@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Science, Faculty of"@en, "Physics and Astronomy, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Neufeld, Carl Richard"@en ; dcterms:issued "2011-09-29T20:43:08Z"@en, "1963"@en ; vivo:relatedDegree "Master of Science - MSc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description "Photoelectric measurements were made of the shock-excited spectrum of a mixture of helium and argon. The electron density behind the shock wave and the temperatures of the plasma components were deduced from the spectroscopic measurements, assuming thermal equilibrium conditions in the shock plasma. The two temperatures were in fairly good agreement, supporting the equilibrium assumption. On the other hand, the temperature and electron density differ significantly from values expected for a one-dimensional shock wave."@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/37701?expand=metadata"@en ; skos:note "AN EXPERIMENTAL INVESTIGATION OF EQUILIBRIUM CONDITIONS IN A SHOCK PLASMA b y CARL RICHARD NEUFELD B . S c . , Queen's U n i v e r s i t y , 1962 A.THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department o f PHYSICS We accept t h i s t h e s i s as conforming to the r e q u i r e d s tandard THE UNIVERSITY OF BRITISH COLUMBIA October , 1963 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t 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 per-m i s s i o n 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^. I t 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 w r i t t e n p e r mission. Department of PH'VStCS The U n i v e r s i t y of B r i t i s h Columbia,. Vancouver 8, Canada. Date NOV. 2 3 , / 3 6 2 ABSTRACT P h o t o e l e c t r i c measurements were made o f the s h o c k - e x c i t e d 'spectrum o f a mix tu re of he l ium and argon. The e l e c t r o n d e n s i t y beh ind the shock wave and the temperatures o f the plasma compon-ents were deduced from the spec t ro scop i c measurements, assuming thermal e q u i l i b r i u m c o n d i t i o n s i n the shock plasma. The two temperatures were i n f a i r l y good agreement, suppor t ing the e q u i -l i b r i u m assumption. On the o ther hand, the temperature and e l e c t r o n d e n s i t y d i f f e r s i g n i f i c a n t l y from va lues expected f o r a one-dimen-s i o n a l shock wave. ACKNOWLEDGEMENTS I wish to thank my supervisor, Dr. A.J. Barnard, for the suggestion and supervision of the project described in this thesis. I am also grateful to Mr. W . V , Simpkinson for able assistance with the experimental research. Thanks also to Mr. J.H. Turner, Mr. Peter Haas, and Mr. John Lees for aid in construction and maintenance of the apparatus. Financial assistance during this project in the form of an N.R.C. Award is gratefully acknowledged. - i i -TABLE OF CONTENTS ABSTRACT i LIST OF ILLUSTRATIONS i v ACKNOWLEDGEMENTS v I INTRODUCTION 1 I I THEORY S p e c t r o s c o p i c Theory (a) Temperature De te rmina t ion from S p e c t r a l I n t e n s i t i e s 6 (b) S t a r k Broadening o f Hydrogen L i n e s 11 Shock Theory 17 I I I EXPERIMENTAL DESIGN AND CONSTRUCTION Shock Tube 23 M i x i n g Chamber 26 S p e c t r o s c o p i c Equipment 28 E l e c t r o n i c Equipment 29 IV EXPERIMENTAL WORK P r e l i m i n a r y I n v e s t i g a t i o n 30 Measurements 33 A n a l y s i s of Data 36 - i i i -V RESULTS De te rmina t ion o f Ng from E,^ Broadening 38 Observed L i n e I n t e n s i t i e s 38 Comparison W i t h Shock Theory k l V I CONCLUSION 1*2 APPENDIX U6 BIBLIOGRAPHY hi - i v -LIST OF. ILLUSTRATIONS FIGURE 1. P l o t of pkT v s . L 12 2. Schematic Diagram of Apparatus 2k 3 . D r i v e r 25 U. S w i t c h 27 5. S p e c t r a l I n t e n s i t y Traces 35 6. Spectrophotometer S e n s i t i v i t y 37 - 1 -CHAPTER I INTRODUCTION . Much has been said and written about the attractiveness, of 'controlled fusion power generators, and the role plasma\"physics 12 might be expected to play in such devices, ' While this attrac-tiveness has not diminished, the possibility of imminent success appears almost as remote as ever. It is now generally realized that not much is known of the processes which occur in.plasmas, and much current research is concentrated on studying these processes using plasma generators which are not expected to pro-duce a self-sustaining fusion reaction. Information thus gained may be useful in designing an operative controlled fusion device. One method of generating a plasma for study employs the electro-magnetic shock tube. The shock tube produces a low tem-perature high density plasma from which useful observations can be made. In this device, electrical energy stored in a capacitor bank is partly transferred, in a short time, to a gas under low pressure. There are two basic types of•electro-magnetic shock tubes - the electrodeless discharge type and the electrode type. In the electrodeless discharge type, the energy of the charged capacitor is discharged through a coil around one end of the shock tube. The gas in the tube breaks down because of the - 2 -high electric fields associated with the time-varying current wave-form. The gas absorbs energy from the coil and a shock wave is subsequently generated. In the electrode type shock tube, the energy of the capa-citor bank is discharged through a spark gap situated in one end of the shock tube. Some of the energy is transferred to the gas near the spark gap and a shock wave is generated. Spectroscopic diagnostic techniques are well suited to shock plasma studies. At the temperatures of laboratory shock plasmas (approximately 10^ °K) there is a generous radiation of light, A decided advantage of spectroscopic techniques is the fact that no mechanical devices such as probes need be inserted into the plasma. Although probes are useful tools, i t is often difficult to determine how much the presence of the probe affects the local value of the parameter under observation. Assuming thermal equilibrium, the line spectra of the gas under study can be readily related to a plasma temperature. Most laboratory plasmas contain hydrogen as an impurity, and electron densities can be determined from the broadening of the or H p lines. It is instructive to compare spectroscopic, determinations of plasma temperature, and electron densities with results ob-tained from shock theory, A fairly comprehensive shock theory has been worked out for the case of a plane advancing shock front, - 3 -assuming thermal equilibrium behind the front. Such comparisons 3 were made by Barnard, Cormack and Simpkinson using helium and argon plasmas in an electrode type electro-magnetic shock tube. Their work revealed discrepancies between the spectroscopic and shock theory values for temperature and electron density. Since the writing of the above paper, a Kerr Cell high-speed camera has become available for analysis of the plasma. The Kerr Cell photographs revealed that the front face of the advancing plasma slug was definitely not plane, A description of this work is given by Cormack.^ Thus the standard shock equations are in-applicable. It is also possible that the condition of thermal equilibrium is not met, so that a unique temperature cannot be assigned to the plasma, \"The processes within the gas should be considered more closely to outline the nature of the problem of temperature determination. Laboratory plasmas normally consist of electrons and gas ions and atoms interacting for a short period of time. The electrons, much lighter and usually having a greater thermal velocity than the gas atoms and ions, rapidly attain a Maxwellian velocity distribution by frequent collisions among themselves. Calculations for the times taken to achieve this state have been made by Spitzer' and Jankulak^ and' are of the order of 10\"^ se-conds for the low temperature dense plasmas studied. These times are much shorter than the time, of the order of 10~^ seconds, when observations of laboratory plasmas are usually \"made. Thus, under normal conditions of observation, a unique temperature as determined be the velocity distribution can be assigned to the electron gas. The atoms and/or ions (hereafter referred to as 'ions\") will also possess a velocity distribution which may or may not be Maxwellian. If the distribution is Maxwellian,. the tempera-ture i t determines may or may not be the same as the electron temperature. The ions collide with each other and with electrons. The time for ions to come to equilibrium with each other (ion-ion -9 relaxation time)is of the,order of 10 seconds, (see Jankulak) The ions will also collide with the electrons, gradually establishing thermal equilibrium between these two plasma com-ponents with an electron-ion relaxation time of the order of 10\" seconds. The state of thermal equilibrium is characterized by the following considerationst (1) A unique temperature can be assigned to the gas. This implies the electron temperature and the ion temperature are the same, (2) The populations of the various electron energy levels of an ion vary as exp (-Em/kT), where E is the energy level of the m-th excited state of the m i-th stage ion .< k i s Boltzmann's constant T i s the temperature. The latt e r two relaxation times referred to above apply-to elastic collisions. The inelastic electron-ion and ion-ion relaxation times are considerably longer. 7 Griem concludes that, i n laboratory plasmas, the level populations w i l l not be s t r i c t l y i n accordance with an expo-nential law. Some of the excited levels may be populated i n this manner, but the ground state w i l l almost certainly not be. Where an exponential law can be f i t t e d , the temperature i n the expres-sion w i l l be the electron temperature. In cases of. thermal equi-librium, this temperature w i l l also be the ion temperature. In view of the above considerations, i t seemed advisable to investigate the problem of equilibrium experimentally. A mix-ture of argon and helium was used and line intensities of ad-jacent spectra of each element were measured. From each of these measurements a temperature could be calculated assuming thermal equilibrium conditions. By comparing the two temperatures i t was hoped that an estimate could be made of the completeness of elec-tron-ion interactions at the time of the observations. Adjacent spectra are spectra of an atom and an ion (or of two ions) each possessing the same nucleus but whose complements of1 electrons differ by one. 6 CHAPTER I I • THEORY Spec t ro scop i c Theory (a) Temperature De te rmina t ion from S p e c t r a l I n t e n s i t i e s S p e c t r a l i n t e n s i t i e s can be used to c a l c u l a t e a temperature f o r a p lasma . {See I n t r o d u c t i o n ) . Al though l i n e s of the same spectrum can be used a more s e n s i t i v e de te rmina t ion can be made u s i n g l i n e s of adjacent s p e c t r a . The d i f f e r e n c e i n the i o n i z a -t i o n energ ies o f adjacent spec ies o f an atom or i o n i s f a r g r ea t e r than the d i f f e r e n c e i n e x c i t a t i o n l e v e l s o f a s p e c i e s . Thus the l e v e l p o p u l a t i o n s , depending on exp (-E / k T ) , are l e s s n e a r l y equal when adjacent s p e c t r a are cons idered and a more accura te temperature de t e rmina t ion i s p o s s i b l e . The abso lu te 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 an e l e c t r o n t r a n s i t i o n between energy l e v e l s E and E of an i - t h ' • J m n 8 stage i o n i s g i v e n by; (See f o r example Condon and S h o r t l e y ) j i ' i l ^ A d 4 - ( ) where? N^m) i s the d e n s i t y of i = t h stage ions of energy E m g^ i s the degeneracy of the energy l e v e l E m \"A ^ i s the wavelength of the l i n e - 7 -c i s the speed of l i g h t S 1 i s the t h e o r e t i c a l l i n e s t r e n g t h o f the t r a n s i t i o n E - E (here and hencefor th E i s cons ide red the upper m n m l e v e l ) . F o l l o w i n g Condon and S h o r t l e y , the term l i n e s t r e n g t h i s taken to mean the sum o f the squares o f the e l e c t r i c d i p o l e m a t r i x e lements . The l i n e • s t r e n g t h f o r the he l ium and argon l i n e s 9 used i n t h i s experiment were eva lua ted by Simpkinson us ing the Coulomb approx imat ion as desc r ibed by Bates and Damgaard.^\"0 The r e s u l t s are t a b u l a t e d i n the Appendix . I n thermal e q u i l i b r i u m a t a temperature T^ the va lue o f N^\"(m) can be g i v e n ass N V ) - C e x p / - J ! - ) . . . ( 2 ) h kT /j where G i s a cons t an t . Thus 4 . „ , A o ) , ' / E m \\ N i(o) , g o 8 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 the i ~ t h stage i o n s . N 1 ( o ) i s the d e n s i t y o f i ~ t h stage i o n s i n the ground s t a t e ^ ( E o - 0) g 1 i s the s t a t i s t i c a l weight of these i o n s . Here we have se t C = ^ . ^ i S 0 From equa t ion (3) N^(m) N i ( o ) / \" E \\ N 1 / E m \\ _ . m _ — exp [- — L — exp ( - —) . .-.(U) g£ g j V kT/ Z 1 V kT / - • N i ( m ) \" On s u b s t i t u t i n g f o r - j — i n equa t ion (l) we get g m . 6 U / i s i N 1 / E m \\ I 1 = _ _ exp I - — \\ . . . ( 5 ) 3 A i Z 1 \\ kT / W r i t i n g Saha ' s equa t ion i n a form g i v i n g the r a t i o o f the numbers of ions i n v a r i o u s stages of i o n i z a t i o n we have, approximate ly , jji+1 z i 2 /2 JJ M^ j^X 3/2 / v ^ i i + i ° — — r — j e x p — , , , ( 6 ) N Z 1 X N I ii / \\ kT where: N i s the number d e n s i t y o f e l e c t r o n s e m i s the mass of an e l e c t r o n e i s the i o n i z a t i o n energy o f the i - t h stage i o n (the energy r e q u i r e d to remove the ( l + l ) - t h e l e c t r o n ) h i s P l a n c k ' s c o n s t a n t . A n improvement on Saha ' s equat ion i s sometimes w r i t t e n by - 9 -i n c l u d i n g a f a c t o r o f the form e 3 / N \\ 1 / 2 / l \\ 3 / 2 on the r i g h t hand s i d e o f equa t ion ( 6 ) . The second term i n the b r a c k e t a r i s e s from the s h i f t i n g of the e x c i t a t i o n l e v e l s of an atom or i o n by the e l e c t r i c f i e l d s i n the p lasma. Equa t i on (6) i m p l i e s the n e g l e c t i n g of t h i s c o r r e c t i o n te rm, A c a l c u l a t i o n f o r the c o n d i t i o n s of t h i s experiment d i s c l o s e s t ha t t h i s procedure in t roduces an e r r o r o f about $% i n the p o p u l a -t i o n s of the v a r i o u s i o n s . S i n c e the dependence on the i n t e n s i t y term i s l o g a r i t h m i c (see equa t ion (9) ) the e r r o r i n o m i t t i n g the c o r r e c t i o n term i s n e g l i g i b l e . I f we w r i t e equa t ion (5) f o r ( i + l ) - t h stage ions as and combine equat ions (5)j> (6) and (7) we f i n a l l y a r r i v e a t I 1 ^ n N / h 2 y / 2 Q i /v.+E-E / v i + l e / S l p m I / Q\\ I Al 2 \\^2//m ekT/ S 1 + x \\ kT / - 10 -Tak ing l o g 1 0 of bo th s ides of equa t i on (8) and r ea r r ang ing we get ~ F T T ( V . + E - E ) kT - 2.303 ^ i p , ^ 1 + 1 3/2 l o g 1 0 kT + 3 / 2 l o g 1 0 f 2 / T m e V l o g ^ / S I n s e r t i n g numer i ca l values, i n (9) we o b t a i n 1 (V. + E - E •) . : 2.303 * ' i p • m / i ~ i i ,,1+1 3/2 l o g . . - kT •+• 21.8 + l o g . . . r A j ° x u 1 i + 1 . U \" . 1 X * where kT i s i n e l e c t r o n v o l t s . We see t h a t equa t ion (10) i s of the form ^ \" 3/2 l o g ^ 0 kT +.B which i s an i m p l i c i t equa t ion i n kT w i t h th ree unknowns kT, A , and B . T h i s equa t ion can be s o l v e d g r a p h i c a l l y by i n t r o d u c i n g a s c a l i n g parameter p such t h a t pA i s cons t an t . F o r convenience pA i s se t equa l to 10 so t h a t equa t ion ( l l ) f i n a l l y becomes - 11 f j r - 3/2 l o g 1 0 ( p k T ) - (B + 3/2 l o g 1 ( ) - L . . . (12) A p l o t o f L versus pkT i s g i v e n i n F i g , 1 from which kT can be ob ta ined f o r g i v e n v a l u e s o f A and B , (b) S t a r k Broadening of Hydrogen L i n e s We note tha t a p p l i c a t i o n o f the theory developed i n p a r t (a) of t h i s chapter r e q u i r e s a knowledge of the e l e c t r o n number d e n s i t y , N , An es t imate o f N can be ob ta ined by l i n e broadening t echn iques , Q Q . . . . The p r i n c i p a l l i n e broadening mechanisms a f f e c t i n g the emis s ion spectrum o f a l i g h t source a r e : (1) the Doppler e f f e c t i n f l u e n c i n g the observed f requenc ies because of the,random thermal motions of the r a d i a t i n g atoms and i o n s j (2) p e r t u r b a t i o n o f one o r bo th o f the a s s o c i a t e d energy l e v e l s o f the atom or i o n by the e l e c t r i c f i e l d s due to ne ighbour ing ions'-and e l e c t r o n s (S t a rk e f f e c t ) ; (3) p e r t u r b a t i o n o f energy l e v e l s by van der Waals f o r ce s between atoms and/or ions (pressure b roaden ing ) . The above processes are w i d e l y d i s c u s s e d . A good rev iew a r t i c l e on the sub jec t i s one by R . G , Breene J r . \" ^ I t can be shown t h a t , under the c o n d i t i o n s of t h i s experiment (a dense, low tempera-- 13 -tu re plasma) the Eopp le r and pressure broadening are on ly a few tenths of an angstrom. Thus S t a r k broadening i s the dominant p r o -c e s s . The S t a r k e f f e c t can c o n t r i b u t e to l i n e broadening and l i n e s h i f t i n g . L i n e broadening w i t h o u t s h i f t i n g r e s u l t s from the l i n e a r S t a r k e f f e c t . The spectrum o f hydrogen, p resen t as an i m p u r i t y i n a lmost a l l l a b o r a t o r y plasmas, e x h i b i t s the most pronounced l i n e a r S t a r k e f f e c t . The broadening o f one of the .hydrogen l i n e s (H=c) was measured i n t h i s experiment . 12 I n 1919, Holtsmark developed the f i r s t theory f o r l i n e broadening due to the l i n e a r S t a r k e f f e c t . He c a l c u l a t e d the e f f e c t due o n l y to the f i e l d of the s t a t i o n a r y i o n s , . o n the assumption tha t the frequency o f pe r t u rba t i ons by e l e c t r o n s was too h i g h to a l l o w the energy l e v e l s to respond. The c a l c u l a t i o n s were c a r r i e d out f o r stationary-;, s i n g l y charged ions o f number d e n s i t y s u r -rounding a r a d i a t i n g atom. A n a t u r a l u n i t , a r i s i n g out of these c a l c u l a t i o n s , f o r the f i e l d s t r e n g t h i s F q where F Q = 2.61 e-Nj 2 / / 3 . . . ( 1 3 ) where e i s the e l e c t r o n i c charge, L 8 x 1 0 \" ^ s ta tcoulombs . F q i s u s u a l l y c a l l e d the.. Holtsmark normal f i e l d s t r e n g t h . 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 can be represen ted on a s i n g l e curve - I k -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 A X oC = F ' o where AX i s the d isplacement i n angstroms from the l i n e c e n t r e . The Holtsmark theory can be g e n e r a l i z e d to i n c l u d e m u l t i p l y 13 charged i o n s us ing r e s u l t s d e r i v e d by Chandrasekhar. We mere ly r e p l a c e N i n equa t ion (13) by an ' e f f e c t i v e d e n s i t y ' g i v e n by Kr* - N T + 2 3 / 2 N o + 3 3 / 2 N , + . . . = 2 i 3 / 2 N , . . . ( l k ) e f r 1 2 3 i where S i s the degree o f i o n i z a t i o n of the most h i g h l y charged i o n p r e s e n t . The e l e c t r o n d e n s i t y N q , can be approximated by f o r a modera te ly i o n i z e d gas.The e l e c t r o n d e n s i t y i s a c c u r a t e l y g i v e n b y S N q - N ± + 2 N 2 + 3 N 3 + ... - 2 i N ± . . . (15 ) A more r ecen t theory o f l i n e broadening has been developed by Gr iem, Ko lb and S h e n . ^ As w i t h the - Holtsmark theory , the r e -s u l t s app ly to a plasma o f atoms, e l e c t r o n s and s i n g l y charged i o n s . Account was taken o f e l e c t r o n i c and i o n i c f i e l d s , and the numer i ca l c a l c u l a t i o n s of l i n e p r o f i l e s have shown b e t t e r agreement - 1 5 -w i t h Experiment than the Holtsmark theory . The t h e o r e t i c a l p r o f i l e s o f Griem e t a l are moderate c o r -r e c t i o n s to the Holtsmark t h e o r y . Thus i t w i l l be assumed t ha t , as be fo re , g e n e r a l i z a t i o n to m u l t i p l y charged ions can be e f f e c t e d by r e p l a c i n g N G by as g i v e n by equa t ion ( l k ) . A l s o we now have F » 2.61 e N 2 ^ 3 . . . (16) o e • The va lue o f F q i n a l a b o r a t o r y plasma can be ob ta ined by comparison o f an e x p e r i m e n t a l l y determined l i n e p r o f i l e w i t h a t h e o r e t i c a l p r o f i l e c a l c u l a t e d f o r a temperature and e l e c t r o n den-s i t y neares t t h a t a n t i c i p a t e d i n the plasma. From AA = « O F Q . . . ( 1 7 ) the cons tan t by which i s m u l t i p l i e d to get the best f i t i s F , which can be used to f i n d N „„. e x i The above f i t i s made q u i t e s imp ly by r e p l o t t i n g , on a l o g -l o g s c a l e , the t h e o r e t i c a l p r o f i l e ( s p e c t r a l response versus X) and the exper imen ta l curve ( s p e c t r a l response versus A X ) . The h o r i -z o n t a l s c a l e i s i n bo th cases the same. The h o r i z o n t a l s h i f t r e -q u i r e d to a l i g n the p r o f i l e s i s F . The v e r t i c a l s h i f t r e s u l t s • from the cho ice o f i n t e n s i t y s c a l e s and I s un impor tan t . I t shou ld be remembered t h a t l i n e broadening measurements may g ive o n l y N G ^ ' (see equa t ion ( l h ) ) and not N q as r e q u i r e d f o r - 16 -i n s e r t i o n i n equa t ion (10) . I n such cases , ^eff i s used i n equa-t i o n (10) to so lve f o r the f i r s t approximat ion to kT . S a h a ! s equa t ion i s then s o l v e d , us ing these ' approx imat ions to N p and kT, to f i n d the p o p u l a t i o n d e n s i t i e s of the v a r i o u s stages of i o n s . Then, u s i n g e q u a t i o n s ( l k ) and (15), an improved va lue of N g w i l l be found . T h i s v a l u e can then be s u b s t i t u t e d i n t o equa t ion (10) to f i n d a second approximat ion to kT, The procedure i s repeated u n t i l c o n s i s t e n t va lues o f N and kT are o b t a i n e d . e The above method i s de sc r i bed f o r a plasma i n which t h e ambient gas i s composed o f o n l y one k i n d of atom o r m o l e c u l e . I n t h i s exper iment , a mix tu re of gases was used^ so a s l i g h t e x t e n s i o n of the theory i s r e q u i r e d . We cons ide r a plasma conposed o f two types of atoms X and Y whose r e l a t i v e abundance i s g i v e n by ^ =• R , . . ( l 8 ) where R i s g r ea t e r than o r equal to 1. I t i s now p o s s i b l e to analyze the spectra, of the plasma com-ponents i n the manner o u t l i n e d above to o b t a i n the f i r s t a p p r o x i -mat ion to N g and kT , The second approx imat ion can be made w i t h the he lp of equa t ion (18) i n c o n j u n c t i o n w i t h e q u a t i o n s ( l k ) and (lp). - 17 -Shock Theory An estimate of the parameters N and kT can also be made by applying the shock equations to the plasma. We consider a shock-heated plasma generated by the rapidly-moving 'piston' composed of dr i v e r gas. The dr i v e r gas, near the d r i v e r at the onset of the discharge, i s heated by the arc and moves down the shock tube at a high v e l o c i t y . We w i l l consider a strong, one-dimensional shock wave propagating into a gas mixture at r e s t . The symbols which appear i n the analysis are tabulated' below. Table I Symbol Meaning V shock v e l o c i t y v f flow v e l o c i t y n,n' i n i t i a l density of gas atoms of types A and B r e s p e c t i v e l y ahead of the shock. m,m' masses of gas atoms of types A and B r e s p e c t i v e l y V v i t o t a l i o n densities of gas atoms of types A and B r e s p e c t i v e l y behind the shock n. ,n'. l * 1 dens i t i e s of i - t h stage ions of types A and B re s p e c t i v e l y behind the shock N e el e c t r o n density behind the shock T temperature behind the shock P pressure behind the shock U i n t e r n a l energy per i o n behind the shock V v i i o n i z a t i o n p o t e n t i a l s of the i - t h stage ions, as defined on page 8, - 18 -Assuming'complete mixing 1 b e h i n d the shock, we may w r i t e n n_ - . n» ttnf - ™ We a l s o w r i t e n ' = x * . . . ( 2 0 ) and, u s i n g equa t ion (20) n i = x n i . . . ( 2 1 ) S i n c e a s t rong shock i s cons ide red , we have P 0 < < PI U << U, where the s u b s c r i p t s r e f e r to c o n d i t i o n s ahead o f the shock. The shock equat ions f o r the c o n s e r v a t i o n of p a r t i c l e s , l i n e a r momentum, and energy become (n * n'O v o ( n j + nj.) (v ~ v f ) ....(22) p = (n^m * n£m«) (v - v f ) v f . . . ( 2 3 ) 2 p v f = jKmiij + m ' n p (v v ) v f + (rij + h p (v - v f ) . U . . . ( 2 1 0 We a l s o know tha t the e l e c t r o n d e n s i t y i s g i v e n by N Q S 2 i ( n i + n p . . . ( 2 5 ) i - 19 -We now w r i t e n . nj — - r . s - 4 - r! ...(26) n I 1 n i 1 From equat ions (21) and (26) i t f o l l o w s t ha t n | _ n! - A » x ~ - x r ' . . . ( 2 7 ) n^ nj. 1 We can now w r i t e N e \" = Rj. 2 i ( r ± . . + x r p - n^. r . . . ( 2 8 ) i r - S i ( r , + x r p . . . ( 2 9 ) i Us ing equat ions (20 ) , (21) and (28) we can r e - w r i t e equa-t i o n s (22) , (23) and (2k) as . . . ( 3 0 ) . . . ( 3 1 ) n 9 n n p «* J(m * x m') — ( ^ - n) v \" +• ( l + x ) - — U . . . ( 3 2 ) n T - n V f a—h— V p « (m + x m») n ( n T - n) n . - 20 -• S o l v i n g equat ions (31) and (32) f o r n we f i n d n = 2(1 + x ) P U + p / n j • ' • ( 3 3 ) From equa t ion (30) we f i n d p / n j + 2(1 + x ) U v • — — — ; . . . ( 3 4 ) . (2(m + x m») (1 4 x ) U ) ' Equat ions (33) and (34) express the e x p e r i m e n t a l l y known q u a n t i t i e s n and v i n terms of the unknown quan t i t e s p , n^ and U , These : three unknowns depend on kT and N and i t might appear t ha t r e - a r r a n g i n g the equat ions would y i e l d e x p l i c i t express ions f o r kT and N . However, .the q u a n t i t i e s p , n T , and U are compl i ca t ed func -t i o n s of temperature and e l e c t r o n d e n s i t y and the equat ions r a p i d l y become i n t r a c t a b l e . We w i l l proceed i n the s o l u t i o n o f the problem by w r i t i n g express ions f o r p , n ^ , and U i n terms of kT and N G and s u b s t i t u t i n g these va lues i n t o equat ions (33) and ( 3 4 ) . Assuming thermal e q u i l i b r i u m between ions and e l e c t r o n s , we can supplement equat ions (33) and (34) w i t h the equa t ion o f s t a t e and the equa t ion f o r the i n t e r n a l energy of an i d e a l gas: p = ( N q + i i j + ru\\) kT ' . . . ( 3 5 ) (Hj. + nJ<) U -.3/2 k T ( N E +• + nj.) + n ^ + n ^ + + . . . + njV^ + n ' O P + V | ) + . . , . . . ( 3 6 ) Equa t i on (36) i m p l i e s n e g l e c t i n g the e x c i t e d s t a t e s of the v a r i o u s stages o f i o n s i n the gas m i x t u r e . I n t h i s experiment the temperature i s of the order o f 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 o f an i o n , g i v e n by £ E n g n exp ( - E n / k T ) E . 2 £ g n exp ( - En/kT) n i s s m a l l compared w i t h the i o n i z a t i o n energy. W i t h the a i d of equat ions (20), (21) and (28) we can w r i t e equat ions (35) and (36) as p « ( N e * n j ( l + x ) ) kT . . . (37) (1 + x ) U - 3/2 kT (1 * x + r) + r . V + r 0 (V + V n ) +., .• J. O £ 0 J . + x(r»V' * r« (V + V») • » . . . ) . . . ( 3 8 ) i O £ O 1 Assuming therraal e q u i l i b r i u m , the are g i v e n by the Saha equa t ions , 2 Z' , /2/7m kTN\\3/2' / V \\ _ ^ £ = ^ ^ t i • e x p - - £ ] . . . ( 3 9 ) N z V h / V. kr / P e p v where Z ^ i s the p a r t i t i o n f u n c t i o n f o r the q - t h stage i o n , and by L> r, a 1 . . . ( L 0 ) i - 22 To use the shock theory d e s c r i b e d above i n c a l c u l a t i n g va lues of kT and N s a t i s f y i n g the exper imen ta l c o n d i t i o n s , a s emi—i te ra t ive e method was adopted. F i r s t , es t imates were made o f the expected va lues o f N and kT, Equa t i on (39) was then used t o f i n d the r. © 1 and r £ . Next equa t ion (29) was used to c a l c u l a t e r. Equa t i on (28) was used to f i n d n ^ , wh ich was then used i n equa t ion (37), a long w i t h the es t imate of N to c a l c u l a t e p . E q u a t i o n (38) was used to f i n d ( l + x) U . Then equat ions (33) and (3k) were s o l v e d f o r n and v . These two r e s u l t s were compared w i t h the known v a l u e s . The i n -i t i a l es t imates of N g and kT were then adjus ted t o o b t a i n a second approx imat ion to n and v . The process was repeated u n t i l the c a l -c u l a t e d n and v agreed w i t h the known v a l u e s . I t may be remarked t ha t a f u l l y i t e r a t i v e method would be s u p e r i o r t o the somewhat clumsy approach adopted above. Such was a l s o the o p i n i o n of the author a t one t i m e . The equat ions above were r e -a r ranged to permi t i t e r a t i v e s o l u t i o n s f o r N g and kT and a s o l u t i o n a t tempted. However, the i n t e r v a l of convergence of the method was so s m a l l t h a t none of the at tempted s o l u t i o n s converged. Th i s method was subsequent ly abandoned. - 23 CHAPTER I I I EXPERIMENTAL DESIGN AND CONSTRUCTION Shock Tube The shock tube used i n t h i s experiment was a quar tz tube of 2 .5 cm, i n s i d e diameter , approximate ly 1,5 meters l o n g . An e l e c -t rode type e l ec t ro -magne t i c d r i v e r was p l a c e d a t one end of the tube , A schematic, drawing o f the apparatus i s shown i n F i g , 2 . The d r i v e r (see F i g , 3) was of the co -p l ana r t y p e . The copper e l ec t rodes were embedded i n epoxy r e s i n . C o n s t r u c t i o n o f the d r i v e r proceeded by pou r ing succes s ive l a y e r s of epoxy r e s i n , a f t e r a l l o w i n g the p rev ious l a y e r to harden. The d r i v e r has proved to be q u i t e s t u r d y , even a t v o l t a g e s up to 20 k v . The d r i v e r geometry g i v e s f a i r l y c l o s e c o u p l i n g of the arc cu r r en t to the cu r r en t i n the b a c k s t r a p . T h i s c o u p l i n g g ives the arc a s t r o n g m a g n e t i c . r e -p u l s i o n , thus a i d i n g i n a t t a i n i n g a h i g h shock v e l o c i t y . The c a p a c i t o r bank c o n s i s t e d o f three 5j^£, c a p a c i t o r s capabable o f o p e r a t i n g a t 20 k v . The des ign p e r m i t t e d the use of one, two o r a l l three of these c a p a c i t o r s i n p a r a l l e l . P r e l i m i n a r y exper imenta t ion seemed to i n d i c a t e t h a t the 'maximum shock v e l o c i t y f o r a g i v e n energy i n the c a p a c i t o r bank occu r red when the cap-ac i t ance was a minimum. The r i n g i n g frequency o f the e l e c t r i c a l c i r c u i t ( c a p a c i t o r s , s w i t c h , l eads and d r i v e r ) was h ighes t when FIG. 2 S C H E M A T I C D I A G R A M OF A P P A R A T U S not to scale (gi s h u t - o f f v a l v e This port ion r e m o v a b l e for c l e a n i n g D r i v e r To v a c u u m p u m p - ^ To p r e s s u r e g u a g e -*= To a r g o n s u p p l y *s. To h e l i u m s u p p l y r= •Cold trap • M e t e r i n g v a l v e Capacitor b a n k -M i x i n g c h a m b e r FIG. 3 D R I V E R not to scale e p o x y r e s i n S h o c k t u b e b u t t s a g a i n s t h e r e G l a s s w o o l r e i n f o r c i n g C o n n e c t i o n to s w i t c h Q u a r t z t u b i n g S p a r k g a p - 2 c m . A l u m i n u m b a c k i n g p l a t e Copper e l e c t r o d e s M o u n t i n g h o l e C o n n e c t i o n to c a p a c i t o r b a n k F N O - 2.6 -only one capacitor was used. This experiment involved one capacitor charged to 12 kv. Thus the energy i n the capacitor bank before dis-charge was 36O joules. The switch used (see Fig k) was-an open a i r spark gap switch, triggered by a high voltage pulse. The switch was of very simple de-sign and incorporated an adjustable gap to allow use of various f i r -ing voltages. The only wear noted i n over one year of operation was a slight erosion of the tungsten f i r i n g pin; The shock velocity was measured by noting the time interval between the responses of two photomultipliers, stationed at differ-ent positions along the shock tube, to l i g h t from the luminous front following the shock. Mixing Chamber The experiment used a mixture of gases i n the shock tube. The mixture was prepared i n a mixing chamber. The chamber was a cylindrical brass container of about ii . 5 l i t r e s f i t t e d to allow evacuation by means of the same pump used to evacuate the shock tube, (See Fig 2 ) . Connections were also made to allow admitting helium and argon gas from separate storage bottles. An aneroid guage (O-76O mm.) indicated the pressure in the chamber, and the gas mixture was introduced into the shock tube through a F I G 4 S W I T C H not to scale Copper c y l i n d e r I n s u l a t i o n T r i g g e r pin A d j u s t i n g screw Copper spark e l e c t r o d e s Copper c u r r e n t leads ;/////. A/ / / / / ; /./^ / ; / s r-r •—1 1 ' 1 1 1 - i ,-. 1 —i—J T e f l o n i n s u l a t i o n L u c i t e i n s u l a t i o n Copper r e t u r n lead P l y w o o d s u p p o r t L u c i t e d a m p s - 28 -metering valve to the tube. The ratio of helium to argon was assumed to be the same as the ratio of the pressures of the two gases in the mixing chamber. 15 The shock tube is similar to the one described by Cormack. The only innovations are the capacitor bank, the driver, and the mix-ing apparatus. Spectroscopic Equipment A Hilger E l spectrograph was used to obtain time-integrated spectra of the shock luminosity. These spectra were used to iden-tify the various emission lines from the ambient gas,and the im-purity lines present. The choice .of lines used for the final in-tensity measurements was made on the basis of the time-integrated spectra. The f i r s t time-resolved measurements were made using a Bausch and Lomb grating monochromator. Two photocells were avail-o able, an RCA IP 28 photomultiplier in the region 3000 - 6000 A and a Phillips 150 CVP photomultiplier for wavelengths in the region hOOO - 8000 A. During the experiment a Jarrell-Ash grating monochromator model 82-010 became available for use. The latter instrument had a greater resolving power than the former. The same photoelectric cells were used on the new instrument. Electronic Equipment The electronic equipment used consisted of a 0-20 kv. power supply, two variable, calibrated 0-1.5 kv. supplies for the photomultiplier tubes, a Theophanis^ trigger pulse unit and a Tektronix type 55l dual beam oscilloscope fitted with a single input preamplifier, a difference preamplifier and a Dumont trace recording camera. The outputs from the two monbchromator photomultipliers were led into cathode followers of standard design. The cathode follower outputs were led through shielded cables to the single input preamplifier on the oscilloscope. The output of the velo-city photomultipliers was led through shielded cable directly into the difference preamplifier, A small pick-up coil near the main current leads was used to trigger the oscilloscope from the main discharge current. The variable high voltage power supplies for the photo-multipliers allowed adjustment of the photomultiplier output pulses without varying the s l i t widths. Thus spectral lines of widely different intensities could be studied without varying the monochromator geometry, Camparing two spectrophotometer pulses obtained with different photomultiplier voltages required a cal i -bration to determine the dependence of response on supply voltage. - 3 0 -CHAPTER IV EXPERIMENTAL WORK Preliminary Investigation Three sets of time-integrated spectra were taken^ using f i r s t argon, then helium, and lastly a mixture of argon and helium as the ambient gas in the shock tube. The shock velocity could be changed by varying the energy stored in the capacitor bank. Ade-quate exposures resulted from ten firings of the bank. The spectra obtained were analyzed with the aid of an iron arc reference spectrum taken on the same plates. After analysis, certain lines were chosen for time-resolved studies. Choice was made on the basis of remote-ness from proximate impurity lines and i f possible, proximity to other lines of the same and adjacent spectra. At the time of the experiment there was no way to check the spectral sensitivity of the monochromators, Manufacturer's data giving spectral sensi-tivity versus wavelength for the Bausch and Lomb spectrophoto-meter were available. A subsequent experimental calibration of the monochromator-photomultiplier combinations by Simpkinson, was in reasonably good agreement with the manufacturer's values. The preliminary results showed that He I and A III lines were visible in time-integrated studies. An ambient gas of 1 part argon to 20 pa^rts helium at about hOOpressure and a bank voltage - 31 -of lh kv, were used*--- It should be noted that (in the region 2500-o 5000 A) the equipment for time-resolved studies gave a strong re-sponse to lines which were weak on the spectrograph plates. In o particular, the Hell line of wavelength U686 A gave a strong re-sponse on the monochromator, but was not visible on the spectro-graph plates. There may be several reasons for this. The ex-planation may be merely a difference in sensitivity of the two optical instruments, one responding to weaker signals than the other. Also, the shape of the time-resolved pulse is important, A reasonably intense line of short duration would give a good time-resolved signal while appearing very weak in time-integrated o studies. The line He II 1*686 A. was well separated from impurity lines. As a check, the monochromator was set to respond to this line when pure helium was the ambient gas in the shock tube. Adding a small amount (5$) of argon reduced the pulse by about $0% and when the mixture contained l\\.0% argon, the line disappeared. Several lines were chosen for time-resolved studies in the gas mixture. These lines weres He I He II A II A III 5876 A 1686 A 3388.17 A 3301.88 A 3336.13 A - 32 -The settings of the monochromators for these lines were determined by scanning the relevant spectral regions when the ambient gas was either pure argon or pure helium. This was par-ticularly necessary for A II lines, since these were almost com-pletely absent from the spectrum of the gas mixture. The lines thus located were also examined in the mixture to determine their intensities under the final experimental conditions. The presence of the H,^ impurity line in the gas mixture was also verified. The H to CD 1 I , _ f _ 1 1 — + • 1 * ~ 3j5 40 45 50 55 6 0 65 70 75 - 38 -CHAPTER V RESULTS V Determination of N from H^ Broadening The H^ profile as determined by the method described in chapter II was fitted best by the theoretical profile for ..' N o 1 0 1 7 cmT3, T = 20,000°K. The ratio - F for the best e ' o f i t was approximately 800 statvolts/cm. From F Q = 2 . 6 l e N e f f,^ N = N „ „ = 5 x 1 0 1 7 cmT3 e eix This value of N was substituted into equation (10) when solving to obtain the first approximation to kT. The value of N Q is lowered after using this value of kT.and an approximation to the populations of various ionized states to solve equations (lL) and (l£) for the second approximation to N . ( v Observed Line Intensities The intensities of the various spectral lines were assumed to be proportional to the maxima of the luminosity traces. Strictly speaking, the area under the profile when intensity is plotted against wavelength in the region of the line is the correct measure of intensity. The instantaneous line profile for a narrow line - 39 -like He I 5876 A is difficult to determine. Time-integrated spec-tra on the spectrograph plates revealed that the He I and He II lines had approximately equal widths, while the A III lines were broader than the A II lines. If i t were assumed that, at any time, the line profiles are in the same proportion as on the spectral plates, the helium intensities would not be much changed, while the A III spectrum would be weighted over the A II spectrum. As will be seen later, such a procedure would not change the nature of the conclusions arrived at from the experiment. The observed line intensities are displayed in table II, along with upper energy levels E m, and ionization energies V.^ as 17 found in Moore, Table II Multiplet 0 Line A Intensity E (ev.) m (upper level) He I (W 5876 12.8 22.97 He II V.Q » 2L.46 ev. (1) U686 6.9 50.80 A II V_ • 10,68 ev, 0 (96) 3388.5 0.3 23.53 A III -V = 27.76 ev. (1) 3311.25 5.3 25.25 ~ ho -The intensities are merely corrected values of the spectrophotometer voltage pulses at a certain supply voltage. The important quantity i s , of course, the ratio of the two helium intensities and of the two argon intensities, so actual values of the intensities are not important. The intensity values shown above were used in equation (11) to determine a value of kT for the argon and the helium spec-tra as described in chapter II. The resulting temperatures were used to determine the second approximation to kT. The following table shows the results. Table III N in cm.\"3 e kT (ev.) Argon Helium First approximation 5.1 x 1 0 1 7 3.35 3.66 Second approximation 5.0 x 1 0 1 7 3.28 3.66 The discrepancy between the final two temperatures is about 12%. - l a -Comparison With Shock Theory The method outlined in chapter II was used to calculate the values of N and kT as determined by shock theory. The ex-perimental conditions were an i n i t i a l pressure of ,375 mm. Hg at 78° F (corresponding to a total i n i t i a l particle density (n + n1) of l.hk x 10 cm. ) and a shock velocity of k.5 cm/ytf sec. The results are given in table IV. along with the spectroscopically determined values for comparison. It will be noted that kT is greater, and N smaller than the values given by the spectroscopic observations, Table IV -3 N in cm. kT (ev.) Shock theory 2.15 x 10 li.10 Spectroscopic theory Argon 5.0 x 1 0 1 7 3.28 Helium 5.0 x 1 0 1 7 3.66 CHAPTER VI CONCLUSION The two spectroscopic temperatures calculated in this thesis are equal within experimental error 10$). It should be remem-bered that there is some uncertainty in the argon spectrum, and the quoted argon temperature is probably lower than the true value. There are two reasons for thiss (1) the difference in the profiles at A II and A III lines as seen in the spectrograph platesj (2) the uncertainty due to the portion of the argon spectrum that could be observed. The only strong lines were A III lines; the A II spectrum was barely present; no sign could be found of A IV lines. If a temperature of 3.66 ev, is assumed instead of 3.28 ev, and Saha's equation used to determine ion populations for argon, the greatest percentage change in the abundance of any species is 20$ for A TV (a change from 2,1$ to 2 .5$). The value of 3.6.6 ev, for the temperature of argon would thus seem to give values com-patible with spectroscopic observations, although the A IV spec-trum should perhaps be observable at this temperature. The determining of N by H^ broadening appears to be a good technique. The line broadening theory, is not strongly de-pendent on thermal equilibrium. The time-resolved analysis used in - 10 -this work is superior to time-integrated measurement since the latter is heavily weighted by additional luminosity due to ring-ing of the circuit. The driver current associated with this apparatus is an oscillatory discharge of high frequency. This experiment measured electron level populations in an attempt to gain insights into the problem of thermal equilibrium in a plasma. The levels were found to be populated in a manner con-sistent with an assumption of thermal equilibrium. The question remains as to how accurate a method this is of checking the assump-tion. It is certainly possible, for example, that the ion temp-erature is different from the electron temperature in spite of the above mentioned results. The general nature of comparison of the shock theory and spectroscopic values of N and kT is the same as that found by Barnard et a l . The argon temperature is much lower than the shock temperature while the helium temperature is in reasonable agreement with the shock -temperature.- Had the comparisons for the gas mix-ture differed substantially from those for the pure gases used by Barnard et al, some new information regarding the mechanism pro-ducing the discrepancy might have been obtained. In view of the known non-planarity of the shock front, comparison with the stan-dard shock theory can serve at best as an approximate guide. Pre-ionization ahead of the shock may also be taking place, but i t is - i l k -d i f f i c u l t to see how t h i s mechanism would e x p l a i n the anomolous temperature s i n c e one would expect i t to cause the shock tem-pera ture to be lower than the s p e c t r o s c o p i c temperature. The methods developed i n t h i s experiment may be the be -g inn ings of a p romis ing t echn ique . Plasmas c o n s i s t i n g of m i x -tures o f gases have d e s i r a b l e spec t ro scop ic c h a r a c t e r i s t i c s , s ince observable s p e c t r a l l i n e s come from i n i t i a l l e v e l s o f w i d e l y v a r y i n g energy. A more accurate de te rmina t ion o f l e v e l popu l a t i ons than i n the case o f a pure gas i s t he re fo re p o s s i b l e , A q u e s t i o n wh ich remains to be answered i s how good a measure of the temperature of a mix tu re can be ob ta ined by s p e c t r o s c o p i c 18 measurements. T r i c h e d i scusses the s t eady- s t a t e d . c . arc spec-t r a of mix tu re s and concludes t h a t c a l c u l a t i o n s fromi such s p e c t r a w i l l l e a d to i naccu ra t e temperature de t e rmina t i ons . U n f o r t u n a t e l y h i s t reatment i s of a p u r e l y q u a l i t a t i v e nature and cannot be r e a d i l y used to assess the accuracy o f the experiment de sc r i bed i n t h i s t h e s i s . F u r t h e r work shou ld be d i r e c t e d , i n p a r t , to the processes o c c u r r i n g i n mix tu res and t h e i r e f f e c t s on l e v e l popu-l a t i o n s . Exper imen ta l i n v e s t i g a t i o n o f l i n e broadening theory may be p o s s i b l e u s i n g mix tu res of gases . S p e c t r a l da ta o f l i n e p r o -f i l e s c o u l d be ob ta ined from the emiss ion s p e c t r a of two d i f f e r e n t gases f o r which t h e o r e t i c a l l i n e p r o f i l e s have been c a l c u l a t e d . - 16 -An obvious p a i r o f gases i s hydrogen and h e l i u m . S ince the e l e c t r o n number d e n s i t y i s the same f o r bo th s p e c t r a , a comparison of t h i s q u a n t i t y u s i n g emiss ion l i n e s from the two elements should g ive the same r e s u l t s . Such work would r e q u i r e some ref inement i n the t e c h -niques of measuring the p r o f i l e s of narrow l i n e s . F u r t h e r work should i n c l u d e the r e s u l t s of c a l c u l a t i o n s from a more complete s e t of s p e c t r a l i n t e n s i t i e s . A, b e t t e r i d e a o f the c o n s i s t e n c y o f the r e s u l t s would be p o s s i b l e . The spectrum of he l ium was r a t h e r sparse under the c o n d i t i o n s o f the exper iment , and more argon l i n e s from v a r i o u s spec ies of ions would be d e s i r -a b l e . Perhaps d i f f e r e n t c a p a c i t o r energies o r gas pressures shou ld be t r i e d , as w e l l as v a r i o u s d r i v e r de s igns . I t i s somewhat d i f f i c u l t , a t t h i s s tage , to assess the v a l i d i t y of the exper iment . More s o p h i s t i c a t e d experiments might a i d i n such an assessment. The r e s u l t s are encouraging enough to i n s p i r e f u r t h e r exper imenta t ion and re f inement , and a u s e f u l technique may e v o l v e . - us -APPENDIX OSCILLATOR STRENGTHS The t a b l e o f o s c i l l a t o r s t r e n g t h s , S, g i v e n be low i s ex-t r a c t e d from the M . S c , t h e s i s of S impkinson , i n which the theo-r e t i c a l j u s t i f i c a t i o n f o r the va lues can a l s o be found . Tab le V L i n e Wavelength i n jL S He I 5876 32.9 He I I 4686 126 A I I 3388.5 9.2 A I I I 3311.25 10.8 - hi -BIBLIOGRAPHY 1, Bishop, A . S . , Project Sherwood, Doubleday, I960, chap. 1 2, Rose, D . J . , and Clark , C.., J r . , Plasmas and Control led Fusion, M . I . T . and Wiley , 1961, chap. 1 3 , Barnard, A . J . , Cormack, G .D . , and Simpkinson, W.V. , Can, Jour. Phys. UO, 531 (1962) i i . Cormack, G . D . , Ph.D. Thesis , Univers i ty of B r i t i s h Columbia, 1962 5. Sp i t ze r , L . , J r . , Physics of F u l l y Ionized Gases, In te r -science 3, 1956,pp. 76 f f . 6. Jankulak, F . J , , M.Sc. Thesis , Univers i ty of B r i t i s h Columbia, 1963 7. Griem, H.R. , Phys. Rev. , 131, 1170 (1963) 8. Condon, E . U . , and Short ley, G . H . , Theory of Atomic Spectra, Cambridge, 1935 9. Simpkinson, W.V. , M.Sc. Thesis , Univers i ty of B r i t i s h Columbia, 1961 - L8 -10. Bates, D .R. , and Damgaard, A . ? P h i l . Trans. Roy. Soc. A 2h2, 101 (1900) 11. Breene, R . G . , J r . , Rev. Mod. Phys. 29, 9k (1957) 12. Holtsmark, J . , Phys. Z e i t . 20, 162 (1919) 13. Chandrasekhar, S . , Rev. Mod. Phys. 15, 1 (I9k3) lk. Griem, H.R. , Kolb, A . C . , and Shen, K . Y . , P h y s . Rev. 116, k (1959) See also Naval Research Laboratory Report No. 51*55, I960 15. Cormack, G . D , , M,Sc. Thesis, Un ive r s i ty of B r i t i s h Columbia, I960. 16. Theophanis, G . A . , Rev. S c i . Ins t . , 31, L27 (i960) 17. Moore, Charlotte E . , A M u l t i p l e t Table of Astrophysical Interest , Nat ional Bureau of Standards, Technical Note 36, 1959 18. Tr iche , H . , C.R. Academie des Sciences, 256, No. ii,907 (1963) "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0085300"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Physics"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "An experimental investigation of equilibrium conditions in a shock plasma"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/37701"@en .