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Jaul has been accepted towards fulfillment of the requirements for Ph.D. degreein Mechanical Engineering flaw/J / flézz 7 Major professor Date fiw Lie/”5‘ 0-7639 '"dvanoue FINES: 25¢ per day per item RETURNING LIBRARY MATERIALS: Place in book return to renew charge from circulation recur THEORETICAL AND EXPERIMENTAL EXAMINATION OF PULSED 16 um CO2 TRANSFER CHEMICAL LASERS By Warren K. Jaul A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Mechanical Engineering 1980 ABSTRACT A THEORETICAL AND EXPERIMENTAL EXAMINATION 0F PULSED 16 um C02 TRANSFER CHEMICAL LASERS By Warren K. Jaul An experimental and theoretical investigation of hydrogen- halide C02 16 um laser systems was made. The experiments employed a pulsed hydrogen-halide chemical laser to optically pump a cell containing a mixture of HX, C02, and diluent. Similar experiments using deuterium instead of hydrogen were also performed. Initially a computer model was developed simulating laser oscillation in a DF/CO2 and HBr/CO2 device. The model used a rate equation approach to compute the time histories of the concentra- tions of both the lasing and non-lasing species. Rotational non- equilibrium of both C02 and HX molecules was permitted. Non- equilibrium of the rotational population could be the result of lasing or preferential pumping. Kinetic mechanisms important to 16 um lasing were identified using the results of the computer simulation. The predictions of the HBr/CO2 model were compared to the experimental results of Osgood [7, 8], who reported 16 um laser output from an optically pumped HBr/COZ/Ar gas mixture. The model predictions compared favorably with the experi- mental results of Osgood in all but one instance. Experimental results demonstrated that increasing Ar partial pressure increased 16 um pulse power while the computer simulations predicted the opposite trend. The computer program was subsequently modified to more accurately simulate the absorption of the optical input pulse. The results of the computer calculations were again compared to the experimental observations of R. M. Osgood and also to the experimental observations of N. Barnes [22]. In both instances the model predictions agreed with experimental results. The model correctly predicted that increasing the partial pressure of Ar raised 16 um pulse power while lowering pulse energy. Because of the potential for higher output powers and ener- gies from HF lasers compared to HBr an HF pumped HF/CO2 16 um laser would be desirable. To demonstrate the feasibility of such a device experiments were performed using an HF laser to optically pump an HF/COZ/He gas mixture. Due to HF polymerization at low temperatures it was necessary to maintain the gas mixture above 260°K in contrast to the HBr device of Osgood that could operate at 193°K. No evidence of laser output from the HF/CO2 device was ever observed. To attempt to explain these results the computer model was modified to simulate the chemical kinetics in an HF/CO2 gas mix- ture. The results of the computer calculations predicted very weak 9.4 um lasing (approximately 2% of HBr output at 9.4 um) and no 16 um laser output. A combination of slower energy trans- fer between HF and CO2 compared to HBr and a vibrational self- deactivation rate two orders of magnitude greater for HF than for HBr appeared to be responsible for these results. ACKNOWLEDGMENTS I express my appreciation to my thesis adviser Dr. Ronald Kerber for his encouragement and support particularly during the. preparation of this dessertation. I thank the faculty members who served on my doctoral guidance committee: Dr. Jes Asmussen, Dr. Martin Hawley and Dr. Mahlon Smith. Their constructive advice was very helpful. To the Department of Mechanical Engineering and the Division of Engineering Research go my thanks for-providing me with teaching and research assistantships that allowed me to complete my studies. The expert typing of the final version of this dissertation by both Carol Cole and Vicki Brock and the excellent preparation of the figures by Pam Detine is gratefully appreciated. Most of all though, I thank my parents whose constant faith in my ability to finish this work helped me to do so. 1'1 TABLE OF CONTENTS Page LIST OF TABLES ........................ v LIST OF FIGURES ....................... - vi 1. INTRODUCTION ....................... 1 1.1 History ....................... 1 1.2 Present Work .................... 6 2. COMPUTER SIMULATION AND DISCUSSION OF IMPORTANT KINETIC MECHANISMS IN THE HYDROGEN-HALIDE 602 LASER ....... 11 2.1 Introduction .................... 11 2.2 CO2 Kinetic Model .................. 14 2.2.1 Transfer Between Fermi Resonance States . . . 15 2.2.2 Reactions Peculiar to the Addition of N . . . 18 2.2.3 Reactions Peculiar to the Addition of D . . . 19 2.2.4 Reactions Peculiar to the Addition of HBr . . 21 2.3 Theoretical Model .................. 22 2.3.1 Laser Simulation ............... 22 2.3.2 Summary of Important Relaxation Mechanisms . . 26 2.3.3 Laser Performance Characteristics ...... 27 2.4 Parametric Variation ................ 39 2.4.1 Optically Pumped COz/He Mixtures ....... 39 2.4.2 Optically Pumped DF/HE/CO Mixtures ..... 43 2.4.3 Optically Pumped HBr/Ar/COZ Mixtures ..... 46 2.5 Comparison of Model and Experiment ......... 46 2.6 Summary ....................... 51 m“ 3. PREDICTIONS OF A COMPUTER SIMULATION FOR A 16 um HBr/CO2 LASER .......................... 3.1 Introduction .................... 3.2 Theoretical Model .................. 3.3 Parametric Variation and Comparison With Experiment . 3.3.1 Effects of Changing HBr and CO2 Partial Pressures .................. 3.3.2 Effect of Argon ............... 3.4 Summary ....................... 4. FEASIBILITY OF AN HF-COZ 16 um LASER: EXPERIMENT AND THEORY .......................... 4.1 Introduction .................... 4.2 Experimental Study ................. 4.2.1 Pump Laser and Saturation Pulse Laser . . . . 4.2.2 COZ-HF Gas Mixture Cell ........... 4.3 Experimental Results and Discussion ......... 4.3.1 Attempts to Observe Rotational Lasing in HF . 4.3.2 Attempts to Produce Lasing in Optically Pumped HF- and DF-CO2 Gas Mixtures ......... 4.4 Computer Simulation of an HF-COz/Ar Gas Mixture and Comparison With Experiment ............. 4.4.1 Introduction ................. 4.4.2 Reactions Peculiar to the Addition of HF . . . 4.4.3 Parametric Variation: Comparison With the Results of the HBr-C02 System ........ 4.4.4 Effect of the V-R Mechanism and Initial Rota- tional Distribution on HF-CO2 Energy Transfer 4.5 Summary ....................... 5. SUMMARY AND CONCLUSIONS ................. APPENDIX A. RECOMMENDED RATE COEFFICIENTS FOR THE 16 um C02 LASER SYSTEM .................. APPENDIX B. RATIO OF PERFORMANCE FOR HX-CO2 TCL DEVICES . . . APPENDIX C. NOMENCLATURE .................. REFERENCES .......................... iv 52 52 53 61 62 67 76 79 79 82 82 93 94 94 102 115 115 115 124 132 135 137 142 148 151 154 Table 2.1 2.2 3.1 3.2 4.1 A.1 C.1 LIST OF TABLES Effect of rotational relaxation on laser outpUt (weak 9.4 um saturation); 2 torr C02; 10 torr He ........ . ................ Effect of line selected operation on 16 um laser output parameters (strong 9.4 um saturation), 20 torr C02; 10 torr He ............. Effect of C02 pressure of 16 um power; comparison between experimental and computer results Effect of HBr pressure on 16 um power; comparison between experimental and computer results Observed HF rotational laser transitions . . Recommended rate coefficients for 16 um CO2 laser systems ..................... Nomenclature ................... Page 36 37 63 64 98 142 151 Figure 1.1 2.1 2.2 2.3 2.4 2.5 LIST OF FIGURES Diagram summarizing the two-step process of photon absorptionandcxfllisional transfer of energy from species HX to CO2 .................. Vibrational energy level diagram for C02 kinetics including the DF transfer energy. The states (0330) and (0220) are deleted for clarity. These states are included in the model and have reaction mechanisms similar to (0310) and (0220), respectively. In addi- tion, the detailed kinetic modeling between the (02°:O) (0220), and (10°C) states is included. The arrows indicate some of the energy exchange and relaxation processes included in our model ........... Detailed diagram of kinetic mechanisms that relax the lower level of the 9.4 um band (02°C) (the upper level of the 16 um band) .................. Net reaction rates for a typical case. Plots (a)-(d) show net reaction rates for processes most important to 16 um lasing. The dashed line indicates the rate for the reaction running in reverse. The subscripts refer to the collisional species (M) number ..... Schematic diagram of a possible configuration for an optically pumped 16 um CO2 laser ........... (a) Time histories of power on selected transitions of the 16 um laser (b) Time histories of species concentrations for the levels controlling 16 um lasing ......... vi 12 13 28 3O 32 Figure 2.6 2.8 2.9 2.10 2.11 2.12 Diagram showing the effect of rotational hole burning caused by restricting the number of rotational bands lasing (a) Power on lasing bands at three distinct times during the run (b v Schematic showing the effect on the rotational concentration of the lasing levels. Solid lines represent equilibrium populations; dashed lines, the concentrations due to rotational hole burning; the arrows represent the lasing transitions Lasing on a single rotational transition; the solid lines represent medium gain 0f selected rotational bands. Power time history for the P(21) band is represented by the dashed line ......... . Effect of input energy on conversion efficiency (a) Effect of total (9.4 um and 4.3 um) input energy. Input energy is normalized by C02 pressure (b) Effect of 9.4 um saturation ........... Effect of pressure on pulse energy and pulse duration (a) Effect of He pressure (b) Effect of total mixture pressure ......... Effect of mixture composition on pulse energy and pulse duration for a DF/C02/He mixture pumped by a DF laser (a) Effect of C02 pressure (b) Effect of He pressure .............. Effect of initial gas temperature on pulse energy and pulse duration .................... Effect of mixture composition on pulse energy and pulse duration foran HBr/COZ/Ar mixture pumped by an HBr laser ...................... Page 34 38 4O 42 44 45 47 Figure 2.13 Comparison of experiment and theory (a) Experimental results of Osgood [4] (b) Effect of level of saturation as predicted by the model ...................... (c) Effect of Ar as predicted by the model (d) Laser performance of an optically pumped DF/COz/He mixture. The gas mixture is DF = 20 torr, C02 = 2 torr, and He = 10 torr. Pumping is such that IDF(1)]/[DF(O)] = 9 at t = O with no 9.4 um saturation .................... Effect of HBr rotational relaxation probabilities upon bleaching. The standard case is P = 1.0 ....... Time history of photon emission in HBr/C02 cavity. Included are the HBr input pulse, the 9.4 um pulse, and 16 um pulse ................... Effect of C02 partial pressure on both 16 um and 9.4 pm lasing and 16 um pulse duration ....... Effect of HBr partial pressure on delay of 16 um and 9.4 pm lasing and 16 um pulse duration ........ Experimental results of Barnes; effect of varying Ar partial pressure on 16 um pulse energy ........ Experimental results of Osgood; effect of varying Ar partial pressure on 16 um pulse power ....... . The effect of Ar and He partial pressure on 16 um pulse energy as predicted by the computer model The effect of Ar partial pressure on 16 um pulse power as predicted by the computer model .......... Net reaction rates for a typical case. Plots (a) and (b) show all reaction rates involving Ar which affect the (02°O) level. The dashed line indicates the rate for the reaction running in reverse ......... viii Page 48 49 55 58 59 6O 68 69 7O 71 72 Figure Page 3.10 The effect of Ar partial pressure on the net reaction rate of HBr(v = 1) + CO (00 0) Z HBr(v = 0) + o 2 C02(00 1) ...................... 75 3.11 The effect of Ar partial pressure on 9.4 pm and 16 um pulse delay and on the duration of 16 um oscillation . 77 4.1 Schematic diagram of experimental setup to produce 16 um lasing using a pulsed HF laser to optically pump an HF/COZ gas mixture. The C02 laser is used to opti- cally saturate the 9.4 pm transition in CO2 to enhance 16 um lasing ..................... 83 4.2 (a) Diagram of Marx bank discharge circuit used to electrically initiate the SF6/H2/He gas mixture . 85 (b) Circuit used to triger spark gaps in high-voltage discharge circuit in Figure 4.2a. 4.3 Photograph of HF laser facility at Michigan State University ...................... 86 4.4 Gas handling system that provided calibrated gas mix- tures for the SF6-H2 laser .............. 87 4.5 Diagram of pulsed 10.6 um (9.4 pm) COg-N laser facil- ity. The screen box served to isolate t e detection equipment from outside electrical noise ....... 89 4.6 A typical 10.6 um pulse profile 1 usec/div,200 mV/div. The lower trace shows the current trace of the dis- charge circuit. Measured using a Pearson Electronics pulse current transformer calibrated at 0.1 V/10 mA . 91 4.7. Circuit used to trigger spark gap for application of pulse high voltage across discharge electrodes in the C02 system in Figure 4.4 ............... 92 4.8 Diagram of gas handling system and pressure monitoring devices for the HF-CO2 gas mixture cell ....... 95 4.9 Shown are the rotational levels preferentially pumped in v = 1 level of HF and the two rotational levels in the v = 0 to which relaxation would be most likely to occur ........................ 97 4.10 Shows the end view of three arrangements of electrodes used to electrically initiate the SF6/H2/He gas mixture ...................... . 101 Figure Page 4.11 HF dimer mole fraction (X ) versus temperature at four different pressures (atm) ............ 103 4.12 HF polymer mole fraction (Xi) versus temperature for a pressure of 0.1 atmospheres ............ 104 4.13 HF polymer mole fraction (X1) versus temperature for a pressure of 0.01 atmospheres ............ 105 4.14 HF polymer mole fraction (X1) versus temperature for a pressure of 0.001 atmospheres ........... 106 4.15 HF polymer mole fraction (X1) versus temperature for a pressure of 0.0001 atmospheres ........... 107 4.16 A typical DF pulse profile .2 usec/div, 200 mV/div. The output is from the P1(7) transition in DF . . . . 114 4.17 Comparison of the effect of temperature on the rate coefficient for energy transfer from HBr, DF, and HF to C02 ........................ 122 4.18 Comparison of the effect of temperature on the rate coefficient for deactivation of C02(00°1) by DF, HBr, and HF ........................ 123 4.19 Time history of the small signal gain on the 9.4 um transition having maximum gain for the HBr-602 and HF-CO2 systems ....... ‘ ............. 125 4.20 Net reaction rates in the HF—CO system for a small signal gain case. The rates shgwn are those important to transfer of energy into and out of the C02(OO°1) level ........................ 127 4.21 Net reaction rates in the HBr-€02 system for a small signal gain case. The rates shown are those important to transfer of energy into and out of the C02(OO°1) level ........................ 128 4.22 Time histories of species concentrations for levels controlling 9.4 pm lasing in an HF-CO2 device . . . . 129 4.23 Comparison of the time histories for 9.4 um laser oscillation in the HBr-CO2 and HF-CO2 systems . . . . 131 CHAPTER 1 INTRODUCTION 1.1 History Isotope enrichment by selective ionization of a molecular species is an important use of lasers. The tunability and narrow frequency spread of the output enable the laser or a combination of lasers to ionize one molecular species while having little or no effect upon its isotope. In particular, lasers operating near 16 um provide an efficient means of separating isotopes of uranium. This wavelength selectively ionizes fissionable uranium 235 from its non-fissionable isotope, allowing relatively easy and inexpensive separation to take place. It is the objective of this thesis to determine the feasibility of developing an HF/CO2 or DF/CO2 transfer chemical laser to produce 16 um lasing which could be a component in the uranium enrichment process. The transfer chemical laser (TCL) makes use of vibrationally excited state distributions of one molecule for the creation of population inversions in a second molecule. The device is a chemical laser since the vibrationally excited states of the first molecule are produced from a chemical reaction. The hydrogen- and deuterium-halides and C02 produce the most important TCL's. The exothermic chain reactions of H2 + F2 and D2 + F2, with their potential for large laser output, make the HF 1 and DF systems attractive as a pumping species. A strong V + V coupling exists that permits transfer of the vibrational energy from the hydrogen- and deuterium-halide product molecules to the (0001) level of coz. There are two types of TCL's, depending upon how the chemically reacting system gives up its energy to C02: 1. The chemical reaction and the transfer process take place in the same cavity via the following V + V,R process: 0 + _ ' O 00 0) + HX(v — n - 1, 02) + C02(00 1) + BE (28)* HX(v = n, J + CO 1) 2( 2. The chemically reacting system lases and optically pumps the resonant transition in a spearate gas mixture: HX(v = n) + hv + HX(v = n + 1) (1.1) and then transfers its energy to C02 via process (28). This two-step process is summarized in Figure 1.1. Chemical pumping of CO2 was first reported by Gross [1] and Chen et al. [2], who observed lasing at 10.6 um as CO2 was added to pulsed DF and HC1 chemical lasers. The CD2 quenched DF and HC1 lasing and replaced it by stronger laser action from C02. The first continuous wave chemical transfer lasers were developed by Cool et al. [3, 4] in 1969. In these systems the exothermic reaction took place in the same cavity with C02. Chang and Wood [5, 6] observed 10.6 um lasing from an HBr-CO2 system optically pumped *The reaction numbers correspond to the numbers listed in Table A.1 in Appendix A. 3846 «6' HF COLLISIONAL "—— TRANSFER goao cfi' DF 2439 cm" H3.- / __—0 9.4 pm , io°o 02°o hv ”W" OPTICAL PUMPING _.__01°o HF DF HBr V=0 Figure 1.1. Energy level diagram summarizing_the two—step process of photon absorption and collisional transfer of energy from species HX to C02. by an HBr laser. Osgood [7, 8] observed 16 um laser oscillation from a similar apparatus. However, laser oscillation at 16 pm from either an HF or DF optically pumped HF/CO2 or DF/CO2 gas mixture has not been reported. The advantages of using HF gas are the higher output of HF lasers as compared to HBr or DF lasers, and, compared to DF, HF lasers are less expensive to use. With the HF optical transfer laser system, one has externally variable input power from the highly exothermic chain reaction of the H2 + F2 system. The exothermic pumping reaction is separate from the HF/C02 cell, hence there is little or no temperature rise in the gas mixture. For a multilevel system such as C02, in which the lower level of the lasing transition is not the ground state, preventing a temperature rise implies that higher population inversions are possible. The mechanisms for the transfer process are shown in Figure1.1. The output pulse from the pump laser is absorbed in the COZ-HF cell by HF. Through molecular collisions the HF energy is transferred to the first asymmetric stretch mode of CO2 by reaction 28. The energy defect AE for HF is much larger than for DF or HBr. However, the rate coefficient for energy transfer for HF is nearly equal to that of HBr, and Bott et al. [9] postulate that the excess energy from HF goes into rotational motion of the HF molecule. Experiments by Manuccia [10, 11] in which an electrically initiated HF/COZ gas mixture produced 16 um lasing are further con- firmation than an HF pumped 16 um C02 1659? IS feasible. In addition to the experimental work, the development of a computer model that will accurately predict operation of the TCL laser device is highly desirable. A computer simulation that suc- cessfully approximates the actual performance of a laser is important for two reasons. First, if the laser is expensive to operate, a computer model may be less expensive to use to predict laser output under varying conditions. Secondly, if the model accurately predicts laser performance, one may use the model to study the kinetic mecha- nisms responsible for laser oscillation. Using experimental observations, a simple rate equation model was developed by Airey [12] in 1970, and was used to identify several important mechanisms in an HCl laser system. However, the first such model to describe an HF chemical laser system was done by Emanuel [13] in 1971. A two-level continuous wave laser was simu- lated using a rate equation approach. Laser action took place between only two vibrational levels. The rotational levels were assumed to be in thermal equilibrium at the translational tempera- ture. Improved models, capable of computing the time histories of many vibrational transitions simultaneously and modeling in detail the effectiveness of cavity parameters, soon followed [14, 15, 16]. These models were complex and expensive to run. Several simplified versions were developed that could be used under restricted condi- tions to approximate the results of the large models at a greatly reduced cost [17, 18]. The assumption of rotational equilibrium used in all of these models prevented any of them from accurately predicting the spectral output from a laser. The first model to assume rotational non-equilibrium was used by Schappert [19] to examine the rotational relaxation effects in a C02 amplifier. J.J.T. Hough, intfissdoctoral thesis [20], uses a more comprehensive model to describe the output of an HF laser. The rotational levels of each vibrational level were allowed to differ from their thermal equilibrium values in the model. The non-equilibrium values for these populations could arise from lasing or preferential pumping (i.e., a pumping mechanism that populates levels in a non-Boltzmann manner). Another assumption critical to an accurate prediction of output spectra is to allow the gain on a particular vibration rotation band to vary with time during lasing. Again, the model of Hough was the first to demonstrate the effect of gain fluctuations during lasing. 1.2 Present Work To date, these models have been almost exclusively applied to the study of pulsed HF and DF lasers. Efforts to improve the operation of the TCL devices would benefit from a similar effort directed at modeling the transfer process. Enhanced performance from the continuous wave, HF-CO2 system of Manuccia could be accom- plished by an experimental and theoretical study of a pulsed HF-CO2 laser. To determine the feasibility of the HF/CO2 16 pm laser requires a detailed knowledge of the kinetic mechanisms in the system. To accomplish this task the following goals were identified for this thesis: 1. A computer model of the HF-CO2 system is created to examine the characteristics of the 16 um CO2 laser. It is used to offer suggestions for further research. Analysis of the kinetic mechanisms provides insight into the relative importance of various processes affecting laser oscillation. 2. Before a 16 um HF-CO2 model can be used with confidence, a model to compare with the experiments of others is developed. Such a model will simulate 16 um laser output from an HBr-CO2 gas mixture. 3. An experimental apparatus has been constructed to verify 16 um lasing from an HF-CO2 mixture. 4. Attempts are made to perform a similar experiment using a DF-CO2 mixture. The following sections of this thesis describe the computer model in its sequential phases of development. The models described in this thesis assume that the initial HX-CO2 and diluent gas mixture is homogeneous throughout the cavity. All processes are also assumed uniform in the cavity. A rate equa- tion approach is used to solve for the time history of concentrations of both lasing and non-lasing species. During lasing the gain on any transition is allowed to vary rather than remain fixed at the threshold value. This allows for a detailed examination of the interaction of the pumping and deactivation mechanisms with the output intensity. The interesting feature of such an assumption is that the gain rises significantly above threshold before laser action begins. The model also allows the rotational populations of a given vibrational level in C02 to vary from their equilibrium values. The non-equilibrium of the rotational levels may be due to preferen- tial pumping, or lasing. Rotational relaxation is modeled using a rate coefficient for time process suggested by Polanyi [21] and given by e-CAE/RT k = PZ (1.3) CO M 2, where ZCOZM is the binary collision frequency for a unit concentra- tion of C02 and species M. The term AE represents the energy dif- ference between the J and J - 1 levels and P is the probability that relaxation will occur upon collision, and C is a constant which indicates the dependence of the relaxation rate on the value of the rotational state. In the final stages of deyelopment, the model also assumes rotational non-equilibrium in the HX molecule. The effects of pref— It. erential optical pumping are clearly evident. Rotational hole burning and bleaching of a particular vibrational-rotational transi- tion are easily simulated with this model. With the assumptions of non-constant gain during lasing and rotational non-equilibrium the model is capable of predicting the time resolved spectral output from the laser. These features allow simultaneous lasing on as many transitions as reach threshold and the result is that multiline lasing is predicted. Detailed balancing is maintained for each reaction mechanism in the model. Thus, for all the reactions listed in Table A.1 the rate coefficient for the reverse reaction is calculated from the equilibrium constant for the particular reactions where products and reactants are unchanged except for their vibrational or rota- tional state. [‘3 = e-AE/kT kf where AE is the energy difference between reactants and products and kf and kB are the rate coefficients for the forward and backward reactions, respectively. Initially the model simulated output from a DF/CO2 and HBr/CO2 system. These results were used to study the competing mechanisms in the device. The model predictions for the HBr/CO2 laser were compared to the experimental observations of Osgood [7, 8]. In Chapter 3 an improved computer model is discussed. The model moni- tors the time histories of the first fifteen rotational levels of HBr which enable it to simulate the optical input pulse. The 10 predictions of this model are-again compared to the experimental results of Osgood and to the results of another experiment performed by Barnes [22]. In both cases the model compares favorably with experiment. Finally, a computer model was developed to simulate an HF/CO2 laser system. A discussion of this model is postponed until the end of Chapter 4 so that its predictions Can be compared with the experimental results. An HF/CO2 laser was constructed to experimentally determine whether this system was capable of producing 16 um laser output. The results of the experiment are presented in Chapter 4. CHAPTER 2 COMPUTER SIMULATION AND DISCUSSION OF IMPORTANT KINETIC MECHANISMS IN THE HYDROGEN-HALIDE C02 LASER 2.1 Introduction Development of an optically pumped CO2 laser at 10.6 um has been reported by Chang and Wood [5, 6]. The pumping source was a transverse discharge HBr laser with output in the range 4.02 - 4.61 pm as described in Reference [23]. More recently, optically pumped 16 um C02 lasers have been reported by Osgood [7], Manuccia et al. [10, 11], and Buchwald et al. [24]. Optical pumping of a C02 laser pennits one to selectively populate levels in C02 with a minimum of heating. This is possibly a significant advantage for laser oscillation at 16 pm. The kinetics of vibrational energy transfer in such a C02 laser can best be understood by referring to the energy level diagram in Figure 2.1. (The states (0330) and (0220) are deleted from Figure 2.1. for clarity.) However, these states and their reaction kinetics are included in our modeling studies. The most important reaction paths for 16 um lasing are shown in Figure 2.2. The upper level of a standard CO2 laser (0001) is located '1 above the ground state. The lower level (1000) is at 2349 cm located 961 cm'1 below it. The various wavelengths observed at 300°K in this laser are typically associated with J levels of 11 12 - ----- — VT REACTION ~--— INTERMOLECULAR vv REACTION ——-— INTRAMOLECULAR vv REACTION DF(V)_DF(V_H --— TRANSFER REACTION V 3000 — + I 0 .— I20 29 + 3 O4°0 29 .__5 _ ——6 IS —g , —9 z I E 2000—— l l a l I I e K) A A < I l I 3 I , :II I I fix; I [I l I I I I | I I I I l IOOOF-I I | I . ' l I .QI I'Iu I I 0 00°0 z: Figure 2.1. Vibrational energy level diagram for C02 kinetics including the DF transfer energy. The states (0330) and (0220) are deleted for clarity. These states are included in the model and have reaction mechanisms similar to (0310) and (02°0), respectively. In addi— tion, the detailed kinetic modeling between the (02°0), (0220), and (10°C) states is included. The arrows indicate some of the energy exchange and relaxation processes included in our model. 13 2000 wave number, cm 2 c 1000 (0000) Figure 2.2. Kinetic mechanisms that relax the lower level of the 9.4 pm band (02°C) or the upper level of the 16 um band. 14 transitions near P(20). The detailed chemical kinetics of the various levels associated with this laser have been carefully examined [25, 26]. With this background, a computer model of a laser capable of lasing on selected J levels of transitions between the (0200) + (0110) levels was developed. The basic kinetic mecha- nisms controlling laser performance with a C02 mixture being pumped by HBr or DF lasers are examined. Finally, the model is compared with the observations of Osgood [7] for an HBr pumped HBr/C02 mixture. 2.2 C02 Kinetic Model An extensive theoretical study of the rates of W and VT reactions of COZ-CO2 and COZ-N2 has been made by Herzfeld [27, 28]. We use his work as the basis for selecting the reaction paths for this system and we use Reference 28 as a guide for estimating rates when experimental measurements are not available. In addition, many of the reactions in the model are common to those reviewed by Taylor and Bitterman [26] and Kerber et al. [25]. The states (0310) and (0330) are assumed in equilibrium and statistically com- bined. We denote this combined state as (030) and adjust the kinetics accordingly. The small energy difference, 73 cm'l, between these states is neglected, and both states are assigned the energy of (0310). A schematic of the overall C02 kinetics is shown on an energy level diagram in Figures 2.1 and 2.2. The vibration-translation (VT) energy transfer reactions are denoted by dotted lines, 15 intramolecular vibration-vibration (VV) reactions are shown as solid lines, and the intermolecular VV transfer reactions are denoted by dashed lines with arrows to the final states. Initial states of these intermolecular VV reactions are C02 (0000) and the C02 state at the tail of the dashed arrow. Reactions involving the state (0220) are similar to those for (0200), but have been omitted from Figure 2.1 to preserve clarity. The detailed kinetic mechanisms 00), (02°0), and (0220) are included individually for the states (10 in the computer model (see Figure 2.2). This detailed modeling for the 602 laser system was first presented in Reference [25] and will be re-examined later in the text. We have limited our model to the level (0001) and the levels below it. For comparison, Figure 2.1 shows three higher levels. This work draws heavily on References [25] and [26]; it includes data prior to these studies only when necessary. In fact, the kinetics for the interaction of N2 with the CO2 system are taken entirely from Reference [26], since little new information on these processes has recently become available. All reactions and rate coefficients are the same as those given in Reference [17] except those specifically discussed in the following sections. The kinetic relaxation system used in this study for DF-CO2 and HBr-CO2 is given in Table A.1. 2.2.1 Transfer Between Fermi Resonant States. Theoretical SSH calculations (based on short range force interactions) by Herzfeld [28] and Seeber [29] for pure C02 indicate 16 that the rate of energy transfer between the strongly coupled levels in Fermi resonance 1 (15“) C02(1000)+M : 002(0220) + M + 102.8 cm‘ It = 0 is fast. However, these calculations also show that the reaction coupling the levels not in Fermi resonance, (152), is faster than (150). Recently, Stark has measured what is interpreted to be kgs [30]. He finds the value to be about two times that predicted by Seeber. Bulthuis and Ponsen [31] have measured the rate of decay of (1000) to (0110). Interpretation of this result is difficult since several kinetic paths are possible; however, any interpreta- tion of this result would yield a rate an order of magnitude lower than calculated values. Another experiment by DeTemple, Suhre, and Coleman [32] only adds to the confusion. Stark has reviewed these results and interprets the measurements of Rhodes, Kelly, and Javan [33] and DeTemple et al. [32] to be only a measure of an effective rotational relaxation rate. The laser fluorescence measurements of Rhodes et al. [33] at 300°K in pure CO2 indicate that kIS or kIS is possibly ten times faster than the calculated rate coefficients of Reference [28], which vary as T1’5. Very recent measurements and interpretations of Jacobs et al. [34] have tried to answer some of these questions. They have mea- sured the reverse of kIS for C02, He, and N2. They find* *All rate coefficients are in units of cc/mole—sec. 17 O _ 12 _ K_15 - 5.6 x 10 M - (:02 = 1.5 x 1012 M = He = 5.6 x 1012 M = N2 Seeber's calculated result is approximately seven times smaller than that obtained by Jacobs et al. [34]. While the value cal- culated by Sharma [35] (utilizing long range forces to determine the ratio) is about three times larger. In light of this recent data, it seems advisable to adjust the expected value of rate con- stants to be between these theoretical predictions. Also, since the trend with temperature of the two calculations is in the oppo- site direction for the majority Of cases, we temporarily assume that these rates are independent of T. Clearly more work is needed here to remove some of these uncertainties from the value of these rate coefficients. Therefore, we assume 0 _ 12 kl5 - 8.0 X 10 2 _ 12 Development of a 16 um C02 laser and its characterization will be a significant step in determining these rate coefficients. Herzfeld's calculations also show that N2 is nearly as efficient as CO2 for these reactions. In Reference [25], the rate coefficient for each species was adjusted such that all have nearly the same probability per collision as C02; we retain that assumption for the present time. This is roughly the result found by Jacobs et al. [34] for He and N2. The transfer between the other states in Fermi resonance, (1110),(0310), is given in Reaction (10): (10) 002(1110) + M : 002(0310) + M + 144 cm'1 Although Herzfeld does not compute this rate, he does compute the 10) state to total rate of deactivation of the combined (1110, 03 be twenty times slower than Reaction (150) at 300°K. This is prob- ably a lower limit on klo; we estimate k /10 ~ 0 10 = k15 In our model, Reaction (10) includes that relaxation between the levels (1110) and (0330) that are not in Fermi resonance. In most cases, Reaction (10) is of very little importance during lasing on either the 9.4 or 16 um bands. 2.2.2 Reactions Peculiar to the Addition of N2 It is often favorable to add N2 to enhance laser performance in traditional C02 lasers. That same advantage may also be found when lasing at 16 pm is desired. Additional reactions associated with the addition of nitrogen are listed below. Nitrogen can be utilized as a vibrational energy reservoir through the following resonant V—V energy exchange. (20) c02(0001) + N2(0) I 002(0000) + N2(1) + 18 cm'1 19 Taylor and Bitterman [26] have reviewed rate coefficient data for this reaction and their “best fit" in the temperature range from 300-1600°K 15* 2.49 e-3.390 k = 1.32 x 103 T 20 Collisional deactivation of N2(1) has also been examined in Ref- erence [25]. The associated V-T reaction is (21) N2(1) + M : N2(0) + M and the "best fit“ to the experimental data is for M = N2 -5 T4.51 e13.560 k21 = 1.16 x 10 for M = He [(21 = 3.36 X 10"2 1.3.44 e-4.679 2.2.3 Reactions Peculiar to the Addition of BF The DF-CO2 system has been well studied [25, 17, 36] and Cohen has given revised estimates of the D2 + F2 system since then based primarily on his measurements with Bott [37, 39]. Therefore, only a list of the kinetic mechanisms and their associated rate coeffi— cients is given.+ *Where 0 = - (103/RT), and R = 1.987 cal/mole - °K. 1”Deactivation of CO2 by DF has been included earlier. 20 DF vibration-vibration relaxation: (23a) DF(v) + DF(v) Z DF(v - 1) + DF(v + 1) _ 15 -1.0 (23b) DF(v) + DF(v + 1) Z DF(v - 1) + DF(v + 2) = 3 x 1015 T'l'O k 27b (23c) DF(v) + DF(v + 2) : DF(v - 1) + DF(v + 3) _ 15 -1.0 k27c — 1.5 x 10 T and finally DF vibration-translation relaxation. (24) DF(v) + M I DF(v - 1) + M k28 = v x (4.5 x 104 T2'2 + 5.3 x 1016 T'Z'O) DF(v) k _ -6 4.7 28Ar — 2.7 v x 10 T V k = 2.3 v x 103 T2‘2 28N 2 The DF—He rate is taken as twice the DF-Ar rate and C02 is assumed to be as efficient at N2 in deactivating DF(v) to translational energy. 21 2.2.4 Reactions Peculiar to the Addition of HBr Addition of HBr to CO2 mixtures for optical pumping with an HBr laser has been accomplished both for conventional 10.6 um lasers [5, 6] and 16 um lasers [7]. In this section, we formulate the kinetic mechanisms associated with HBr—CO2 mixtures. Rate coeffi— cients are of primary interest at 200°K since a main goal of our HBr/C02 modeling is to compare with the experimental results of Osgood [7]. The V-V transfer reaction is of primary importance for this HBr-C02 mixture: (25) HBr(v) + c02(0000) : HBr(v - 1) + 002(0001) For this reaction, we use the rate 12 k = 5.22 x 10 v 25 as given by Stephensen, et al. [25] at 300°K and adjust its value to 193°K using the same temperature dependence as that for DF. Vibrational-vibrational relaxation of HBr(v) is given by (25) HBr(v) + HBr(vl) : HBr(v - 1) + HBr(vl + 1) 1 The rate coefficient for v = v = 1 is taken as 4.12 x 1012 at 300°K as measured by Burak et al. [40]. We assume that this rate scales with v and T similar to the DF-DF VV rate. Vibrational- translational relaxation of HBr(v) (27) HBr(v) + M : HBr(v - 1) + M has been measured by Zittel and Moore [41] at 189°K for self relaxa- tion. This rate is used without temperature correction for the 22 comparison with the results of Osgood. The rate for M = He has been measured by Hopkins and Chen [42] at 300°K. We use this result with the same vibrational and temperature scaling as the DF-He V—T rate. Efficiencies for other species are scaled relative to M = He as has been assumed for DF V—T relaxation. The complete kinetic model for the C02 laser is given in Table A.1. In addition, the individual rotational populations associated with the lasing tran— sitions are modeled separately, with R-T relaxation given by 2 1L C02(v1,v2,v3,J) + M Z C02(v1,v2,v3,J1) + M The rate for rotational relaxation was taken from the measurements of Jacobs et al. [43]. 2.3 Theoretical Model 2.3.1 Laser Simulation The laser computer simulation developed in this study is similar to the one described in Reference [25]. A brief resume of its features is presented here. Rate equations are used to represent the chemical kinetic and stimulated emission processes occurring in a representative unit volume within a Fabry-Perot cavity. All processes are assumed to be uniform throughout the cavity. Only the P-branch of the (0001) — (0200) and (0200) - (0110) bands are permitted to lase, and a Boltzmann distribution is assumed for the rotational levels that are not involved in the lasing process. 23 The vibrational and rotational exchange reactions may be written, for reaction r, in the form k ZGINJIZBINJ (21) 1 ri i kfr i ri i ' where [Ni] is the molar concentration of species i, ari and Bri are stoichiometric coefficients, and k+r are the forward and back- ward rate coefficients. The rate of change of concentration of 002(0001,J) is given by d[C02(0001,J)] 0 dt = ' X(19J + 1) + Xch(00 lsJ) + YO pt (2.2a) For C02(0200,J), we have d[C02(0200,J)] 0 "‘“"“at“"“ = x(1,a) - x(2,J + 1) + Xch(02 0,J) (2.25) and for C0(0110,J), we have d[C02(0110,J)] 1 ——dt—— = x(2,J) + xch(01 0,11) (2.2c) and for all other species d[Ni] . dt = Xch(1) (2.2d) For the case of HBr pumping the optical pumping rate is denoted by YOpt' The photon emission rate, x(1,J), is the rate of change of concentration resulting from stimulated emission on the (0001) - (0200) band, and J is the rotational quantum number for the lower 24 level of a particular transition within the 9.4 un band. The photon emission rate x(2,J) is a similar quantity for the (0200) +-(0110) band. The designations 1 and 2 shall be used throughout this thesis to denote upper and .lower bands, respectively. The rate Of change of species concentration resulting from collisional relaxa- tion is XChU) = 2) (BY‘I " OLY‘IM'Y‘ (2.3a) r where O . B . _ rJ _ . OPJ Lr - kr g Nj k_r J NJ (2.35) The laser cavity is assumed to have a uniform photon flux with active medium length L, mirror spacing t, and mirror reflec- tivities R0 and RL' The rate equation for photon flux, f(i,J), is 21—: (in) = 3,4 [a (1.4) - 04mm f(i,J) (2.4) The threshold gain is given by qthr(i), where athr(i) = "2E 1n(R0RL(i)) i = 1,2 (2.5) Note that the product RORL(i) will in general be different for the two lasing bands. Only P-branch transitions are considered; thus, the gain of a transition with lower level J(J') is hNA 20 + 1 a(1,J) = 7fir-w1(J)B1(J)¢1(J){§j—:—T [C02(0001,J - 1)] (2.6 ) - [C02(0200,J)]} a 25 and “N 2 20'+-1) 0425') = 4—15 520' MIN >520: )I—gfi- [cozmz0 0,J' - 1)] - [C02(0110,J')]} (2.6b) where the wavenumber of the transition is w1(J)[w2(J')] and B1(J)[B2(J')] is the Einstein isotropic absorption coefficient based on the intensity [44]. Ijruebroadening constants and resonance con- stants used in the Voigt profile 01(J)[¢2(J‘)] at line center are those of Reference [25]. Planck‘s.constant, the speed of light, and Avogadro's number are denoted as h, c, and NA, respectively. The photon flux terms are related to photon emission rates through the relation x(i,J) = d(i,J)f(i,J) i = 1, 2 (2.7) and the output lasing power per unit volume for a band given by Pi(t) = 3: P(i,J) (2.8a) and the power on a given transition is P(i,J) = hCNAw1(J)x(i,J) i 1, 2 (2.8b) A numerical integration routine may be used to solve Equa- tions (2) and (4) to determine species concentrations and the photon flux on all transitions; here, this work uses the Runge-Kutta inte- gration method of Shampine et al. [44]. 26 The laser pulse energy per unit volume is given by t0+t c E1 = j~ Pi(t)dt i = 1, 2 (2 9) t0 where t0 is the time of pulse initiation and tC denotes the time lasing terminates. 2.3.2 Summary of Important Relaxation Mechanisms , \Now we shall review and discuss the kinetic processes impor- tant to the 16 um laser band. Mechanisms affecting lasing at 16 um may be understood by examining the kinetic mechanisms that deacti- vate the upper and lower levels of this band. First, we examine mechanisms that relax the upper level (0200). These mechanisms are shown in Figure 2.2. The rate Of change of the (0200) population due to kinetics is given by 9I9§g_l = + kg[0001][0000] - k92[02°O][O1IO] + kg[030][0000] - k95[0200][0110] - kg[0200][0000] + k97[0110][0110] + kgl[1110][M] - k911[0200][M] + k13[030][M] - kg3[0200][M] + k15[1000][M] - k915[0200][M] 27 + kg7[0220][M] - k917[0200][M] - k28[0200][M] + k918[0110][M] The three significant paths for deactivation of (0200) are as follows: 2 1. The VT relaxation of (0200) to (02 0) through Reaction (17) followed by VV relaxation of (0220) from Reaction (72). 2. Direct V-V relaxation of (0200) by Reaction (70). O 3. The VT relaxation of (0200) to (10 0) through Reaction (150) followed by vv relaxation of (1000). Path 1 is the most significant as can be seen by the time history of net reaction rates shown in Figure 2.3 for a typical case. The dashed curves indicate the magnitude of reactions running in reverse. Relaxation of (0110) results primarily from V-T processes with He. Self relaxation of (0110) by C02 is two orders of magni- tude slower for the present mixture. 2.3.3 Laser Performance Characteristics In this section,the relative importance of the kinetic mecha- nisms is examined and assessed as a function of the strength of optical pumping conditions and optical extraction parameters. A schematic diagram of a possible configuration for the Optically pumped 16 um C02 laser simulated in this seCtion is shown in Figure 2.4. 28 Fccowmw__oo esp ow Loews mpawsomnzm ash mp6s one mmpmowncw m:w_ umcmwv asp moans coepomms am: 302m ADV use Acv moo—a uum z .5:— oe.om_ no.8: oo.mo ca.m. oa.a~ p b .Lmn525 sz mmwowam .wmcm>we cw oceans; cowpommc as» Low .mcwmmp E: 0H ow pcwpsoaew pmoE mommwoosa com rIII 1 60-.- (18190-1 Il'l 60-53 " 60-:- r 00'1- .wmwo Pageazp a Low mmpms cowpumms pmz .n.mm.m acumen own z .u:.» oo.om. oo.». ao.;. oe.m. oo.;u eo.o IIIIIIII w HHHHIIIIIIII é: . II Iawanw.I.I.IIII ”r an »i IIIIIIIIII .% .epz .I . m . I. “pi .w y I: .w Amy n 00‘1- 29 , .Lmnszc sz mmmomam chowmwppoo mcp op Loews mpnwcomasm ash .mmsm>mc cw mcwcczs cowpomm; one see one; any mmpwomucw wch uwzmmc use .mammp E: 0H on ucwucoase “mos mammmoosa so; mmpms cowuomms pm: 305m Auv can on mpopa .mmmo Fwowaxp 6 so» moves cowpoemc umz .c.om.m mesmed wow 2 .82.. cum 2 .u=_~ oo.oo- oc.&o Oc.fin oo.fiw OO.&N 00.9. 06.0Jj OO.&I OD.£G OO.WW Oo.ml 60.6. pI ”I IllIlIlIIIlIIIIIIIIIlIIIlIIIIIII w. .m ceszz .m eyeza ” n IIIII "r hr \\ T.” N I.” II . .2zg . ~zs:z n. ~ y .w1 ._:¢ .» Onu IO -Omw 0 52.5 H m we: H j at n... lllllllllllll .w -w e==_¢ .IIII . . I IIIIIIIII .lI.lIIIIII. W lllll fir aezx IIII .m ~==_¢ lllll .IIII em .m e W 00"- (181001 3O DFIHBr Pump Laser us.__/u ------ A / 9.4/um C02 Laser / / U:__/ [In/"71) / / ‘6- -Y\___/ 16,um COZ Laser Figure 2.4. Schematic diagram of a possible configuration for an optically pumped 16 um C02 laser. 31 The time—resolved spectral output for direct optical pumping of a 12 torr, 1 C0225 He mixture at 300°K is shown in Figure 2.5a. This case simulates direct pumping to C02(0001) (by an HBr laser) and instantaneous saturation with a 9.4 um C02 pulse which results in 10% of the c02(0000) population initially residing in 002(0200). Unless otherwise noted, the cavity used for the present calculations has R0 = 0.9, RL = 1.0, and L = 2 = 20cm. Lasing was restricted to the four P-branch transitions shown in the figure. The effect of this restriction will be assessed later in this section. The strongest lasing is observed on transitions at the boundary between lasing and nonlasing rotational levels. For this case, the time histories of excited state species concentrations important to laser performance is shown in Figure 2.5b. The abrupt change in concen- trations Of (0110) and (0200) near 20 nsec corresponds to the onset of lasing as shown in Figure 2.5a. The lack of simultaneous abrupt changes in the (0220) and (1000) concentrations was surprising. However, the relaxation rates into and out of these levels were not sufficiently rapid (when compared to stimulated emission) to propagate the concentrations jumps to nonlasing transitions. Instead the observed effect was a smooth change over a period of time. The relative importance of the net vibrational relaxation mechanisms for this case, illustrated in Figure 2.3, was discussed earlier. The pulse terminates at 100 nsec; therefore, any relaxa- tion occurring after this point is of little importance. 32 .mcmeF E: mH mewFFocpcoo mFm>oP mgu Low mcowpwspcwocoo mmwomqm eo mmeOHmFL week Aav .mem— E: ofi wcp mo mco_uwmcmcp umpomem :o smzoa mo woes0me; wepp Amy m.N essay; .82.. us: can 5 “2: 8. a 8 s a o 8 s a a . .— [IlliIll I\lIlIl Sac: ) 8%? I on 3 m 3 m I 9 HI. . -. m m 5%: Mk I S W m m m I 8 6.5 I 2 .8. 3. i, as. ou— 22—55—5 5.; .o :53 .2 :2 2 a8 :2 N :85... E: 5.8.. 33 Recall that initially we have a very high population in (0200) as a result Of the Optical pumping. Hence, we see that the con- trolling mechanisms are those reactions that relax this level to those closely coupled to it; i.e., reactions (5), (72), (152), (17), and (18°). For the present gas composition, the VT mechanisms with He are stronger than C02 self-relaxation through VT relaxation (again see Figure 2.3). The model includes detailed R-T relaxation mechanisms. For the present case, lasing was limited to P(17), . . . P(23). This somewhat artificial limit to the number of lasing transitions causes a hole to be burned in the rotational population. As a result, the"0utsidE"lines in the rotational manifold become the strongest lasinglines as a result of rotational relaxation from the popula— tions outside the lasing band to those at the edge of the lasing band. This phenomenon is most significant near termination. We observed this behavior for both four and six transition lasing cases. In Figure 2.6a, we examine the relative time evolution of power on the four lasing transitions. The figure clearly shOws the effect Of burning a hole in the rotational population. This hole causes transitions internal to the lasing rotational manifold to exhibit weak lasing relative to transitions on the boundary, especially near termination. The lower level has a "negative" hole in its population. This rotational relaxation mechanism is shown schematically in Figure 2.6b. The standard rotational relaxation rate used is that given by Jacobs et al. [43]. 34 .mnowpemcosu mnemop onu ucomonaos oxenso onp ”onwnnsn opon Focowpopos op ozo mnowponpnoo Inoo one .monWF oonmmc mmnowpopzaoa Eswnnw—msco pcomonaon mo:WF nepom .mpo>op mnemoP on» to nonpospnoonoo Ponowpopon onp no poommo one mnwzonm unpoaonom Anv .23; one mnwnso moswp ponwumvo oonnu no monon mnemop no Lozom on .mnwmop monon Ponoenopon eo conga: one mnwpowspmoc >n oomzoo onenczn open Fonowuopoc to pooomo one onwzonm Eonmowo .25: e358 2252. .q :3. . 5:2 mm s w. = P you c of! «5:75.. actfl A" 8:338 5.5.338: I I I I u: c _.n||| 8.538 52.535 I|II InIun human umnnflduwuflmfluva ”a (W ”Md 3. .3 3355—3. 1.3.. 0225 a. :2 2 n8 .3: 3.5.2:... 53.. I... .e.~ ocsmen 35 In Table 2.1, results using this rate are compared with results using a rate twice the standard. The time t1% is the time for the power to drop to 1% of its peak value, Pp. The results shown here are similar to those Observed earlier for HF lasers [46, 47]. More rapid rotational relaxation increases pulse energy and pulse duration. Accurate modeling of rotational relaxation permits the assessment of the amount Of energy extractable on a given line or set of lines. In Table 2.2, we compare the results of calculations for extracting energy on six and four lines with single line lasing. The mixture and initiation used for this table was higher pressure C02 with stronger pumping and 9.4Tflnsaturation. (This strong pump- ing case corresponds to initially placing 50% of the ground state population in (0200).) These results indicate that line selection may yield approximately 50% or more of the multi-line energy in a single line. Of course, these results are sensitive to composition and initiation conditions. It is interesting to examine the gain time histories for a single line case; see Figure 2.7. Single line lasing simulates the use of a grating for one reflector of the cavity. For this condition, only P(21) reaches threshold, although the other lines experience gains well above the threshold for P(21). The dashed line in Figure 2.7 is the power on P(21). Note, the gain of P(21) remains at a quasi-steady value for nearly 50 nsec after it drops below threshold. The quasi-steady condition is a result primarily Of rotational relaxation into (out Of) the upper 36 So. 0 mi owm .o NI“ 5. . o NIm 92.0 NIm 0%. o nmnoo no Amnono noon? no poommm .m.m onzmwn a... 5...: .65.: 22.55.: e5... :8. - u... 552. 5.... . 7... v... m... . a. ... a ... n o e 1 u 1 —.e d q q 1 e m I — m m m n m $23.8 1 a w m w I 2 m m m m. n. m m 1 ~... {on . _ t . o: 2... n 2 v.88. . . :23 . n a. . nNo8 . me— .n. .m. 41 to the spatial distribution of the pump laser, etc. From the figure, one may conclude that the conversion efficiency increases with input strength over the region shown. Of course, this trend cannot and dOes not continue indefinitely. The highest input energy plotted corresponds to putting half of the ground state population into C02(0200), which is probably a realistic maximum coupling of pump energy. Over this range of practiCal interest stronger pumping yields higher conversion efficiencies. Basically, the phenomena observed results from the competition between optical extraction at 16 um and relaxation of C02(0200). The conversion efficiency of the 9.4 pm saturation pulse is shown in Figure 2.8b. For this figure, the strength of the HBr pumping pulse was held constant at a value that corresponds to putting 10% of the initial C02(0000) population into C02(0001). Hence, this case corresponds to very strong HBr pumping. In general, strong HBr pumping requires lower 9.4 pm saturation to achieve and sustain lasing. The 16 um laser pulse begins more rapidly and with much higher initial power as the 9.4 pm saturation level is increased. Clearly, Figure 2.8b shows that increasing the 9.4 um saturation strength may not be efficient. However, under certain conditions one cannot observe 16 um lasing without 9.4 pm saturation. For the case in this figure, lasing was present even without9.4innsaturation. The effect of He concentration on the pulse duration and pulse energy is shown in Figure 2.9a. The pulse energy is found to be relatively insensitive to He, while the pulse duration decreases 42 PULSE DURATION (nsec! R— .cowpwczu wmpsa vcm xmcwcm mmrza :o wczmmmca do pomewm :3: gang: Nazca! 3— R a “as. . . 3.1.8" 3. um um 351M .mczmmwcn mcszwe Pave» we aowwwm PULSE DURATION (nut) .wcsmmmga m: we powmwm Es. :33: :. 8. 8 S 3 a .. . c . . . 1 . c 2 I. a .3. a. ,IIIIIIIIIIILAHHHHWIIIIIM.. 8— $.— § -3 seam . . :38 . N8 .2. Am. (rm mam 351M .m.N me:m.. 43 with He concentration. For the region where He j_C02, we find that increases in He result in increased 16 um laser power, without sig- nificant changes in pulse energy. The increased power is a result of more efficient relaxation of (0110) through Reaction (19b). As expected, the effects of pressure scaling on laser per- formance are to increase pulse energy and decrease pulse duration with increasing mixture pressure. This trend is confirmed by the calculations shown in Figure 2.9b. For these calculations, the input optical pump energy was increased proportionally to the pres— sure so that the fraction of CO2 placed in (0200) was held constant. Therefore, the total effect of pressure scaling shown in the figure results from kinetics and pressure broadening. 2.4.2 Optically Pumped DF/He/C02 Mixtures For these calculations, very strong DF pumping was assumed. The net result of the DF pump laser was to place 90% of the DF con- centration in DF (1). The effects of C02 and He concentrations on 16 um laser performance are shown in Figures 2.10a and 2.10b, respectively. In general, increasing the COZ/DF ratio tends to increase pulse energy and decrease the pulse duration until the DF/CO2 concentrations are equal. Increases in the He/DF ratio decrease pulse energy and increase pulse duration. In Figure 2.11, the effect of mixture temperature on 16 um laser performance is compared over the range of practical interest. Our calculations show that pulse energy may be expected to increase by about a factor of five for 200°K mixtures relative to room temperature experiments. 44 mI\NOU\.o e PULSE DURATION lunc) .mgzwmwga m: we powwwm Anv .wxzmmeQ moo mo pummmm Am. .mem_ no m An emasza m.:pst co. cowpmczv mmpsa new Amcmcm mmpza :o cowpmmoasoo mcszws $0 pomwmm :5. 253.... s. :5. =33... N8 a e .m cm .... . e o a J. .... n. .. .. - .e w w m s n . 2. 3 . 1 m m m m m w . . .s m :2... . a. :28 . a . S . 2. . L 3 :8. . . to: . N8 Lne—B I ma mn DIN 35104 .o..m ma:u.. PULSEENERGYIJH) Figure 2.11. 45 20~ -20 DF - 20torr .0 1.5_ He - 20torr _1_5 5 C02 - 2torr F" U C 2 2: E L0- _ 10 E? 3 Q5_ _05 O 1 L I 0 am am an TEMPERATURE (°K) Effect of initial gas temperature on pulse energy and pulse duration. 46 These conclusions should be tempered by the fact that confidence in the selected value of most rate coefficients decreases with tem— perature as a result of the availability of experimental data. 2.4.3 Optically Pumped HBr/Ar/C02 Mixtures For these calculations, we simulate pumping a HBr/Ar/CO2 mix— ture with a pulsed HBr laser. The HBr pump is assumed to deliver 1.06 J/R that is absorbed by the mixture in a sinusoidal pulse with a 200 nsec duration. The mixture temperature for these calculations was taken to be 193°K. For the composition examined in Figure 2.12, we find that the pulse energy is a maximum for a C02:HBr ratio of s 2.5:1. The pulse duration decreases monotonically with CO2 pres- sure. Further examination of HBr/CO2 mixtures will be made in the next section. 2.5 Comparison of Model and Experiment The pulsed experiments of Osgood [7], for a HBr pumped HBr/ COZ/Ar mixture, are compared with the computer model in this section. The output observed by Osgood from an apparatus similar to that depicted in Figure 2.4 is shown in Figure 2.13a. From the measure— ments reported, quantitative estimates of the energy absorbed by the 16 um cell from the HBr pump laser pulse and the 9.4 pm satura- tion pulse were difficult to determine. In Figure 2.13b, model predictions are shown for conditions with and without 9.4 pm satura- tion; all other conditions were set to reflect the conditions of the experiment. 0.1 0.03 e 5 0. 00 E 55 a: —I a 0.04 O. 02 47 - 10 Hm -Ofimn Ar - 3t0n' T - 193°K - 8 as (965d) NOIIVHI‘IO 3510c] O. 01 0 C02 1 HBr Figure 2.12. Effect of mixture composition on pulse energy and pulse duration forauiHBr/COZ/Ar mixture pumped by an HBr laser. .Fwnoe map >2 empowumLQ mm cowpmezpmm we Fw>wF wo pumwwm An. .mvg uoommo wo mppzmm. prcwswcmaxm Am. .xgomgp ccm pcwewcqum $0 cemvcwaaou .MH.N mesmwm 48 .si .2: 33$ .2: m N _ V m N _ o _ I— d 9 _ — O o . .< I lo M m .. m 5:223 Elvd 02 W W x m .o u. I J .1. u m o 2 .M m n w w... fl 6 I to; . .< 8:228 E5... .82. :2 n .v . a. I :2 2 .o . woo 3 to. .. ... . .2. 3 5.163522 525.22.. 49 .co..m.=.mm a: ¢.m 0: e..3 o u o be m u HAoV.Q.\H....Q. was» seam m. mcwasza .Lcop OH 0 m: can .ccoa N u moo .Lcop om u .o m? mcszws mmm och .wcszws m:\woo\uo uwasza xppmowaao cm mo mucmscowcma comm. Au. .Fmvos ago he umaowcwca mm .< 40 pomymm on .xcomcp cam ucmswcmgxm we cemwcwgsou .mH.N mgzmwm as... .2: caiws: a. . “w L 8. W to; . ..< 8 w W v :32 o: 1 m o W. m o m n I. u as .W m :2£5.~8 to. m. .o . .2. 50 _ As expected, addition of the 9.4 pm saturation pulse increases pulse energy and shortens the time for 16 um lasing to reach thresh- old. Note that "weak" or “strong" 9.4 um lasing as discussed in I thiSthesis would show little difference in Figure 2.13b. The very abrupt increase in pulse power at threshold predicted by the model was not observed inthe experiment. All efforts to demonstrate with the model the gradual increase in power observed in the experi- ment have failed. One possible explanation of this discrepancy is the fact that the present model has no provision for the 16 um laser cavity to also lase at 3-4 um on DF or HBr. In the experiment, such a mechanism would tend to give results more consistent with those observed by Osgood.- The only condition where the model pre- dicted a smooth shaped pulse was for a weakly pumped DF/CO2 mixture at 300°K, as shown in Figure 2.13d. Note, all the HBr/CO2 mixtures examined are at about 200°K; hence, perhaps some of the observed difference is a result of an erroneous temperature dependence of a rate coefficient. Finally, in Figure 2.13c, the effect of argon on the predicted 16 um output is examined. The trend shown in this figure is opposite to that observed by Osgood. For calculations examining the effect of argon, the 9.4 pm saturation pulse was not present. Fortunately, the credibility of the present model is some- what redeemed since the two trends that have been predicted by our model, which are contrary to the experiments of Osgood, have been recently observed by Barnes [22]. Barnes has found that under the conditions of his experiment that 16 um pulse energy decreases with 51 Ar, and he also sees a more abrupt increase in 16 um power at initiation. 2.6 Sumnary This chapter presented a computer model which revealed the important kinetic mechanisms in the DF/CO2 and HBr/CO2 TCL laser devices. Some comparison with experiment was performed and the results show the model to be deficient in some regimes of interest. The next chapter is devoted to the description of an improved version of the computer model. More attention is given to comparing the model's predictions with experimental results. CHAPTER 3 PREDICTIONS OF A COMPUTER SIMULATION FOR A 16 um HBr/co2 LASER 3.1 Introduction The results of calculations of a previous laser simulation for HBr/COZ/Ar mixtures [48] were compared to the experimental observations of Osgood [7, 8]. This model was successful in pre- dicting many of the observed results. Certain predictions of the first model, however, did not coincide with the experiment. Accord- ing to Osgood, as Ar partial pressure is increased, the 16 um pulse power increases. The model implied the opposite trend. It also predicted pulse shapes that were too sharply peaked when compared to those actually seen by Osgood. Several changes have been made on the computer model to allow more accurate modeling of the laser system. The results of this improved simulation were again compared to Osgood. The model calculations were also compared to the results of experiments performed by Barnes[22]. In both cases, the model predicts results similar to those obtained experimentally. The model predicts that increasing Ar pressure increases pulse power in agreement with Osgood. The model also predicts that increasing Ar pressure decreases pulse energy in agreement with Barnes. The utility of this model, however, is greater than reproduc- tion of experimental results. The observations of the experiments 52 53 of both Barnes and Osgood can be explained by analyzing kinetic mechanisms. In short, this computer simulation is capable of demon- strating those kinetic mechanisms responsible for producing these results. In addition, the model is also used to predict results in regimes of interest that have not been examined by experiment. 3.2 Theoretical Model The computer model described in this chapter simulates an HBr/COz/Ar gas mixture in a laser cavity being pumped by an external HBr laser. Details of the model formulation are described in Chap- ter 2. The significant difference between the model described there and the present model is the method by which the optical input pulse is simulated. In the first model, it was assumed that the popula- tion inversion of HBr occurred instantaneously (i.e., in a time short, compared to the rate of the transfer of energy from HBr to COZ)’ and the initial HBr rotational population was taken as a Boltz- mann distribution in equilibrium with the translational temperature, l' (for“ all cases examined T = 193°K unless otherwise noted). Although this is a good approximation for many systems, it does mask effects that are significant. The most important of these is the result obtained by varying Ar partial pressure. These results, obtained from an experiment, cannot be predicted without the more detailed formulation. The second model determines the time history of the gain of the first fifteen rotational levels for the first two vibrational levels of HBr. Rotational nonequilibrium mechanisms of the HBr 54 levels are modeled in detail. Rotational nonequilibrium effects in CO2 were included in the first model also. Absorption by HBr occurs in selected rotational levels of the O-1 vibrational transi— tion. The gain of each level is: 0.1 = TWA... (0)31. (0)0101) [ng—H- HBr(v = 1) - HBr(v = 0)] (3.1) where mi = wavenumber of the transition; Bi = Einstein B-coefficient for the transition; ¢i = line shape function for the transition. The input pulse, the number of HBr photons/sec-cmg, f, is modeled as a time rate of change of HBr photon flux % = E1 sin (wt/2 ) (3.2) where E1 is a constant which adjusts the total input energy to a specified value. Since the rate of increase of the flux is propor- tional to the flux input, the integral of the function is set equal to the total energy available from the HBr pump laser. The value of 80 md of Osgood [7] is used. Cavity losses are included. Effects such as bleaching of a particular vibrational-rotational level are modeled in detail. One parameterthat controls bleaching is the rotational relaxation rate of HBr. As this rate increases the ability to bleach a particular transition decreases. The graph in Figure 3.1 illustrates this effect. The rate constant for rotational relaxation is 55 Gas Mixture HBrzCozzAr P'|.0 I 5.33:4 '5 P = 7.75 torr " T = 193'k P==0.l 2 '0 -- 'E z: 2‘ S. {g :5 > c: 23 E. 33 E 5__ E .5 P=(10l O ' f i L0 2.0 TIME I/usecl Figure 3.1. Effect of HBr rotational relaxation probabilities upon bleaching. The standard case is P = 1.0. 56 k = PZHBr-M (3'3) where Z is the binary collision rate between HBr(v,J) and species M. The parameter P is the probability per collision that relaxation occurs. For molecules with large moments of inertial such as the hydrogen halides, there is uncertainty in both the mag- nitude of the rate constant and the rotational quantum number depen- dence of rotational relaxation. Polanyi and Noodall [21] suggest that the rate constant k is of the form given in Eq. (1.3). Although experiments for HCl and HF have shown this to be the correct form for k, there is disagreement as to the value of P and of C. The experimental results of Hinchen [49, 50] suggest rotational relaxa- tionof HF decreases rapidly from gas kinetic values at low J'to less than 50% gas kinetic for J greater than 7. The data of Hinchen predicts a value of 0.10 for C. Milkins' [51] data showseavariation from 0.45 to 0.10 times the gas kinetic rate as J increases from one to fifteen giving a value of 0.52 for C. Polanyi et al. [52] predict C to be 0.917 giving even a larger J dependence for the relaxation rate of HF. Although these effects are less dramatic for HCl and HBr, there is little or no recent data to demonstrate that rota- tional relaxation rates for these species are known with certainty. Thus, the model assumes that the rotational relaxation constant is independent of AE. The parameter P is set equal to one, cor- responding to a rate equal to binary collision rate. For low J values (J < 6) this assumption is realistic. The model assumes 57 optical pumping (Ml the J = 2 and «J = 4 levels of the HBr O-l transition. There are factors other than rotational relaxation rates influencing whether or not a particular transition will be bleached with optical saturation. As expected, bleaching increases as pulse energy increases or pulse duration decreases, i.e., as the input intensity increases. There exists an optimum input pulse beyond which the vibrational rotational transition appears to be bleached. Multiline operation, however, generates a very complex distribution where bleaching may be difficult to isolate and the general trends of pulse conversion efficiency, as a function of input pulse strength, are dependent on the particular transitions selected. The time history of photon emission occurring in the HBr/CO2 cavity is illustrated in Figure 3.2. The dip in the 9.4 pm pulse profile coincides with the onset of 16 um lasing. Oscillation on 16 um begins and ends during 9.4 pm laser action. The long power tail on the 9.4 pm pulse suggests that collisional relaxation of HBr is not a significant mechanism since lasing continues long after the end of the 4.3 pm input pulse. The delay between the input pulse and the commencement of lasing on 9.4 pm and 16 pm is important when one is concerned about pulse conversion efficiency. The effect of CO2 and HBr partial pressure on pulse delay is shown in Fig- ures 3.3 and 3.4. The curve in Figure 3.3 describing the delay of 16 um lasing illustrates that this delay decreases as CO2 pressure increases until a minimum is reached. Although the exact pressure suf- ficient to eliminate 16 um lasing through deactivation of the (0200) level 58 .mo. x2 cmwpawppzs ma u_:o;m czogm $32. In “2» 2.8... Amoflxv 5.532. of. .33.. a: 3 m5 new .33.. :3 7m 93 .mmpza “sac? gm: mgp mcm emus_o:H .zpw>mo Nou\cm: cw cowmmwsm cowosa we acoamvg weep .N.m mesmw. 33$ .2: m .. .... m. .. fl . n o a O M 3 HO w m. we; m 2 xOMO~ u .—. to. a .. . .. .sxm .., i... s e ”N ". .<.~oon.m: $5.5... 2o 5...: 59 GAS MIXTURE HBr:C02;Ar 1:1.33X:4 94/” T = 193°K 0.05 ‘_ P (3.75 + Zx)t0rr __ 10 Q 3 5 3 8 E; 0.03-n g5 25 -- 5 53 g a a s} 0.01 «- 0 0 : I 0 5 10 C02 PRESSUREfiorfl Figure 3.3. Effect of CO partial pressure on both 16 um and 9.4 pm lasing, and T6 um pulse duration. 60 GAS MIXTURE HBr:C02:Ar 1. 33X: 2 : 4 P =(4.5+x)t0rr T = 193°K +0.1 .- 9J®uni g -- 2. 0 .\ >— 5 Lu O I... 16,um U3 "J.5 _I 2 G. -.ILO +0.02"‘ "115 0 1 -0.02 i . 0 0 2 4 HBrPRESSUREtmrr) Figure 3.4. Effect of HBr partial pressure on delay of 16 um and 9.4 um lasing and 16 um pulse duration. Pulse delay time is relative to the completion of the optical output. Thus negative delays imply onset of lasing during optical pumping. 10,..m PULSE DURATION (fisecl 61 was not determined, 16 um lasing was not predicted for a CO2 pressure of 50 torr. This corresponds to an infinite delay time. This result is, of course, dependent on input pulse strength and gas mixture conditions. Increasing CO2 partial pressure shortens.the delay before the onset of 9.4 um lasing by increasing the rate at which energy is collisionally transferred to C02. Finally, 16 um pulse duration is decreased at higher C02 pressures because of the enhanced deactivation of the (0200) level. Increasing HBr partial pressure has a dramatic effect upon 9.4 um pulse delay, as the graph in Figure 3.4 illustrates. Not only does HBr enhance the rate at which energy is transferred to CO2 but, since the gain is a linear function of pressure in the lower pressure regime, the absorption of input flux is increased in proportion to the HBr partial pressure. As expected, 9.4 pm pulse delay and 16 um pulse duration decrease at higher HBr pres- sures due to increased energy transfer to CO2 and the increased rate of deacivation of the (0200) level. 3.3 Parametric Variation and Comparison With Experiment In this section the results of parametric studies performed by Osgood and Barnes are compared to the parametric predictions of the model. The cavity conditions, such as mirror reflectivity, cavity length, and input pulse strength, reflect the experimental conditions of OSgood. The input pulse energy from an external HBr laser is 80 mJ, with 67% of the energy available on the 0-1 transi- tion of HBr. The CO2 cavity has a length of 20 cm and a mode volume 62 of 0.62 ml. Only partial pressures of the constituent gases were varied in the computer simulations. 3.3.1 Effects of Changing HBr and 002 Partial Pressures The results of an experiment carried out by Barnes [22] demon- strate the effect of CO2 partial pressure and HBr partial pressure on 16 um pulse power. Optimum HBr and CO2 pressures were found in the experiments. The partial pressures of CO2 and HBr were varied in the model: the results are summarized and compared to the experi- mental values in Tables 3.1 and 3.2. An optimum 002 and HBr pressure were found. The diagram of kinetic mechanisms affecting the population of the (0200) level of C02 is shown in Figure 2-2~ The equation describing the time rate of change of the C02(0200) population due to chemistry and lasing is: d[C02(0200,J)l dt = XCH(020,J) - X(2,J+1) + x(1,J) . (3 5) The terms X(1,J), x(2,J+1) represent lasing on 16 um and 9.4 um, respectively. The XCH(020,J) term represents the net rate of change of C02(0200) due to collisional energy transfer. The reactions corresponding to the four most significant rates are listed below. (25) 002(0000) + HBr(v==1) I 002(0001) + HBr(v = 0) (15°) 002(0200) + M‘I 002(1000) + M (17) 00 (0200) + M : 002(0220) + M 2 (18°) 002(0200) + M‘i 002(0110) + M 63 .39.... .o 2...... 2: E .82.. 8.8% a... m... .o 8:38.. .28.. 2: m. 8:63. 8.3.2.... 3.2.5 x .2 8.2233 2. 2 2:8. 2: .. gem... .m a. 8 8.8.2.. -2 x mmm A. $2.3 5:2...828 .o .E: 2... 8:82: 8.335.. 32.5 ... .. . .om......e..fm..m.... ... "mam. u... .2 "N8 a... “:35... 2.. . a... 8.3.2.. 23. am an E 880...... 2.582 23. -o- E .3 .9 mg m. p.808. .82 . 35.5 852. 5.2.3.... 2.5: a... o... a... o... o... .5 e. a... Emmi»... .825... 2...... .53. .mppzmm. .muzasoo vcm Fmpcwewcmaxm cmmmen cemwcwasoo ”.mZOa E: o. :o mczmmmca moo mo pomwwm .H.m m_nmh 64 an: a h is 3 3. u a ~32; c1095: 9.352 mg EN Rm 2m 2: m2 .mEOE . EBA—Eco AmmZmmc cw mcwcczg cowpommc asp cow mum; msp mmumuwu:_ mew, umgmmv «sh .Fw>m_ Aeomov mgu “gamma gown: L< mc_>Fo>:_ mmpmg cowpommg FFw sogm any new Amy myopa .wmwu pmumazp a cow mmumc cowpomm; gmz 6:552: .83 us: cm 3 o... ~.o 3 ~._ 3 a. o. v. ~. . 1. + o. u n I, w u ” 2- x :2. E l! “0 It .I 1 IV m II T m . 11 O. u . l , . . / l _ fl / ~ — II “I / \ II “I . / \ ._ . / I \ ._ I E I. II \ _ \__ .02. E E. E \ \ x \ ._ .. .. """"""" l‘ \ \ 1.- No ll O. .09. E Anv Amy .m.m mcsmwe U!” 901 73 discussed previously, these reactions are important deactivation mechanisms for CO2 and HBr. Increasing Ar partial pressure increases deactivation and leads to an earlier pulse termination and lower energies. It is important to point out that the rate coefficient for Ar is smaller by at least a factor of sixteen than for 002, HBr, or He. The effect of He on pulse energy is shown in Figure 3.8. Clearly, He is more efficient in deactivating the upper level of the 16 um transition. The effect of Ar is only significant at rela- tively low CO2 and HBr pressures. The consequence of increasing Ar partial pressure on pulse power is less obvious. To enhance 16 um power the addition of Ar must increase the rate at which the 002(0200) level is populated, or favorable relax the (0100) level of 002. There are two paths by which Ar can increase the rate of populatingthe (0200) level of 002; one way is to increase a reaction which deactivates the upper level of CO2 and populates the (0200) level; or, another way is to enhance 9.4 pm power. The importancecfi’Ar in relaxing excited state CO2 into the 002(0200) level is ruled out. Any relaxation into the (0200) level is orders of magnitude less than the relaxa- tion rate out of the (0200) level by Reactions (17) or (15°) involv- ing argon. This same argument rules out the importance of Ar relaxation of 002(0100). Instead, increasing argon pressure increases 9.4 pm pulse power. This is done by increasing the col- lisional transfer reaction between HBr and 002 due to the increased rate at which the v = 1 level of HBr is populated. This effect is 74 illustrated in Figure 3.10, in which the magnitude of Reaction (25) is compared for two values of Ar partial pressure. The effect Ar has upon the rotational relaxation rate of HBr is important to increasing this transfer mechanism. The rate at which rotational relaxation occurs is assumed to be proportional to ZAB’ the binary collision frequency between species A and species B, which is given by: 1 2 z = [HBr] [Ar] [8“kT] /‘ (3.6) . “AB HBr,Ar where “AB is the reduced mass of species A and B. This rate is proportional to the partial pressure of Ar. Increasing Ar partial pressure increases the collision frequency. Next, we examine the equation describing the absorption of input flux by the HBr popula- tion, given by: df(v,J) ‘dt )f(v,J) (3.7) = C(a(V,J) - “thr where a(v,J) is defined in Equation (3.1), c is the speed of light, and a is the threshold value of the gain for an HBr transition. thr Since the term a(v,J) is proportional to the population difference of the HBr (v,J) and-HBr (v 2 1, J + 1) levels, maintaining the largest possible difference insures that a(v,J) is large. The term “thr is a constant for a particular laser simulation, the rate of absorption of incoming photon flux is then proportional to a(v,J). The rotational levels above and below the level being pumped serve as reserviors. Rotational relaxation replenishes the population of the lower level lost due to absorption. The increase in the 75 GAS MIXTURE HBr: C02 : Ar 2: 1 :1.33X P = (2. 25+x) torr T =193°K Ar =10torr 0.20 -- / 2%. e gg E“. < m E : 0.15 " Q < “a: 0.10-- : ' : 0.1 0.5 THHE Luaec) Figure 3.10. The effect of Ar partial pressure on the net reaction rate Of HBr(v = 1)+C02(0000):HBY‘(V:0) + C02(00°l). 76 'population at the v = 1 level caused by absorption is spread to other rotational levels by J‘+ J - 1 deactivation. An increased rotational rate enhances this effect. Clearly, the faster the energy is absorbed by HBr, the quicker the population of the upper level of HBr is increased, raising 9.4 um power and subsequently improving 16 um power. The increased rate of optical extraction at both 9.4 pm and 16 um, however, shortens the pulse duration. Previously, the model assumed that the rotational levels of HBr (v = 1) were populated in a Boltzmann distribution. This is equivalent to assuming an infinite rotational relaxation rate and a change of Ar partial pressure within reasonable limits have no effect upon pulse power. Increasing Ar partial pressure as illustrated in Figure 3.11 delays both the onset of 9.4 um lasing and the onset of 16 um lasing. The pulse delay is due to competition between two factors: (1) the increased rate of absorption of photon flux by HBr due to enhanced rotational relaxation as previously discussed, and (2) the lower value of the gain at line center due to pressure broadening by addition of Ar. The pumping mechanism must overcome this increased deactivation. The result is the delayed pulse. There is no pulse delay with increased Ar pressure in the Doppler broadened regime. As expected, pulse duratiOn decreases with increased Ar partial pressure. 3.4 Summary The model is capable of exhibiting many kinetic mechanisms and its predictions compared well with experiment. The most significant result is the reversal of the trend of Ar partial pressure and its 77 GAS MIXTURE 1 . 2 : 1.33X P = (2. 25+x) torr 0. 32 -- T - 193°K ~2J) 0.24 "' 16,..m 9.4m g 5 >- 5 Lu o b‘a“ 0.16 "' "1.0 -—l :3 Q (108 I F* O O 5 10 Figure 3.11. Ar PRESSURE (torr) The effect of Ar partial pressure on 9.4 pm and 16 um pulse delay and on the duration of 16 um oscillation. 16,um PULSE DURATION (yuseCI 78 effect on pulse power. It is a direct consequence of the detailed modeling of the optical input pulse. We have in several instances used the model to generate results under conditions that are of interest, but where experiments have not been performed. The com- puter simulations may be used to study the effect of various rate coefficients, some of which have been questioned in the literature, and to assign magnitudes consistent with experiment. More detailed experiments are needed which study the amount of energy in the optical input signal lost due to imperfect mode matching and mirror losses. Obviously, each pump laser will have a different spectral output and this needs to be specified in the experimental results. CHAPTER 4 FEASIBILITY OF AN HF-CO 16 pm LASER 2 EXPERIMENT AND THEORY 4.1 Introduction Because of the potential for high electrical conversion effi- ciency in the production of 16 um laser oscillation, the hydrogen and deuterium halide C02 chemical transfer lasers have been widely studied. Chang and Wood [5, 6] have reported 10.6 um lasing from HBr/C02 gas mixtures optically pumped by an HBr laser. More re- cently, Osgood [7] has observed 16 um lasing from a similar apparatus. A similar system using an HF or 0F pump laser rather than HBr would be highly desirable. The advantages of using HF gas are the higher output of HF lasers compared to HBr or DF lasers, and when compared to DF, HF is less expensive to use. Experiments by Manuccia [10, 11] in which an electrically initiated HZ/FZ/COZ gas mixture produced 16 um lasing is confirmation that an HF pumped pulsed 16 um C02 laser may be feasible. It is proposed in this thesis to optically pump the HF/CO2 gas mixture using an HF laser. With the HF optical transfer laser system, one has externally variable input power from the F + H2 system. The exothermic pumping reaction is separate from the HF/CO2 cell; hence there is little or no temperature rise experienced in the test cell. Foralnultilevel 79 80 system such as 002, in which the lower level of the lasing transi- tion is not the ground state, higher population inversions are possible. The upper level of C02 is pumped by the following reaction: (28) 002(0000) + HF (v,0) 2:.HF (v - 1, 0') + 002(0001) + AED where AED is the energy defect between reactants and products. For J = J' = 3, AED is equal to 1612 cm‘l. In comparison, the value for the HBr-CO2 and DF-CO2 systems is 209 cm'1 and 558 cm'l, respec- tively [53]. Laser induced fluorescence measurements [38, 55, 56, 57, 58] have shown, however, that the rate coefficient, k28’ for HF is nearly as large as that for HBr or DF and that all three have values larger than 3% of the gas kinetic rate. This efficient transfer of energy from vibration to vibration between the hydrogen halides and CO2 cannot be predicted by the accepted theories of energy transfer used before 1969 [54], in which the excess energy was assumed to go directly to increasing the trans- lational motion of one or both colliding species. Several schemes have been postulated to explain where this relatively large amount of excess energy given up by HF goes [58, 59]. Changes in the rotational quantum number of CO2 are ruled out [54]. The spacing between adjacent levels in C02 is approxi- 1 and a change of approximately eighty levels would mately 20 cm- be required to minimize AED. Changes in the rotational level of HF could easily be expected to absorb the vibrational energy defect 81 in the reaction minimizing AED. A change of six rotational quanta [54] would yield a AED < 60 cm"1 for the transfer process. The change in rotational quantum number of HF is the basis of a V +-V-R theory [60] developed to explain the large measured value of the vibrational deactivation of HF by the following reaction: (30HFM) HF (v,J)l+, HF : HF (v",J'_) + HF + AED' In the same manner as above, AED' is minimized by letting J' differ from J. Experiments employing differing methods have attempted to verify the existence of this V-R mechanism with only limited. success.* Reaction (3OHF(V)) is important to the operation of an HF-CO2 TCL device since rapid self-deactivation of HF may be an important kinetic mechanism in controlling 16 um lasing. Because of this, the experiment described in this chapter will examine this V-R mechanism as it affects HF self-deactivation. An HF-CO2 computer model will be used to examine the V—R mechanism responsible for energy transfer from HF to C02 (Reaction (28)). In addition to the experiments that examine the V-R mechanism in HF, the major portion of this chapter describes the efforts made to produCe 16 um laser oscillation in optically pumped HF/CO2 and DF/COZ gas mixtures. The computer model mentioned above was *For a complete discussion of this mechanism and a bibliography the reader is referred to the Ph.D. thesis of Robert C. Brown, Reference 61. 82 developed to simulate lasing in the HF/CO2 TCL device. The results of an analysis that examines the kinetic mechanisms that are impor- tant to both 9.4 pm and 16 um oscillation are also presented. Three questions may be answered by the results of both the experiment and theoretical analysis: 1. Is there a significant amount of HF transfer to C02 or does HF-HF deactivation predominate? 2. At what level in CO2 are the deactivation mechanisms signifi- cantly fast to extinguish possible laser action? 3. How does the HF-CO2 system compare to similar systems employing DF or HBr? 4.2 Experimental Study 4.2.1 Pump Laser and Saturation Pulse Laser A schematic diagram of the apparatus is shown in Figure 4.1. Several different geometries were tried and these will be discussed in detail later. Referring to the figure, the HF pump laser con- sisted of a plexiglass cavity 40 cm long and 6.25 cm wide. The CaF2 windows were held in aluminum holders, each 17 cm long, machined to the Brewster angle for CaFZ. The maximum reflector M4 was 97% reflective over the 2-3 pm regime. A grating (7200 lines/cm blazed at 10.6 um) could be substituted for the mirror M4, depending on the experiment. The pump laser worked by electrical initiation of an SF6/H2/He gas mixture. The reaction proceeded as shown below: 83 M1 M2 M3 M4 / I\ X] (g 7.7 COT"? HF PUMP ‘ M5 16 um CAVITY LASER GRATING "-‘-“i [ MONOCHIOMAtoT] I ABSORBTION l CELL I ouscroa I I- — — — I I scum | / I [ monommno: ] sox : assume»! I I cinema I L._._.__._.__ -I I I co: GAIN cm. I osmunscore I L _. _ __ _. _ _.- \w / C02“ "2‘“. 10.6.9.4 um LASER \ N = M6 Figure 4.1. Schematic diagram of experimental setup to produce 16 um lasing Using a pulsed HF laser to optically pump an.HF/C02 gas mixture. The C02 laser is used to optically saturate the 9.4 um transition in C02 to enhance 16 um lasing. 84 ' + F SF + e- ZSF5 6 F + H21: HF + H The He was used as a diluent to reduce the translational tem- perature during lasing. A Marx bank discharge circuit shown in Figure 4.2a used two 0.04 uf capacitors charged to 30 W to deliver approximately 36 joules to the gas mixture. The spark gap labeled (a) in the figure physi- cally rested on top of the cavity and was directly attached to the capacitor labeled (1). The minimum spacing between elements of the circuit helped to lower the circuit inductance to improve the laser performance by producing a more homogeneous electrical dis- charge in the SF6/H2/He gas mixture. Two copper flat plate electrodes 36.5 cm long and 3.5 cm wide, separated 2.54 cm, were used to produce the discharge in the gas mixture. The spark gaps (a) and (b) (Maxwell Model 40065) were filled with 5 psig dry nitrogen and were fired using the trigger circuit shown in Figure 4.2b. A photograph of the complete system, including the tWo charg- ing capacitors and spark gaps, is shown in Figure 4.3. In Figure 4.4 a schematic diagram Of the gas handling system shows the method of monitoring the flow rates of each of the three gases and the total pressure inside the HF laser cavity. The pres- sure was measured using a bourdon tube gauge (Heise). For the HF laser a 6H2:35F6:1 He gas mixture maintained at 150 torr total 85 R l I ———‘.‘V‘V3\Mfi———+ H V \ 1 \1/ 0.04;“ 0.04“, 323 50 MO. (2 Figure 4.2a. Diagram of Marx bank discharge circuit used to elec- trically initiate SF6/H2/He gas mixture. 100 M09 9 —NVVVV\NWV\N——v 2.5 M09 D HV flAAfiAAAAA/_fi l I 0.5 u‘ SPARK ‘“" GAP ‘— ~ 4.vawv~————- 5 M09 Q /500 pl (E‘—ii :: Figure 4.2b. Circuit used to trigger spark gaps in high-voltage discharge circuit in Figure 4.2a. 86 Figure 4.3. Photograph of HF laser facility at Michigan State University. V - VERNIER VALVES R - LOW-PRESSURE REGULATORS _®__< :> HEISE GAUGE V3 CHECK VALVE __ LASER 7 fl CONTROL COM pOyAELNVE ‘ L__®g HEISE .IiflfliI ‘_Q§75 78*‘<:>GAUGE "T‘ EXHAUST HASTINGS 'THER MOCOUP LE VACUUM GAUGE Figure 4,4, Gas handling system that provided calibrated gas mixture for SF6-H2 laser. 88 pressure were optimum for this particular cavity. The total energy was found to be between 150-200 mJ, as measured by a Hadron model 101 thermopile and a 141 nanovolt null detector (Voltronics). The spectral output from the HF laser is in the 2.5 to 2.8 um region. With the use of a grating the HF laser could be operated on a single vibrational-rotational transition. The output from the HF laser was detected using an Au:Ge photodiode detector (Raytheon QKN 1568) operated at 77°K. The output was displayed on a fast-rise (1.2 nsec) Tektronix 485 oscilloscope or a fast-rise (<0.5 nsec) dual beam Tektronix 7844 oscilloscope. A 0.5-m monochrometer (McKee-Pedersen) measured the wavelength of the output. As shown in Figure 4.1 the system also contained a COZ-NZ-He TEA laser. This consisted of a plexiglass cavity 1.6 m long and 2.54 cm in diameter. The system used NaCl windows held in aluminum holders machined at the brewster angle for NaCl. Details of the gas handling system are similar to those shown in Figure 4.4. The flow rates of each of the three gases were moni- tored using Matheson 601 flow meters, and the total pressure in the cavity was monitored using a bourdon tube gauge (Heise). A detailed diagram of this laser is shown in Figure 4.5. The mirror M1 was silver coated and had a 3.5-m radius of curvature. The flat output coupler was dielectric coated and was 95% reflective at 10.6 um and 9.4 pm. | I I I I I l I METERED news I gout-557°“ I CO2! N2' H. I ‘ I I MONOCHROMATOR I L-—“--—--4 Figure 4.5. 89 SCREEN BOX V r ------- q OSCI LLOSCOPE 125.391-93'55 I}; 1.... 3g u__,. WW—fi ’ powea SUPPLY—w so M9 r" ----- - - -—-] GEE I -—-vvv\—-oI-l GH I so Mg yoLTAGEI II— ' I ,I/ 1 I CAPACITOR I —-0 I TO VACUUM PUMP Diagram of pulsed 10.6 um (9.4 um) COz-NZ laser facility. The screen box served to isolate the detection equipment from outside electrical noise. 90 This laser was capable of oscillation on 10.6 pm or 9.4 pm and could be used to saturate these transitions in the HF-C02.gas_ mixture to enhance 14 pm or 16 um lasing. A 70 cm long plexiglass low-pressure cw'gain cell and a 10 cm plexiglass absorption cell were placed inside the resonator cavity. The cw'cell contained a 1 N2:1.85 C02:3.85 He gas mixture at 7 torr total pressure. Operating below lasing threshold, the REGULAIORS MCLEoo I- T T “I @— GAUGE I l DRY I I ICE | ‘ com “I“ _9_ MANOMETER I I 8 (D HEISE L _ _ _ _'J GAUGE I. now 3; MEIER . ..... 1 I ‘ . ”“3“” I —MIRR0R ' PIP-CO: I I L I DRY ICE METHANOL SLUSH BATH PUMP Figure 4.8. Diagram of gas handling system and pressure monitoring devices for the HF-C02.gas mixture cell. 96 in such a way as to verify the existence of the V-R mechanism dis- cussed earlier. The fact that sufficient population inversion between rotational levels can exist to promote rotational lasing has been substantiated by the results of various experiments [64, 65, 66, 67]. Deutsch [69, 70], using an electrical discharge in a CF4 + H2 gas mixture, has observed rotational lasing from levels as high as J = 18 in HF. Chang and Wood [5] also report rotational lasing using an SF6 + H2 gas mixture. In fact, energy from rotational lasing may be a significant percentage of the total output from the HF laser. Chen et al. [71] estimate that as much as 10% of the output from their 1.5 joule laser had a wavelength of 16 um or greater, implying rotational lasing. If the V-R mechanism is significant (Reaction (29HF(V))), then, it should be possible to optically pump an external cell containing HF gas using an HF laser oscillating on one or two tran- sitions in the P1(3) - P1(8) range. After V-R relaxation, one would expect to see rotational lasing from different J levels in the v = 0 band depending upon the level being preferentially pumped. By minimizing the energy defect and assuming that the v = 1 level of HF is optically pumped, the diagram in Figure 4.9 shows the two rotational levels in the v = 0 level that would be most likely populated by V-+V,R relaxation from any given level. Table 4.1 lists the value of the wavelength for various rotational lasing transitions. The large stimulated emission cross section for these rotational transitions [72] implies that a relatively small popula- tion inversion could produce a large value for the gain of the 97 5500 - —\J=Ib \ \ J=7 5000 - ”,,/””/”’::>r—____- _____ .hls ___ J_6 § \ / . 4500 - \\ so cogowz mocmgmymm Ant—+nn>v A ch gpmcm_m>83 a: meowp_m:mgp Commp .mcowgmgog a: nm>gmmno .P.q m—QMH 99 transition. Stimulated emission cross sections are about two orders of magnitude larger than for the corresponding V-V transition [72]. 4 For an excited state population of molecules of 10' torr [72] a 1 can be expected. small signal gain of up to 1 cm- For this experiment mirror M1 was 98% reflective over the region 14.3 to 20.0 pm. The mirror M2 was 98% reflective over the same region and was 60% transmissive at 2.5 - 3.0 pm. The experimental procedure consisted of flowing HF gas through the cell. The HF pump laser was operated on a single vibrational- rotational transition, usually at P1(6), P1(5), P1(4), or P1(3) since these lines would be expected to produce rotational lasing at wavelengths in regimes where the mirrors were highly reflective and where the Hg Cd Te detector was operative. There is no stated optimum HF pressure for such an experiment; while at low pressures rotational relaxation (which would deplete excited state rotational population) is reduced, it is also true that the V-R mechanism which depends upon collisions is also reduced. At high pressure the reverse is true. Absorption of the optical pulse is also pressure dependent with the absorption increasing as the pressure increases up to a point at which the pulse will be totally absorbed in a finite length. Thus, the experiments were run at pressures which varied from 0.1 torr to 500 torr. Initially we recorded output which we measured using the mono- chrometer and found that it corresponded to emission from the J = 15 + J = 14 transition. It was found, however, that this was merely a reflection of the original HF pulse that was entering the 100 detector. Once stray output was prohibited from entering the detector no other output was observed. Increasing the output energy and power from the pump laser was proposed to increase the energy absorbed in the HF absorption cell. To accomplish this the pump laser cavity was modified. Originally two copper flat plate electrodes 36.5 cm long by 3.5 cm wide transferred the electrical energy to the gas. These plates were separated 2.54 cm, thus putting the energy into a volume of 0.322 2. Incorrect or uneven gaping of the plates frequently caused inhomogeneous discharges. Thus, the top plate was replaced by two rows of 100, 1000, resistors. A comparison of these two cavi- ties is shown in Figures 4.10a and 4.10b. The width of the resistor rows was 1.27 cm and thus the discharge volume was reduced by more than one-half. The change, however, produced no noticeable change ’in the HF outputsignal. The last configuration tried is shown in Figure 4.10c, in which the bottom plate electrode was replaced by a 0.95 cm diameter copper rod to further decrease the volume into which the electrical energy is placed. A small increase (5-8%) in the HF output signal was found using this arrangement. The experiments to observe R-R lasing were repeated using the new cavity in the pump laser; however, there was still no evi- dence that rotational lasing was occurring. 101 r— H.V. FLAT PLATE | — [ ELECTRODES F"""] l RESISTORS FLAT PLATE I'_"_l l J :1 RESISTORS COPPER ROD Figure 4.10. Shows the end on view of three arrangements of elec- trodes used to electrically initiate the SF6/H2/He gas mixture. 102 4.3.2 Attempts to Produce Lasing in Optically Pumped HF- and DF-COZ Gas Mixtures The HF pump laser could be run either single or multi-line. When running single-line, the following procedUre was used: first, the wavelength of the HF line was verified using the monochrometer; second, HF gas was added to the HF/CO2 cell cooled to 200°K and absorption of the line was recorded. Finally, CO2 was to be added and various HF/CO2 mixture ratios and total pressures were examined. During absorption measurements, however, it was found that the absorption coefficient calculated for HF was significantly less than predicted. Polymerization of HF at low temperature was found to be the cause of the lowered absorption by HF. Measurements [73, 74] show that a significant percentage of HF is in the form of polymers below 260°K as can be seen from Figure 4.11. This is the case at pressures as low as 1 torr and .less, as shown in Figures 4.12 through 4.15. This was a major setback in achieving laser oscillation at 16 pm from an HF-CO2 gas mixture. Cooling the sample cell was exepcted to be necessary to increase the (0000) population of CO2 to increase the transfer process, Reaction (28). Cooling would also deplete the C02(0110) population to enhance 16 um lasing. Osgood [7] found that cooling was necessary for 16 um lasing in the HBr-CO2 gas mixture. The (0110) level is the lower level of both the 14 pm and 16 um transitions in C02. At 300°K, 4.1% of the total population of C02 is in the (0110) level, while at 200°K only 0.82% of the population resides in this level. A factor of 103 10°F Io'II— ' ' 2 10'2- 9 y— 2’ E 5.164 163 Id2 16' -3 IO _ In J ‘2’ 16‘- 165 l L L L L L I J 220 260 300 340 O r( K) Figure 4.11. HF dimer mole fraction(X ) versus temperature at four different pressures (atm . Where the subscript 2 represents dimers. 104 0 10 r Io‘I — 2 9 Id“- .— U < 3 L In ‘5 1635 IE Id‘I- 165 1 I 220 260 300 - 340 W K) Figure 4.12. HF polymer mole fraction (X1) versus temperature for a pressure of 0.1 atmospheres. Where i = 1, for monomers, 2 for dimers, and so on. 105 10°F- "I I6' — z "2 Q I— . U IO]- < K IL US x3 '6' 2 IO:- x4 16“— 105 I 1 l . 1 L I J 220 260 300 340 T(°K) Figure 4.13. HF polymer mole fraction (X1) versus temperature for a pressure of 0.01 atmospheres. 106 IOOI'" xI IO."- 2 9. .2 .- IO '- U < a u. I» "" -3 o 10- Io"- 165 I Figure 4.14. HF polymer mole fraction (Xi) versus temperature for a pressure of 0.001 atmospheres. 107 xI 16'- X2 2 9. .. ,_ 10- U < a: :4. x3 m d G o 10 - 12 X. 10“- Id, 1 I I L g L I J 200 240 280 320 360 T(°I<) Figure 4.15. HF polymer mole fraction (X~) versus temperature for a pressure of 0.0001 atmosp ere. 108 five difference in concentrations at these two temperatures may quench lasing on this transition. Thus the experiments initially set out to observe either 10.6 pm or 9.4 pm lasing from the HF-CO2 gas mixture. This decision was reinforced by the results of the computer simulation which also predicted 9.4 pm (10.6 pm) to be more probable than either 16 pm (14 pm) lasing, even if a saturation pulse at 9.4 pm (10.6 pm) is used to populate the upper level of these transitions. Since the ratio of transition probabilities for 10.6 pm to 9.4 pm is 0.34 to 0.2 [43], unless one forces oscillation on 9.4 pm by preferentially absorbing 10.6 pm, the 10.6 pm transition will be the most likely to sustain laser oscillation. Thus for this experiment the following procedure was used. The grating (7200 lines/cm blazed at 28 um) was used to force oscil- lation on a single vibrational-rotational transition in HF. The wavelength was verified using the monochrometer. Second, HF gas was added to the HF/CO2 cell and absorption of the line was recorded. Finally, CO2 was added and various HF/CO2 mixture ratios and total pressures were examined. No lasing was observed. The experiments had been carried out at pressures ranging from 0.5 torr to 5 torr. From our modeling studies it was found that 9.4 um (10.6 um) lasing was enhanced by runningat.higher pres- sures of HF and 002. Therefore, the experiments were performed at mixture pressures ranging from 5 torr to 100 torr. Losses due to collisional deactivation predominate above this pressure. Although no lasing was observed, a significant problem was brought 109 out during these relatively high pressure experiments. It was found that HF expanding through the orifice was condensing on the down- stream side and causing pressure fluctuations and thus disturbing the flow rate. The vapor pressure of HF is 0.69 atm at 300°K; thus cooling at lower pressure could cause condensation. The flow system was, therefore, abandoned for a static fill of the HF-CO2 cell. This change of procedure demonstrated a deficiency in the HF/CO2 gas cell. The plexiglass and to a lesser extent the copper of which the cell was constructed was susceptible to corrosion by HF. The absorption coefficient of the HF pulse by the resonant gas in the cell would decay as a function of time. This implied that HF was disappearing due to wall reactions. Passivating the cell slowed the process but did not eliminate it. The plexiglass end pieces were finally replaced with aluminum window holders. Although the cell could not be completely passi- vated, the mixture lifetime was significantly increased. Mixture lifetime is an important variable when using a non- flowing system. The gases are added in three stages until the final desired pressure is reached. However, the delay between filling the system and actually taking data may be as long as three hours for low pressures [59]. The longer the delay, the more homogeneous the mixture becomes. The long delays also lead to a highly contaminated mixture when corrosive gases such as HF are used. The technique which pro- vided the most successful results involved filling the cavity with each of the gases used, in the proper ratio, to a total pressure 110 equal to that of atmosphere. Before taking data the cavity was pumped down to the desired pressure. This had the advantage of quicker mixhng times and it eliminated any leak rate problems during this mixing time. It did increase wall reactions, however, but the effect on absorption was not noticeable. In fact, down to pressures at the limit of accuracy of this system (approximately 200 mtorr) the HF pulse (operating on a P1(J) transition) was com- pletely absorbed. In the case of P1(6),which has an absorption coefficient mea- 1 torr'l, in a length of 50 cm sured [75] at 300°K to be 0.71 cm- at 100 mtorr only 3% of the original pulse intensity will remain. At normal operating pressures from 0.5 mtorr to 5 torr of HF the pulse was absorbed in a fraction of the total length. To increase the power density in the absorption cell a focusing lens was purchased (1" diameter, CaFZ, 50 cm focal length (Janos 0ptics)). The effect of the lens can be estimated by calculating the beam diameter of the pump pulse Us given by [76]: w = LA- 1/2 21:- -' L3 ‘1/4 5 2n R R2 where A is the wavelength of the HF output and L is the length of the HF pump laser. For this system Us is .72 mm, giving a diameter Of1.44HML 111 where U0 is the beam waist at the center of the cavity. 0_2_§_ Since beam divergence is small Us is approximately the diameter of the input pulse in the center of the absorption cell without the focusing lens. The aCtual beam diameter for this configuration may have been smaller than calculated since the surface area of the resistor ends was considerably smaller than a flat plate electrode of the same length and width of the resistor bank. Thus, the active medium may not have been as large as possible. This may have been respon- sible for the fact that a change to this new cavity resulted in no increase in output power from the laser. The CaF2 lens was placed between the pump laser and the absorp- tion cell. This focused the input pulse at the center of the absorp- tion cell. The experiments were rerun with this configuration; however, the results of all cases showed no oscillation in C02. Various amounts of the He were added to the HF-CO2 gas mixture. This was suggested by results of the computer model which predicted (see Chapters 2 and 3) that He was an effective deactivator of the (0200) level (and similarly (1000)). Although this is detrimental to 16 um (14 um) oscillation, it benefits 9.4 um (10.6 um) oscilla- tion by removing lower level population that arrives due to lasing or deactivation. An additional advantage to the presence of He is 112 the increase in rotational relaxation of HF to increase absorption of the optical pump pulse (see Chapter 3). Mixture pressures ranging from 1 torr with 0% He to pressures as high as 600 torr with 95% He were tested with no observation of lasing in the C02 gas mixture. Finally, an attempt was made to lower the threshold value of the absorption cell cavity. The value of the threshold is given by equation (2.5) where R0 and RL are the mirror reflectivities at 10.6 pm. For this system athr was equal to 5.96 x 10.4 cm'l. The com- puter model operating under similar conditions predicted gains of approximately 5 x 10'3 cm'l. All cavity loss mechanisms have been included in the R0 and RL terms. The only mirrors available for this setup were both flat. It can be demonstrated that for such a system there exists only one point of alignment [76] at which a stable resonator exists. All other alignments produce an unstable cavity in which the light rays can "walk out" of the cavity. The alignment technique uses a He-Ne (Metrologic) laser operating at 6328 A to visually align the mirrors, M1 to M4, in that order. The success of the technique depends upon both front and back surfaces of the mirrors being paral- lel to one another. If this does not hold, a mechanism for loss can be introduced into the system. To decrease threshold a 3.5-m radius of curvature silvered metal mirror was substituted for M1. This was 100% reflective at all wavelengths. The smaller radius of curvature would make mirror 113 alignment less critical. A mirror was used to obtain any signal reflected from one of the brewster windows‘on the HF/CO2 cavity. The monochrometer was removed from the system and the signal was sent directly into the HngTe detector. The threshold gain for “thr for such a system is calculated to be 1.68 x 10'4, a reduction of more than 70% in the value of O‘thr’ In addition, a long pass filter (1 > 3.2 pm) was used to pre- vent the HF pump pulse signal from entering the detector. The results of all trials with this geometry showed no evidence of lasing in the HF/COZ/He gas mixture. An attempt was made to perform a similar experiment using DF rather than HF. The DF pump laser was identical to the HF system except 02 was substituted for H2. A trace of the DF output is shown in Figure 4.16. Several tries at using DF to absorb the output from the DF laser demonstrated that no DF was present. The original bottle of DF was obtained from BIO-RAD industries and had been stored for several years. Upon purifying the bottle according to the procedure previously described it was found that no DF remained. The replacement cost for DF at this stage of experimentation pro- hibited any further attempts with this device. It was concluded that all reasonable methods to produce laser action in CO2 with the available apparatus had been attempted. To explain these negative results, a computer model developed during the course of the experiments will be used to identify the important kinetic mechanisms in the HF/CO2 gas mixture. 114 Figure 4.16. A typical DF pulse profile .2 nsec/div, 200 mV/div. The output is from the P1(7) transition in DF. 115 4.4 Computer Simulation of an HF/COZAr Gas Mixture and Comparison With Experiment 4.4.1 Introduction The description of a computer simulation which approximates lasing on 9.4 up and 16 pm from both a DF/CO2 and an HBr/C02 gas mixture was given in Chapters 2 and 3. In Chapter 3, a detailed description of the comparison between the computer model and two sets of experimental results [7, 8] was presented. The .conclusions reached were that the model compared favorably with the experiments and was capable of predicting, for an HBr-C02 system, results in regimes where no experiments have yet been performed. The model has been modified to simulate a laser cavity con- taining an HF/COz/Ar gas mixture. The use of Ar rather than He in the computer model allowed a direct comparison to the experimental results of Osgood to be made, where Ar was uSed as a diluent. Because the experiments described in the first part of this chapter failed to demonstrate lasing either on 9.4 pm (10.6 pm) or on 16 pm (14Lm0, it is hoped that such a computer simulation may offer an explanation for these negative results. The HF-CO2 model is similar to that described in the previous two chapters except for those reactions affected by the addition of HF. 4.4.2. Reactions Peculiar to the Addition of HF The following reactions involving HF are assumed to be the possible important kinetic mechanisms. 116 1. Vibration to vibration energy exchange (29a) HF(v + 1) + HF(v + 1)‘Z HF(v) + HF(v + 2) (29b) HF(v + 1) + HF(v + 2)‘Z HF(v) + HF(v + 3) (29c) HF(v + 1) + HF(v + 3) ::HF(V) + HF(v + 4) 2. Vibration to translation energy transfer (30 ) HF(v) + M'Z HF(v - 1) + M HF(v) The magnitudescfliReactions (29b) and (29c) are expected to be small compared to Reactions (29a) and (3OHF(V))irIthis system since optical pumping is assumed to take place on only the 0-1 transition of HF. There is some discrepancy in the measured value of Reaction (3OHF(V)) which Bott and Cohen and others [77-82] have measured. Bott [83], however, appears to have resolved this controversy and we use his corrected rate. The temperature dependence given by Cohen for this rate [84] is: k = 1 x 1014 T'°°8(v) + 2.5 T3'5(v), M = HF 3OHF(V) For Reactions (29a), (29b), and (29c) the temeprature dependent rate coefficients are: 117 _ 12 0.5 k29a - 1.5 x 10 T _ 11 0.5 . _ 11 0.5 For the rate coefficients involving the HF-CO2 energy transfer and deactivation the following reactions are possibly significant: (28) HF(v = n) + 002(0000) ::.HF(v = n - 1) + 002(0001) 02(1001) (28') HF(v = n) + 002(0000) :zHF(v = n - 1) + > 002(0201) I ‘ ' 0 i 002(1001) 0 002(10 0) o i ' t + 002(00 0)‘: I > + 002(00 1) 002(0201) 002(0200) ‘ J L J ' 0 0 (28") HF(v = n)_+ 002(00 0) Z: HF(v = n - p) + 002(00 1) (30002) HF(v==n)i-002(0000) :: HF(v = n - 1) + 002(nm£0) (8d,9d) 002(0001) + HF(v II 0) :: _HF(v = 0) + 002(nm20) (8a,9a) 002(0001) + co :: C02(nm£0) + co 2 2 118 The (0001) level of co2 is populated by Reaction (28), (28'), or (28"), or a combination of all three. For both the initial and final states of HF having the same rotational quantum numbers, the energy defect for Reaction (28) is approximately 1600 cm'l. For Reaction (28") the energy defect is still larger. Reaction (28') was proposed [58] as an alternative to (28) and (28"); it provided a means of transferring energy to CO2 where the energy defect was only a few hundred wavenumbers. Measurements have shown these trans- fer mechanisms to proceed quite rapidly; approximately 0.3% of the gas kinetic rate at 300°K. If Reactions (28) and (28") were the dominant reactions, this would indicate the mechanism is not very sensitive to energy defect, and such a result is not typical of reactions involving vibrational energy exchange. Experimentally, it is difficult to determine which of the three reactions is actually taking place. Simply monitoring 4.3 um fluorescence gives no indication. The levels (1001) and (0201), populated by the intermediate state model (ISM), as Reaction (28') is called, have fluorescence bands which fall within the range of the 4.3 pm bandpass filters used in most laboratory experiments. However, Hancock and Green [56, 81] have shown evidence that the populations of the (1001) and (0201) levels are small and that the direct transfer method, process (28), dominates. Thus, the present calculations neglect the reaction path of the (ISM). The explanation for where this excess energy goes, if not into trans- lation, is offered by Lucht and Cool [58], who claim that excess vibrational energy goes into exciting rotational modes of HF as 119 previously discussed. The effect of initial rotational level dis- tribution on the value for the net rate of energy transfer has not been measured for HF in the first or second vibrational levels. It is possible to use the model to assess this effect, and the results of this calculation are presented later. Douglas and Moore [85] claim that there is no effect of initial rotational excitation when HF is in the v = 3 or v = 4 state. A list of both measured and calculated values for Reaction (28) + Reaction (30a) is given in Table 2 of Reference [54]. It is necessary to specify the sum of these two rates since in the case of some hydrogen-halides it is difficult or impossible to determine the final state of C02. For comparison the values for the transfer rates of the HBr-CO2 and DF-CO2 systems are also listed. The value of ke can be measured directly for HBr-CO2 energy transfer [38]. For the DF-CO2 case, Lucht and Cool [58] point out that Reaction (30C02) should be negligible compared to Reaction (30C) with HF replaced by DF and M = DF should exceed the rate constant for Reac- tion (30002) for DF, since the interaction in the latter reaction is weak compared to that of Reaction (30HF(V))' Thus, an upper bound on the value for k28 can be specified and this value is listed in Reference [54]. For the HF-CO2 reacting mixture, the rate co- efficient for Reaction (30HF(V)) is so large that it is impossible to estimate the value of k28’ It is still assumed, however, that k >> k30 for HF. Thus the model assumes that CO2 is as efficient as N2 in deactivating HF. 120 Several scenerios have been developed to explain the HF-CO2 transfer mechanism. The theory of Dillon and Stephenson [87,.88, 89] uses a model containing semi-classical Vi+ V-R transfer mecha- nisms to estimate the rate coefficients. Their results compare favorably with those measured experimentally. A comparison between both measured and calculated values as a function of temperature is given in Figure 4.17. The rates show a negative temperature dependence over this temperature range. The results of Lucht and Cool [58] show a Tn dependence for this rate constant where n is approximately -1.3. Bott's results approximate n to be -0.4. Bott has also measured this rate to 1010°K and finds a positive tempera- ture dependence from 750°K to 1012°K [90]. There is no evidence to suggest which of these two sets of measurements is correct; thus the model will initially use Bott's results and assess the effect of varying this rate up to the value as measured by Lucht and Cool. The temperature dependent rate constant from Bott's results is: 12 -0.4 k28 = 7.15 X 10 T for T between 300°K and 750°K. As previously mentioned, it is assumed k28 >> k30 and therefore k3O ’will be neglected. CO 602 2 121 The vibrational level dependence of this rate has been measured by Bott [90, 91] and he finds the rate to scale as v", where n is between 1.9 and 2.0 for energy transfer from HF to C02. Measurements of the deactivation of CO2 by HF (Reactions 8 and 9), as a function of temperature, are shown in Figure 4.18. The values for CO2 deactivation by DF are provided for comparative purposes. A comparision is made between measured and calculated values in the same figure. The calculations of Shin [92, 93] could have proved significant, since it was his aim to specify the final state of CO2 for Reaction (8d, 9d). He assumed that deactivation of C02(0001) by DF would produce C02 in the (0100) level while the final state of C02 after collision with HF was (0000). However, the temperature dependence of the rate is the reverse of that measured by Lucht and Cool [58]. The measurements of the temperature dependence of this rate by Chang et al. [94] agree with those of Shin, except they present only two measurements and thus no conclusions can be drawn. How- ever, at 305°K there is agreement amongst the measurements and cal- culations and therefore we use Lucht and Cool's rate at 299°K with some confidence. We assume the final state of CO2 is either (1110) or (0310) as predicted by Herzfeld [27] for DF-CO2 deactivation. And, we also assume the probability for deactivation to be in the same ratio as for DF. This procedure is used since, as can be seen in Figure 4.18, the rates have a similar temperature dependence and their magnitudes appear to differ over the temperature range by a constant factor. 122 O LUCHT, COOL o BOTT, COHEN ao- A/HBr'<302 a STEPHENSON, FINZI, MOORE o ADP-Co2 o DILLON, STEPHESON 25- ,,’DF-00é RATE COEFFICIENT (seé'torf') l l l l o soo soo 900 I200 T (°K) Figure 4.17. Comparison of the effect of temperature on the rate coefficient for energy transfer from HBr, DF, and HF to C02. 123 4u6P 454- ‘0' o LUCHT,COOL 3 ST EPHENS, COOL A CHANG, MC FARLANE. A 3‘6 ' VIOLGA T;- § 34 [- To 0.) :2 3.0 '- I- 2 E2 52 Ll. 2.6 I- I: O 2.4 - (J I‘." < 2.0 - 0: 1.6 (- L4 - I.o .- ' L I . 300 600 900 I200 'T(°KZ) Figure 4.18. Comparison of the effect of temperature on the rate coefficient for deactivation of C02(00°1) by DF, HBr, and HF. 124 When comparing the values of k28 and k8,9 for the HF-CO2 and DF-CO2 system using Figures 4.17 and 4.18 for the DF-CO2 system, the value of k28 exceeds the value of k8,9 by almost an order of mag- nitude. For the HF-CO2 device the rate of deactivation of the (0001) level is similar in size to the rate of transfer of energy to the (0001) level. The significance of this will be discussed when evaluating the performance of the HF-CO2 laser device. 4.4.3 Parametric Variation: Comparison With the Results of the HBr-C02 System For purposes of comparison,we initially chose the HF cavity conditions to resemble ones chosen for the HBr-CO2 systemas described in Chapters 2 and 3. An optimum HBr/COZ/Ar gas mixture of 0.75:9:3:0 is used and the HF/COZ/Ar gas composition is identical. This mixture produced the highest output power in the HBr-CO2 system. The input power was adjusted such that the input photon flux as a function of time was equal in both the HF- and HBr-CO2 systems. Thus, the ratio of the power and energy of the optical pump pulse for the HBr-CO2 and HF-COZ system was inversely proportional to the frequency of the output signal for HBr and HF, respectively. This not only provided an easier means by which to judge relative performance of the two systems, but also reflects the fact that HF optical power and energy is typically larger than that of HBr. First a small signal gain case was performed to assess the potential for lasing on 9.4 pm in the HF-CO2 system. A similar case using HBr was also run. The results are presentedin Figure4ul9. The transition having the largest gain was used (P(14) for HBr-C02 10 -2 IO - GAIN (cm—l) 0.263 P (14) 125 GAS MIXTURE C02: HX: Ar 9.0 : 0.75: 3.0 coz-Har (TH93°K) P06) (Oz-HF(T=300°K) Figure 4.19. TIME (nsec) Time history of the small signaI 931“ 0” the 9'4 “m transition having maximum gain for the HBr-C02 and HF-CO2 systems. 126 at 193°K and P(16) for HF-CO2 at 300°K). The value of “thr specifies the threshold gain of the cavity for both systems. The significant rates affecting the system peculiar to the addition of HF are shown in Figure 4.20. These same rates involving HBr are shown in Fig- ure 4.21. It is evident that the transfer rate for Reaction (28) for n = 1 is much larger for HBr in comparison to the other reaction rates than for the HF gas mixture. This is an obvious result given the relative size of the rate coefficients. However, the fact that the rates for Reaction (28) for n = 2 and Reaction (29) are significant in the HF system implies that HF-HF relaxation and redistribution are larger than for HBr. Reac- tions (29a) and (29b) involving HF are responsible for this result. Consequently, energy is not efficiently coupled to 002. While some energy is stored through vibrational quanta exchange reactions, much is lost to translational heating of the gas. The most significant mechanism for losses in the HF-CO2 device is the deactivation of CO2 by HF, Reactions (8d, 9d). The magnitude of the rate coefficient for the sum of these reactions is comparable to the size of the transfer rate constant. This is not the case for the HBr system, as demonstrated in Figure 4.21. Finally, it is this fast transfer rate in comparison to all other reaction rates which explains the sharper peak in the gain profile in Figure 4.19 for the HBr gas mixture. Next, the HF system was allowed to lase on 9.4 pm. Although lasing did occur at 9.4 pm, no 16 um transition reached threshold. The reason for this is illustrated in Figure 4.22, where populations LOG (RT). 127 RT (30:) GAS MIXTURE COZ: HF I A! 9.0 3 0.75! 3.0 RTI ZBIVII R RTIZI) V82 TIME (,GEC) Figure 4.20. Net reaction rates in the HF-002 system for a small signal gain case. The rates shown are those important to transfer of energy into and out of the C02(00°1) level. 128 16‘- Imzsma GAS MIXTURE C02; HBr 3 Ar .6‘- so : 0.75 : 3.0 L R7188) ;: 2__ EE 4 (9 IO " <3 4 II- 13- " RTIZ'Ic) RT m Id' 1 ' 1 O 4 6 8 IO 12 TIMEIFSEC) Figure 4.21. Net reaction rates in the HBr-CO system for a small signal gain case. The rates shown are those important to transfer of energy into and out of the 002(00°1) level. 167 /cc) 3. O 129 ,C02IOOI) /l IO" -coz(o2‘0) POPULATION (MOLES /.16' A100) GAS MIXTURE C02 2 HF : Ar 9.0 :0.75 = 3-0 0 I Figure 4.22. I TIME ([ASEC) Time histories of species concentrations for levels controlling 9.4 um lasing in an HF-CO device. The total pressure is 12.75 torr at T = 3 0°K. The nota- tion x10n means that the actual values are 10n times the values shown on the graph. 130 of various levels of CO2 are plotted as a function of time. The (0200) level, the upper level of the 16 um band, shows a large increase at approximately 1.75 usec corresponding to the onset of 9.4 pm lasing. The (1000) level of CO2 in Fermi resonance with (0200) absorbs this population nearly as fast as it is deposited due to lasing. The remaining excess population is transferred to the (0220) level. The speed with which the population of (0200) is increased due to lasing is controlled by the rate of transfer of energy from HF(v = 1) to 002(0001). In the HBr system, the rate of depositing population into (0200) is faster than the rate of decrease due to all sources except lasing. The time history of 9.4 pm power output from both the HBr and HF devices is shown in Figure 4.23. The power predicted by the HBr-002 laser oscillation is twenty times greater than that from HF-COZ. This is directly attributable to a slower transfer rate in the HF gas mixture along with competition from HF deactiva- tion of the (0001) level as discussed above. The effect on pulse decay and output power of changing the value ofiflmarate coefficient for Reaction (28) to the value as measured by Lucht and Cool is also shown in Figure 4.21. For an increase in the rate by a factor of 1.8, the power is increased by the same amount and the pulse delay is decreased by an equal amount. Deactivation of HF by itself and 002(0001) is still sufficient to inhibit 16 um lasing. Finally, an optimum HF pressure was sought which would produce the largest 9.4 pm power. For a 1 He:3 002:0.33XHF gas Inixture at a total pressure of (12 + X) torr. The optimum pressure of HF POWER (WATTS/CC) Figure 4.23 131 600- 5°°' II GAS MIXTURE C02 : HX : A? 9.0 :o.7s : 3.0 —HBT‘C02 40°” N USES LUCHT ANo COOL'S VALUE OF THE TRANSFER RATE + USES BOTT'S VALUE OF THE TRANSFER RATE 300— 200- 100)- ” + HF-C02 //\HF-C02 A / l \ :— 0 2 0 I TlME(/.4SEC) Comparison of the time histories for 9.4 pm laser oscillation in the HBr-CO and HF-COZ systems. Also shown is the effect on 9.fi pulse delay and power of changing the value of the transfer rate. 132 was found to be between 7 and 12 torr. This is directly opposite to what is expected when comparing it with the HBr-CO2 results, in which 9.4 pm power only increased with larger HBr pressure. Deactivation by HF is large and case by case comparison with HBr shows significantly lower 9.4 pm powers and energies for any given HF pressure. That the optimum HF pressure exists is due to the significant HF V-V and V-T relaxation mechanisms. These reactions act to absorb large amounts of the input energy. The rate of absorp- tion of energy by optical pumping is proportional to the HF concen- tration (see Equation (3.1)). The deactivation rates are propor- tional approximately to the concentration squared. Eventually the deactivation mechanism overcomes the absorption term, thus lowering 9.4 um power. Even at this optimum pressure, however, the model did not predict 16 um laser oscillation in the gas mixture. 4.4.4 Effect of the V-R Mechanism and Initial Rotational Distribution on HF-C02 Energy Transfer» As previously stated, the large quantity of excess vibrational energy of HF given up during the pumping of the (0001) level of CO2 is thought to go to exciting the rotational modes of HF. Thus, in Reaction (28) O 0 HF(V,J) + C02(00 0)': HF(v - 1, J') + C0 00 1) + AED 2( where J was previously constrained to equal J' this constraint is now relaxed and J' is chosen such that AED is minimized. For example, if an HF molecule resides initially in the v = 1, J = 3 level, upon 133 collision with C02 the final state of HF would be v = 0, J = 9. This gives AED = 53 cm‘l. In the model this procedure was followed for all (v = 1,J) and (v = 2,J) states of HF for J = 0-13. For J states above this, the final rotational state equaled the initial state. This was necessary since the model computed only the first sixteen rotational levels of HF. The error resulting from this procedure is small since optical pumping took place on levels below J = 5. Initially, the model simulated a case in which the rotational distribution peaked at J = 4, and this was compared to a case where the distribution peaked at J = 3. Only a 3% reduction in the overall transfer rate and a similar reduction in peak power were observed. The explanation for this result is two-fold. As the rotational quantum number increases, the level spacing is further apart and thus, as the initial rotational state of HF increases, a change of fewer rotational levels is required to minimize AED. The other half of the explanation rests on an artifact of the model, that rotational relaxation, in the model, is assumed to be independent of the rotational number. The assumption of rotational quantum number independence for relaxation follows from the discussion in Chapter 3. Although rotational relaxation rate is probably J depen- dent for HF, the results of Hinchen [49, 50], Wilkins [51], and Polanyi [52] differ as to what this dependence is. They do suggest that the rate is of the order of the gas kinetic rate at low J. Thus, the assumption of this model that the rotational relaxation rate is independent of rotational quantum number and equal to the gas kinetic rate is not an unrealistic one. 134 The time for relaxation TR is equal between any two J levels. Therefore, the higher the initial rotational distribution of state V, the less the rotation non-equilibrium in the V-l state. Replenish- ment of these low rotational states is faster the higher the initial rotational distribution is. This replenishment is necessary since these are the levels being preferentially pumped by the optical input pulse. Thus, the overall effect of the V-R mechanism is to lower absorption by displacing the rotational population such that it peaks ata J level much higher than is being pumped. The higher the initial distribution the less absorption is affected. It is interesting to note that if rotational relaxation is J dependent and is slower for higher J levels, as predicted by Hinchen [49, 50] and others [51], then changes in the initial rota- tional distribution-will have less effect. As mentioned earlier, this was the result Douglas and Moore [89] found in their experiments. An interesting effect of this V,R mechanism for energy trans- fer from HF to CO2 is the potential fOr highly non-equilibrium rotational distributions in the HF(V = 0) level. BecauSe of the large cross section.for emission, Hinchen [74] predicts gains of 1 cm'1 fOr population inversions of 10'4 torr. Such p0pulation inversions are not predicted by the model, however, when the V-R mechanism is assumed. This is probably due to the slow rate of transfer of energy from HF to C02 compared with the fast rotational relaxation rate. 135 4.5 Summary, This chapter has included the record of the various attempts made to produce laser action in an HF-CO2 diluent gas mixture and to observe R-R lasing in preferentially pumped HF gas, with no suc- cess in either case. I Various methods were tried to optimize the transfer of HF energy to the HF-CO2 system. Lowering cavity loss mechanisms to reduce the laser threshold were also undertaken. The fact that the temperature was critical to HF dimer formation, which required the system to remain above 260°K, ruled out attempts to optimize the system for 16 um lasing. Optimization at 16 pm would have included optical saturation at 9.4 pm. The corrosiveness of HF was also the cause of many problems that resulted in special handling to reduce system contaminants. The expense of special non-reactive steels, such as monel, to con- struct the cavity prevented their use in the experiments; however, if the experiment were to be rerun it would be desirable to use monel for the interior walls of the cavity to reduce this problem. The computer model developed simultaneously during the period of experimentation offered several suggestions for improvement of the procedure predicting beneficial effects by the addition of a diluent to the HF/CO2 gas mixture. Still, no lasing was ever observed. Finally, the computer model was used to examine the important kinetic mechanisms in the HF-CO2 gas mixture. The kinetic model was similar to the one developed to examine the HBr-CO2 system. 136 Simulation results indicate that the HF-CO2 is plagued by large self deactivation rates along with strong coupling between HF and C02, both for energy transfer and deactivation. The V-V,R mechanism, although important to energy transfer, does not have a Significant effect upon measured quantities such as pulse power and energy. The most significant result from the model is that the higher level of initiation, due to increased HF laser output, is still not sufficient to overcome slightly slower transfer rates to C02 and increased V-T deactivation of HF by itself. CHAPTER 5 SUMMARY AND CONCLUSIONS This thesis has presented computer models which simulate laser oscillation in three different hydrogen halide chemical transfer lasers. In each of the three cases a hydrogen or deuterium-halide laser is used to pump a COZ-HX gas mixture. Rate equations are used to solve for the time history of concentrations of both lasing and non-lasing species. The model also predicts the time resolved spectra of both power and energy on selected vibrationalarotational bands. All processes are assumed uniform throughout the cavity. During lasing the gain of any transition is allowed to vary rather than remain fixed at the threshold value of the gain. This allows observation of the interaction of gain and photon flux during lasing. Rotational levels of both the HX and CO2 molecules are allowed to differ from their Boltzmann equilibrium value at the translational temperature. Rotational relaxation is modeled using a mechanism suggested by Polanyi [24]. Effects (rf single line operation, rota- tional hole burning, and bleaching of a particular band are examined in detail. The optical pump pulse was modeled in two different ways. The first assumed that the HX(v = 1) level was populated instan- taneously (i.e., in a time short compared with the rate of transfer 137 138 from HX to C02) in a Boltzmann distribution at temperature T. The second method necessitated computing the time history of the values of the first sixteen rotational levels of HX(v = O) and HX(v = 1) and modeling in detail absorption of input flux on selected rota- tional transitions. The models were used to investigate the relative performance of the HBr-, DF-, and HF-CO2 chemical transfer lasers. The experi- mental data available in the literature was used to provide a test of the validity of the models' predictions of the HBr-CO2 laser device operating at 16 pm. The model, using the method of instan- taneous populating of the first excited vibrational levels, pre- dicted results which compared favorably with those results observed experimentally by OSgood and Barnes. The kinetic mechanisms impor- tant to the production of 16 um laser oscillation are revealed by examination of the modelS' predictions. The disagreement between the observations of Osgood's [7] experiment and the model predictions concerning the effect of argon pressure of output pulse power reveals a shortcoming of the first model. The second generation model attempted to more accurately simulate absorption of the optical input flux. Again, the model predictions were compared to the experiments of Osgood and Barnes. The model reveals the effect of Ar on enhancing 9.4 pm and 16 um power. Argon served to increase the rotational relaxation rate of HBr which prevented the bleaching of the transitions being opti- cally pumped by the HBr laser. The rate at which energy is absorbed was increased, which increased the rate at which energy is transferred 139 to C02, and finally the laser output power was raised. The mechanism would not have been evident without the more detailed modeling of rotational nonequilibrium in HBr. The validity of the model results in regimes of interest was found to be sufficient to allow the development of a computer simulation which should predict the per- formance of an HF-CO2 laser device. A goal of the thesis was to demonstrate the feasibility of a 16 um HF-CO2 laser system. The potential for larger output power and energy of the HF pump laser compared to HBr were incentive enough to develop such a device. The experiments failed to yield the expected results. No evidence of either 9.4 (10.6) um or 16 (14) um lasing was found experimentally. Therefore, the purpose of the model became centered on an attempt to explain the experimental results. The model demonstrated the significant deactivation mechanisms present in the HF-CO2 gas mixture. Previously, experimental mea- surements had shown that the rate of energy transfer between HF and CO2 was no larger than the rate of deactivation of CO2 by HF. However, even more significant to the reason for poor performance of the HF-COZ system compared to HBr is the large value of the rate coefficient for self deactivation of HF. This is the dominant mecha- nism that reduces the 9.4 pm laser output and prevents 16 um oscil- lation in the model. The reason the experiments of Manuccia [10,11], where an HZ/FZ/COZ gas mixture is electrically initiated, succeeded in producing 16 um lasing is because of the lack of ground state HF initially in the system. 140 In a series of experiments performed by Buchwald et al. [24] various isotopes of C02 were used to absorb an HF input pulse directly. Laser oscillation in the 16-17 pm region was observed. The technique of Buchwald et al. overcomes the problem on the HF-COZ system of slow energy transfer from HF to CO2 and the large rate of energy deactivation of C02 and HF by HF. The conclusions of this thesis are not evidence that 9.4 um or 16 um laser output is impossible from an optically pumped HF-CO2 gas mixture. In fact, the model predicts 9.4 um oscillation. It does point out that laser action will be difficult to initiate. It is possible that cavity losses such as system contamination due to wall reactions involving HF and poor mode matching between the pump laser and the absorption cell might raise the threshold of the cavity to a value that quenched laser oscillation. The effect of wall reactions involving HF was one of the most significant variables affecting system performance. The use of either stainless steel or monel steel for cavity construction would have reduced this problem; however, the cost for such a system pro- hibited this. Although passivating the cavity lessened the problem, it was not a permanent solution. The repeatability of experiments suffer for such a system. The experiment did serve to point out areas in which special attention should be made to provide ideal conditions. The results of the experiment and model combined may help to understand the important mechanisms in the TCL device. 141 To this end, a simple expression is developed (see Appendix B) which for a C02 optically pumped transfer laser will provide some indication whether 16 um laser oscillation is likely to occur. This expression takes into account the ratio of important energy gain to energy loss mechanisms in the gas mixture as predicted by the comprehensive models. Comparing the HBr-CO2 and HF-CO2 systems gives the ratio of performance to be 1.12 and 0.402, respectively. The large self deactivation rates of HF as compared to HBr are primarily responsible for the difference of these two values. . As pointed out previously, lasers employing an electrically initiated H2/F2/CO2 gas mixture do not suffer from large quantities of HF present in the system. Due to pre-reaction or slow discharge times larger than desired quantities of HF may exist. Thus, future research on these types of devices Should concentrate on alleviating these problems as a means of increasing 16 um output energy and power and thus raising the device efficiency. APPENDICES APPENDIX A Recommended rate coefficients for 16 um C02 laser systems. 142 m N N m N an o u . a oH x H.H u mx Ho Hovmoo+Ho ~c.~oo + Ho ocvmoo+Homcvmoo m m.o HH H o + a o a CH x H.H n «x .o Hc.~oo+.c ovaou + He ccvmoo+Homov~oo H m.o a H a + o a cH x m.p u mx Ac HcHNoo+Ho cH.~oo + .o covmoo+Ao HHV~oo m m.o oH H . a + o H a s OH x ~.H n NH Ha Ho.~oo+.c Novwoo + Ha oov~oo+HH covmoo N a m.~ H a H c + a o ,o a. .9 OH x v.m u Hx Ho Hc.~oo+Ho cHH~ou + Ha cc.~ou+HH ocvmoo H 2.3.0 m.~ H H .. o + c o Qucwfinvfiuwmoo ”H5“ 5 COHUOMQNN o “0mm”— .msmumxm cmmmp moo E: 0H cow mucmHUHmeoo mpmg amucmssoomm .H.< m—nmp 143 oH~.Hm m.me mcH x pm.n u mwx m: + HooNc.~oo H m: + Homcv~oo HH emem.°o mh.ma a.m u NHH ms + .occH.~oo H m: + HcHHH.~oo NH qu.qo m.~a qu x a.» u me m: + HcNNc.~oo H m: + .oHHH.~oo NH omo¢.om aH.He mTH: x o.o u wa m: + Hoomcvuoo H m: + .cHHH.~oo OH m.Hs acH x Hm.H u on m: + Honc.~oo H m2 + HoHHHv~oo oH ~.owa HHoH x mn.H n max on + Homovmoouu on + .Hoocvmoo 6a ~.o-s HHcH x H.H u oax H: + Hamo.~oo H m: + HHcocvmoo om oomH.N-w m.waHHTOH x A.» u nag m: + HomeHNOU H a: + .Hooc.~oo no 33.79359 73 x as n «as. H: + 88KB H H: + 5818 2.. o.H-a H.HoH x 6v.~ n wax 0:. + HoHHH.~oo_HM on + .Hooovmoo 6m o.HTe «HcH x mq.H u 6&3 m: + HoHHHv~oo H H: + .Hocovmoo om oomv.~uw m.ms H...H.H x MH.H n cox H.z + .oHHvaoo H v: + HHoocvmou nm onH.HTm mh.ee v.oH x ma.» n max H: +..oHHH.~oo u H: + HHcoc.~oo mm m.ce NHoH x ~.H u mg .cHHovmou+HcHHa.~ou H .ooao.~oo+Hc-o.~oo NH m.ca HHcH x m.H u ”x .oHHo.~oo+.oHHc.~ou H .cccc.~oo+.oo~c.moo ch m.os HHeH x m.H u ex HOHHc.~oo+HcHHo.~oo H Accco.~oo+HocoH.~oo o nucmfioamumoo mum: acofiuomwm .uommm A.u.H:ouv .H.< mHQHH 144 o.H-s H.HOH x «m.H u omwx mz+HoHHoV~oo N mz+Ho-cv~oo N2: 0236-6 3&9 m3 x H.H u ammo. a hz..8H::~8 u {£3318 ~an cm.Hm Hm.me NcH x o.o u amwx mz+HcHHovwoo H mz+Ho-ovmoo N2: c.Hua H.HOH x em.H u on“: mz+AOHHo.~oo H mz+Hoo~c.~oo oomH ommqm.onm mm.~e mcH x o.~ u amwx hzioHHSNoo H hzicomsNoo can oq.Hm H.ma HOH x q.~ u name oz+HcHHov~oo H mz+Hoo~oV~oo camH m.Ha mcH R m.m u pHx m2+.¢o~c.~oo H mz+Hc-ov~oo EH c.Hna mHcH x H.H u ome az+HcHHc.~oo H az+Hocchmoo noH ommqm.cum mm.~e moH x m.H u awa hz+SHH8~oo H BzicocHVNoo an omv.Hm o~.ms NOH x «.4 u ame mz+HoHHovmoo H oz+HoooHv~oo muH . m.Ha mS x mm.m u mmx mz+Hc-c.~oo N mz+Hcoch~oo mmH m.He mOH x em.H u mwx m=+Hco~ovwoo N mz+HccaHV~oo omH aeo.Hm Ho.ma mcH x m.v u HHH mz+Hcoch~oo H mz+Homovmoo HH o-.Ho ~m.me NoH x >.m u mmx mz+Ho-oV~oo H m=+HcHov~ou NHH nucowoflmmmoo Guam woodwommm .uomom .H.U.H=oav H.< aHan 145 N.N.H u > “NommH u NH> °HoH x mN.N u oNNx mz+HHn>vum= N mz+H>.Hm= oNN N.N.H u > Hem.va > HioH x mo.v n nNNx N2+HHT>.um: H N2+H>Vum= oNN m.N.H u > “N.Na > mcH x H.H u mNNx Hz+HHu>vum= H H=+H>Vum= mNN . wN . . H N >u .x X . H I> > .H > .H N N H > H c.Hna_H>u>_m mHoH «N H x HH+H>vumm+HH Hum: H HH V m=+H V m: 6N mN N N s s N > u > x o n . l> > .H N N H mm.cua vHoH Nm N x .Hooov oo+HH .um: H .oooov oo+H v m: mN >oqN . N N N . . . . II. 6 6 N |> > U m H > vmm.mno HN.wa >HHnonvv N x z+HH vmo H z+H Vma «N >nvN N N § 0 o 0 s u h x O " II> > m H > mw.ve >muoH N m x 2+HH Hun M 2+. .ma nvN m.....H u >“N.Na >NOch.H n >anx Hz+HHu>Vmo N H=+H>vmn mHN NN . X . u > I> > > o.Huax_H>u>_Hm vmeoH o m x HH+H VHQ+HH can H HH an+H can NN . NN N N X N |> > mm.oua > «HoH m H x HHooov oo+HH can H Hoooo. oo+H can NN HN U x o N oNe.vT NH.NB NuoH on m H Nz+Hosz H.Nz+.Hsz HN eN N N N N x o N onm.mlm NH.NB mueH Nm H x AH. z+Hcocov oo M Ho. z+HHecc. ou ON a a oH x Hm.v u oaHx mz+Hc cchoo + N2+HH oc.Nou omH ommmon Nm.m H- o + a . _ . u an N N N N ommvmosw mm.Ne NoH x NN N x 2+.ooocv on H 2+HoHHcv oo nNH o a oH x NH.N u mme m=+Hc ochoo + w=+Hc HovNoo «NH onH.H- NH.N N: c + H ucwwowmumoo mumm / :oHuomwm .uowmm a M A.u_HcooV .H.< aHnaN 146 .391. m.N + .3??? NHOH x OH R ocmx 3: + 2:3,; M 32+ 3;: com 355.9 :3 x o.H u Homo. HVz + 2.3% M 3:33: nom ENHTH. 22 x 8.... u moms. H: + 3.3% H Hz+ Emu mom m.N.HuH> “may _H>N>_m. .x NHonmH u mmx HH+H>ZE + .Hnimz H HH>Tm=+ .35. mm 233.6 35.99 HHS x 3N u NNH :ooeNoo+ 2.3%. H SooSNoo+ 3:5 NN. nuamwoflmwooo mumm MCOHuommm .uomwm H.H.Hcouv .H.< aHnaH 147 .AHHH :oHuowm mom. cmocsocoum 00u on awe wocowcommo musumquEwu mHse w .Xon mHOE\Hmo Nam.H mH m can xo :H w« B UnaumummEmu on» wuws3 .Hex\mOHvI u o yuHucmsv mayo .ucmumsoo EDHHQHHHSUU may Eouu vmcHEkumc mH ucmHonumoo mum“ mCHmmHE may .coHuommu sumo Mom Comm can .mEo .mUHOE mo mEumu :H muHcs :qu .>H0>Huommmmu .mmumu ©Hm3xomn can vumzuom wumcmHmmc Ix can +x mucmHonumoo mama 0293 um: u a: N2 u m: me u m: w: n N: .mmN .Nc n N: m: "OH: RN .6: u v: New n H: "mmHUme oHumeumum H.H.Hcoov .H.< aHnaN APPENDIX 8 Ratio of performance for HX-CO2 TCL devices. APPENDIX B RATIO OF PERFORMANCE FOR HX—CO2 TCL DEVICES It would be highly desirable for the HX-CO2 chemical transfer system to have a simple analytic expression that would serve as an indicator of performance. Although there is no one sure test for whether laser oscillation at 16 pm is possible or not, a good indication can be found from examining the derivative of the HX(v) population given by leéév)I = kVTEHX(V)] [M] - kVV [HX(v)] [HX(v')] v'fO - kt[HX(V)I [coz<0000>1 where kVT is the rate coefficient for vibrational to translational relaxation and kVV is the rate coefficient for intramolecular transfer and kt is the rate coefficient for energy transfer'between' HX and co 0000). 2( Examination of the terms shows that the first and second terms are energy loss mechanisms, and the third term is an energy gain mechanism. Thus, simply taking the ratio of the third term to the sum of the first two should give a value that might be used to sug- gest the likelihood that CO2 will lase at 16 um. kt[HX(v)] [c02(0000)] = kVTEHX(V)] [Mli'kvv [HX(VlISEHXIV')I v'fO R 148 149 Next, an estimate for the concentrations is necessary. From the equation it is evident that the population of HX(v) can be cancelled in all three terms of the ratio, giving 0 kt[C02(OO 0)] R = k M] + k . [HX( ')] VTI VV v'fO v The 002(0000) population can be set equal to the total population of CO2 since even a total population inversion between (0001) and (0200) requires only a few percent of the ground state population to be vibrationally excited. The concentrations of the species M are just the total populations of 002, HX, and diluent present in the gas mixture. Finally, the HX(v') population is a maximum of 50% of the total population (neglecting degeneracy factors) assuming that one can optically bleach the 0-1 transition of the HX species. Thus, the ratio R becomes: kt[C02] = kVT[C02] + kVT[HX] + kVT[(diluent)] + kvv 0.3[HX] R «Evaluation of R for two specific cases inVolving the HF-COZ. and HBr-C0 systems respectively yields the following results. 2 For equal concentrations of 002, HBr, HF, and diluent the value 'of R for the HF-CO system is 0.4 while for the HBr-C02 system 2 R equals 1.0. 150 This model ignores the affect of HX deactivation of c02(oo°1) which for the HF system is comparatively larger than for HBr. The model is only concerned with examining the relative magnitude of the energy transfer rate between HX(v) and CO2 to that of the rate of energy deactivation of HX(v) in the gas mixture. The preceding calculation thus yields a simple expression that can be used to judge whether one is likely to observe sufficient population inversion in a gas mixture to enable lasing to occur or whether deactivation mechanisms will predominate. APPENDIX C Nomenclature 151 Table C.1. Nomenclature Symbol in Text Definition B(v,J) Einstein isotropic intensity absorption coeffi- cignt, for transition with lower level (v,J) cm /molecule-J-sec 10 Speed of light, 2.997925 x 10 cm/sec Rotational energy of state v,J, cm'1 Energy defect between products and reactants in a chemical or relaxation reaction, cm' Laser output energy per unit volume, joules- cm‘ Number density of free electrons moles-cm-3 Photon flux, mol-cm'Z-sec"1 Number density of HX molecules in the vth vibrational level, Jth rotational level, moles-cm‘ Number density of CO molecules having v , quanta in the symetric stretch made, v2 quanta in the bending mode and V3 quanta in the asymetric stretch mode, moles-cm-3 34 Plank's constant, 6.6256 x 10' J-sec Energy of a single photon with oscillation fre- quency v, Joules Boltzmann's constant, 1.38054 x 10' Forward and backward rate constants, in terms of moles, centimeters, and seconds Length of active medium, cm Distance between mirrors on laser cavity, cm 152 Table C.1 (cont'd.). Symbol in Text Definition Ni Concentration of species i, mol-cm'3 .flfli Time-derivative of N1, mol-cm-3-sec'1 dt NA Avogadro's number, 6.02252 x 1023 molecules- mol‘1 PL Power density of laser output, N-cm-3 P(i,J) Output lasing power per unit volume on the (i,J) transition, watts-cm‘ Pi(t) Output lasing power on a single band as a function of time watts-cm‘3 P Peak outpgt lasing power during the pulse, p watts-cm' RO’RL Mirror reflectives R Universal gas constant, 1.98725 cal-mol'1-°K'1 t Time, sec T Temperature, °K t17 The time necessary for the lasing power to ° reach 1% of the peak power, sec ZAB Binary collision frequency for species A and B, moles /cm3-sec a(V,J) Gain of transition with lower level (v,J), cm' or ’Br Stoichiometric coefficients of reaction r of i i species i Threshold gain, cm-1 Table C.1 (cont'd.). 153 Symbol in Text Definition ¢(v,J) Yopt X(I9J) Xch(V1V2V3’J) Normalized line profile of transition with lower level (v,J), cm Optical pumping rate, moles-c'm3-sec-1 Rotational relaxation time constant, sec Rotational relaxation time constant for species M with collision partner N, sec Laser beam diameter at the mirror, cm Laser beam waist, cm Wavenumber of transition with lower level (v,J), cm“ Photon emission rate for transition I with lower level J, I = 1, 9.4 um I = 2, 16 um, moles/cc-sec Rate of change of species cozfvlvgv3,J) due to chemistry, moles-cm'3-seC' Rate of change of species N due to chemistry, moles- -cm 3-sec Reduced mass for species A and B, gm LIST OF REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] LIST OF REFERENCES R.w.F. Gross "Chemically pumped C02 laser," J. Chem. Phys. 59, 1889-1890 (1969). H.L. Chen, J.C. Stephenson, and 0.3. Moore, "Laser-excited vibrational fluorescence of HCl," Chem. Phys. Lett. 2, 593- 596 (1968). T.A. Cool, R.R. Stephens, and T.J. Falk, "A continuous-wave chemically excited 002 laser," J. Chem. Kinet. 2, 495-497 1969 . T.A. Cool, T.J. Falk, and R.R. Stephens, "OF-002 and HF-CO continuous-wave chemical lasers," Appl. Phys. Lett. 25, 31 - 320 (1969). T.Y. Chang and 0.R. Wood II, "Optically pumped atmospheric- pressure 002 laser," Appl. Phys. Lett. 22, 19 (1972). T.Y. Chang and 0.R. Hood, "Optically pumped 33-atm 002 laser," Appl. Phys. Lett. 22, 370 (1973). R.M. Osgood, "Optically pumped 16 um C02 laser," Appl. Phys. Lett. 28, 342-345 (1976). R.M. Osgood, “Sixteen micrometer CO2 laser," Opt. Comm. l§g 123-124 (1976). J.F. Bott and N. Cohen, "Temperature dependence of V-V, V-R, T energy transfer measurements in mixtures containing HF," J. Chem. Phys. 58, 4539-4549 (1973). T.J. Manuccia, J.A. Stregack, N.w. Harris, and B.L. Wexler, "14 and 161flngasdynamic C02 lasers," Appl. Phys. Lett. 29, 360 (1976). B.L. Hexler and T.J. Manuccia, "The effect of H2 on the 14 um and 16 um C02 lasers; improved performance and cw oscillations," 5th Conference on Chemical and Molecular Lasers, April 18-20, 1977, St. Louis, MO. J.R. Airey, "Cl + HBr pulsed chemical laser: a theoretical and experimental study," J. Chem. Phys. §2, 156-167 (1970). 154 [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] 155 A. Emanuel, "Analytical model for a continuous chemical laser," J. Quant. Spectrosc. Radiat. Transfer 2;, 1481-1520 (1971). R.L. Kerber, G. Emanuel, J.S. Whittier, "Computer modeling and parametric study for a pulsed H2 + F2 laser," Appl. Optics 2;, 1112-1123 (1972). J.G. Skifstad, "Theory of an HF chemical laser," Combustion Science and Tech. 6, 287-306 (1973). S.N. Suchard, R.L. Kerber, G. Emanuel, and J.S. Whittier, "Effect of H2 pressure on pulsed H + F laser. Experiment and theory," J. Chem. Phys. 52, 50 5-40 5.(1972). R.L. Kerber, "Simple model of a line selected, long chain, pulsed DF-CO2 chemical transfer laser," Appl. Optics 22, 1157 1973 . G. Emanuel and J.S. Whittier, "Closed-form solution to rate equations for an F + H2 laser oscillator," Appl. Optics 1;, 2047 (1972). G.T. Schappert, "Rotational relaxation effects in short-pulse C02 amplifiers," Appl. Phys. Lett. 22, 319 (1973). J.J.T. Hough, "A Theoretical and Experimental Investigation of the Mechanisms of the Hydrogen-Fluoride Pulsed Chemical Laser," Ph.D. Thesis (1975). J.C. Polanyi and K.B. Woodall, “Mechanism of rotational relaxa- tion," J. Chem. Phys. §§_(4), 1563-1572 (1972). N.P. Barnes, private communication, Los Alamos Scientific Laboratory (1978). 0.R. Wood and T.Y. Chang, "Transverse-discharge hydrogen halide lasers," Appl. Phys. Lett. 29, 77 (1972). M.I. Bushwald, 0.R. Jones, H.R. Fetterman, and H.R. Schlossberg, "Direct optical pumped multiwavelength CO2 laser," Appl. Phys. Lett. 22, 300 (1976). R.L. Kerber, N. Cohen, and G. Emanuel, "A kinetic model and computer simulation for a pulsed DF-CO2 chemical transfer laser," IEEE J. QE. QE-9, 94 (1973). R.L. Taylor and S. Bitterman, "Survey of vibrational relaxa- tion data for processes important in the COZ-Nz laser system,” Rev. Mod. Phys. 42, 26 (1969). [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] 156 K.F. Herzfeld, "Deactivation of vibration by collision in C02," Discussion, Faraday Soc., 88, 22 (1962). K.F. Herzfeld, "Deactivation of vibrations by collision in the presence of Fermi resonance," J. Chem. Phys. 48, 743 (1967). K.N. Seeber, "Radiative and collisional transitions between coupled Vibrational modes of C02," J. Chem. Phys. 88, 5077- 5081 (1971). E.E. Stark, "Measurement of the 1000-0200 relaxation rate in C02," Appl. Phys. Lett. 28, 335 (1973). K. Bulthuis and G.J. Ponsen, Chem. Phys. Lett. 24, 613 (1972). T.A. DeTemple, 0.R. Suhre, and P.D. Coleman, "Relaxation rates of lower laser levels in CO ," Appl. Phys. Lett. 22, 349 (1973). 2 "‘ C. K. Rhodes, M. J. Kelly, and A. Javan, "Collisional relaxation If the 1000 state in pure C02," J. Chem. Phys. 48, 5730-5731 1968 R. R. Jacobs, Ké J. PetBipiece, and S. J. Thomas, "Rate constants for the CD2 0200 - 10 0 relaxation," Phys. Rev. A 11,54 (I975). R.D. Sharma, "Kinetics of equilibrium of 1388 cm'1 level of cog," J. Chem. Phys. 48, 5195-5197, 1968. vibrational W. Baumann, J.A. Blauer, S.N. Zelazny, and W.C. Solomon, "Kinetic model and computer simulation of continuous wave DF-CO2 chemical transfer lasers," Appl. Optics 28, 2823 (1974). N. Cohen, A Brief Review of Rate Coefficients for Reactions in the D2-F2 Chemical System, Aerospace Corp. Report TR-OO74 (4530)-9, January 1974, Los Angeles, CA. For example, see J.F. Bott, "Temperature dependence of vibra- tional energy transfer for DF (9 = 1) to several diatomics," J. Chem. Phys. 88, 427 (1974) and references therein. J.C. Stephenson, J. Finzi, and C.B. Moore, "Vibration-vibration energy transfer in COZ-hydrogen halide mixtures," J. Chem. Phys. 88, 5214 (1972). I. Burak, Y. Noter, A.M. Ronn, and A. Szohe, "Vibration- vibration energy transfer in gaseous HCl," Chem. Phys. Lett. 11, 345 (1972). [41] [42] [43] [44] [45] [46] [47] [A8] [49] [50] [SI] [52] [53] 157 P.F. Zittel and C.B. Moore, “Vibrational relaxation in HBr and HCI from l44°K to 584°K,” J. Chem. Phys. _8, 6636 (J973). B.M. Hopkins and H.L. Chen, ”Vibrational relaxation of HBr (v = I) state in methane, water, helium, and hydrogen gaseous mixtures,” J. Chem. Phys. 88, 1495 (1973). R.R. Jacobs, J.J. Pettipiece, and S.J. Thomas, “Rotational vibration rate constants for C02,“ Appl. Phys. Lett. 28.(8), 375 (I97l). H. Statz, C.L. Tang, and G.F. Koster, “Transition probabili- ties between Iaser states in carbon dioxide,” J. Appl. Phys. _81, 4278 (I966). L.F. Shampine, H.A. Watts, and S.N. Davenport, “Solving non- stiff ordinary differential equations r the state of the art,“ SIAM Review 48, 376 (I976). The integration routine used here is RKFAS. J.J.T. Hough and R.L. Kerber, “Effect of cavity transients and rotational relaxation on the performance of pulsed HF chemical lasers: a theoretical investigation,” Appl. Optics ii, 2960 (I975)- R.L. Kerber and J.J.T. Hough, ”Rotational nonequilibrium mechanisms in pulsed H2 + F2 chain reaction lasers, I. Effect on gross laser performance parameters, “Appl. Optics 41,2369(1978). R.L. Kerber and W.K. Jaul, ”Kinetic mechanisms in a 16 um C02 laser,” J. Chem. Phys. Zl_(5), 2299-2312 (1979). J. J. Hinchen and R.H. Hobbs, “Rotational population transfer in HF,” R77-952-595-l, United Technologies Research Center, East Hartford, CN (August I977). Also, see J. Appl. Phys. 88, 628 (I979)- J.J. Hinchen and R.H. Hobbs, “Rotational relaxation studies of HF using ir double resonance,” J. Chem. Phys. 88, 2732- 2739 (1976). R.L. Wilkins, ”Mechanisms of energy transfer in hydrogen fluoride system,” J. Chem. Phys. 82, 5838-5854 (1977). N. C. Lang, J. C. Polanyi, and T. Wanner, Chem. Phys. 23, 2l9- (1977)- K. Bulthuis and G. J. Ponsen, “0n the relaxation of the lower laser level of 002,” Chem. Phys. Lett. 44, 6i3-6l4 (I972). [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] 158 R.W.F. Gross and J.F. Bott, Handbook of Chemical Lasers (New York: John Wiley and Sons, 1976). J.F. Bott and N. Cohen, "Temperature dependence of V-V and V-R,T energy transfer measurements in mixtures containing HF," J. Chem. Phys. 88(10), 4539-4549 (1973). J.K. Hancock and W.H. Green, "Laser excited vibrational re- laxation studies of hydrogen fluoride,” J. Chem. Phys. 88_(5), 2474-2475 (1972). J.F. Bott and N. Cohen, "Temperature dependence of several vibrational relaxation processes in DF-CO2 mixtures," J. Chem. Phys. 88_(1), 447-452 (1973). R.A. Lucht and T.A. Cool, ”Temperature dependence of vibra- tional relaxation in the HF, DF, HF-CO , and DF-COZ systems,” J. Chem. Phys. 88 (3), 1026-1035 (1974I. R.R. Stephens and T.A. Cool, "Vibrational energy transfer and de-excitation in the HF, DF, HF-CO , and DF-COz systems," J. Chem. Phys. 88_(12), 5863-5878 (1972). H.K. Shin, "Vibration-rotation-translation energy transfer in HF-HF and DF-DF," Chem. Phys. Lett. 28, 81-85 (1971). R.C. Brown, "A Theoretical Assessment of Vibrational Rotational Energy Exchange in Hydrogen Fluoride Chemical Lasers" Disser- tation, Michigan State University (1980)., A. Girard, "The effects of the insertion of a CW, low pressure 00 laser into a TEA CO2 laser cavity," Opt. Comm. 4;, 346-351 1 74). A. Gondhalekar, N.R. Heckenberg, and E. Holzhauer, "The mech— anism of single-frequency operation of the hybrid-CO2 laser,” IEEE J. Quantum Electronics QE-ll, 103 (1975). E.R. Sirkin, E. Cuellar, and G.C. Pimentel, "Laser emission between high rotational states of HX resulting from photo- elimination of halogenated olefins," 5th Conference on Chemical and Molecular Lasers, April 18-20, 1977, St. Louis, MO. N. Skribanowitz, I.P. Herman, R.M. Osgood Jr., M.S. Feld, and A. Javan, "Anisotropic ultrahigh gain emission observed in rotational transitions in optically pumped HF gas," Appl. Phys. Lett. 28, 428-431 (1972). [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] 159 D.P. Akitt and J.T. Yardley, "Far-infrared laser emission in gas discharges containing boron trihalides," IEEE J. Quantum Electronics QE-6, 113-116 (1972). E. Cuellar, J.H. Parker, and G.C. Pimentel, "Rotational chemical lasers from hydrogen fluoride elimination reactions," J. Chem. Phys. 82, 422-423 (1974). W.W. Rice, R.C. Oldenborg, "Pure rotational HF laser oscilla- tions from exploding-wire laser," IEEE J. Quantum Electronics QE-13, 86-88 (1977). T.F. Deutsch, "Laser emission from HF rotational transitions,” Appl. Phys. Lett. 24, 18-20 (1967). T.F. Deutsch, "Molecular laser action in hydrogen and deuterium halides," Appl. Phys. Lett. 18, 234-236 (1967). H. Chen, R.L. Taylor, J. Wilson, P. Lewis, and W. Fyfe, "Atmospheric pressure pulsed HF chemical laser,” J. Chem. Phys._8;, 306-318 (1974). R.E. Meredith and F.J. Smith, "Investigations of Fundamental Laser Processes Vol. II: Computation of Electric Dipole Matrix Elements for Hydrogen Fluoride and Deuterium Fluoride," 84130-39-T(II), The Environmental Research Institute of Michi- gan, Ann Arbor, MI (November 1971). R.L. Jarry and W. Davis Jr., "The vapor pressure, association, and heat of vaporization of hydrogen fluoride," J. Phys. Chem. 81, 600-604 (1953). G.T. Armstrong and R.S. Jessup, ”Combustion calorimetry with fluorine: constant pressure flame calorimetry,” J. Research 84A, 49-59 (1960). L.M. Peterson, C.B. Arnold, and G.H. Lindquist, "Pulsed HF chemical laser linewidth measurements using time-resolved bleachable absorption of HF gas,” Appl. Phys. Lett. 24, 615- 617'(1974). B.A. Lengyl, Introduction to Laser Physics (New York: John Wiley and Sons, 1966). J.F. Bott and N. Cohen, "Shock tube studies of HF vibrational relaxation, J. Chem. Phys. 88 (8) 3698-3706 (1971). [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] 160 J.F. Bott, "HF vibrational relaxation measurements using the combined shock tube-laser-induced fluorescence technique," J. Chem. Phys. 8Z_(1), 96-102 (1972). J.J. Hinchen, "Vibrational relaxation of hydrogen and deterium fluorides," J. Chem. Phys. 88_(1), 233-240 (1973). R.M. Osgood, A. Javan, and P.B. Sackett, "Measurements of V-V exchange rates for excited vibrational levels (2 §_V §_4) in hydrogen fluoride gas," J. Chem. Phys. 88, 1464-1480 (1974). J.K. Hancock and W.H. Green, "Vibrational deactivation of HF (v = 1) in pure HF and in HF-additive mixture," J. Chem. Phys. 8Z_(11), 4515-4529 (1972). J.L. Ahl and T.A. Cool, "Vibrational relaxation in the HF-HCI, HF-HBr, HF-HI, and HF-DF systems," J. Chem. Phys. 88, 5540- 5548 (1973). J.F. Bott, "Gas dynamic corrections applied to laser-induced fluorescence measurements of HF(v = 1) and DF(v = 1) deactiva- tion," J. Chem. Phys. 8l_(8), 3414-3416 (1974). N. Cohen, "Review of rate coefficients on the H2 + F2 chemical laser system," TROO73(3430)-9, The Aerospace Corporation, El Segundo, CA (1972). D.J. Douglas, and C.B. Moore, "Vibration relaxation of HF (v = 3,4) by H2, 02, and 002," J. Chem. Phys. Z8_(4), 1969- 1773 (1979). R.A. Lucht and T.A. Cool, "Temperature dependence of vibra- tional relaxation in the HF-DF, HF-COZ, and DF-COZ systems, II,” J. Chem. Phys. 88_(9), 3962-3970 (1975). T.A. Dillon, and J.C. Stephenson, ”Energy transfer during 'orbiting' collisons," J. Chem. Phys. 88_(11), 4286-4288 (1974). T.A. Dillon and J.C. Stephenson, ”Calculation of vibrational and rotational energy transfer between HF, DF, HCL, and 002," J. Chem. Phys. 88_(5), 2056-2064 (1973). T.A. Dillon and J.C. Stephenson, ”Effect of straight path approximation and exchange forces on vibrational energy trans- fer,“ J. Chem. Phys. 88 (9), 3849-3854 (1973). [90] [91] [92] [93] [94] 161 J.F. Bott, "Vibrational relaxation of HF(v = 1, 2, and 3) in H2, N2, and C02," J. Chem. Phys. 88_(10), 4239-4245 (1978). J.F. Bott, "Vibrational relaxation of DF(v =1- 4) in 0 H2, N2, HF, and C02," J. Chem. Phys. Z8_(9), 4123-4129(1979). H. K. Shin, "Temperature dependence of V- R, T energy transfer probabilities in C02(OO°1) + HF/DF,"J . Chem. Phys. 88 (5), 2167- 2168 (1974). H. K. Shin, "De- excitation of CO (000 )by Hydrogen Fluorides,” J. Chem. Phys. 8Z_(8) 3484- 3496 (1972) R.S. Chang, R.A. McFarlane and G.J. Wolga, "Vibrational Deactivation of CO by HF and DF at 75 and 100°C," J. Chem. Phys. 88_(1) 667-6 9 (1972).