Scientific Contributions of Lee H. Sentman III

D. L. Carroll1 and W. C. Solomon2

1CU Aerospace, Champaign, IL 61820

2University of Illinois at Urbana-Champaign, Urbana, IL 61801

Lee H. Sentman III (1937-2010) contributed to many fields in aerospace sciences for nearly five decades before his passing. He pursued his passion for flight and aeronautics through education, science, teaching, and decades of flight experience. He specialized in non-equilibrium gas kinetic flows and was the first to demonstrate the importance of quantum rotational non-equilibrium to high-energy lasers. He was honored by the AIAA through election as a Fellow and as the recipient of the Plasmadynamics and Lasers Award for his lifetime of outstanding achievements. In this paper we will review his scientific contributions and their impact to our understanding of various complex aerospace-related phenomena.

I. Introduction Lee Hanley Sentman III was born 27 January 1937 in Chicago, Illinois, and spent the first six weeks of his life in an incubator. He was the eldest of three brothers. His father (born on 7 March 1910 in Wyoming, Delaware) was a civil engineer who graduated from the University of Illinois at Urbana-Champaign (UIUC) in 1931 and was a track and field star at UIUC. His mother Esther Dore (born on 14 November 1907 in Chicago, Illinois) also attended UIUC where she received her degree in Education and taught in the Chicago Public School system for her career. His parents met at UIUC and were married in Chicago on 26 December 1931 a few months after graduation. Lee followed in his parents’ footsteps and graduated from UIUC in 1958 with a degree in Aeronautical and Astronautical Engineering. Lee was on the UIUC fencing team as was awarded the Big Ten conference medal for achievement in academics and athletics, the same award his father received in 1931; they are the only father – son combination to win the award. Soon thereafter, Lee worked at Lockheed Missiles and Space Company (LMSC) in Sunnyvale, California, while simultaneously obtaining his Ph.D. from Stanford University in 1965. His dissertation advisor was Prof. Krishnamurty Karamcheti, who was a former graduate student of the esteemed Prof. Hans Liepmann. Sentman moved back to his home state of Illinois in 1965 and joined the faculty of his undergraduate years. While teaching at UIUC over the next 37 years he was known for being a tough but fair Professor, winning UIUC’s prestigious W.L. Everitt Undergraduate Teaching Excellence Award, and twice winning the department’s Outstanding Teacher of the Year award. After retiring in 2002 as Professor Emeritus he continued working as a consultant for CU Aerospace on multiple programs and providing invaluable insight to the understanding of challenging new technologies. During the last two decades of his life he took up his old passion for flying, built his own RV-6 experimental aircraft, and after two years of flying his own plane, doing what he loved, he died tragically in an airplane accident in March of 2010. This paper summarizes the important scientific contributions of Lee H. Sentman III in the areas of (1) rarified gas dynamics, (2) chemical kinetics, (3) chemical lasers, and (4) laser physics.

II. Rarified Gas Dynamic Contributions During the 1950s there was an ever increasing desire to understand the aerodynamics of different types of bodies (missiles and early satellites) in upper atmospheric rarefied gas flow conditions, but there was very little quantifiable data for this type of aerodynamic situation at the time. LMSC put Lee to work studying this very problem from a theoretical standpoint to try to determine reasonably accurate approximations of the aerodynamic coefficients for missiles, and Prof. Karamcheti acted as Sentman’s Ph.D. advisor to guide this effort.

1 Vice President, CU Aerospace, 2100 S. Oak St. – Ste 206, Champaign, IL 61820, Fellow AIAA. 2 Prof. Emeritus, Univ. of Illinois at Urbana-Champaign, 104 S. Wright, Urbana, IL 61801, Fellow AIAA.

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4 - 7 January 2011, Orlando, Florida

AIAA 2011-1137

Copyright © 2011 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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In his earliest published work on this topic, Sentman computed the aerodynamic coefficients for a body in free molecule flow using detailed kinetic theory and compared the results with several approximate theories. He found that the approximate theories, which do not completely account for the random motion of impinging molecules, were satisfactory at predicting CN and CM for molecular speed ratios at satellite altitudes. However, a critical finding was that these approximate methods were inadequate for predicting CA for elongated bodies at small angles of attack, Figs. 1 and 2 [Sentman, 1961].

Figure 2: Variation of the axial force at zero angle of attack with L/D for a cylinder. [Sentman, 1961; Fig. 6]

Figure 3: Aerodynamic coefficients for the idealized satellite shape for a molecular speed ratio S of 7 [Sentman, 1962a; Fig. 3]

Following this work, Lee investigated the effect of the thermal accommodation coefficient, α ≡ (Ei – Er) / (Ei – Ew), and found that it can have a significant impact on predictions of the aerodynamic coefficients CN, CM, and CA for molecular speed ratios at satellite altitudes, Fig. 3 [Sentman, 1962a]. Experiments would be required to better determine what values of thermal accommodation were most realistic, but Sentman’s theoretical calculations were able to “bound” the problem for missile and satellite designers. He further showed analytically that the treatment of the atmosphere as a single species with the average molecular weight of the mixture was a valid assumption [Sentman, 1962b]. Sentman and Karamcheti tackled the theoretical problem of predicting rarefied gas flow around a sphere [Sentman, 1969]. A series of calculated plots, Fig. 4, shows how a ridge of increasing density with increasing speed ratio S would form and extend downstream. It was hypothesized that the first high-density ridge develops into a shock wave as collisions become important and would appear to form first in the downstream region; these observations agreed with those of Grad [Grad, 1959]. These results were important in that they indicated that a shock should indeed form in a free molecular flow at high speed ratio.

Figure 1: (a) Idealized satellite shape used for kinetic theory calculations. [Sentman, 1961; Fig. 4]

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(a) S = 0.25 and S = 1

(b) S = 3

(c) S = 5 and S = 10

Figure 4: Constant-density contours for rarefied flow around a sphere. (a) S = 0.25 and S = 1, (b) S = 3, (c) S = 5 and S=10

Sentman continued to work with rarefied gas dynamics and kinetic theory over the next two decades as he studied the kinetic equations for a gas under the action of non-conservative forces [Karamcheti, 1968], the interpretation of molecular beam experiments [Klavins, 1970], tangential velocity effects in gas-surface scattering [Sentman, 1974], a new kinetics model for rarefied gas dynamic problems [Forster, 1974], a kinetic description of the initial stages of shock formation in the classic piston problem [Sentman, 1977a], and a computer aided design method for determining the free molecule aerodynamic and solar radiation forces and moments on the space station [Sedlund, 1989]. For 25 years he taught a graduate level “Kinetic Theory” course and a related class entitled “Environmental Effects on Spacecraft Motion” that included the fascinating intertwined influences of rarefied gas dynamics, solar radiation pressures, and magnetic field torques on satellite dynamics as a function of orbital altitude.

III. Chemical Kinetics and Chemical Lasers

In the summers of 1971 and 1972, Sentman worked at the Rocket Propulsion Laboratory at Edwards Air Force Base. It was during this time that he began to put his skills and talents to work on the detailed kinetics problems associated with rocket propulsion and the new exciting field of high energy chemical lasers. 3.1 Chemical Kinetics Studies Lee began to investigate the kinetics of vibrational and rotational molecular energy transfer with a paper in 1972 [Blauer, 1972]. HF was the molecule of choice for energy transfer studies because of its broad importance in application to rockets and chemical lasers. Agreement with the existing theory was marginal at best, however, and studies of HF relaxation at high temperature in the presence of other diatomic molecules showed that a variety of mechanisms (V-V, V-T, and V-R) of energy transfer were found to be operating. Sentman developed a better theory and model [Sentman, 1973a] to describe the results from experiments which points out the role of molecular vibrational-rotational states, Fig. 5, in energy transfer in the absence of other affects. Agreement between data and theory improved in a variety of cases, for example in HF-HF, Fig. 6. This work was expanded to model many other molecular species including DF-HF, DCl-DCl, HCl-HCl, HBr-HBr, DI-DI, HI-HI, N2-DI, N2-HI, HF-O2, HF-D2, DF-NO-HF-NO, DF-N2, and HF-N2 [Sentman, 1973a; Sentman, 1973b].

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Figure 5: Collision geometry for the interaction of two vibrating rotators. [Sentman, 1973a; Fig. 1]

Figure 6: Relaxation times for HF and DF. Data (×, •, ☐, etc.), Sentman model (⎯), and Shin theory (⎯ ⎯). [Sentman, 1973a; Fig. 2]

3.2 Chemical Laser Modeling and the BLAZE–II Code Shortly thereafter Sentman and colleagues at Bell Aerospace Textron (BAT) built the BLAZE–II computer model [Sentman, 1977b] to perform extensive chemical laser simulations that included the detailed kinetics of HF, DF, and DF-CO2 chemical lasers, Figs. 7 and 8. Early fluids and kinetics only versions of BLAZE–II had evolved at BAT, and Sentman added the lasing equations to the model during the years that he consulted there. Over the next 30 years, BLAZE–II became a workhorse code for Sentman and his students. It proved to be an excellent tool for predicting laser gain and output powers with very reasonable accuracy, and significantly helped to guide the rapid development of the laser systems at BAT and later at UIUC and CU Aerospace. The legacy of the BLAZE code lives on in the most recent dramatically enhanced versions BLAZE–IV and –V [Palla, 2007; Palla, 2010].

Figure 7: Schematic of two-stream mixing represented in the BLAZE-II model [Sentman, 1977b; p. 69]

Figure 8: Schematic of the Fabry-Perot resonator used in the BLAZE-II model [Sentman, 1977b; p. 70]

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With an established body of work, Sentman contributed to the construction of a detailed kinetic model that described a completely different DF-CO2 laser [Zelazny, 1976]. Unlike most chemical lasers this laser had kinetics that were slow enough to allow operation at up to several hundred torr. Kinetic modeling of this transfer laser was also able to describe the laser performance as a function of cavity pressure quite nicely, Figs. 9 and 10. This helped to demonstrate the BLAZE–II model’s flexibility in treating a wide variety of reacting flow systems.

Fig. 9: Comparison between computed number densities in the upper laser level and experimental results (Fig. 1 from [Zelazny, 1976]).

Fig. 10: Comparison between predicted and experimental zero power gain for the six optical cavity pressures for a DF-CO2 transfer laser (Fig. 4 from [Zelazny, 1976]).

3.3 Hot Pumping Reaction and Importance of Collisional Decomposition Most HF chemical laser studies addressed a system characterized exclusively by what was called the “cold reaction”. However, his study of the so called “hot reaction” was a classic case where the kinetics of the higher HF v-levels were addressed with BLAZE–II to characterize the combined situation [Sentman, 2001; Detweiler, 2005]: “Cold reaction” F + H2 → HF (v,J) + H v =1,2,3 –ΔH=31.5 kcal/mol “Hot reaction” H + F2 → HF (v,J) + F v = 3,4,5,6 –ΔH=98.0 kcal/mol This study included the critical collisional decomposition reaction, H + HF(v=3) → H2 + F. This reaction and its corresponding heat release dramatically reduced the exceptional potential expected by the very energetic “hot reaction”. The inclusion of the collisional decomposition reaction brought the model into reasonably close agreement with data and explained the disappointing laser performance experiments that were achieved in several laboratories over many years. Additionally, this study elucidated conditions and geometry changes under which the energy advantages of the “hot reaction” might be obtained. 3.4 Rotational Non-Equilibrium One of the most significant, and initially controversial, contributions by Sentman was the hypothesis and demonstration that rotational non-equilibrium was significant and in fact could explain certain aspects to HF/DF chemical laser data that had previously been unexplained. Lee mechanized the theory to examine the role of rotational non-equilibrium in describing the behavior of vibrationally pumped lasers and showed that certain behaviors, such as simultaneous multi-line lasing, could only be described by very fast, but measurably finite [Polanyi, 1972; Hinchen, 1975], rotational relaxation in the case of fast pumping and rapid collisional deactivation, Fig. 11 [Sentman, 1975]. Simultaneous multi-line lasing on a single v-level was not allowed by any other existing model, all of which considered only rotational equilibrium. The populations of lasing v-J levels, multi-line lasing and cut-off were well described by rotational non-equilibrium. This involved the development of an entirely new kinetics code called NORO-II (later MNORO) which solved the rotational non-equilibrium kinetics, while utilizing

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the fluid dynamic, and mixing profiles determined from the faster running BLAZE-II code; this coupling of the two codes together provided for a computationally efficient approach to this complex problem (in the days when punch cards were still used and there was no substitute for computational efficiency!).

Fig. 11: Comparison of results from a rotational equilibrium calculation (left) and one with rotational non-equilibrium (right) [Sentman, 1975]. Rotational equilibrium shows only single line lasing at any position X and the sequential increase in rotational line J as each line encounters lasing cutoff. Rotational non-equilibrium shows simultaneous lasing on several lines and generally lasing on lower J lines; both of these characteristics were in agreement with data whereas rotational equilibrium was not.

Further, using rate constants given by Cohen [Cohen, 1972], Sentman compared his results to laboratory experiments at the time and obtained very good agreement. He further applied the rotational non-equilibrium model to describe conditions that could partially suppress the multi-line lasing and showed that quite good performance could still be obtained employing this technique [Sentman, 1976]. Using Hinchen’s data [Hinchen, 1975] he solved the following equations to determine two critical constants from data in Polanyi and Woodall’s groundbreaking rotational transition probability paper [Polanyi, 1972], Fig. 12 [Sentman, 1977c].

His work of rotational non-equilibrium modeling continued for over twenty years with a number of papers elucidating the details. These are best summarized in a seminal review [Sentman, 2001]. As will be seen in Sect. 4, these kinetic studies directly impacted the advanced work on laser oscillations in unstable resonators as well as a detailed understanding of HF overtone lasers 3.5 Sodium and COIL Systems Lee’s understanding and study of kinetic effects also led him into the area of chemically pumped electronic states with a study of the electronically excited Na*(4d2D) which is produced by resonant transfer from excited SiO [Stephens, 2001], as well as into the realm of chemical oxygen-iodine lasers (COIL) [Carroll, 2000; King, 2010].

Figure 12: Comparison between theory and data [Sentman, 1977c; Fig. 3].

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IV. Experimental and Theoretical Laser Physics

In the early 1980’s, Lee recognized that he needed to have his own experimental laboratory in order to study the underlying detailed physics these HF/DF chemical lasers. With AFOSR support he established an HF chemical laser lab at UIUC and embarked on more than twenty years of in depth studies into the fundamental physics of the complex interactions between the kinetics and optical physics of these quantum electronic systems. It is notable that some of his colleagues from graduate student days were supportive, but skeptical that this to-date “complete theoretician” would be able to pull off any meaningful experiments; their skepticism was happily proven unfounded within only a couple of years. 4.1 Time-dependent Oscillations in Unstable Resonators He extended his rotational non-equilibrium study to include physical optics of unstable resonators in an iterative code that would pass information back and forth between the rotational non-equilibrium kinetics and a wave optics module, Fig. 13 [Sentman, 1978]. The power spectral distribution in the multi-line lasing cases for rotational equilibrium and non-equilibrium were found to be much better described in the latter model, consistent with his earlier findings. The consideration of rotational non-equilibrium coupled with physical optics is responsible for accurately predicting the power spectral distribution within a real resonator [Sentman, 1980; Sentman, 1981; Zelazny, 1982]. An important finding from this work was the prediction of oscillations that occurred on lines whose saturated gain zone did not fill the unstable resonator, Fig. 14. Further, the amplitude of the fluctuation was determined by the fraction of the resonator filled by the saturated gain zone of the oscillating line, and the frequency of the fluctuation was determined by the location of the intensity peak of the oscillating line [Sentman, 1978; Sentman, 1985].

Fig. 13: Schematic of the wave propagation through the unstable resonator in the coupled rotational non-equilibrium and wave optics model [Sentman, 1978; Fig. 1].

Fig. 14: Outcoupled power vs iteration number predicted by the rotational non-equilibrium unstable resonator model. The predicted powers from the kinetics and wave optics portions are shown [Sentman, 1978; Fig. 8].

The appearance of a 40 ns oscillation, Fig. 15, in experiments at Lee’s UIUC laboratory led to another series of papers with a focus on explaining the physics of this phenomenon. From detailed modeling, these oscillations were hypothesized to be a competition between chemical pumping and radiative deactivation of the upper HF laser levels. The oscillations occurred only when the media was not strongly coupled to the optical fields diffractively or geometrically [Sentman, 1989a]. Two conditions were later found that would reduce or eliminate the oscillations: (1) a resonator Fresnel number < 3, and (2) the number of passes required for a wave to exit the Fresnel core of the resonator was > 4 [Palla, 2005]. These predictions were tested and confirmed experimentally using a lower magnification resonator, as well as shorter and longer resonator mirror separations [Mayer, 2005].

Figure 15: Oscilloscope trace showing 7 ns oscillation superimposed on top of a 40 ns oscillation [Sentman, 1987; Fig. 7].

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4.2 Master Oscillator Power Amplifier Studies HF master oscillator power amplifier (MOPA) experiments showed that between 1/3 – 1/2 of the device’s oscillator output must be input to the amplifier to obtain amplifier output equal to the device’s oscillator performance [Sentman, 1987; Sentman, 1992; Waldo, 1992]. Further, when time-dependent oscillations were a part of the oscillator beam, the amplitude modulation of the output beam was reduced by a factor that equaled the amplification ratio of the amplifier. An amplifier performance model was developed that was in good agreement with experimental data and determined that a single 4 m oscillator would be sufficient to drive 8 similarly sized amplifiers [Waldo, 1993]. 4.3 Examination of Quantum Physics Approximation While the inclusion of rotational non-equilibrium into the kinetics enabled the prediction of a variety of physical phenomena that the rotational equilibrium assumption could not simulate, Sect. 3.4, the predicted spectra generally lased with a peak on a lower v, J transition than was measured experimentally. The 3-level v, J version of MNORO, called MNORO3, used the classic “rigid rotator harmonic oscillator” approximation for the energy levels of the different v, J states. Sentman hypothesized that this assumption may have been the source disagreement between predicted and measured spectra and replaced this assumption with the exact quantum physics expression for Ev,J. The new model resulted in a spectral shift of 1 – 2 J-lines higher which was in significantly better agreement with data, Fig. 16 [Sentman, 1989c]; this demonstrated yet another refinement to the modeling and understanding of these systems that had not previously been tested. 4.4 HF Overtone The demonstration of the first HF Overtone laser by Jeffers [Jeffers, 1989] in which there is a multi-quantum jump of 2 vibrational levels (v = 2 → 0) that enabled the high energy HF laser to operate at a more attractive wavelength range of 1.35 – 1.40 µm rather than at the fundamental (v = 2 → 1, and v = 1 → 0) wavelength range of 2.5 – 3.0 µm set off a new wave of detailed experimental and theoretical studies by Sentman and his students. The overtone wavelengths were of significant interest to the military for both atmospheric transmission and laser “brightness” [Horkovich, 2006] reasons. The MNORO3 rotational equilibrium model (now including the exact expression for Ev,J) was updated to allow lasing on the overtone transitions and renamed ORNECL. The students led by Sentman proceeded to demonstrate the highest HF Overtone efficiencies of >70% relative to the fundamental performance [Carroll, 1993a], Fig. 17, and measured the gain suppression of HF fundamental v, J lines while simultaneously lasing on the HF Overtone [Theodoropoulos, 1996a]. The gain suppression data

Figure 16: Comparison between HF fundamental spectral data and the MNORO3 and ORNECL models [Sentman, 1989c; Fig. 5]. ORNECL includes the exact expression for Ev,J and is in better agreement with data.

Figure 17: HF Overtone efficiency as a function of reflectivity compared with Rigrod theory [Carroll, 1993b; Fig. 9].

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proved to be a painstaking process, but ultimately determined that the fundamental gains on the low J transitions P1(4-6) and P2(4-6) were suppressed by 41-96%, whereas the gains on the high J fundamental transitions P1(7-9) and P2(7-9) were only suppressed by 3-44%. The explanation for this phenomenon appears to be tied to the rotational relaxation rates [Theodoropoulos, 1996b]. Sentman’s group also measured performance as a function of gain length and demonstrated linear scaling in both the fundamental and overtone as expected [Sentman, 1993]. The HF Overtone gains were on the order of 0.1% cm-1, significantly lower than the much higher gain fundamental transitions which were typically 4-10% cm-1. This led to the investigation of some general laser physics issues for systems having low gain and how best to extract the desired energy in the form of a laser beam from these systems [Carroll, 1993b], and would have a considerable impact on the demonstration and evolution of the electric oxygen-iodine laser system [Carroll, 2005]. 4.5 Line Selected Performance Due to the fact that the atmosphere absorbs some HF wavelengths dramatically more than other wavelengths, there has been considerable interest by the military over the years in determining just how much power can be extracted from a single- or two-line HF resonator as compared to a typical multi-line (6-12 lines) HF oscillator. Early modeling work indicated that with the proper line choice, > 50% of the multiline power might be obtained in a single line mode [Sentman, 1976]. Detailed experiments and modeling followed two decades later in which measurements were made showing 25% of the multiline power in a single line with a Littrow configuration, and 54% in a cascade pair of lines relative to the multiline power [Sentman, 1993; Gordon, 1997; Sentman, 1999a]. 4.6 Mixing Enhancement in Chemical Lasers Sentman’s early experiments utilized entirely subsonic HF chemical lasers. While these proved extremely useful for scientific study devices, they lacked the direct connection to the large supersonic HF laser systems in terms of some of the complex fluid mechanics and mixing effects. As such, Sentman and his students designed a small-scale supersonic device as the final project for a graduate class, and later built and tested this system in the late-1980’s [Sentman, 1989b]. This supersonic laser became the workhorse test device for Sentman and his students over the next 12 years. The work with this device turned towards a more detailed investigation of the effects of trip injectors on mixing/performance enhancement [Sentman, 1999b]. The trip jets cause a distortion and stretch the reactant interface such that the reactant gases mix and react more rapidly thereby increasing the laser gain and decreasing the losses; these effects are best described in a pair of papers by Driscoll [Driscoll, 1986; Driscoll, 1987]. Sentman’s group demonstrated a dramatic 60% laser power enhancement when they switched from a more classic parallel slit nozzle (PSN) array to an array of the HYSIM nozzles, Fig. 18, that included gas trip jets inside the supersonic portion of the nozzle flow [Sentman, 1999b]. Sentman also had notches added to the HYSIM array, but measured no appreciable enhancement to performance; it was believed that the notches were too small to significantly further enhance the mixing and performance of the test hardware. The team also investigated the effects of boundary layer thin film cooling effects upon performance [Sentman, 1999b]. Using room temperature helium as the thin film injected behind the nozzle blade, Sentman’s group measured approximately a 10% drop in nozzle blade temperature thereby demonstrating the anticipated effect of cooling the nozzle blades. The laser performance however was not enhanced in this experiment, which was believed to be a consequence of the design being originally optimized for performance without thin film cooling.

Figure 18: Comparison of HYSIM and HeFilm supersonic nozzles [Sentman, 1999b; Fig. 8].

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V. Concluding Remarks Lee Sentman relied on a very deep fundamental education to provide his own research interests. He used this to guide himself through a wide variety of investigations in topics ranging from space physics, the details of chemical kinetics and molecular energy transfer, chemical laser performance and more. His fundamental understanding of the properties of atoms and molecules essentially freed him to use his natural investigative nature to go to places that most scientist-engineers can only dream about. In his graduate level courses, textbooks were rarely used and exams were frequently oral and never easy (return visits were more frequent than not). It was a constant treat to wander through the great lessons of literature with Lee as both student and fellow educator, and he constantly hammered home the necessity to cross check calculations with real experiments. The far ranging research, addressed above, is first rate; however, his insistence on teaching his loyal students the importance of doing things the “right way” is his most important legacy.

Acknowledgments This paper is dedicated to the memory of Lee H. Sentman III, our friend and mentor whose guidance has been invaluable through the decades. The authors would like to thank Jan Sentman (wife), Jeanne Griswold (daughter), John Sentman (brother), Munson Kwok, and George Emanuel for conversations regarding Lee’s life and memories.

References Blauer J A, Solomon W C, Sentman L H, and Owens T W, “Catalytic Efficiencies of H2O, D2O, NO, and HCl in the

Vibrational Relaxation of HF and DF,” J. Chemical Physics, 57 (8) 3277-3281 (1972) Carroll D L, Sentman L H, Theodoropoulos P T, Waldo R E, and Gordon S J, “Experimental Study of Continuous

Wave Hydrogen-Fluoride Chemical Laser Overtone Performance,” AIAA Journal, 31 (4) 693 (1993a) Carroll D L and Sentman L H, “Maximizing Output Power of A Low-Gain Laser System,” Applied Optics, 32 (21)

3930 (1993b) Carroll D L, King D M, Fockler L, Stromberg D, Solomon W C, Sentman L H, and Fisher C H, “High Performance

Chemical Oxygen-Iodine Laser Using Nitrogen Diluent for Commercial Applications,” IEEE J. Quant. Elect., 36 (1) 40-51 (2000).

Carroll D L, Verdeyen J T, King D M, Zimmerman J, Laystrom J, Woodard B, Benavides G, Kittell K, Stafford D, Kushner M J and Solomon W C, “Continuous-wave laser oscillation on the 1315 nm transition of atomic iodine pumped by O2(1Δ) produced in an electric discharge,” Appl. Phys. Lett. 86 111104 (2005)

Cohen, N,“A review of rate coefficients for Reactions of the H2-F2 System” Aerospace Corp. Report TR-0073 (3430), The Aerospace Corp., El Segundo, CA, (1972)

Detweiler G L, Sentman L H, and Carroll D L, “The Possibility of Hot Reaction Enhancement of CW HF Laser Performance,” AIAA Paper 2005-5042 (2005)

Driscoll R J, “Mixing Enhancement in Chemical Lasers, Part I: Experiments,” AIAA J, 24 (7) 1120 (1986) Driscoll R J, “Mixing Enhancement in Chemical Lasers, Part II: Theory,” AIAA J, 25 (7) 965 (1987) Forster T J, Sentman L H, and Grimm A D, “An Investigation of the Utility of a New Kinetic Model for Rarefied

Gas Problems,” Proc. of the Ninth Int. Symp. On Rarefied Gas Dynamics, Gottingen, Germany, A.3 (1974) Gordon S J, Sentman L H, Jenkins D S, and Ayre A J, “Line Selected Performance of cw HF Lasers,” AIAA Paper

97-2424 (1997) Grad H, “Equations of Flow in a Rarefied Atmosphere,” Rept. R-339, RAND Corp. (1959) Hinchen J J, “Rotational population transfer in HF,” J. Appl. Phys., 45 1818 (1974) Horkovich J A, “Directed Energy Weapons: Promise & Reality,” AIAA Paper 2006-3753 (2006) Jeffers W Q, “Short Wavelength Chemical Lasers,” AIAA Journal, 27 (1) 64-66 (1989) Karamcheti K and Sentman L H, “Kinetic Equations for a Gas Under the Action of Nonconservative Forces,” J

Chem Phys, 48 (5) 2181-2184 (1968) King D M, Field T H, Carroll D L, Laystrom-Woodard J K, Driscoll R J, Sentman L H, Ragheb A M, Elliott G S,

and Solomon W C, “Performance of a Multi-Stream Injection Coil with Starlet Ejectors,” AIAA Paper 2010-4754 (2010)

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Klavins A and Sentman L H, “The Interpretation Error in Molecular Beam Experiments, Rev of Scientific Instruments, 41 (11) 1560-1567 (1970)

Mayer S J, Palla A D, Sentman L H, and Carroll D L, “Experimental Study of Time-Dependent Oscillations in a cw HF Chemical Laser Confocal Unstable Resonator,” AIAA Paper 2005-5364 (2005)

Palla A D, Sentman L H, and Carroll D L, “Simulation of Time-Dependent Oscillations in a cw HF Chemical Laser Confocal Unstable Resonator,” AIAA Paper 2005-5365 (2005)

Palla A D, Zimmerman J W, Woodard B S, Carroll D L, Verdeyen J T, Lim T C and Solomon W C, “Oxygen Discharge and Post-Discharge Kinetics Experiments and Modeling for the Electric Oxygen-Iodine Laser System,” J. Phys. Chem. A 111 6713-6721 (2007)

Palla A D, Carroll D L, Verdeyen J T, Zimmerman J W, Woodard B S, Benavides G F, Day M T and Solomon W C “Modeling of Recent ElectricOIL Gain Recovery Data,” AIAA paper 2010-5041 (2010)

Polanyi J C and Woodall K B, “Mechanism of Rotational Relaxation,” J. Chem. Phys., 56 (4), 1563 (1972) Sedlund C, and Sentman L H, “A CAD Method for the Determination of Free Molecule Aerodynamic and Solar

Radiation Forces and Moments,” AIAA Paper 89-0455 (1989) Sentman L H, “Comparison of the Exact and Approximate Methods for Predicting Free Molecule Aerodynamic

Coefficients,” ARS Journal, 1576-1579 (1961) Sentman L H, “Effect of Degree of Thermal Accommodation on Free Molecule Aerodynamic Coefficients,” ARS

Journal, 1408-1410 (1962a) Sentman L H, “The Single Species Assumption in the Application of Free Molecule Theory in the Earth's

Atmosphere,” ARS Journal, 1933-1934 (1962b) Sentman L H and Karamcheti K, “Rarefied Flow Past a Sphere,” AIAA Journal, 7 (1) 161-163 (1969) Sentman L H, “Vibration-to-Rotation and Vibration-to-Vibration Energy Transfer Between Diatomic Molecules,”

Chemical Physics Letters, 18 (4) 493-500 (1973) Sentman L H, and Solomon W C, “Kinetics of the Vibrational Relaxation of the HF-N2 System, J Chemical Physics,

59 (1) 89-91 (1973) Sentman L H, and Chrisman C C, “Tangential Velocity Effects in Gas-Surface Scattering,” Chemical Physics

Letters, 26 (3) 407-413 (1974) Sentman L H, “Rotational Nonequilibrium in CW Chemical Lasers,” J Chemical Physics, 62 (9) 3523-3537 (1975) Sentman L H, “Line Suppression and Single Line Performance of a CW HF Chemical Laser,” Applied Optics, 15

744 (1976) Sentman L H, and Grimm A D, “Kinetic Description of the Initial Stages of Shock Formation in the Piston

Problem,” Physics of Fluids, 20 (1) 10-17 (1977a) Sentman L H, Subbiah M, and Zelazny S W, “Blaze II: a chemical laser simulation computer program,” Bell

Aerospace Textron, Buffalo, NY, Tech. Repp. H-CR-77-8 (1977b) Sentman L H, “Rotational Relaxation of HF,” Journal of Chemical Physics, 67 (3) 966-969 (1977c) Sentman L H, “Chemical Laser Power Spectral Performance: A Coupled Fluid Dynamic, Kinetic, and Physical

Optics Model,” Applied Optics, 17, 2244 (1978) Sentman L H, “Rotational Nonequilibrium Effects in CW Chemical Lasers,” J de Physique, 41, C9-17 (1980) Sentman L H, and Rushmore W, “Computationally Efficient, Rotational Nonequilibrium cw Chemical Laser

Model,” AIAA Journal, 19 (10) 1323-1332 (1981) Sentman L H, Nayfeh M H, Townsend S W, King K, Tsioulos, G, and Bichanich J, “Time-dependent Oscillations in

a CW Chemical Laser Unstable Resonator,” Applied Optics, 24, 3598 (1985) Sentman L H, Carroll D, Gilmore J, Theodoropoulos P, Waldo R, and Gumus A, “CW HF Chemical Laser MOPA

Performance,” AIAA Paper 87-1449 (1987) Sentman L H, Gilmore J O, and Carroll D L, “Mechanism for Time-Dependent Oscillations in a CW HF Chemical

Laser Unstable Resonator,” AIAA Paper 89-1897 (1989a) Sentman L H, Theodoropoulos P, Nguyen T, Carroll D, and Waldo R, “An Economical Supersonic CW HF Laser

Testbed,” AIAA Paper 89-1898 (1989b) Sentman L H, Carroll D L, and Gilmore J, “Modeling CW HF Fundamental and Overtone Lasers,” AIAA Paper 89-

1904 (1989c) Sentman L H, Waldo R E, Theodoropoulos P T, Nguyen T X, and Carroll D L, “Hydrogen Fluoride Chemical Laser

Amplifier Performance: Experiment, AIAA Journal, 30 (1) 138 (1992) Sentman L H, Otto J W, Gordon S J, and Carroll D L, “Effects of Gain Length on HF Overtone Performance and

Line Selection on HF Fundamental Performance,” AIAA Paper 93-3185 (1993) Sentman L H, Cassibry J T, Wootton B P, and Eyre A J, “CW HF Laser Line Selected Performance,” AIAA Paper

99-3468 (1999a)

12

Sentman L H, Eyre A J, Wootton B P and Cassibry J T, “Comparison of CW HF Laser Performance for Several Nozzles,” AIAA Paper 99-3469 (1999b)

Sentman L H, “Mechanisms of HF Laser Performance,” XIII International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, Florence, Italy, 2000, SPIE Vol. 4184, 137 (2001)

Stephens J M, Gole J L, Sentman L H, and Zaczek M, “Potential for a Chemically Pumped Sodium Laser,” AIAA Paper 97-2425 (1997)

Theodoropoulos P T, Sentman L H, Carroll D L, Waldo R W, Gordon S J, and Otto J W, “Continuous Wave Hydrogen Fluoride Overtone Lasing Saturation Effects on Fundamental Gain Suppression,” AIAA J, 34 (6) 1216 (1996a)

Theodoropoulos P T and Sentman L H, “Fundamental Gain Suppression Mechanisms in a Continuous Wave Hydrogen Fluoride Overtone Laser,” AIAA Journal, 34 (8) 1589 (1996b)

Waldo R E, Sentman L H, Theodoropoulos P T, and Carroll D L, “HF Chemical laser Multiple Pass Amplifier Performance, AIAA Paper 92-2978 (1992)

Waldo R E and Sentman L H, “Effect of Gain Length on Hydrogen Fluoride Chemical Laser Amplifier Performance,” AIAA Journal, 31 (11) 2090 (1993)

Zelazny S W, Blauer J A, Wood L, Sentman L H, and Solomon W C, “Transfer chemical laser: modeling of a cw DF-CO2 laser, Applied Optics, 15 (5) 1164 (1976)

Zelazny S W, Rushmore W L, Raymonda J W, Subbiah M, and Sentman L H, “Rotational Non-equilibrium influences on cw HF/DF Chemical Lasers,” Proc. 13th Int. Symp. on Shock tubes and Waves, 438 (1982)