.9 and 3376.5 are abnormally low; the Coulomb approximation seems to break down f o r these l i n e s . Helium Line Strengths The l i n e strengths of helium were obtained from the absor p t i o n o s c i l l a t o r strengths. The absorption o s c i l l a t o r s t r e n g t h , f , i s r e l a t e d to the l i n e strength, S, by f = K - \u00C2\u00A7. A \u00C2\u00A7n where ^ i s the wavelength of the l i n e , g n i s the degeneracy of the lower energy l e v e l and K i s a constant which w i l l be taken as u n i t y here as only r a t i o s of f or S are used i n c a l -c u l a t i o n s . The o s c i l l a t o r strengths of n e u t r a l helium were ob-tained from the work of T r e f f e t z et a l (1957) while those of i o n i z e d helium are simply those of hydrogen (see f o r example - if7 -Unsold). The values of f, g n , and S f o r the helium l i n e s to be studied i n t h i s experiment are tabulated below. Hel H e l l f A( cmxlO^) g n S= Ag nf f A( cmxlO^) g n s= A g n f .057 3.888 3 .665 .151 3.203 50 2H-.2 .623 5.876 9 32.9 .81+2 H-. 686 32 126 BIBLIOGRAPHY Bates, D.R., and Damgaard, A., P h i l i s o p h i c a l Transacations of the Royal Society A2^ +2, 101, 1950. Breene, R.G.Jr., Reviews of Modern Physics 2\u00C2\u00A3, 1957. 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