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An imploding detonation expansion laser Armstrong, Bruce Allan 1974

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AN IMPLODING DETONATION EXPANSION LASER BY BRUCE ALLAN ARMSTRONG B.Sc, University of Saskatchewan, 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THE DEPARTMENT OF PHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER, 1974 In p resent ing t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements fo 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 t h a t permiss ion for e x t e n s i v e copying o f 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 r e p r e s e n t a t i v e s . I t i s understood that copying o r 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 ga in s h a l l not be a l lowed without my w r i t t e n p e r m i s s i o n . 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 October 7 , 1 9 7 4 A B S T R A C T An imploding detonation expansion laser has been b u i l t and some preliminary work has been done to determine i t s properties. Optical and pressure measurements were per-formed both i n the detonation chamber and the nozzle. Gain measurements at CO and CO2 wavelengths were made as a function of s t a r t i n g mixture, throat height and pos i t i o n i n the nozzle. A b r i e f attempt to make the system lase was not successful. More e f f o r t w i l l be expended a f t e r repairs to the machine have been made. T A B L E O F C O N T E N T S Page ABSTRACT i i LIST OF TABLES . . . . . v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS x i CHAPTER ONE: Introduction 1 CHAPTER TWO: Theory . . . . . . . . . 5 2.1 Steady Nozzle Theory 5 2.2 Nonequilibrium E f f e c t s i n a Laval Nozzle . . . 8 2.3 Gas-Dynamical Lasers . . . . . . . . . . . . . 18 2.4 Chemical Lasers . . . . . . . . . 21 CHAPTER THREE: Machine Design, Construction and Operation . . . . . 27 3.1 Construction of the Detonation Chamber . . . . 30 3.2 The Nozzle . . . . . . . . . 33 3.3 Operation of IDEL I 35 i i i Table of Contents, continued CHAPTER FOUR: Optical and Pressure Measurements . . . 38 4.1 Detonation V e l o c i t i e s 38 4.2 Membrane Rupturing Time 41 4.3 Pressure as a Function of Time 45 4.4 Pressure as a Function of Posit i o n . . . . . . 50 4.5 Pressure as a Function of Starting Mixture . . 54 CHAPTER FIVE: Gain Measurements 56 5.1 Methods of Determining Population Inversion . 57 5.2 J i t t e r of the Probe Laser Beam 59 5.3 Results of the CO2 Gain Measurements . . . . . 63 5.4 CO Gain as a Function of Starting Mixture . . 66 5.5 CO Gain as a Function of Throat Height . . . . 70 5.6 CO Gain as a Function of Po s i t i o n . . . . . . 72 5.7 Conclusions . . . . . . . . . . 74 CHAPTER SIX: The Laser Cavity . . . . . . . . . . . . 76 6.1 Construction of the Laser Cavity . . . . . . . 76 6.2 Alignment of the Laser Cavity . . . . . . . . 78 6.3 Did IDEL I Lase? 80 CHAPTER SEVEN: Conclusions, Summary and Future Improvements . . . . . . . . . . . . . 81 iv Table of Contents, continued Page BIBLIOGRAPHY . . . . . 8 3 APPENDIX A: . . . . . . . . 85 V L I S T O F T A B L E S Page Table I Nozzle Shape 33 v i L I S T O F F I G U R E S Page Figure 1 I l l u s t r a t i o n of p r i n c i p l e s behind IDEL I . . . 3 2 Dependence of pressure, temperature and area of a c a l o r i c a l l y i d e a l gas on the Mach number. M* = 1.2 9 3 Dependence of pressure, temperature and area of a c a l o r i c a l l y i d e a l gas on the Mach number. M* = 1.8 10 4 Temperature p r o f i l e s of a diatomic gas i n a Laval nozzle 12 5 V i b r a t i o n a l modes of CO2 . . . . . . 14 6 Energy l e v e l diagram of CO2 and N 2 . « . • • • 16 7 Temperature p r o f i l e s of a mixture of C 0 2 , N 2 and H 20 i n a Laval nozzle 17 8 Temperature r a t i o s below which p a r t i a l popula-t i o n inversion for P-branch t r a n s i t i o n s are possible. T,. = maximal r o t a t i o n a l temoera-^ lim ture. The abscissa gives the r o t a t i o n a l quantum number of the lower laser l e v e l . For instance: Population inversion of the P(10) l i n e of HF i s obtained i f T ./T .. < 0.1. . . 22 v i i L i s t of Figures, continued Page Figure 9 Relative population inversion of P-branch l i n e s ( v i b r a t i o n a l quantum number of the upper state V = 1) as function of r o t a t i o n a l temperature T t . P = r o t a t i o n a l quantum number of the lower state . . . . . 23 10 Relative populations of v i b r a t i o n a l l e v e l s i n CO immediately aft e r the chemical reac-t i o n 0 + CS CO + S + 82 kcal/mole 24 11 Scheme of molecular relaxation process. The c h a r a c t e r i s t i c times shown are average values for room temperature and atmospheric pressure. 25 12 Schematic i l l u s t r a t i n g the p r i n c i p l e s of oper-ation of IDEL I 28 13 The evolution of the detonation front i n the detonation chamber . 29 14 Detonation chamber 30 15 Electrode configuration . . . . . . . . . . . 32 16 The Laval nozzle and apex of the detonation chamber 34 17 Schematic of IDEL I 36 18 Experimental arrangement used to obtain fram-ing camera photographs . . . . . 39 19 Framing camera photographs of the luminous front i n the detonation chamber and the noz-zle. . . . . . . . , . . . . 20 Experimental arrangement used to detect the influence of the membrane on the detonation front 40 42 v i i i L i s t of Figures, continued Page Figure 21 Graph showing the a r r i v a l and departure times of the detonation front referenced to the nozzle throat . . . . . . . 44 22 Traces of oscillograms of pressure as a function of time i n the detonation chamber and the noz-23 Transit times of the pressure pulse i n the de-tonation chamber and the nozzle . . . . . . . 48 24 Correlation of the pressure pulse and the lumin-ous front 49 25 Pressure as a function of po s i t i o n i n the de-tonation chamber and nozzle for d i f f e r e n t s t a r t -ing mixtures . . . . . 52 26 Schematic showing the evolution of the pressure pulse i n the detonation chamber and the nozzle 53 27 Pressure measured i n the detonation chamber at a point 6 cm from the throat as a func-t i o n of t o t a l f i l l i n g pressure and s t a r t i n g mixture 55 28 Laser gain method of determining whether a population inversion e x i s t s . . . . . . . . . 58 29 Experimental arrangement used to measure gain 60 30 Mode patterns . 62 31 Traces of oscillograms of gain measurements f o r CC>2 as a function of s t a r t i n g mixture . . . . 65 32 Traces of oscillograms of gain measurements for CO as a function of s t a r t i n g mixture . . . . 68 ix L i s t of Figures, continued Page Figure 33 Traces of oscillograms of gain measurements for CO as a function of throat height 71 34 Traces of oscillograms of gain measurements for CO as a function of p o s i t i o n i n the nozzle . . 73 35 The laser cavity . . . . „ . 77 36 Alignment system 7 9 37 The construction of the probe laser and i t s power supply 85 x A C K N O W L E D G E M E N T S I to thank Dr. Boye Ahlborn f o r suggesting and supervising the course of t h i s work and also for his a s s i s -tance with the experiment. I should l i k e to thank Paul Redfern for designing and constructing the detonation chamber and nozzle. I wish to o f f e r thanks to Dr. Shigeo Mikoshiba for his assistance with the experiment. I wish to o f f e r s p e c i a l thanks to Dr. John T u l i p of the University of Alberta for his assistance with the gain measurements and also for the discussions held with him. The loan of the CG^ and CO probe lasers from the ele c -t r i c a l engineering department of the University of Alberta i s g reatly appreciated. Thanks go to Connie f o r typing t h i s t h e s i s . F i n a n c i a l assistance from the National Research Coun-c i l i s g r a t e f u l l y acknowledged. xi - 1 -C h a p t e r 1 INTRODUCTION We believe i t possible to operate a gas-dynamical l a s e r i n which the working f l u i d i s v i b r a t i o n a l l y "hot" before i t enters the nozzle. A l l gas-dynamical lasers use a molecular gas as the working f l u i d . These molecules can be produced i n a chemical reaction which often leaves the molecules i n a v i b r a t i o n a l l y excited state. I f these excited molecules could be used as the working f l u i d entering the throat of a gas-dynamical l a s e r then much higher inversions should be obtained and higher laser powers would be achieved. This thesis describes an attempt to b u i l d and operate such a lase r which has fea-tures of gas-dynamical as well as chemical l a s e r s . In order to achieve high lase r power i n an ordinary chem-i c a l l a s e r the mass flow rate must be high, as lase r power depends on the mass flow rate into the o p t i c a l cavity m u l t i p l i e d by the number of laser quanta per unit mass. The mass flow rate i n turn depends upon the flow v e l o c i t y and density. In stan-dard chemical lasers the flow v e l o c i t y , which cannot exceed the flame v e l o c i t y , i s subsonic and the density i s far below -2-atmospheric density i n order to keep the c o l l i s i o n a l d e a c t i -vation time down. For these reasons, the power output of a chemical lase r i s small, often being below 1 watt. In order to increase the l a s e r power, the flow rate should be made supersonic and the density must be increased. Both conditions are obtained i n a detonation where the mass flow rate i s t y p i c a l l y three orders of magnitude larger than i n a flame reaction. Our mass flow rate was t y p i c a l l y . 5 kilograms per second which i s of the same order of magnitude as big gas-dynamical l a s e r s . To f a c i l i t a t e l a s i n g of the detonation, two things have to be done. F i r s t l y , one must attempt to f l a t t e n the detona-ti o n by imploding i t . The smoothing e f f e c t of imploding a detonation was previously demonstrated by Huni [1]. Secondly, i t i s advisable to expand the reaction products behind the detonation front by l e t t i n g the material flow into an expanding nozzle a f t e r the detonation has reached the apex of the con-verging channel. This provides a wider detonation front which should a l l e v i a t e problems associated with the smoothness of the front. Both these e f f e c t s are i l l u s t r a t e d i n figure 1 . This experimental arrangement expands the reaction products i n the Laval nozzle immediately a f t e r they are formed. These molecules w i l l act l i k e ordinary molecules i n a gas-dynamical laser but may s t i l l "remember" t h e i r recent chemical formation i . e . they may have a very high v i b r a t i o n a l temperature. -3-IMPL0D1N 6 DETONATION Figure 1 I l l u s t r a t i o n of p r i n c i p l e s behind IDEL 1. -4-With these considerations and hopes i n mind we started to investigate an Imploding Detonation Expansion Laser (IDEL I ) . In Chapter 2 the theory pertinent to the experiment i s discussed. Steady flow nozzle theory i s developed and used to predict pressures i n the nozzle. Non LTE nozzles and the p r i n c i p l e s behind gas-dynamical lasers are discussed i n order to show how an expansion through a Laval nozzle can produce a population inversion. In the l a s t section l i t e r a t u r e i s c i t e d to show that the products of a chemical reaction are often "inverted". In Chapter 3 the design, construction and operation of IDEL I are presented. In Chapter 4 the o p t i c a l and pressure measurements made on IDEL I are discussed. From the o p t i c a l measurements the membrane rupturing time and detonation v e l o c i t i e s are c a l -culated. Pressure measurements as a function of time, p o s i t i o n , and s t a r t i n g mixture are given. In Chapter 5 gain measurements at CO and C O 2 wavelengths are discussed. Problems encountered during C O 2 gain measure-ments and the r e s u l t s of the measurements are given. CO gain i s discussed as a function of s t a r t i n g mixture, throat height and p o s i t i o n . In Chapter 6 the mechanics of a l i g n i n g the laser cavity are presented. The r e s u l t s of the search for laser action are also given. In Chapter 7 a summary i s given along with the conclu-sions. Future improvements are discussed. -5-Chapter 2 THEORY A l l l a s ers require a population inversion of the ex-c i t e d states which i s obtainable only i n a non-equilibrium s i t u a t i o n . In t h i s l a s e r there are two mechanisms leading to a non-equilibrium s i t u a t i o n : the f a s t flow of the molecular gas through the Laval nozzle and the chemical formation of molecules i n the chemical reaction. I t would be good to know i n i t i a l l y how much population inversion can be expected. Unfortunately, a comprehensive theory of such an imploding detonation expansion l a s e r i s at present not ava i l a b l e , mainly because the chemistry of an overdriven detonation i s not known. A f e e l i n g for the magnitude of the inversion can, how-ever, be obtained by analyzing molecular nozzle flow and by discussing the inversion following a chemical reaction separately. Nozzle theory and the p r i n c i p l e s behind gas-dynamical lasers are therefore reviewed i n sections 2.1, 2.2 and 2.3, and chem-i c a l l a s e r action i s reviewed i n section 2.4. 2.1 Steady Nozzle Theory - 6 -The symbols which w i l l be used to describe steady, isen-t r o p i c i n v i s c i d flow i n one dimension of an i d e a l gas are: Y — gas constant h = enthalpy u = p a r t i c l e v e l o c i t y P = pressure a = speed of sound P - density m = mean molecular weight T = temperature M = mach number A area A symbol with no asterisk r e f e r s to conditions i n the nozzle while a symbol with an ast e r i s k r e f e r s to throat con-d i t i o n s . Conservation of energy implies: 2 2 h * + = h + -n + 2 n + 2 ( 1 ) The equation of state for a gas i s : h • F T TT <2> Also a = JZM. * m (3) -7-and u = Ma (4) Substituting the value of h from (2) into (1) and using (3) and (4) we f i n d : T* 2 + (y-1) M 2 T 2 + (y-1) M*2 ( 5 ) For an is e n t r o p i c process one has: Y p*/P = ( T * / T ) Y _ 1 (6) p*/p = ( T * / T ) r l Conservation of mass implies: A _ p *u* A* - p u (7) ( 8 ) The r a t i o s of p*/p and u*/u are now introduced with the equa-tions (7) and (4) and (5) so that we have: Y+l A _ M* lo x. / v - n M 2 \ 2 (Y-1) A* M I 2 + (y-1) M*V. Equation (9) indicates that the Mach number i n a nozzle i s a function of the area r a t i o A/A* only and f o r a p a r t i c u l a r nozzle A/A* i s of course known as a function of p o s i t i o n . Therefore, given a value of y and M**, M can be calculated t If a gas i s accelerated from a stagnant reservoir into a Laval nozzle M* = 1, but i n our case the gas i s already moving at supersonic speeds i n the detonation chamber. There i s some uncertainty i n choosing M* so two values, hope-f u l l y the upper and lower l i m i t s , were chosen. - 8 -as a function of p o s i t i o n . When M i s known then the temper-ature, pressure and density r a t i o s can be calculated using equations (5), (6) and (7) respectively. Setting y = 1.2 and 1.4 and M* = 1.2 and 1 .8 the temper-ature, area and pressure r a t i o s have been plotted as a func-tion of the Mach number (figures 2 and 3). The figures show that there i s a strong dependence of the r a t i o s on the values of y and M * . As the gas expands through the nozzle both the trans-l a t i o n a l temperature and pressure drop. The lowering of the t r a n s l a t i o n a l temperature, as w i l l be seen i n the following sections, can produce a population inversion. The use of steady nozzle theory to predict conditions i n our nozzle w i l l of course not be accurate but the general trend should p e r s i s t . 2.2. Nonequilibrium E f f e c t s i n a Laval Nozzle A molecular gas can store energy i n the form of random t r a n s l a t i o n a l motion, r o t a t i o n a l , v i b r a t i o n a l , e l e c t r o n i c e x c i t a t i o n , d i s s o c i a t i o n , and i o n i z a t i o n . Each of these modes or degrees of freedom may be characterized by a temper-ature T. , T ., T , which a l l agree i f the gas i s tran' r o t ' v i b ' ^ ^ in l o c a l thermal equilibrium. I f the gas i s temporarily d i s -turbed, by extracting some energy out of any one of these - 9 --10--11-modes, i t w i l l take some time and require a number Z of gas k i n e t i c c o l l i s i o n s u n t i l a new equilibrium i s obtained. E q u i l i b -rium i s reached quickly within rotation and t r a n s l a t i o n by themselves, since Z = Z. = 1 - 1 0 [2-4]. Energy ex-rou tran change between these two degrees of freedom i s also very rapid, with Z t_ r = 10 - 100 c o l l i s i o n s [2-4]. E q u i l i b r a t i o n between t r a n s l a t i o n and v i b r a t i o n , however, takes much longer. Num-2 7 bers of Zfc v~= 10 - 10 are quoted [2-4] . Thus v i b r a t i o n a l energy can be i s o l a t e d from r o t a t i o n a l and t r a n s l a t i o n a l energy for some time. I f , for instance, a diatomic molecular gas i s expanded i n a Laval nozzle, the t r a n s l a t i o n a l and r o t a t i o n -a l temperatures are r a p i d l y lowered while the v i b r a t i o n a l temperature nearly maintains i t s i n i t i a l value. This e f f e c t i s i l l u s t r a t e d i n f i g u r e 4. I t w i l l be shown in section 2.3 that i f T ., > T . a v i b r o t p a r t i a l population inversion i s produced. These nonequilibrium e f f e c t s , i n the case of CO, can be enhanced by the addition of Ar and N 2. A further lowering of the t r a n s l a t i o n a l temperature may be accomplished using s t r i c t l y thermodynamic e f f e c t s by adding to the CO large f r a c t i o n s of a monatomic gas to increase the e f f e c t i v e gas constant y. Argon i s p a r t i c u l a r l y suitable for t h i s purpose because, as a heavy c o l l i s i o n partner, i t also reduces the rate of v i b r a t i o n a l energy loss to t r a n s l a t i o n through V-T c o l l i s i o n s . MacKenzie [5] has calculated and - 1 2 -DISTANCE FROM THROAT F i g u r e 4 Temperature p r o f i l e s o f a d i a t o m i c gas i n a L a v a l n o z z l e . demonstrated the e f f e c t i v e n e s s of Ar f o r enhancing the l a s e r power o f a gas-dynamic CO l a s e r . Another n o n e q u i l i b r i u m e f f e c t important t o CO l a s e r s i s the exchange of v i b r a t i o n a l energy from N 2 to CO. Because n i t r o g e n i s a homonuclear d i a t o m i c molecule, m o l e c u l a r n i t r o -gen e x c i t e d t o v a r i o u s v i b r a t i o n a l l e v e l s of the e l e c t r o n i c ground s t a t e cannot decay r a d i a t i v e l y and i s t h e r e f o r e extremely l o n g l i v e d . Through c o l l i s i o n s the e x c i t e d N 2 t r a n s f e r s i t s energy to the v i b r a t i o n a l s t a t e s of CO. By expanding a mix-ture of CO and N~ through a L a v a l n o z z l e , the v i b r a t i o n a l -13-temperature of the CO remains higher than i t would i f i t was expanded alone, since the N 2 acts as a v i b r a t i o n a l energy reservoir. MacKenzie [5] has calculated and demonstrated the effectiveness of N 2 i n lengthening a CO l a s e r pulse. In Ar d i l u t e d mixtures the continued addition of N 2 enhances laser power only s l i g h t l y u n t i l the remaining CO content becomes too small and laser power decreases [5]. The ineffectiveness of N 2 addition to Ar d i l u t e d mixtures i n -dicates that the several hundred c o l l i s i o n s that occur between N 2 and CO molecules during the short period i n which they flow through an o p t i c a l cavity are not adequate to transfer any s i g n i f i c a n t amount of N 2 v i b r a t i o n a l energy to the expended CO laser states [5]. This completes the discussion of nonequilibrium e f f e c t s i n diatomic molecules. There i s , however, another nonequili-brium e f f e c t which can occur i n a polyatomic molecule as they have two or more v i b r a t i o n a l degrees of freedom which do not have to be i n equilibrium with each other. The C 0 2 molecule i s a good example. However, to understand the d e t a i l s we have f i r s t to give a b r i e f d e s c r i p t i o n of the C0 2 energy l e v e l s . Carbon dioxide being a triatomic l i n e a r symmetric molecule has three degrees of v i b r a t i o n a l freedom: the symmetric stretch (vj) (figure 5a), the bending mode ( V 2 ) (figure 5b) and the asymmetric stretch ( V 3 ) (figure 5c). -14-(a) o SYMMETRIC STRETCH (V.OO) (b) BENDING (ov/o) (c) ASYMMETRIC STRETCH (OOH) Figure 5 V i b r a t i o n a l modes of co 2. The molecule can vibrate i n more than one mode at the same time and can possess more than one quantum of v i b r a t i o n a l energy i n each mode. The v i b r a t i o n a l l e v e l s are normally designated by four numbers representing the number of v i b r a -t i o n a l quanta associated with each mode and written i n the form (vi v2 V 3 ) . The number %, which represents the number of quanta of angular momenta associated with the bending mode, w i l l not concern us. The (001) •*• (100) v i b r a t i o n a l r o t a t i o n a l t r a n s i t i o n s produce in f r a r e d r a d i a t i o n near 10.6 microns and the (001) -»• (020) t r a n s i t i o n s produce in f r a r e d r a d i a t i o n near 9.6 microns. -15-Anderson [6] and T u l i p and Sequin [7] have considered the expansion of a hot mixture of C0 2, and H20 through a Laval nozzle. They assumed the molecular model shown i n f i g -ure 6. There i s an extremely f a s t , near resonant v i b r a t i o n a l energy exchange between the V = 1 l e v e l of N 2 and the (001) l e v e l of C0 2 as well as a very fast exchange between the (100) and (020) l e v e l s of C0 2 due to Fermi resonance [8]. In addition, v i b r a t i o n a l energy i s ra p i d l y transferred among the lower excited states of the degenerate mode V 2 i n CC»2 due to the nearly equal spacing of these l e v e l s . Hence, these f a s t t r a n s i t i o n s appear to j u s t i f y a v i b r a t i o n a l model which groups the p a r t i c i p a t i n g l e v e l s into two modes (modes I and II i n figure 6) which are assumed to be i n equilibrium within themselves but not with each other. The authors of [6] and [7] have calculated that when a mixture of C0 2, N 2 and H 20 i s expanded through a Laval nozzle, a nonequilibrium s i t u a t i o n a r i s e s as shown i n figure 7 . Their r e s u l t can be understood p h y s i c a l l y i f i t i s r e a l i z e d that excited N 2 has a long l i f e t i m e since r a d i a t i v e t r a n s i -tions are forbidden and therefore acts as a v i b r a t i o n a l energy reservoir for the (001) l e v e l of C0 2. Thus, Tj does not equ i l i b r a t e with T t r a n during the time the gas takes to pass through the nozzle. However, as emphasized i n [8], the e q u i l i b r a t i o n of Mode I with Ti_r_tn i s enhanced by the presence of H 90 i n the mixture -16-2 0 0 0 cm-1 u cc UJ m JL => Z U l > 3C 1000 cm*1 MODE TJ MODE I (001) (V=1) 23&9.3cm-1 2329.7 c m - 1 (000) Y (ooo) (ooo) I COa(ya) C0 2(r 3) Figure 6 Energy l e v e l diagram of CO,, and N 2 « -17-F i g u r e 7 Temperature p r o f i l e s o f a mixture o f C0 2/ N 2 and H 20 i n a L a v a l n o z z l e . as the (010) l e v e l o f C0 2 i s q u i c k l y depopulated by c o l l i s i o n s w i t h H 20. The r e l a x a t i o n o f the v i b r a t i o n a l energy of H 20 i s very r a p i d as i t s energy i s transformed i n t o t r a n s l a t i o n a l energy by c o l l i s i o n w i t h o t h e r water molecules owing to the l a r g e a t t r a c t i o n f o r c e s due to the d i p o l e - d i p o l e i n t e r a c t i o n of the H 20 m o l e c u l e s . These n o n e q u i l i b r i u m e f f e c t s l e a d to a p o p u l a t i o n i n v e r -s i o n , t h a t i s , the upper l a s e r s t a t e (mode I ) has a h i g h e r -18-number density than the lower laser states (mode I I ) . Some sample population inversions have been calculated i n [6] and [ 7 ] , Although these c a l c u l a t i o n s were done for reservoir tem-peratures of less than 2000°K and the temperature i n our deton-ation chamber i s much higher, the general trend hopefully would p e r s i s t . 2.3 Gas-Dynamical Lasers In section 2.2 we showed how nonequilibrium e f f e c t s could produce a s i t u a t i o n i n which the v i b r a t i o n a l temperature was greater than the r o t a t i o n a l temperature. In t h i s section, we s h a l l show how t h i s condition pro-duces a population inversion. Molecular lasers operating on v i b r a t i o n a l r o t a t i o n a l t r a n s i t i o n s require e i t h e r a complete or p a r t i a l population inversion. In the f i r s t case the number of molecules i n the upper v i b r a t i o n a l state N v i s larger than the number N ' i n the lower laser state. In the second case inversion i s only present for c e r t a i n t r a n s i t i o n s such that N _ > N ' ' while v,J v ,J there i s no inversion for other l i n e s of the same and other bands, and i n p a r t i c u l a r N v < N v'. Such a p a r t i a l population inversion i s found i n molecular gases with high v i b r a t i o n a l -19-temperature and low r o t a t i o n a l temperature. The p r i n c i p l e may be e a s i l y understood i n the l i m i t i n g case where T r Q t •* 0 and T ., > 0. In t h i s case the molecules i n a l l v i b r a t i o n a l vib states have the r o t a t i o n a l quantum number J = 0 so that the lower state for the P(l) l i n e s (with J = 0 -*• J = 1) i s com-pl e t e l y empty. The population of the J-th r o t a t i o n a l l e v e l ( r o t a t i o n a l energy F(J)) within the V-th v i b r a t i o n a l l e v e l ( v i b r a t i o n a l energy G(V)) i s given by (10)[9], = H Q ^ T e x p 1 T T l T - ^ T ^ / ; ( 1 0 , where N i s the t o t a l number of molecules and Q and Q_ are v J the v i b r a t i o n a l and r o t a t i o n a l p a r t i t i o n functions and g_ = J 2J + 1 i s the s t a t i s t i c a l weight of the l e v e l . The p a r t i t i o n functions are approximated as usual. 00 -he Q v = 1 + I exp 2£ G(V) V N=l (11) k T . n - rot Q J " h B. g f-hc /G(V) F(J) 0 The v i b r a t i o n a l and r o t a t i o n a l energies can be given as: G(V) = (W V - X W V 2) = W V e e e e F(J) = B e J (J + 1) (12) where B e, Wfi and X e are spectroscopic constants [9]. We -20-assume that the temperatures T ., and T . are defined i n -^ vib rot dependently and are not equal. Minimum requirement for laser emission i s that a v i b r a t i o n a l r o t a t i o n a l population inver-sion e x i s t s . - V 2 1 . i N > 0 (13, The prime refers to the lower laser state, thus for P branch tr a n s i t i o n s (AJ = +1 i n emission) v' •*• v - 1 and J ' -*- J + 1. By s u b s t i t u t i n g (10) into (13) one obtains for the r e l a t i v e population inversion: A N v J N g r (he /G(V) F(J) \" = b~o~ l e x p i " X IT + T / " y v u J L "vib -rot'-/ . ( he /G(V-l) F (14) (J+l)'~ ' 1 1 exp r o t Obviously to make t h i s expression p o s i t i v e the expres-sion i n the brackets has to be p o s i t i v e . With some rearrange-ment a l i m i t i n g condition for a population inversion i s ob-tained as f i r s t proposed by J.C. Polanyi [9]. T . AF(J) B T = T~^- mm = 2 ( J + 1 ) VT <15> For a given molecule B /W i s a constant so that the e e temperature reduction x necessary to reach the threshold of inversion depends l i n e a r l y on the r o t a t i o n a l quantum number -21-J. Inversion i s p o s i t i v e below the threshold l i n e s x = 2(J+l)B e/W e given i n figure 10 for several molecules. Of course only the ordinates of integer numbers J have physical meaning. Figure 9 [10] gives the r e l a t i v e population inversion AN/N as a function of the r o t a t i o n a l temperature T r Q t f o r several l i n e s of the P branch of HF . The v i b r a t i o n a l quantum number of the upper laser i s 1 and an i n i t i a l tem-perature of T v ^ b = 5000°K i s used. 2.4 Chemical Lasers In section 2.2 i t was assumed that the s t a r t i n g stagna-ti o n temperature was i d e n t i c a l for v i b r a t i o n and r o t a t i o n , however, t h i s need not be so. G. Hancock et. a l . [11] have done i n f r a r e d emission studies of the reaction O + CS -*• CO* + S + 82 kcal/mole and found that i n i t i a l l y about 85% of the a v a i l a b l e energy appears as v i b r a t i o n a l energy i n the CO product. Figure 10 gives the r e l a t i v e v i b r a t i o n a l population densities imme-dia t e l y a f t e r reaction. Other reactions have been studied and s i m i l a r r e s u l t s found [12 - 15]. - 2 2 -1 2 3 4 5 6 7 8 9 1 0 Figure 8 Temperature r a t i o s below which p a r t i a l population inversion for P-branch t r a n s i t i o n s are possible. T.. = maximal r o t a t i o n a l tenroerature. The ab-lim s c i s s a gives the r o t a t i o n a l quantum number of the lower l e v e l . For instance: Population inversion of the P(10) l i n e of IIF i s obtained i f T r o t / T v i b i O- 1-Figure 9 R e l a t i v e p o p u l a t i o n i n v e r s i o n of P-branch l i n e s ( v i b r a t i o n a l quantum number of the upper s t a t e V = 1) as f u n c t i o n of r o t a t i o n a l temperature T . P = r o t a t i o n a l quantum number of the l£wer s t a t e . -24-a u ui m z i 1 2 Z = 10 z < Cf < z o < cc CD 8 2 4 P O P U L A T I O N D E N S I T Y Figure 10 Relative populations of v i b r a t i o n a l l e v e l s i n CO immediately a f t e r the chemical reaction O + CS -*• CO* + S + 82 kcal/mole. This t o t a l population inversion does not l a s t long but soon relaxes into a p a r t i a l population inversion. Typical relaxation times are given i n figure 11 [2]. This s i t u a t i o n implies a rather high v i b r a t i o n a l tem-perature. For instance, Foster and Kimbell [16] found T ^ = 25000°K for CO molecules generated i n the reaction of oxygen and carbon disulphide. -25-I RELAXATION TIME;— |^  Chemical r e a c t i o n T o t a l i n v e r s i o n P o s s i b l e d i s e q u i l i b r i u m i n v i b r a t i o n , r o t a t i o n , t r a n s l a t i o n | R+R, T-*T, R-*T P a r t i a l i n v e r s i o n R e l a x a t i o n w i t h i n each degree of freedom but s t i l l n onequilibrium between v i b r a t i o n and r o t a t i o n / t r a n s l a t i o n Total relaxation F i g u r e 11 Scheme o f m o l e c u l a r r e l a x a t i o n p r o c e s s . The c h a r a c t e r i s t i c t i m e s shown a r e average v a l u e s f o r room t e m p e r a t u r e and a t m o s p h e r i c p r e s s u r e . -26-Under such conditions r o t a t i o n a l cooling i n a Laval nozzle can either improve the e x i s t i n g p a r t i a l inversion or create the inversion i f ^ X Q t i s too high i n i t i a l l y to permit l a s i n g . Many CO chemical lasers have been b u i l t i n previous years [17 - 21] but a l l of these are low power, the largest being about 2kw. This i s due l a r g e l y to the low mass flow rate as the density i s low and the v e l o c i t y of the chemical reactants i s subsonic. Our design t r i e s to overcome the low mass flow rate by increasing the pressure to over 10 atm and making the flow supersonic. These and other considerations w i l l be expanded upon i n chapter 3. -27-Chapter 3 MACHINE DESIGN, CONSTRUCTION AND OPERATION The plan to enhance the inversion of a gas-dynamical laser by chemical nonequilibrium led to a machine design which i s described i n t h i s chapter. The apparatus should have the following features: 1. I t should generate a detonation front which i s plane over the length of the laser c a v i t y . 2. This detonation front should be ra p i d l y admitted into the expansion nozzle i n the i n t e r i o r of the laser cavity. The reason for 1. i s that i f the detonation i s not planar or homogeneous across the laser cavity axis, l a s e r action w i l l be i n h i b i t e d . The reason for 2. involves the freshly formed reaction products. If they are not emitted quickly into the laser cavity, the population inversion w i l l have had time to relax. These features are i l l u s t r a t e d i n figure 12. -28-Figure 12 Schematic i l l u s t r a t i n g the p r i n c i p l e s of operation of IDEL I . One method of achieving a plane detonation front i s to implode i t [1]. I f a rather plane detonation front can be produced over the e n t i r e area at region A shown i n figure 12, then a plane detonation front should be produced some time l a t e r at the entrance to the nozzle. This i s i l l u s t r a t e d i n figures 13(c), 13(d) and 13(e). Previous experiments i n our laboratory had shown that i f a small detonation front was produced at region B i n figure 13, i t would expand as the plenum chamber expanded u n t i l i t f i l l e d the entire area at region A. Figure 13 The e v o l u t i o n of the detonation f r o n t i n the detonation chamber. -30-3.1 Construction of the Detonation Chamber With the considerations of the previous section i n mind, the detonation chamber as shown i n figure 14 was designed and constructed by Paul Redfern. Figure 14 Detonation chamber The detonation chamber i s constructed of 1/4" s t e e l plate welded together. I t i s b u i l t i n two sections which bo l t together by means of flanges at the point of largest area. I n i t i a l l y we believed that the 1/4" s t e e l plates of the detonation chamber should be strong enough to withstand the -31-pulse loading of the detonation. However, afte r about 50 f i r i n g s the plates of the converging sections near the nozzle entrance had bulged outwards about 5 mm. To strengthen t h i s section, 3/4" s t e e l plates were welded to i t both on the top and the bottom. For the i n i t i a t i o n of the detonation a 1.6 juF capacitor was charged to 18 kv using a Sorensen 1-2Okv, 30 mA power supply. The capacitor, switched by a spark gap, was discharged through two electrodes which were i n t e r i o r to the detonation chamber at region B. The i n i t i a t i o n of the detonation was more d i f f i c u l t than anticipated. When using the electrode configuration i n figure 15(a) the a r r i v a l times of the luminous fronts at the nozzle varied from .6 msec to > 10 msec. Such a v a r i a -tion indicated that the detonation was not spontaneously i g -nited and sometimes not i g n i t e d at a l l . The next s t a r t i n g system had the electrodes protruding into the detonation chamber s i m i l a r to a spark plug i n an i n t e r n a l combustion engine (figure 15(b)). This design, although an improvement, was not yet s a t i s -factory. In order to launch a detonation one must create a shock of a v e l o c i t y larger than the detonation v e l o c i t y . The f i n a l l y used electrodes (figure 15(c)) had a small c a v i t y around them which helped to amplify the shock strength of the i n i t i a l spark. -32-Figure 15 E l e c t r o d e c o n f i g u r a t i o n . -33-3.3 The Nozzle An expansion nozzle cast from aluminum was bolted to the detonation chamber as shown i n figure 16. The shape of the nozzle i s given i n table I . DI S T A NC E FROM T H R O A T (cm) 1 2 3 4 5 6 7 9 11 13 15 18 HEIGHT OF N O Z Z L E (cm) 1.0 1.8 2.6 3.3 3.8 4.2 45 4.9 5.2 5.4 5.5 5.6 Table I Nozzle shape The vacuum seal between the nozzle and detonation chamber was made with "viton" gaskets so as to minimize the d e t e r i o r -ating e f f e c t of the hot gases. The gases from the detonation chamber entered the nozzle through a s l i t of width 20 cm and height v a r i a b l e from 0 to .80 mm. The nozzle height adjustment was accomplished by ex-tending the detonation chamber so that the converging plates came closer together. This method has the e f f e c t of imploding the detonation more i f the nozzle height i s made smaller which has a deleterious side e f f e c t i n that i t raises the tempera-ture of the detonation front leading to a shorter relaxation time of the v i b r a t i o n a l e x c i t a t i o n . PLEXIGLASS PLATE Figure 16 The L a v a l nozzle and apex o f the detonation chamber. -35-The sides of the nozzle and the apex of the detonation chamber were covered with 3/4" l u c i t e so that o p t i c a l measure-ments could be made on the detonation front. The l u c i t e plate covering the nozzle had f i v e 1/2" diameter ports located at 1.3, 5.1, 8.9, 12.7 and 2 0.3 cm downstream as measured from throat so that the detonation front could be studied through infrared transmitting windows at d i f f e r e n t times during i t s evolution. Due to cracking of the l u c i t e p l a t e , i t proved impossible i n t h i s work to use the port c l o s e s t to the throat. The gases a f t e r leaving the nozzle entered a c y l i n d r i c a l dump tank of volume 550 l i t r e s . This dump tank could be iso l a t e d from the nozzle by means of a s l i d i n g plate valve. Figure 17 i s an i l l u s t r a t i o n of the complete system ex-cluding dump tank. 3.4 Operation of IDEL I For the operation of the device a .001" thick mylar mem-brane was i n s t a l l e d between the nozzle and the detonation chamber i s o l a t i n g them from each other. The enti r e system was then evacuated to below 2 t o r r and then the detonation chamber was f i l l e d with t y p i c a l l y 50 t o r r C 2H 2, 100 tor r 0 2, 100 tor r CO~. This s t a r t i n g mixture was then detonated and Figure 17 Schematic of IDEL I. -37-the detonation f r o n t would t r a v e l to the other end of the chamber i n about .6 msec and rupture the membrane. The deton-a t i o n products would then enter the nozzle and supposedly have a p o p u l a t i o n i n v e r s i o n . For the next shot, the membrane was rep l a c e d and the procedure repeated. - 3 8 -Chapter 4 OPTICAL AND P R E S S U R E M E A S U R E M E N T S Before venturing into extensive gain measurements of the f l u i d i n IDEL I the properties of the flow had to be known. For t h i s purpose the luminous front i n the converging and diverging section was studied and pressures were measured as a function of p o s i t i o n , time, and s t a r t i n g mixture. A framing camera and two photo diodes were used to measure detonation v e l o c i t i e s and the membrane rupturing time (figure 18) . 4.1 Detonation V e l o c i t i e s From framing camera photos (figure 19) i t was possible to determine the v e l o c i t y of the leading edge of the detona-tion front i n both the detonation chamber and the nozzle Knowing the time between each frame and the distances involved, the v e l o c i t y of the leading edge i n the detonation Figure 18 Experimental arrangement used to o b t a i n framing camera photographs. chamber was c a l c u l a t e d to be 2 ± .2 km/sec w h i l e i n the n o z z l e i t was 2.5 ± .2 km/sec. The v e l o c i t y of the t r a i l i n g edge of the detonation f r o n t i n the nozzle was 2.2 ± .2 km/sec so t h a t the f r o n t expanded as i t t r a v e l l e d through the n o z z l e . 4 0 -qure 19 Framing camera photographs c f the luminous f r o n t i n t h e d e t o n a t i o n chamber a n d t h e nozzle. -41-The v e l o c i t y of the detonation front was not constant from shot to shot but varied about ± .4 km/sec from the values stated above. The detonation v e l o c i t y was probably a function of how well the detonation was started and how homogeneously the gas was mixed. This would depend on how well the s t a r t i n g mixture was mixed. No s p e c i a l attention was paid to the amount of time given to mixing. The detonation v e l o c i t y was measured as a function of sta r t i n g mixture but no dependence was found. The accuracy of the v e l o c i t y measurements of ± .2 km/sec was not s u f f i c i e n t to allow a measurement of any weak dependence. This experimental accuracy was due to the uncertainty i n determining the p o s i t i o n of the somewhat fuzzy edge of the detonation front on the framing camera pi c t u r e s . The detonation v e l o c i t i e s were measured independently using two photo diodes and also two pressure probes. The re s u l t s were consistent with each other. The detonation v e l o c i t i e s were lower than what was ex-pected from [1]. At t h i s time no explanation has been found. 4.2 Membrane Rupturing Time It i s important to know the membrane rupturing time for i f the detonation front stagnates at the membrane too long, - 4 2 -the f r e s h l y formed molecules w i t h t h e i r chemical i n v e r s i o n w i l l have a chance to r e l a x . This w i l l , of course, hinder l a s e r a c t i o n . To determine the membrane r u p t u r i n g time, two sets of osc i l l o g r a m s were taken under i d e n t i c a l c o n d i t i o n s except f o r the presence of a membrane ( f i g u r e 2 0 ) . PHOTO DIODES VALVE TO DUMP TANK CLOSED A B GAS FLOW DETONATION CHAMBER NOZZLE FRAMING CAMERA Figure 2 0 Experimental arrangement used to de t e c t the i n f l u e n c e of the membrane on the detonation f r o n t . - 4 3 -In both cases the throat height was .80 mm and the same st a r t i n g mixture was used. The valve separating the nozzle and the dump tank was closed so that the dump tank would not be f i l l e d with the s t a r t i n g mixture. F a i l u r e to close the valve would lead to a premature termination of the experiment and possibly the experimenter. The former part was sometimes tempting. The f i r s t set of oscillograms was made with no membrane present. The time taken to t r a v e l from A to B (figure 2 0 ) was recorded by the photo diodes. The framing camera recorded the shape of the front and also gave a check on the photo diodes. The second set of oscillograms was taken with a membrane present but with a ti n y hole i n i t to allow the s t a r t i n g mixture to f i l l the nozzle as i t did when no membrane was present. The photos of the second set taken by the framing camera were indistinguishable from the photos of the f i r s t set. The time taken to t r a v e l from A to B as measured by the photo diodes was the same for both s e t s . The l i g h t i n t e n s i t y recorded by the photo diodes does not r i s e very quickly so that the accuracy of the measure-ments i s not better than ± 5 microseconds. Therefore, we only concluded from these measurements that the membrane rupturing time was less than 5 microseconds. A second estimate was obtained by c a l c u l a t i n g the time of a r r i v a l and time of departure of the detonation front from -44-t h e t h r o a t . I t was n e c e s s a r y t o assume a d e t o n a t i o n v e l o c i t y i n t h e d e t o n a t i o n chamber so t h i s e s t i m a t e a l s o has e r r o r . The r e s u l t i s d e p i c t e d i n f i g u r e 2 1 . . 4 ui ° X © 0) © Average " p a t h " o f in c o m i n g d e t o n a t i o n Slow p a t h o f in c o m i n g d e t o n a t i o n F a s t p a t h o f in c o m i n g d e t o n a t i o n Average p a t h o f d e p a r t i n g d e t o n a t i o n F a s t e s t p a t h o f d e p a r t i n g d e t o n a t i o n _ I L i r 8 12 16 DISTANCE FROM THROAT (cm) F i g u r e 21 Graph showing the a r r i v a l and d e p a r t u r e t i m e s o f t h e d e t o n a t i o n f r o n t r e f e r e n c e d t o t h e n o z z l e t h r o a t . -45-The membrane rupturing time as estimated from figure 21 i s probably less than 3 psec. As a further check, aluminum f o i l and Saran Wrap were used as membranes. The framing camera photos and photo diode oscillograms were i d e n t i c a l to those when mylar was used as a membrane. As no differences i n membranes were detected, mylar was used as i t was the easiest to change. 4.3 Pressure as a Function of Time The flow parameters such as density, pressure, tempera-ture and Mach number i n a supersonic nozzle depend only on the r a t i o of the nozzle area to throat area i f the flow i s steady. In t h i s experiment, however, a step wave tr a v e l s into the nozzle so that one cannot assume that the flow conditions are known. For that reason i t was undertaken to measure one of the flow parameters, namely the pressure, as a function of time, p o s i t i o n and s t a r t i n g mixture. Further, the pressure was correlated with o p t i c a l measurements to determine whether the luminous front and pressure pulse arrived simultaneously. Celesco pressure probes model LD-25 were used to measure the pressure i n the detonation chamber and nozzle. The pressure probe i n the detonation chamber was mounted 6 cm upstream from the throat i n the plate which covered the -46-port. The probe's face was f l u s h with the side of the de-tonation chamber. The bottom trace of figure 22 shows a t y p i c a l trace of the pressure signal from the detonation chamber. The oscilloscope was triggered by the noise of the spark gap so the .6 msec before any sign a l appears was the time taken for the detonation front to t r a v e l the length of the detonation chamber. The upper trace of figure 22(b) i s the portion of the pressure pulse that was i n t e n s i f i e d i n the bottom trace. The pressure rose quickly to a constant value and 70 usee l a t e r rose again to almost twice the i n i t i a l value. The i n i t i a l r i s e was caused by the a r r i v a l of the detonation front while the second r i s e was caused by the shock r e f l e c t e d o f f the throat. The pressure was measured simultaneously i n the detonation chamber and the nozzle at a point 1.3 cm downstream from the throat (figure 22(a)). The pressure i n the detonation chamber (bottom trace) rose and f e l l many times as the gas "sloshed" back and fo r t h . In the nozzle (top trace) the pres-sure rose sharply when the detonation front arrived and then again 1 msec l a t e r when the f i r s t "slosh" arrived back at the throat. The second r i s e i n pressure ( f i r s t slosh) proved in t e r e s t i n g when the gain measurements were made. The pressure in the nozzle rose and f e l l many times but a f t e r about 5 msec did not coincide with the pressure r i s e i n the detona-tion chamber. - 4 7 -z> (A in tu a: a. NOZZLE AT X = 1.3 cm DETONATION CHAMBER DETONATION CHAMBER 1 ^ y j ^ f ^ [ ^ ^ 100mv/div 1 msec/div TIME 5 v/div n -I < z 5 v/div 50// sec/div 200/<sec/div Figure 2 2 Traces of oscillograms of pressure as a function of time i n the detonation chamber and the nozzle, The pressure measurements were c o r r e l a t e d w i t h the framing camera photos as f o l l o w s : F i r s t the a r r i v a l times of the luminous f r o n t a t v a r i o u s p o s i t i o n s i n the nozzle were obtained d i r e c t l y from framing camera photos such as those i n f i g u r e 19. The departure of the luminous f r o n t from the t h r o a t -48-was chosen to be t = 0. The path of the luminous front through the nozzle i s i l l u s t r a t e d i n figure 24. Then for determining the a r r i v a l time of a pressure pulse at some pos i t i o n i n the nozzle the arrangement shown i n figure 23 was used. T R A N S I T TIME FROM PRO BE A TO T H R O A T T R A N S I T TIME PROM T H R O A T TO POSITION OF P R O B E B \ N O Z Z L E DETONAT ION C H A M B E R titrm P R E S S U R E P R O B E A M E M B R A N E RUPTURING TIME /////// i TRANS IT TIME * 4 FROM N O Z Z L E • WALL TO PROBE P R E S S U R E PROBE B Figure 23 Transit times of the pressure pulse i n the detonation chamber and the nozzle. Pressure probe A triggered an oscilloscope and pressure probe B si g n a l l e d the a r r i v a l of the pressure pulse at i t s position i n the nozzle. The t r a n s i t time, which w i l l be ca l l e d t , from probe A to probe B was determined from the -49-1 0 0 H 0 4 8 12 16 DISTANCE MEASURED FROM THE THROAT (cm) Figure 24 C o r r e l a t i o n of the pressure pulse and the luminous f r o n t . -50-oscillogram. by The wanted reference time i s t^ which i s related to t t 3 = t - ( t x + t 2 + t 4 ) (15) t^ i s accurate only to about 10 usee as there i s un-certainty i n a l l the terms on the R.H.S. of (15), The uncertainty i n t i s due to the rather slow r i s e of the pressure downstream i n the nozzle. t ^ was calculated assuming a detonation v e l o c i t y of 2 ± .4 km/sec. t 2 , as mentioned i n section 2.2, could range from 0 to 3 usee. As the probe's reach was too short, i t was necessary to recess i t .8 cm from the nozzle's inside wall. t^ could be calculated i f the speed at which gas flowed into the side arm was known. This speed should range between the l o c a l sound speed and the detonation v e l o c i t y . I t was a r b i t r a r i l y assumed to be 1000 ± 500 msec. The r e s u l t s of the c o r r e l a t i o n are shown i n figure 24. 4.4 Pressure as a Function of Posi t i o n In t h i s section, the peak pressures i n the nozzle w i l l be compared to the values predicted by the steady nozzle -51-theory. I t i s not expected that they w i l l be the same as our flow i s unsteady. We wish only to see i f the general trend i s followed. If the pressure at some point upstream of the nozzle throat i s known then the pressure at the throat can be c a l -culated using [1]. This pressure must then be doubled to give the true pressure as the theory i n [1] does not include the e f f e c t of a r e f l e c t e d shock wave. Knowing the throat pressure, the pressure i n the nozzle can be calculated as a function of p o s i t i o n using the theory i n section 2.1. The calculations were done for a detonation chamber s l i t height of 1.25 mm, a nozzle throat height of .80 mm, y = 1.2 and M* = 1.2 Two series of measurements were made using d i f f e r e n t s t a r t i n g mixtures with pressures being measured at one point i n the detonation chamber and at four points i n the nozzle. The r e s u l t s are shown i n figure 25. The experimental values are represented as points while the theory i s represented by s o l i d curves. The error bars are the maximum and minimum pressures measured for d i f f e r e n t shots. Figure 26 traces schematically the evolution of the de-tonation front as i t tr a v e l s from the detonation chamber into the nozzle. The pressure r i s e i n the detonation chamber i s very quick Figure 25 Pressure as a function of p o s i t i o n i n the detonation chamber and nozzle for d i f f e r e n t s t a r t i n g mixtures. - 5 3 -1 1 1 1 i> 1 1 1 1 WW I'.'i'i1!1! l H 1 1 1 1 ' I I I 11 i < " " ' i 1 , 1 , 1 1 1 1 1 1 1 1 i H i " ' . ' I - I 1 ! ' I ' I M ' I l> 1 I I 1 1 1 > I 1 1 ' I' " " 1 1 1 • ! • 1;! 11; I; 1; I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 • • i * •11 * i * i * i 11' 1 11 ' i1111 •ill's'!'!' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 , 1 1 1 1 1 i I I i ' 11 1 1 1 1 1 > 1 1 1 1 * • I ! I ! ! ! I ! ! ' ' ' ! i fill! i " INCOMING DETONATION X=0 Figure 26 Schematic showing the evolution of the pressure pulse i n the detonation chamber and the nozzle. -54-(< lysec) while i n the nozzle the r i s e i s slower, varying from 5 to 2 0 ysec depending on p o s i t i o n . As the luminous front expanded i n the nozzle the pressure pulse broadened also. A s i m i l a r type of expansion i s known from unsteady nozzle flow [22]. 4.5 Pressure as a Function of S t a r t i n g Mixture In an e f f o r t to investigate the detonation process f u r -ther, the pressure i n the detonation chamber was measured as a function of the s t a r t i n g mixture (figure 27). When using a r a t i o of C 2H 2:0 2 of 1:1, the pressure asso-ciated with the detonation f r o n t was l i n e a r with f i l l i n g pres-sure . When the oxygen content was r a i s e d , the pressure increase was small. The mixture of 40 t o r r C 2H 2:160 0 2 produced a pressure r i s e of only 14% compared to 40:40 although the num-ber density was raised 150%. This indicates that the trans-l a t i o n a l temperature was lowered by a factor of about 2. When N 2 was added to a mixture of 40:120 the pressure rose but not l i n e a r l y with f i l l i n g pressure. The mixture of 40:120:160 produced a pressure 55% higher than the 40:120 mixture. Above 160 t o r r of N 2 the detonation pressure appeared to l e v e l o f f although t h i s could not be checked as mixtures with higher N2 content would not detonate. -55-TOTAL FILLING PRESSURE ( t o r r ) Figure 27 Pressure measured i n the detonation chamber at a p o i n t 6 cm from the t h r o a t as a f u n c t i o n of t o t a l f i l l i n g pressure and s t a r t i n g mixture. - 5 6 -C h a p t e r 5 GAIN M E A S U R E M E N T S The main o b j e c t i v e o f t h i s s e r i e s o f measurements was to search f o r a p o p u l a t i o n i n v e r s i o n i n the d e t o n a t i o n r e a c -t i o n p r o d u c t s . As mentioned b e f o r e , i n v e r s i o n i s expected f o r two reasons. F i r s t l y , i n v e r s i o n should occur s i n c e the molecules have been f r e s h l y c r e a t e d by a ch e m i c a l r e a c t i o n . Secondly, an i n v e r s i o n should be produced as the m o l e c u l a r gas expands through the L a v a l n o z z l e . There are s e v e r a l parameters which a f f e c t the i n v e r s i o n . The chemical i n v e r s i o n w i l l "wear o f f " i n time, i . e . w i t h d i s -tance from the n o z z l e t h r o a t . T h i s i s due to the v i b r a t i o n a l e x c i t a t i o n r e l a x i n g through c o l l i s i o n s . The decay o f the chemical i n v e r s i o n w i l l be o f f s e t by gas-dynamical i n v e r s i o n which i n c r e a s e s w i t h the d i s t a n c e from the t h r o a t . The com-p o s i t i o n o f the d e t o n a t i o n mixture w i l l a f f e c t both the chemical and gas-dynamical i n v e r s i o n . Hence, one has the f o l l o w i n g parameters t o v a r y when l o o k i n g f o r an i n v e r s i o n : 1. D i s t a n c e from the t h r o a t . -57-2. Throat h e i g h t — t h i s determines the temperature drop at a fixed p o s i t i o n i n the nozzle. 3. I n i t i a l pressure P q . I f the pressure i s ra i s e d , more c o l l i s i o n s w i l l occur and the gas w i l l relax more quickly. 4. The r a t i o of C^K^rG^. This w i l l determine the amount of CO and C0 2 produced. 5. Addition of other gases such as N 2, Ar, He, CO and C0 2. In order to determine the optimum set of parameters, a fast and simple method i s needed to determine the amount of population inversion. There are two standard methods. 5.1 Methods of Determining Population Inversion The f i r s t method i s shining a probe laser beam through the medium to be investigated and measuring the transmitted i n -tensity as shown i n figure 28. I f the amplitude of the trans-mitted si g n a l increases as i t passes through the medium, a population inversion e x i s t s . This method has the advantage of being simple but has two d i s a d v a n t a g e s F i r s t l y , i t requires a d i f f e r e n t probe laser for each suspected laser l i n e . Ob-viously, no new laser l i n e s can be discovered with t h i s method. Secondly, the gain measurements may be inconclusive i f the -58-MEDIUM :Vx:>:::¥:-Xw>: LASER § j l f g DETECTOR BEAM DEFLECTION DUE TO SCHLIEREN EFFECT Figure 28 Laser gain method of determining whether a population inversion e x i s t s . medium has o p t i c a l inhomogeneities. Beam defle c t i o n s due to the Schlieren e f f e c t , which may make the probe beam miss the detector, (dotted l i n e figure 28) appear as absorption while i n actual fact t h i s may not be the case. The second method involves r e l a t i v e i n t e n s i t y measure-ments of a sequence of l i n e s from which population densities for the various v i b r a t i o n a l r o t a t i o n a l l e v e l s could be deduced. This method allows new laser l i n e s to be found but suffers from being d i f f i c u l t . Also, to be e f f e c t i v e , the medium must be reproducible or comparison of i n t e n s i t i e s i s meaningless. As our medium was not r e a l l y reproducible, the second method was not con-sidered i n earnest. -59-The f i r s t method was chosen because CW CO and C0 2 lasers were available and also the re s u l t s of a gain measure-ment would be available immediately which would allow us to change, a f t e r only one shot, parameter combinations which were not successful. The experimental arrangement i s shown i n figure 29. The predicted ease of obtaining gain measurements proved true i n the case of CO but the C0 2 gain measurements were made d i f f i c u l t by a poor probe laser as w i l l be seen i n the next section. 5.2 J i t t e r of the Probe Laser Beam The probe laser was made at the University of Alberta. Dr. T u l i p was kind enough to loan us t h i s device and to bring i t with him on the occasion of one of several t r i p s he made to the University of B r i t i s h Columbia to consult and help us with t h i s experiment. Unfortunately, the la s e r was damaged during t r a n s i t and i n spite of e f f o r t s to r e f i l l the tube, i t did not reach i t s o r i g i n a l power output. This mishap proved to be very inconvenient since, as a consequence, a l l C0 2 gain measurements were plagued by the noise and problems of a low gain l a s e r . The construction of the probe laser and i t s power supply i s given i n appendix A. -60-Au-Ge detector r THROAT NOZZLE DUMP CO C 0 2 laser Figure 29 Experimental arrangement used to measure g a i n . The f i r s t minor problem was the 120 Hz r i p p l e which appeared i n the laser output. This was reduced to less than .3% by increasing the f i l t e r capacitor i n the power supply from 1 pF to 51 yF. The second more serious problem was connected with the low gain of the CC«2 probe l a s e r . When the gain of a laser i s low, the output power i s very s e n s i t i v e to mirror a l i g n -ment which i n turn i s sensi t i v e to v i b r a t i o n . To reduce the vibrations from the f l o o r reaching the laser, a lab bench was i s o l a t e d from the f l o o r by placing under i t three p a r t i a l l y i n f l a t e d inner tubes. The bench was then f i l l e d with a ton of bricks so as to made a "vibration proof" table. With the laser and detector both on the table, the r i p p l e in output power was < .3%. With the detector i n the p o s i t i o n as shown i n figure 29, the r i p p l e was > 3%. This increase in r i p p l e was caused by the laser beam s t r i k i n g the sides of the ports through which i t had to t r a v e l . I t was impractical to "stop" the laser beam with an i r i s for i f the laser was operating i n the TEM^ mode (figure 30(b)) no i n t e n s i t y would be transmitted to the detector. To a l l e v i a t e t h i s source of noise, the nozzle ports were enlarged from 1/2" to 3/4", t h e i r outer l i m i t set by mechan-i c a l considerations. This reduced the r i p p l e to < .5% but only i f the laser beam was well centred along the axis of -62-the port. As l i t t l e as 1/16" deviation from centre created more r i p p l e . This problem and i t s consequences w i l l be d i s -cussed l a t e r i n t h i s section. To invesitgate what e f f e c t the f i r i n g of the detonation chamber had on the r i p p l e , an aluminum sheet was used as a membrane so that no gas would pass into the nozzle. In t h i s way the e f f e c t of the "operating v i b r a t i o n s " could be deter-mined. Again, i f the beam was well centred, the vi b r a t i o n s had no e f f e c t but a small deviation caused the r i p p l e to increase to over 1%. A l l these noise figures are quoted for the laser i n the TEM mode which has the narrowest beam diameter (figure 30(a)). oo (a) T E M 0 0 (b) T E M U Figure 30 Mode patterns. If the laser was i n any other mode, the beam was larger and more r i p p l e ensued. -63-To summarize the r e s u l t s noted in t h i s section, the r i p -ple of the probe laser could be reduced to <_ .5% i f the laser was i n the TEM mode and the beam was well centred i n the oo port. Vibrations from f i r i n g the detonation chamber had no ef f e c t on the r i p p l e . The f i r i n g of the detonation chamber, although not causing ri p p l e d i r e c t l y , did lead to problems. A f t e r a few f i r i n g s , the mirror alignment would change s u f f i c i e n t l y so that the T E M Q Q mode was no longer produced. After the mirrors were realigned so the T E M q q mode was again produced, the laser beam would no longer point i n the same d i r e c t i o n as i t did previous to the alignment. After every alignment, therefore, the beam would have to be centred i n the port again which took considerable time. For these reasons, i t was too time consuming and f r u s t r a t -ing to achieve the .5% r i p p l e that was possible and r i p p l e of 2 - 5% was accepted. One other source of noise that affected both the CO and C0 2 gain measurements was the stray l i g h t from the luminous gas in the nozzle. To eliminate t h i s l i g h t , the nozzle was wrapped i n black cloths and a bandpass f i l t e r was placed i n front of the detector. 5.3 Results of the C0 o Gain Measurements - 6 4 -Due to the problems discussed i n section 5.2 becoming worse with time, an extensive series of measurements was not possible. Neither the throat height nor the position i n the nozzle was varied. A l l the C0 2 gain measurements were done at a point 8 . 9 cm downstream from the throat with the throat height being f i x e d at .80 mm. Only the i n i t i a l s t a r t i n g mix-ture was v a r i e d . Examples of the gain measured when using d i f f e r e n t s t a r t i n g mixtures are shown in figure 31. Note that i n a l l the oscillograms i n figure 31, there i s a .8 to 1 msec period at the beginning where there i s no s i g -n a l . The o s c i l l o s c o p e was triggered by the noise of the spark gap so t h i s period of no signal i s the time needed for the detonation front to t r a v e l the length of the machine and enter the nozzle. Figure 31(a) i s an oscillogram of a t y p i c a l noise l e v e l measured under operating conditions with the exception that no gas flowed i n the nozzle. The noise l e v e l i s about 3%. The spiking which occurs af t e r 8 msec i n t h i s oscillogram and others i s due to v i b r a t i o n s from the detonation t r a v e l l i n g through the f l o o r and a f f e c t i n g the probe l a s e r . The spiking does not occur i n every oscillogram as the laser was very well aligned for those shots. Using an oxygen lean mixture as compared to the "standard" r a t i o of C 2H 2:0 2 of 1:2, produced severe attenuation for greater than 10 msec (figure 31(b)). This attenuation was expected as carbon p a r t i c l e s , which would attenuate the beam, were - 6 5 -POSITIVE GAIN NUMBERS REFER TO RATIO OF C 2H 2:0 2:N 2'C0 2 (torr) ALL OSCILOGRAMS 1 msec/div > II UJ if) o z T l (a) i > \ T — II z < I _ TV f r i 1 (b) 80.80 >• co cJ II < V (c) n it < 80:160 (d) 50:100:0:50 Figure 31 Traces of oscillograms of gain measurements for CO_ as a function of s t a r t i n g mixture. - 6 6 -produced with t h i s s t a r t i n g mixture. Increasing the oxygen content decreased the attenuation up to a point after which no more improvement was noted. F i g -ure 31(c) was taken with a r a t i o of C 2H 2:0 2 of 1:2. This r a t i o was used as a base point when other gases were added as increasing the oxygen content beyond t h i s gave no improve-ment. No gain above unity was found using only oxygen and acetylene so carbon dioxide was added to the s t a r t i n g mixture. Using a mixture of C 2H 2:C» 2:C0 2 of 50:100 :50 reduced the atten-uation to below the noise l e v e l so that the existence of a small population inversion cannot be excluded (figure 31(d)). A v a r i a t i o n of 50% i n the C0 2 content had l i t t l e e f f e c t but variations greater than t h i s increased the attenuation. Any addition of nitrogen to any s t a r t i n g mixture pro-duced strong attenuation (figures 31(e) and 3 1 ( f ) ) . 5 . 4 CO Gain as a Function of Starting Mixture Of considerable i n t e r e s t i n the f i e l d of chemical and gas-dynamical lasers using an oxygen-carbon working f l u i d are the CO l a s e r s . The wavelengths of CO v i b r a t i o n a l rota-t i o n a l t r a n s i t i o n s f a l l into a band around 5 microns where sensitive detectors are a v a i l a b l e . Laser scattering diagnos-t i c s , 1 aser plasma production and isotope separation with a -67-CO laser would be possible i f a strong CO laser could be de-veloped. To produce maximum gain, the following parameters were varied i n order of th e i r l i s t i n g : 1. the i n i t i a l s t a r t i n g mixture 2. the throat height 3. the pos i t i o n i n the nozzle The CO probe laser had a smaller beam diameter than the C0 2 laser and was not as susceptible to vib r a t i o n s as the C0 2 laser so the problems encountered during the C0 2 gain measure-ments were not serious during the CO gain measurements. The f i r s t set of gain measurements, i n which only the sta r t i n g mixture was varied, was made at a point 12.7 cm downstream from the throat with a throat height of .80 mm (figure 32). No oscillogram of la s e r noise i s given as i t always was < .5%. The spiking seen i n some oscillograms after 6 msec was again caused by vib r a t i o n s from the detonation a f f e c t i n g the probe l a s e r . The i n i t i a l gain measurements i n t h i s set were made with only oxygen and acetylene forming the s t a r t i n g mixture. A ra t i o of 1:1 proved optimum (figure 32(a)) but v a r i a t i o n s i n oxygen of 10% had n e g l i g i b l e e f f e c t . The inversion can be improved by adding argon as i t s addition w i l l lower the r o t a t i o n a l temperature of the expand-ing gas. Using t h i s "optimum" s t a r t i n g mixture, argon was - 6 8 -NUMBERS R E F E R TO RATIO OF C 2 H 2 : 0 2 : A r : N 2 A L L O S C I L O G R A M S % GAIN = 25/div, 1 msec/div J - fa y [ A / \ if • V (a) 75:75 POSITIVE GAIN i 7""*" U (b) 50:50:100:0 1 A, » fi A u 1 n (c) 50:50:0:50 W (d) 50:50np0:50 TIME Figure 32 Traces of oscillograms of gain measurements for CO as a function of s t a r t i n g mixture. -69-added i n increasing amounts u n t i l the mixture would no longer detonate. Ratios of C2H2:C>2:Ar ranging from 1:1:1.5 to 1:1:4 reduced the attenuation to about 1/2%. Lesser or greater amounts of Ar were not as e f f e c t i v e . A mixture of 50:50:100 was used to produce figure 32(b). Again using the "optimum" s t a r t i n g mixture N 2 was added in increasing amounts u n t i l the mixture would no longer de-tonate. Ratios of C 2H 2:N 2 ranging from 1:1:1 to 1:1:3 re-duced the attenuation to about 1/2%. Less N 2 was not as e f f e c t i v e and more N 2 would not detonate. Figure 32(c) was taken with a mixture of 50:50:50. When N 2 and Ar were both added, the gain d i d not increase (figure 32(d)). This e f f e c t was also found by MacKenzie [5] and i s explained i n section 2.2 The e f f e c t of doubling the s t a r t i n g pressure while using the same r a t i o of s t a r t i n g gases was to increase the attenua-tion i f attenuation was present for the lower pressure. If absorbing molecules were present when using the lower s t a r t i n g pressure then t h e i r density would be approximately doubled when using the higher s t a r t i n g pressure and the attenuation would increase. Very l i t t l e work was done at these higher s t a r t i n g pres-sures as the pressure at the convergent end of the detonation chamber was sometimes s u f f i c i e n t to shear the 1/4" bo l t s holding the aluminum sidecovers i n place. -70-Having determined that the optimum s t a r t i n g mixture of C 2H 2:0 2:Ar:N 2 was 1:1:2:1 the throat height was varied. 5.5 CO Gain as a Function of Throat Height The drop i n temperature as a gas expands i n a Laval noz-zle i s a function only of the area r a t i o A/A*. As t h i s r a t i o increases, the temperature drop i n the nozzle increases. How-ever, i n our case there i s an opposing e f f e c t . When the throat height i s made smaller, the gas i s imploded more. This w i l l raise the s t a r t i n g temperature which w i l l tend to decrease the population inversion. The throat height was v a r i e d from .80 mm to .25 mm to .05 mm. For a l l the measurements the s t a r t i n g mixture was 50:50:100 and the p o s i t i o n was 12.7 cm downstream from the throat. Figure 33 shows the r e s u l t s of varying the throat height. Figure 33(a) has the largest throat height while figure 33(c) has the smallest. The e f f e c t on the gain when the throat height was reduced proved to be very s l i g h t but favourable. The increase i n gain may have been due to a greater temperature reduction which would improve the gas-dynamical e f f e c t , but could also have been due to a smaller number of molecules passing through the -71-FOR ALL OSCILOGRAMS %GAIN =.2 5/div 1 msGC/div C 2 H 2 : 0 2 : A r = 50:50:100 ( torr ) u •J I I ' V M THROAT HEIGH T=„80mm POSITIVE .(b) f \J\ - n / V . M i < i I THROAT HEIGHT =.25 mm Figure 3 3 Traces of oscillograms of gain measurements for CO as a function of throat height. -72-laser beam as the density i s decreased when the throat height i s decreased. In order to decouple the throat height and the amount the detonation i s imploded, the detonation chamber would have to be redesigned. In the next section we w i l l see that the CO gain varies considerably with p o s i t i o n 5.6 CO Gain as a Function of Po s i t i o n Variation of p o s i t i o n has two e f f e c t s : with increasing distance from the nozzle, the chemical population inversion i s reduced while the gas-dynamical inversion increases. In t h i s section, the CO gain as a function of p o s i t i o n i n the nozzle i s reported. The measurements were made f o r a s t a r t i n g mixture of 50:50:100 and throat height .25 mm. Figures 34(a) and 34(b) were taken 12.7 and 5.1 cm respec-t i v e l y downstream from the throat. The gain p r o f i l e s shown i n figures 34(a) and 34(b) are almost i d e n t i c a l with the exception of the "spiking" seen after 2 msec i n figure 34(b). This spiking i s very s i m i l a r to the gain that Dr. J . T u l i p has observed i n his gas-dynam-i c a l lasers (private communication)„ An explanation for the spiking occurring at 5.1 cm down-stream but not 12.7 cm i s that the gas, i n t r a v e l l i n g from -73-FOR BOTH OSCILOGRAMS % GAIN = 2.0/div 1 msec/div CjHa'.Og-'Ar = 50:50:100 THROAT HEfGHT = .25 mm — A, X = 12.7 c m P O S I T I V E » G A I N l X=5.1 cm ^ T I M E Figure 34 Traces of oscillograms of gain measurements CO as a function of nonition i n the nozzle. for -74-the f i r s t port to the second relaxed v i a c o l l i s i o n s and thus no inversion was seen at the second port. Unfortunately, the port 1.3 cm downstream could not be used so i t was impossible i n t h i s work to examine the gas just as i t entered the nozzle. With IDEL I I , now under construction, i t w i l l be possible to examine the gas any time during i t s evolution. The peaks of the spikes correspond to about 4% gain and as such i t would be d i f f i c u l t to make the system lase. Never-theless, an attempt was made to operate a la s e r with t h i s ac-ti v e medium (see chapter 6). The a r r i v a l time of the spiking i s rather i n t e r e s t i n g i n that i t does not correspond to the a r r i v a l of the detonation front but rather to the a r r i v a l of the f i r s t "slosh". c 5.7 Conclusions If the reaction products immediately behind the detonation front had been chemically inverted, then a sharp peak i n the gain photos would have been produced as the reaction products intercepted the probe laser beam. The lack of t h i s peak i n -dicates that any chemical inversion, i f i t did e x i s t , had decayed before the gas was examined. The evidence of gas-dynamical laser action was incon-clusive i n the case of C00 due to the high noise l e v e l . The -75-CO g a i n measurements, however, showed some e n c o u r a g i n g s i g n s o f p o s i t i v e g a i n a l t h o u g h a t a l e v e l (< 4%) where the o b t a i n -i n g o f l a s e r a c t i o n cannot be t a k e n f o r g r a n t e d . I n any case an attempt t o make t h e system l a s e was made. The t e c h n i q u e and r e s u l t s a r e g i v e n i n t h e n e x t c h a p t e r . -76-C h a p t e r 6 THE LASER CAVITY In t h i s chapter, the laser cavity and the technique used to a l i g n the cavity w i l l be presented. The r e s u l t s of the attempts to make the machine lase w i l l also be given. 6.1 Construction of the Laser Cavity Because the laser mirrors joined by bellows to the nozzle formed a vacuum seal and also were subject to vi b r a t i o n s from the f i r i n g of the machine, very sturdy mirror mounts had to be b u i l t . A box of one inch aluminum plate was constructed and a mirror was mounted i n each end (figure 35). Holes were cut in the side of the box so that i t could surround the nozzle. To i s o l a t e the mirror assembly from the vibrations of the f l o o r , a table made of bricks was supported by one dozen tennis b a l l s . The aluminum box was set upon the table. As the gain of the system was low (< 4%) the o p t i c a l - 7 7 -F i g u r e 35 The l a s e r c a v i t y . c a v i t y was d e s i g n e d t o h a v e a s s m a l l l o s s e s a s p o s s i b l e . The o u t p u t m i r r o r was a germanium f l a t c o a t e d w i t h a m e t a l d i e l e c t r i c e x c e p t f o r a 2 mm s p o t i n t h e c e n t r e . T h i s m i r r o r w o u l d p a s s a b o u t .75% o f t h e r a d i a t i o n i n c i d e n t upon -78-i t assuming the radiati o n was d i s t r i b u t e d uniformly over the mirror's surface. The back mirror had a radius of 3 metres and was coated with the same d i e l e c t r i c . The d i e l e c t r i c has a r e f l e c t i v i t y of 99.4% over a wavelength range of 3 to 25 microns. Hole coupling was chosen so that the output mirror would be "broadband" and could therefore be used for both the CO and C0 2 laser attempts. 6.2 Alignment of the Laser Cavity To a l i g n the o p t i c a l cavity the la s e r mirrors were re-moved and two helium neon lasers were positioned so that t h e i r beams were coincident with each other and also passed along the axis of the laser c a v i t y (figure 36). To get a s u f f i c i e n t l y long path for laser B so that an accurate alignment could be made, i t was necessary to use a s i l v e r mirror as a wall made a straight path unobtainable. The alignment of the lasers with the o p t i c a l axis was added by using a pinhole i n front of the laser beam to produce a c i r c u l a r d i f f r a c t i o n pattern. After the helium neon lasers were aligned, the back mirror was then i n s t a l l e d and adjusted u n t i l l a s e r A's beam retraced i t s incoming path. The p o s i t i o n of the r e f l e c t i o n of laser B from the rear of the back mirror was marked. The back mirror - 7 9 -LASER B S I L V E R E D ^ M I R R O R 2 m POSITION OF i ^ B A C K MIRROR NOZZL E «... " \ POSITION OF FRONT MIRROR E rvi II LASER A Figure 36 Alignment system. - 8 0 -was then removed and the f r o n t m i r r o r i n s t a l l e d . The same procedure was used t o a l i g n t h i s m i r r o r but w i t h the r o l e s p l a y e d by l a s e r s A and B r e v e r s e d . The back m i r r o r was then i n s t a l l e d a g a i n and a d j u s t e d u n t i l the beam of l a s e r B s t r u c k the spot p r e v i o u s l y marked. T h i s completed the alignment o f the l a s e r m i r r o r s . The m i r r o r mounts proved s t u r d y enough t h a t the alignment d i d not change when the system was put under vacuum. 6 . 3 Did IDEL I Lase? The mixtures which produced the h i g h e s t CO and C 0 2 g a i n were detonated and l a s e r a c t i o n was looked f o r . To t h i s date, no l a s e r a c t i o n has been found although f u r t h e r attempts w i l l be made. When the s i d e o f the n o z z l e i s r e p a i r e d i t w i l l be p o s s i b l e to look f o r l a s e r a c t i o n v e r y c l o s e to the t h r o a t where ch e m i c a l i n v e r s i o n should be g r e a t e s t and f u r t h e r attempts w i l l then be made. -81- \ Chapter 7 CONCLUSIONS S U M M A R Y A N D FUTURE I M P R O V E M E N T S No lase r action has been found to date. This r e s u l t i s not considered f i n a l as we hope to produce l a s e r action at the port cl o s e s t to the throat. When t h i s port has been re-paired, an attempt to produce laser action w i l l be made. Detonation v e l o c i t i e s i n the detonation chamber and the nozzle were measured using a framing camera and pressure probes. The v e l o c i t i e s were found to be 2 ± . 4 km/sec and 2.5 ± . 4 km/sec respectively. These v e l o c i t i e s are lower than what was expected [ 1 ] . The pressures measured i n the nozzle followed the general trend as predicted by steady flow nozzle theory. Gain measurements were done at CC^ and CO wavelengths. No p o s i t i v e gain was detected at CO2 wavelengths although the s t a r t i n g misture of 50:100:50 (C~H9:0~:C09) produced a -82-gain of 1 ± 5%. A p o s i t i v e gain of 4 ± .5% at CO wavelenghts was found using a s t a r t i n g mixture of 50:50:100:50 ^ 2 ^ : 0 2 : Ar:N 2). The p o s i t i v e gain was found at a port 5.1 cm from the throat but not at the port 12.7 cm from the throat. This i n -dicates that the population inversion decayed while t r a v e l l i n g from the f i r s t port to the second. This fact explains our hope of producing lase r action at the port c l o s e s t to the nozzle. We believe that i n order to see the population inversion which i s almost surely formed by the chemical reaction we must look at the reaction products sooner a f t e r t h e i r formation than we have been looking. I t i s f e l t that because of the high temperature and pressure which occur at the throat, no delay of the gas at the throat can be tole r a t e d . To reduce the delay time, a thinner membrane should be used or i d e a l l y a mechanical valve should be used to separate the detonation chamber and the nozzle. The mechanical valve also has the advantage of not introducing impurities into the gas. As hydrogen impurities are detrimental to molecular laser action, a f u e l other than C2H2 should be used. Possible a l -ternatives are CS 2 and CO although there might be some d i f -f i c u l t y i n producing a detonation with those f u e l s . In conclusion, no laser action has been found yet, but our hope i s not dead. -83-B I B L I O G R A P H Y 1. J.P. Huni, Ph.D. Thesis, U.B.C. (1970). 2. W.H. Flygare, Accounts Chem. Res. 1, 121 (1968). 3. R.C. M i l l i k a n and D.R. White, J . Chem. Phys. 39, 3210 (1963). 4. Y.V. Stupochenko, S.A. Losev and A.I. Osipov, "Re-laxation i n Shock Waves" pp. 219 - 222, Springer Verlay, B e r l i n , Heidelberg, New York 1967. 5. R.L. MacKenzie, Phys. Flu i d s 15, 2163 (1972). 6. J.D. Anderson J r . , Phys. Flu i d s 13, 1983 (1970). 7. J . T u l i p and H. Sequin, J . Appl. Phys. 42, 3393 (1971). 8. R.L. Taylor and S. Bitterman, Rev. Mod. Phys. 4_1, 26 (1969). 9. J.C. Polanyi, Appl. Opt. Supp. I I , "Chemical Lasers", p. 109 (1965). 10. B. Ahlborn and K.L. Kampa, "Increase of Chemical Laser E f f i c i e n c y by Gasdynamical Pumping", IPP 1V/10. 11. G. Hancock, C. Morley, and I.W.M. Smith, Chem. Phys. Letters 12_, 193 (1971). 12. K.G. Anlavf, P.J. Kuntz, D.H. Maylotte, P.D. Pacey, and J.C. Polanyi, Discussions Faraday Soc. £4, 183 (1967). 13. K.G. Anlauf, D.H. Maylotte, P.D. Pacey, and J.C. Polanyi, Phys. Letters 24A, 208 (1967). -84-Bibliography, continued 14. N. Jonathan, CM. Melliar-Smith, and D.H. Sl a t e r , Mol. Phys. 20_, 93 (1971) . 15. P.E. Charters, R.G. MacDonald, and J.C. Polanyi, Appl. Opt. 10, 1747 (1971). 16. K.D. Foster and G.H.Kimbell, J . Chem. Phys. 5_3, 2539 (1970) . 17. J.D. Barry, W.E. Boney, and J.E. Brandelik, IEEE J . Quant. Electron. QE-7, 208 (1971). 18. H.S. P i l l o f f , S.K. Searles, and N. Djeu, Appl. Phys. L e t t . 19, 141 (1971). 19. C. Wit t i g , J.C. Hassler and P.D. Coleman, Nature 226, 845 (1970). 20. S.J. Arnold and G.H. Kimbell, Appl. Phys. Lett . 15, 351 (1969). 21. T.V. Jacobson and G.H. Kimbell, J . Appl. Phys. 41, 5210 (1970). 22. H.O. Amann and H. Reichenback, "Recent developments i n shock tube research", Stanford University Press, Stanford, C a l i f o r n i a (1973). -85-APPENDIX A Figure 37 The construction of the probe laser and i t s power supply. 

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