IL34506A - Apparatus for and method of producing a population inversion in a flowing gaseous laser medium - Google Patents

Description

out isa n?»*V Apparatus for and method of producin a population inversion in a flowin gaseous laser medium AVCO CORPORATION C: 32783 ^ DKT. ABRL-77 ^ This Invention relates to a method and apparatus for producing a population inversion in a gas in a chamber.

Optical masers or lasers, as the art has developed, generally involve the establishment of an artificual distribution of bound electrons at energy levels other than the natural distribution in a host environment through the application of a source of energy known as the "pumping energy". This results in a greater number of molecules or atoms in some high energy level than in a lower energy level to which it is optically connected. This is known as a population inversion. The electrons present In the host environment in the artificial distribution then give up their energy and undergo a transition to the lower energy level. The released energy may be in the form of electromagnetic radiation; which, in the majority of devices seen thus far in the art, has been light, either in the visible or infrared.

In optical maser devices currently available in the art there may be employed a gas, such as helium-neon mixture; or, a crystal, such as chromium doped aluminum oxide; or a noncrystalline solid, such as neodymium glass; or a liquid, such as tri-valent neodymium in selenium oxychlorlde, as the environment which responds to the pumping energy, permitting the population inversion of electrons between an excited state and a lower state. The electrons in returning to the lower state give off quanta of light energy or photons in what is known in the art as a radiative transition. When the density of these photons becomes large, the radiative transition probability increases; and, in the presence of a population inversion, electromagnetic modes into which the photons are emitted, in turn, become most readily able to induce further emission therein. This is known in the art as simulated emission of radiation and results in a narrowing of the emission trical discharge or electric current; which, in turn, is used to establish the population inversion.

The recent development of coherent light amplifiers and generators, now generally referred to as "optical masers" or "lasers" has made feasible a host of new uses and applications of electromagnetic wave energy in the optical portion of the spectrum. Light waves produced or amplified by such devices can be very sharply focused to produce energy densities suitable for welding, cutting, drilling and similar purposes. Furthermore, the high degree of monochromaticity obtainable from an optical maser makes it a useful tool for spectroscopic investigations as well as for stimulating various types of chemical and physical reactions. Among the most promising applications of coherent light amplifiers and generators are those in the field of communications where the optical spectrum represents virtually unlimited bandwidth and information carrying capacity. In addition, the directionality of optical maser beams greatly mitigates many problems of interference and security of communications channels.

For communications and other applications it is advantageous to have optical masers operable at many different wavelengths in the light spectrum, which is deemed to Include infrared, visible and ultraviolet energy. As the wavelength emitted by any particular energy transition in a laser medium is tunable only over a small portion of the spectrum, it is important to provide a number of materials adapted for use as active laser media at various light frequencies. A great amount of research has recently been directed to the discovery of such materials and a number have been found. Furthermore, especially for communications use, it is important that laser media be provided which are adapted to continuous wave operation. In general, such media are those characterized by three or more energy levels, at least two ture and emission characteristics of solids, appears more readily achievable with gaseous optical masers.

High gain in a gas laser makes possible the realization of a usef l optical amplifier which is merely the laser without ri any mirrors. When an external light beam passes through the active mixture of an optical amplifier, atoms or molecules in the proper excited state are stimulated to emit, thereby increasing the photon flux. In such a device, the wavelength of the incident light which Is to be amplified must be precisely matched to that which results from the stimulated emission process; for ex*-ample, a helium-xenon amplifier is specific for an amplification of 2.03 micron radiation and a carbon dioxide amplifier is specific for the amplification of 10.6 micron radiation. Optical amplifiers are useful for part of a practical laser communications system.

All known prior art devices are of relatively low power. A high power system (up to one megawatt or more) is possible even for communications applications by utilizing therein the method and/or apparatus according to the present invention. Thus, a high power communications system may comprise a conventional electrically excited CO2 laser for the oscillator and a gas dynamic amplifier embodying the present invention. In this system, in addition to providing a high power CW (continuous wave) operation, mode control, frequency stabilization and modulation lies with the electrically excited laser, where conventional techniques are applicable and the circulating power is low as compared to the output power of the system.

In the Polanyi references identified hereinafter, it is suggested that total and partial inversions may be obtained as a direct result of chemical reaction. Without flow, such inversions are transient. Even if the gas 1B pulsed thermally and permitted is removed by diffusion to the walls. It will be apparent hereinafter, however, that the gas can be cooled by expansion to supersonic speeds which is inherently a volume process that can be performed in any size vessel and at any density consistent with th relevent vibrational relaxation times of the gas. fhe Hurle et al papers also identified hereinafter suggests supersonic expansion as a method of producin population inversion between electronic states by differential radiation relaxation.

While presumably in theory (Hurle et al admit tha they were unable to observe an inversion) an inverted population can be produced in this fashion, the size of a device based on this principle is limited because of radiative trapping and also the stagnation temperatures required to have a signiicant fraction of the energy in the desired electronic level at equilibrium are quite high* I contras to this, it will he seen hereinafter that the operation can be based on transitions between vibrational levels in the ground electronic state which are significantly populated at reasonable stagnation temperatures attainable, for example, by combustio urthermore, in an operation so based, the differential relaxation leading to the inversion is collision dominated and is therefore a volume process leading to no fundamental limits on the size &f.the device.

According to the invention, there is provided a metha of providing a population inversion of €Q2, comprising burning a combustible fue in the presence of a combustion supporting medium to produce a hot gaseous mixture having equilibrium vibrational excitation and consisting of the with first and second auxiliary gases, the first auxiliary gas having a vibrational energy level at least substantially resonant with an upper vibrational energy laser level of the COg and operative to increase the effective relaxation time of this upper laser level, the second auxiliary gas having a vibrational energy level at least substantially resonant with a lower vibrational energy laser level of the C02 and operative to decrease the effective relaxation time of this lower laser level, the lower laser level being intermediate the upper laser level and the ground state of the COg, and then expanding the hot gaseous mixture through a supersonic nozzle. i¾C r.iilr gnn fmm nw.lil I IMIIII ' I 1 .

We also provide an apparatus for carrying out the method, comprising an optical ampli ier having said chamber with an inlet opening for receiving and an outlet opening for exhausting a gaseous mixture, said gaseous mixture comprising (1) a polyatomic gas having an upper laser level, a ground state and a lower laser level intermediate said upper laser level and said ground state, and (2) at least one auxiliary gas, said auxiliary gas having at least one energy level at least substantially re-sonent with one of said laser levels and a relaxation time different from the relaxation time of said at least one of said laser levels operative to increase with respect to the ratio that would exist in said polyatomic gas per se, the ratio of the relaxation time of said upper laser level to the relaxation time of said lower laser level; means for heating said gaseous mixture to a first temperature at a first pressure to provide a substantial portion of the total energy of said gaseous mixture in at least said upper laser level; nozzle means disposed between said heating means and said chamber for receiving said heated gaseous mix-ture at said first temperature and pressure from said heating means and expanding and supplying said gaseous mixture to said chamber at supersonic velocities, said nozzle means providing a flow time in said nozzle that is short compared to the effective relaxation time of said upper laser level and long compared to the effective relaxation time of said lower laser level to provide a second gas temperature and second pressure downstream of said nozzle means that are lo compared to respectively the first temperature and pressure of said gaseous mixture in said heating means to provide a population inversion in said chamber; and means defining a light beam path through the gaseous mixture in said chamber. the vibrational energy of different modes can be quite different. It is this difference in vibrational relaxation times of separate modes which allows the production. of a complete population inversion between vibrational levels of different modes in accordance with the present invention. Thus, the present invention contemplates the rapid expansion of a polyatomic gas through a supersonic nozzle under conditions of density and temperature set forth in greater detail hereinafter such that the effective relaxation time of the upper laser level is long compared to the flow time through the nozzle while the effective relaxation time of the lower laser level is short compared to the flow time through the nozzle .

As the polyatomic gas passes from subsonic to supersonic in the nozzle, the temperature and density drop rapidly with the increasing velocity. If such an equilibrium gas is provided in the subsonic region at a temperature sufficient that considerable vibrational excitation is present and it is expanded to a low temperature in a time less than the vibrational relaxation time for the upper laser level of the gas, then the upper laser level vibrational energy cannot follow this rapid temperature change and remains at a high value. In the expanded region downstream of the nozzle where the pressure and temperature are low compared to their initial values upstream of the nozzle, the upper laser level relaxation time is greatly Increased and the upper laser level vibrational energy can be maintained constant for a distance considerably larger than the nozzle size. Furthermore, in the expanded region, the pressure and temperature are such that the lower laser level relaxation time is substantially less than the upper laser level relaxation time such that the lower laser level vibrational energy remains close to equilibrium with translation and rotation. Thus, in the expanded region down stagnation temperature of the gas while the vibrational energy of the lower laser level is characterized by a temperature close to the downstream gas temperature. Provision of substantially different temperatures in accordance with the present invention produces a population inversion.

The following references and materials cited therein describe some of the background and physical principles involved in the devices under discussion and an insight, to some degree, of application of those principles in the present state of the art: 1 . "Infrared and Optical asers," by A. L. Shawlow and C. H. Townes in Physical Review, Vol. 112 , No. 6, December 15, 1958, pp 1940-1949 . 2 . "Attainment of Negative Temperatures by Heating and Cooling of a System," by N. G. Basov and A.N.

Oraevskii, Soviet Physics JETP, Vol. 17, No. * November, 1963 , PP 1171-H72 . 3. "Population Inversion in Adiabatic Expansion of a Gas Mixture," by V. K. onyukhavand A. M. Prokhorov, JETP Letters, Vol. 3, No. 11, 1 June 1966, pp 286- 288. 4 . "Electronic Population Inversions by Fluid-Mechanical Techniques" by I. R. Hurle and A. Hertzberg, The Physics of Fluids, Vol. 8, No. 9, September 1965. PP 1601 -1607.

. Polanyi, J. C, J. Chem. Phys. £4 3 7 (1961 ) . 6. Polanyi, J. C, Applied Optics Supplement #2 on Chemical Lasers, 109, (1965 ) .

In order that the invention may be fully understood, it will now be described with reference to a specific embodiment in conjunction with the accompanying drawings, in which; and transfer processes; Figure 2 is a plot showing deactivation and transfer times for N2-CO2 system at one atmosphere pressure as a function of kinetic temperature; Figures 3a-d are plots of N2-CO2 gas parameters as a function of position in a supersonic nozzle diagrammatically shown in Figure 3a with differential vibrational freezing; Figure 4 is a plot of specific parameters as a function of nozzle Mach number for an equilibrium gas consisting of 89$ N2/CO, 10# CO2, 1$ ¾0, at a stagnation temperature of l600°K; Figure 5 is a plot of geometric quantities as a function of nozzle Mach number wherein the gas conditions are the same as those for Figure 4; Figure 6 is a plot of parameters as a function of Mach number for operation at the minimum stagnation pressure consistent with diffuser recovery to atmospheric pressure, throat height being such that the product of the throat height and stagnation pressure is 20 mm atm; Figure 7 is a plot of specific parameters as a function of stagnation temperature for a temperature ratio across a suitable nozzle of ,24 for a gas mixture the same as those for Figure 4; Figure 8 is a plot of load lines at several stagnation temperatures showing the power production density as a function of total cavity losses (gainaloss for an oscillating system), intra-cavity flux being the ratio of power density to the gain at any point on the curves, the gas mixture being the same as that for Figure 4; Figure 9 is a diagrammatical representation with parts broken away of a master oscillator-power amplifier including an amplifier in accordance witi the invention; invention; Figure 11 is a perspective view with parts broken away of a metal mirror with hole coupling} Figure 12 is a perspective view with parts broken away showing details of a multi-slit throat nozzle ; and Figure 13 ia a side sectional view taken on line 13-13 of Fig. 12· The performance and operation of a preferred embodiment of the present invention based on differential freezing of vibrational energy may be more clearly understood from a consideration of Figures 1**3 and the discussions of these figures. The required parameters together with a partial energy level diagram for the vibrational energy levels of nitrogen (N^) and carbon dioxide, (CO,,) given by way of example are shown in Figa, 1. In this sjisem, the C(>2 is the active laser mj# A observed (see Patel, C.K.N. , Appl. Phys. Letters 2, 15 (1965 ) and Phys. Rev. Letters I3., 617 (1964 ) ) in static mixtures of N2 and CO2 on the transition (001 ) (100) and pulsed laser action has also been observed on both the transitions (001 ) →· (100) and (001 ) →> (020) . It may be expected that devices in accordance with the present invention will operate on the (001) →> (100) transition although population inversion will exist for both.

Vibrational freezing in a given nozzle and for a given stagnation temperature can be calculated if the vibrational relaxation times, listed to the right of the energy level diagram in Figure 1 , are known. Deactivation of nitrogen vibration by collision with nitrogen is important in that it must be a slower process than resonent transfer of vibrational exciation to the active laser molecule (in this case CO (V3)) for efficient laser operation. This condition sets a lower limit on the concentration of C02 or its equivalent. The energy stored in nitrogen vibration is useless to the laser system if the direct collisional deactivation of nitrogen is a more rapid process than the resonant trans¬ Within CO2 itself the important processes are collision' al deactivation of CO2 (v^) aontaining the upper laser level, and CO2 (vi) containing the lower laser level. Deactivation of the upper laser level indicated by T^^C ^or collisions with CO2 and τβ32Ν or collisions with N2> most likely occurs by exchange of energy with other modes (see Herzfeld, K. F., Discussions of the Faraday Society 33., 22 -27 (1962 ) ) , rather than by direct deactivation. Due to the close energy coincidence between χ l!evels and alternate V2 levels, rapid energy exchange occurs between these modes forcing the relative populations to equilibrate with each other. Thus, the rate limiting process for energy loss from these two modes will be collisional deactivation of C02 (\>2), being the respectively.

If other species, such as ¾0 or I¾, are present then their effect or deactivation of the modes in question must be considered. It should be noted that while loss of vibrational energy from a given mode generally requires a very large number of kinetic collisions, redistribution of energy within a mode occurs with relatively few collisions. Thus, the populations of the various energy levels within a mode tend to an equilibrium. Bpltzmann distribution in a time short compared to the time for loss of vibrational energy from the mode. The degree of exciation of a given mode can therefore be characterized by a vibrational temperature, T , which can in general be different from the temperature characterizing translational and rotational energy and indeed different from the vibrational temperatures characterizing the populations of other vibrational modes.

Knowledge of all of the important vibrational deactivation and exchange rates allows calculation of the populations throughout an expansion through a nozzle. In order to relate the vibrational populations of CO to gain or absorption in a given transition, two additional parameters are required. These are the radiative lifetime for the proposed laser transition and collision-al broadening cross sections for collisions of the radiating CO state with COg and other molecules present in the system. The latter are necessary as at the pressures considered for operation, the line width will be determined by collisions and not by Doppler broadening. The best estimates of all of these parameters will now be outlined.

Several of the vibrational relaxation processes important to the system in question have been investigated experimentally in the development of the invention. One of the important processes, vibrational energy transfer between Ng and COg (V3) has in connection with the above-mentioned studies will now be summarized.

The vibrational relaxation times that are required for 2 -CO2 laser differential freezing calculations are shown as a function of temperature in Figure 2. The relaxation times are plotted plotted in units atm ps. The actual relaxation time is the quantity shown in Figure 2 divided by the partial pressure of collision partner in atmospheres.

The vibrational relaxation time for nitrogen-nitrogen collisions is the longest of all the relaxation times (see Milli-kan, R. C. and White, D. R., J. Chem. Phys. £2, 98 (1961) >. JThe collision deactivation of the lower laser state is controlled by the deactivation of the bending mode V2. This is a quantity which has been measured many times and is accurately known, both for CO -CO2 collisions and for C02-N2 collisions.

Several conflicitng measurements are available for the collisional deactivation of the upper laser level; for its relaxation time the Schwartz, Slawsky, Herzfeld (SSH) theory is used (see the Herzfeld reference cited above). The SSH theory has been found to be in fair agreement with experimental data which are available for the relaxation of the other modes. Since the SSH theory predicted a shorter relaxation time than was actually measured for these other cases, it is felt that it is a conservative estimate to use the SSH theory for the relaxation of the V3 mode.

The laser gain parameters, the transition probability for the (001) →■ (100) transition, and optical broadening] cross sections for this same transition were also measured in the development of the invention. The results are summarized in Table I set forth below.

TABLE I 1. Reciprocal Transition Probability - 2i = .7 Seconds, + 10 TABLE I (Cont.) AT 273° , 1 ATM Pressure Converted to cross section Optical Broadening or0 - 5.7 lO"1^ CM2 Kinetic Cross Sections Prom Viscosity ak - 5.1 x 10~15 CM2 Prom Van Der Waals ak => 6.4 x 10_15 CM2 3. Collision Broadening Cross Sections - Other Gases With the parameters listed in Table I, measurements of laser gain can be related directly to inversion densities and conversely calculations of inversion densities can be related directly to the gain expected.

The relaxation times shown in Figure 2 have also been used in detailed calculations of vibrational freezing in supersonic nozzles. The results of one of these calculations for a specific case are shown in Figures 3a-d. As Indicated in Figure 3a, a hot mixture of nitrogen and CO2 was expanded through a super sonic nozzle to Mach 4. A hot equilibrium gas can be produced in several ways, including transfer heating from a heat source such as a nuclear reactor, shoch heating in a shock tube, or by direct combustion, producing a mixture somewhat different from that shown but having essentially the same properties.

In Figure 3b, the distribution of energy in various parts of the flow field is shown. Energy in thermal translation and rotation in the stagnation region is converted largely into directed kinetic energy of flow in the supersonic region. Energy in vibrational degrees of freedom, which comprises approximately 15$ of the total energy in the equilibrium stagnation region, would, if it remained in equilibrium with translation and rotation, rational freezing the fraction of energy in vibration remains high downstream comprising about 10$ of the total. It is a portion of this nonequilibrium vibrational energy which can be made available as laser energy. The dimension of the sonic throat is an important parameter in determining the maximum stagnation pressure at which vibrational freezing of the upper laser level and nitrogen can be ; obtained, since the rate of decrease of temperature and pressure is inversely proportional to it. For the conditions shown in Figure 3a, the throat was rectangular in shape, one millimeter in minor dimension and of arbitrary major dimension. Essentially the same downstream fractional energy in vibration would be obtained with, for example, a one centimeter throat and 2 atmoshpheres stagnation at the same stagnation temperature and nozzle area ratio.

Figure 3c shows how vibrational energy is divided among the various vibrational degrees of freedom. The temperature in degrees Kelvin characterizing the populations of the various vibrational modes are plotted as a function of position in the nozzle. As can be seen in Figure 3c, the temperatures characterizing the and nitrogen vibrational populations are essentially equal because of the strong vibrational coupling and fall very little through the nozzle, remaining about 1400° downstream of the nozzle. At the low temperature and pressure downstream (as compared to that upstream of the nozzle), the characteristic relaxation length for these modes combined is of the order of meters and thus almost no further decay of these modes is observable in the length scale of the graph. The translational and rotational temperature falls quickly to a low value in the nozzle. The vibrational temperature characterizing the populations of the χ and modes of C02 falls quickly in the nozzle to a low value somewhat above the gas temperature, but is visible relaxing toward the gas temperature on the length scale of the graph. 34506 - population inversion is possible. The fractional populations of the upper and lower laser levels are plotted in Figure 3d. Note that as shown in Figure 3d* in the stagnation region population of the lower (100) level exceeds the population of the (001) level characteristic of an equilibrium situation. However, downstream as the vibrational temperatures become sufficiently separated the population of 002(100) drops below that of 002(001) and population inversion has been produced. Making use of the laser gain parameters summarized in Table I, this population inversion can be interpreted in terms of laser gain. Knowledge of the gain, together with additional computations performed using the vibrational relaxation rates shown in Figure 2, allows theoretical evaluation of the performance of systems in accordance with the invention.

The laser characteristics for a device operating under the gas conditions shown in Figure 3 are listed in Table II.

TABLE II Gas Dynamic Laser Parameters P0 m 20 ATM, T0 = 1600°K, 5# C02, 95$ M2/C0 Zero Power Gain Coefficient G = 2 x 10*"3—5.0 x 10~3 CM"1 Total Gas Power Flux in Flow FQ «■ 24 K /CM2 Laser Power Flux in Flow Fj, « 0.5 KW/CM2 Laser Thermal Efficiency € => FL / FQ = 2.1$ Saturated Laser Power Density Ρχ, Interaction Length L = FL / PL =* 25 - 7 CM Estimated Laser Cavity Flux »PL Q «20 KW/CM2 Specific Fuel & Oxidizer Consumption «60 LB/MEGAJOULE Specific Fuel (C2N2) Consumption ~10 LB/MEGAJOULE For several of the parameters in Table II a range of values is shown. This takes into account the fact that the experimental performance of the gas dynamic laser is actually more ideal than indicated by the detailed calculations. In the case where two num- experimental fact that the upper state freezes at a temperature between the stagnation and throat temperatures and the lower state remains in complete equilibrium with the gas temperatures.

The zero power gain coefficient 6 is believed self-explanatory, the first value being that computed from the populations shown in Figure 3d and the second, that computed using the ideal assumptions which agree more closely with experiments.

The total gas power flux in flow is simply the total energy stored per unit volume in the downstream supersonic region of the nozzle multiplied by the flow velocity. The total energy includes that in vibration, rotation, random translation and directed flow.^ The laser power flux is the flux of available laser energy crossing unit area perpendicular to the flow direction. The available laser energy density is the vibrational energy stored per unit volume in nitrogen, CO if an CO is present, and C02(v ) less the energy remaining in these modes when the vibrational temperature characterizing these modes is reduced to a point where the laser gain is just zero, all multiplied by the ratio of the laser photon energy and the characteristic energy. This energy density, measured in units of joules/cm3 multiplied by the flow velocity in cm/sec yields the laser power flux in watts per square centimeter of downstream flow area.

The thermal efficiency is simply the ratio of these two fluxes and represents the efficiency of the laser system for converting thermal energy in the stagnation region into laser energy in the working section.

The saturated laser power density is the laser power density corresponding to a transition rate between C02(00l) and C02(100) which lowers the vibrational temperature and raises the 002(νχ) temperature to a point where the gain is just zero. This is the maximum rate at which available laser energy length in the flow direction in which all of the available laser energy can be removed by laser action. The first number in each case is obtained from the detailed calculation and is determined largely by the rate at which energy can be removed from the lower state. The second number assumes that only the transfer rate from g to C^Cv^) limits the power density.

The estimated laser cavity flux gives an indication of the intra-cavity circulating intensity necessary to remove the laser power at the maximum rate. This flux is not a fixed number and depends on the details of cavity absorption and coupling losses. The number presented here corresponds approximately to operating at a point where the total cavity losses are one half the total gain, providing reasonably efficient operation. It gives an indication of the mirror heating problems to be faced with this device.

The gas dynamic laser parameters set forth above give an indication of the mass flow rates required for a particular power level. The first of these is simply the total weight of Ng/CO and CO2 which must pass through the device to yield an energy output of one megajoule. Thus, a one megawatt laser under the conditions of the example would have a total mass throughout of approximately 33 lbs/sec. If cyanogen (C N ) is burned with air, compressed directly from the atmosphere, to produce the desired mixture, the specific fuel consumption is the weight of cyanogen burned to produce one megaJoule of output energy.

Further calculations have been made based on ideal assumptions because additional information on basic cross sections is needed before detailed calculations can be carried further.

Shock tunnel experiments have, however, shown that the ideal values can be generated experimentally. Accordingly, several parametric variations were carried out under the following assumptions. The of freedom were assumed frozen at the throat temperature. All other vibrational degrees of freedom were assumed to be in equilibrium at the gas temperature. The gas mixture used in the calculation presented herein corresponds to a possible equilibrium set of combustion products of cyanogen (Cg ) and air with a small amount of hydrogen added. The stagnation conditions assumed for Figures 4, 5* and 6 are a mixture of 89$ N2/C0, 10$ C02, and 1# H20 at a stagnation temperature of 1600°K.

Figure 4 shows the variation of specific laser properties s a function of frozen Mach number, the Mach number based on a sound speed calculated using the effective Y, (Cp/Cv) based on only the equilibrium degrees of freedom.

The stagnation pressure is included in the units of the plotted quantities. € / € 0 is the ratio of the actual thermal efficiency at the indicated shock number to that if the lower state were completely removed from the system (M => ») , For these gas conditions € 0 is approximately 3.6$. is the laser power density limited only by transfer from nitrogen to C02(y3) and is plotted in units of watts/cm3 atm^. Thus, the power density increases with the square of the stagnation pressure since the energy transfer rate involves the product of excited N2/CO and C02 densities. FL, the laser power flux, is proportional only to the first power of pressure since it involves only the stored energy density. The gain, of course, is independent of stagnation pressure since operation is well into the collision broadened limit. The most interesting curve is that showing the saturation cavity flux fa, which varies over a factor of 10^ in the Mach number range shown and is also proportional to the square of the stagnation pressure. Since this flux determines the heat transfer rate to windows and mirrors, which has been found to be an important problem, the selection of the operating Mach number is strongly influenced by the ure 5. Inspection of Figure 5 will show that the interaction length is inversely proportional to the stagnation pressure. The tunnel area ratio is the ratio of the laser channel height to the throat height. The final curve, showing the normal shock stagnation pressure ratio, is important in determining the minimum operating stagnation pressure for systems exhausting into a specified pressure. The stagnation pressure loss in a diff ser is proportional to the normal shock stagnation pressure loss at the operating Mach number. For fixed throat diffusers the loss is essen-tially equal to the normal shock loss, but where variable throat diffusers are used, this loss can be reduced to about half the normal shock loss. Thus, if the normal shock stagnation pressure ratio is 10, then a minimum stagnation pressure of 10 atmospheres will be required to run a nozzle and recover through a fixed throat diffuser to one atmosphere. A stagnation pressure of approximately twice this value can be expected to be required to start the nozzle. Thus, for a burner with a given maximum operating pressure, the above considerations set the maximum Mach number for which recovery to one atmosphere can be accomplished.

Figure 6 combines several of the considerations just discussed. In Figure 6 the stagnation pressure is assumed equal to the normal shock stagnation pressure ratio times one atmosphere. Also, in calculating the aspect ratio, which is the ratio of the interaction length to the channel height, the product of the throat height times the stagnation pressure has been taken equal to 1 mm x 20 atm, parameters which are known to yield the desired differential freezing in the shock tunnel experiments.

Additional computations are shown in Figures 7 and 8 in which the stagnation temperature is varied at constant temperature ratio across the nozzle. The, Mach number varies only slightly throu hout the tem erature ran e. For the tem erature ratio The gas mixture is the same as that used for Figures 4 and 6.

TABLE III Stagnation Optimum Mach Number Stag. Press Temp. (T0) J Mp Area Ratio ratio 3000 25 4.228 16.47 10.7 2800 25 4.225 16.36 10.6 2600 23 4.222 16.23 10.6 2400 23 4.218 16.07 10.5 2200 21 4.212 15.89 10.4 2000 21 4.206 15.67 10.2 1800 19 4.198 15.41 10.1 1600 17 4.188 1 .09 9.9 1400 17 4.175 14.69 9.6 1200 15 4.157 14.20 9.3 1000 15 4.134 13.6O 9.0 The optimum J value is the value of upper state rotational quantum number for which the gain is a maximum. The Mach number shown is the frozen Mach number as defined previously. The area ratio is the ratio of downstream tunnel area to throat area required to obtain a temperature ratio of .24. The stagnation pressure ratio gives the stagnation pressure loss across a normal shock and is important in fixing the minimum stagnation pressure for systems exhausting to atmospheric pressure as discussed earlier.

Figure 7 shows laser quantities as a function of stagnation temperature T0. The quantities are defined in the same manner as those of Figure 4 except that the thermal efficiency plotted here is the actual thermal efficiency and not an efficiency ratio as before.

Figure 8 shows load lines for the gas dynamic laser at several stagnation temperatures for a temperature ration (T/T0) at PL =» o. The load line gives the power production density as a function of gain determined by the gain - loss condition of the resonator. The fraction of this total loss which represents output coupling gives the fraction of the power production density that represents useful output. The intra-cavity flux at any point on the curves is given by the ratio of the power density to the gain at that point. These curves are important for determining optimum -coupling and mirror iieating rates for a given device. < The preceding calculations while theoretical indicate a wide operating lexibility for the gas dynamic laser and allow conditions to be tailored to fit the demands of a particular situation.

A master oscillator-power amplifier arrangement including an amplfier in accordance with the invention, designated by the numeral 11, useful for communications systems, radar systems and the like is shown in Figure 9. Such an arrangement is particularly useful because mode control, frequency stabilization, modulation and the like may- e carried out in the external oscil* lator or driver 12 where conventional techniques are applicable and the circulating power is low, at least as compared to that attainable in the amplifier 11. Broadly, because of high saturation flux in the amplifier 11 that would be present for high power outputs, a highly folded configuration is recommended in combination with a moderately high input signal from the oscillator or driver 12.

The driver 12 may, for example, comprise a conventional low power electrically excited 2 CO2 oscillator and an intermediate amplifier (not shown) if necessary to provide the necessary' drive for the amplifier 11. Thus, as shown, in Figure 9, a master7 oscillator-power amplifier arrangement may comprise a conventional electrically excited N2/CO2 laser 12 and a power amplifier 11 in 34506/2 .se¬ as shown and described in accordance with Figure 3a . Accordingly, the amplifier 11 may comprise a heating region 13 such as a combustion chamber for heating a gaseous mixture of, for example, 89 mole percent N /CO, 10 mole percent CO2, and 1 mole percent HjaO, to a temperature and pressure to provide a substantial portion of the total energy of the gaseous mixture in at least the upper laser level of the polyatomic gas. Such a substantial portion, as is understood in the art, is about 1 - $ of the total energy in the gaseous mixture. For the above gas a suitable temperature and pressure was found to be respectively 1600°K and about 20 atmospheres. The gaseous mixture is preferably as free from impurities as is practically possible. While not exhaustive, other polyatomic gases in addition to carbon dioxide that may be suitable are nitrogen dioxide, sulphur dioxide, nitrous ocide, water and. carbon disulfide. Suitable auxiliary gases in addition to nitrogen that may be suitable are carbon monoxide, oxygen, nitric oxide, water vapor, helium, ammonia and methane. Supersonic nozzle 14 receives the heated gaseous mixture and expands it to supersonic velocities to provide, for example, in the working cham-ber 15 downstream of the nozzle 14 a velocity of about Mach 4, a temperature of about 400°K and a pressure of about 0.1 atmospheres. A light beam path for the input signal 16 from the driver 12 is defined by transparent windows 17 and 18. Accordingly, when an imput signal 16 from driver 12 is supplied to chamber 15 via window 17, this signal emerges from window 18 as an amplified output signal 19. For high power applications, i.e., when optical light flux is in the range of about 1 or more, conventional solid windows may not prove satisfactory and resort to differential pumping techniques or the like may be required as a substitute for the solid windows. Further, a folded configuration may be provided by causing the optical input"- signal to be introduced into the chamber a point -remote from the point at which it entered the chamber.

As pointed out earlier, the gas in the amplifier 11 is cooled by expansion to supersonic speeds. This is of particular significance as such an expansion is inherently a volume process which can be performed in any size chamber and at any density consistent with the relevant vibrational relaxation times. Further, since the principle of operation of the invention is based on transitions between vibrational levels in the ground electronic state which are significantly populated^at reasonable stagnation temperatures attainable, for example, by combustion, and the differential relaxation leading to inversion in chamber 15 of the amplifier 11 is collision dominated and is therefore a volume process, substantially no fundamental limit on the size (and hence the output power of amplifier 11) exists. By contrast, provision of an inversion as a direct result of chemical reaction as suggested, for example, by Polanyi, results in nonequilibrium population produced directly in the chemical reaction. The size of a device for providing an inversion between electronic states by differential radiative relaxation as suggested by Hurle and Hertz-berg, which incidently did not perform successfully, is in any event limited because of radiative trapping. Further, the stagnation temperatures required to have a significant fraction of the energy in the desired electronic level at equilibrium in such devices are quite high.

Combustion driven devices in accordance with the invention have been successfully tested and provided both amplification and laser action. A diagrammatic representation of such a device is shown by way of example in Figure 10. The above-noted tests were carried out with specific fuels and among other things showed that the combustion products of cyanogen (C2 2) behave at least substantially identically to pure 2-CO2 mixtures discussed here 345063 carbon monoxide, . carbon, methane, ethane, benzene and the like. However, in the use of toluene, it appeared that the critical PQh is smaller than that with cyanogen and laser action was only observed at reduced pressures. This is, most likely, the result of large concentrations of water as a constituent of the gas. Although water has a favorable effect ;Ln small concentrations (preferably substantially less than about 10 mole percent) as previously point out, it has been found that large quantities cause too rapid deactivation of the upper laser level. Thus, as compared to the use of cyanogen, when fuels such as toluene are used, either a lower pressure or a smaller nozzle throat is required to reduce the number of kintic collisions occurring during the expansion. The prevention of excessive concentrations of water is, of course, also helpful. However, the hot gaseous equilibrium mixture should have at least 1$ HgO vapour, with from 5 to lOjt C02 and from 85 to 95$ Directing attention now to Figure 10, there is shown a combustion driven device comprising a combustor or burner 31 to which may be supplied a suitable fuel such as cyanogen via pipe 32, and a mixture of oxygen, nitrogen, and hydrogen via pipe 33« The gases are mixed and the fuel burner in the combustor 31 to provide therein a gaseous mixture in substantially complete equilibrium comprised of, for example, about 89 mole percent Hg CO, about 10 mole percent C02» and one mole percent ft^O at a stagnation temperature of about 1600°K and a pressure of about 15 atmospheres, The equilibrium gaseous mixture is exhausted from the combustor 31 via supersonic nozzle 34 and supplied to chamber 35 disposed downstream of nozzle 34· The supersonic nozzle 34 accelerates the gaseous mixture to provide in chamber 35 a velocity of about Mach 4, a pressure of about 0,1 atmospheres, and a temperature of about 300°«500°C, wherefcj there is provided im the chamber 35 the population Inversion as previously flow to provide substantially constant gas velocities, pressure and temperatures. After passing through chamber 35» the gas mixture is supplied to a dif- fuser 36 and, for an open cycle system, thereafter exhausted to the atmosphere. Conventional means 37 and 38 are also provided for controlling the supply of fuel and/or combustion supporting medium to the combustion chamber whereby the combustion of fuel in the combustion chamber provides the polyatomic gas and auxil-liary gas or gasses at the required temperature and pressure.

If the device is to function as an amplifier, oppositely disposed windows transparent at the desired wavelength, such as at 10.6 micron wavelength, need only be provided in the chamber 35. If the device is to function as a generator or oscillator, then, of course, a fully reflective mirror 39 and a partially reflective mirror (see Figure 11) may be substituted for the windows. Because of inter alia, the high heat flux which is encountered on the mirrors, conventional mirrors such as dielectric coated Irtran and salt mirrors have been found unsatisfactory, whereas copper mirrors with hole coupling have operated satisfactorily. The combustor, nozzle, chamber, diffuser, and mirrors and the like must of course be cooled because of the heat fluxes to which they are of necessity exposed. Conventional cooling techniques may be employed to maintain the various components at safe operating temperatures. In addition to usual heat fluxes encountered in combustion driven aerodynamic devices of this type, the heat flux on the mirrors due to laser action imposes an added heat load on the mirrors. This laser heat flux can be adjusted to a suitably low level by those versed in the art, as, for examplet by flowing cool nitrogen over the mirrors to bring to a level comparable to the usual heating encountered in such devices. Accordingly, conventional means of cooling have not been shown for purposes of clarity and a discussion thereof is not deemed necessary.

Mirror losses are of two kinds - geometrical losses and intrinsic losses. Geometrical losses are principally dependent striking the surface of a mirror is greater than the wavelength corresponding to the state of the surface, then the total reflection depends on the reflecting properties of the material, that is, the only total loss, what is termed intrinsic loss, is the loss due to absorption. As a result of the careful use of optical polishing techniques, it is believed that measured absorption values were intrinsic values and were not due to the geometrical effect mentioned above. The aforementioned measured values indicated that as the purity of a satisfactory mirror metal, such as, for example, copper, gold, silver and the like, increases, absorption decreases. Accordingly, the mirror metal preferably is as pure as possible and dead soft. In the case of copper, 99 · 999$ purity and annealing to make it dead soft is recommended.

A copper metal mirror with hole coupling is shown in Figure 11. The mirror 50 may be formed of 99.999$ pure, dead soft copper fixedly carried in a mounting bracket 5 . The active surface 52 is optically polished such that the wavelength of the radiation striking it is greater than the wavelength corresponding to the state of the surface. Holes 53 are provided in the active surface 52 and extend through the mirror to provide coupling out of the chamber 35 · The total area of the holes is selected to provide the necessary percent of transmission. The holes 53 as shown in Figure 11 are arranged and adapted to provide an equilateral array. Passages 5 which define holes 53 preferably extend only a short distance into the mirror and communicate with axially aligned passages 55 having a greater diameter. Such an arrangement facilitates formation of the holes 53 and reduces reflections within the mirror itself. The fully reflective mirror, with the exception of the shape of its active surface and the absence of holes, is identical to the partially transmissive mirror. The partially transmissive mirror is preferably substantially optically mirrors .

As an example, measurements on a copper mirror used successfully in the extraction of 40 watts are given below in Table ■IV: TABLE IV Pre Test Post Test Sphericity ;-+ 0.3 waves at 10.6μ Same radius Pits - 5M dia., .01$ of surSame plus 1μ pits face on 8$ of surface at most dense area. Total number « 10° Scratches - < 2μ, moderate Same Sleeks - None None inclusions - .01$ of surface Same Grain - 1 cm diameter Same Orange Peel - Mild Same Absorptance - 0.8$ 0.8$ Diffuse reflectance 0.7$ 0.7$ Specular and small 98.5$ 98.5$ angle reflectance - Pitting which occurred during the test may have been due to many particles striking the surface a few times each or a small number of particles trapped in the window well and swirled against the mirror many times . The density of the pits varied across the surface in such a way as to make a pattern similar in shape to that given by a Poucault knife-edge test of a telescope mirror with bird-wing defect.

In addition to the pits, particles were seen sticking to the surface. The number density and distribution of these particles were approximately the same as those of the pits resulting from the test. The average size of the particles was estimated to be 2M. Ten blemishes were found having diameters of about .002 inch which were distributed about the mirror with the most severe at the center and a small particle was found on the surface at the center of most of these blemishes. The blemishes, when viewed in white light, had the appearance of the colored interference pattern that would occur 'if carbon were evaporated from a point source at? or above the particle and condensed on the mirror. It is possible that these particles drifted onto the surface of the mirror before or during lasing action and were heated to evaporation temperature by the laser beam; and that some of the evaporant from the particles or their decomposition products condensed on the mirror surface to form the interference patterns noted. Since CN gas was used in the burner, it is possible that carbon particles may be responsible for the blemishes. Accordingly, contaminants, foreign particles such as may result from erosion or otherwise, and the generation of carbon or the like in the gas flowing past the mirrors preferably should be avoided. It should be noted however, that the absorptance and reflectance of the mirror at 10.6 did not change in. spite of the surface damage suffered during the test.

Referring now to Figure 12 , there is shown, by way of example, an elongated multi (in this case three) throat nozzle comprising a first main member 61 defining at its center the majority of the upstream end of the inlet portion 62 of the nozzle, a second main member 63 defining in part at its center the downstream end of the inlet portion 62 and the outermost surfaces 64 and 65 of the outlet portion 66 of the nozzle, and two vane members 67 and 68 removably carried by both the first and second members 61 and 63. The vane members 67 and 68 together with the second main member 63 , as best shown in Figure 13* define three elongated slit nozzles, one above the other and each having a configuration compared to the effective relaxation time of the upper laser level of the gas and long compared to the effective relaxation time of the lower laser level of the gas flowing therethrough. Such a suitable flow time is about Mach 4.

Directing attention now to the first main member 61, it would be seen that it is provided with surfaces 71 and 72 generally convergent in the direction of flow which couple the combustion chamber or heat source (not shown) to the nozzle and direct the heated gas to the various nozzle throats. A plurality of oppositely disposed grooves 73 are provided in the aforementioned surfaces to receive vane member supporting bars 7 . The supporting bars may abut the second main chamber 63, are fixedly attached as by pins 75 to each of the vane members and are adapted for a close fit with the aforementioned grooves 73 to prevent substantially all movement of the vane members and, hence, variation of nozzle position and dimensions.

The upstream end of the second main member 63 is provided with oppositely disposed surfaces 76 and 77 generlly convergent in the direction of gas flow. Surfaces 76 and 77 comprise extensions of surfaces 71 and 72 in the first main member 61. Sur*-faces 76 and 77 in combination with the outermost surfaces 78 and 79 of the upstream end of respectively vane members 67 and 68 define the upstream portion of the outermost nozzle throats. The remaining or inner portion of the upstream end of each vane member of course de ines the upstream end of the inner or middle nozzle throat. The portions 81 and 82 of the vane members downstream of the nozzle throats are provided with a profile that in combination with surfaces 64 and 65 of the second main member define the downstream portion 66 of the nozzle as and for the purposes set forth hereinbefore .

The ends of each vane member are provided with end merit of the vane members both parallel and normal to the direction of gas flow is not only prevented by the supporting bars 7 but also by the end blocks 83 carried in grooves 84. However, clearance should be provided between the outermost surface of the end blocks and the second main member to permit expansion of the vane members in their length direction.

The various components comprising the nozzle may all be formed of copper for heat transfer purposes but the surfaces thereof exposed to gas flow are preferably provided with a thin smooth coat of a highly reflective or polished metal such as gold, silver, chromium and the like. Passages 85 for receiving a coolant are provided in the first and second main members, supporting bars and vane members to maintain these components at temperatures adequate to maintain their integrity and prevent undue erosion of the surfaces exposed to gas flow.

In mounting the vane members in the second main member, it has been found advantageous to attach to the external coolan pipes piston-type seals 86 each having two 0-rings spaced apart and disposed for contact with the second member and with the vane members. Thus* each vane member may be disposed in grooves 8 and the piston seals 86 brought into and maintained in engagement ith recesses in each vane member through passages in the second main member. This arrangement prevents leakage of coolant which in the case of water is very important,; permits expansion of the vane -~-^B&£LES and facilitates removal or replacement of the vane members. surfaces to receive vane member supporting bars 74. The supporting bars may abut the second main member 63, are fixedly attached as by pins 75 to each of the vane members and are adapted for a close fit with the aforementioned grooves 73 to prevent substantially all movement of the vane members and, hence, variation of nozzle positio and dimensions.

The upstream end of the second main member 63 is provided with oppositely disposed surfaces 76 and 77 generally convergent in the direction of gas flow. Surfaces 76 and 77 comprise extensions of surfaces 71 and 72 in the first main member 61. Surfaces 76 and 77 in combination with the outermost surfaces 78 and 79 of the upstream end of respectively vane members ©7 and 68 define the upstream portion of the outermost nozzle throats. The remaining or inner portion of the upstream end of each vane member of course defines the upstream end of the inner or middle nozzle throat. The portions 81 and 82 of the vane members downstream of the nozzle throats are provided with a profile that in combination with surfaces 64 and 65 of the second main member define the downstream portion 66 of the nozzle as and for the purposes set forth hereinbefore.

The ends of each vane member are provided with end blocks 83 which are removably carried in oppositely disposed grooves 84 in the side portions of the second main member. Movement of the vans members both parallel and normal to fche direction of gas flow is not only prevented by the supporting bars 74 but also by the end blocks 83 carried in grooves 84, However, clearance should be provided between the outermost surface of the end blocks and the second main member to permit expansion o£ the vane members in their length direction.

The variouo components comprising the noazls may all be formed of copper for heat transfer purposes but the surfaces thereof exposed to gas flow are preferably provided with a thin, smooth coat of a highly reflective or polished metal such, as gold, silver, chromium and the like. Passage s Si for receiving a coolant are provided in the first and second main members, supporting bars a d vane membe s to maintain theee components at temperatures adequate to maintain their integrity and prevent undue erosion of the surfaces exposed to gas flow.

In mounting the vana members in the second main member, it ha3 been found advantageous to attach to the external coolant pipes piston-type seals S6 each having two O-rings spaced apart and disposed for contact with the second member and with the vane members. Thus, each vane member may be disposed in grooves 84 arid the piston seal3 86 brought into and maintained in engagement with recesses in each vane member through passages in the second main member. This arrangement prevents leakage of coolant which in the case of water is very important, permits expansion of the vane members and facilitates removal or replacement of the vane members.

The various features and advantages of the invention are thought to be clear from the foregoing description. Variou3 other features and advantages not specifically enumerated will undoubtedly occur to those vereed in the art, as likewise will many variations and modifications of the'-preferred embodiment illustrated, all of which may be achieved without departing from the spirit and scope of the invention- as defined by the .following claims:

Claims (11)

1. » A method of providing a population inversion of COg, comprising burning a combustible fuel in the presence of a combustion supporting medium to produce a hot gaseous mixture having equilibrium vibrational excitation and consisting of the CO2 with first and second auxiliary gases, the first auxiliary gas having a vibrational energy level at least substantially resonant with an upper vibrational energy laser level of the CO2 and operative to increase the effective relaxation time of this upper laser level, the second auxiliary gas having a vibrational energy level at least substantially resonant with a lower vibrational energy laser level of the COg and operative to decrease the effective relaxation time of this lower laser level, the lower laser level being intermediate the upper laser level and the ground state of the OO2, and then expanding the ho gaseous mixture through a supersonic nozzle.

2. · A method according to claim 1, wherein the combustible fuel and combustion supporting medium are such that the first auxiliary gas in said mixture is Ng and the second auxiliary gas is Hjp vapor.

3. A method according to claim 2, wherein cyanogen (Cg Ng) and oxygen are used as the combustible fuel and combustion supporting medium, respectively.

4. I . A method according to claim 2, wherein toluene, carbon monoxide, carbon, methane, ethane or benzene is used as the combustible fuel.

5. , A method according to any of claims 2 to I , wherein the burning Is carried out in such a manner that the resulting composition of the hot gaseous equilibrium mixture is from 5 to 10 percent 003» from 85 to 9$ percent N2 and at least 1.0 percent H2O vapor«

6. A method according to claim 3» wherein the hot gaseous equilibrium mixture is produced at a stagnation temperature of about l600° and a pressure of about 15> atmospheres.

7. Apparatus for carrying out the method of providing a population inversion of C02 according to claim 1, comprising a combustion chamber having an outlet for the hot gaseous equilibrium mixture coupled to the upstream side of the supersonic nozzle, means for supplying the combustible fuel and combustion supporting mediura to the combustion chamber, and a working chamber in which the population inversion takes place, said working chamber having its inlet coupled to the downstream side of the nozzle.

8. Apparatus according to claim 7, wherein transparent windows are provided in the working chamber to define a light beam path for laser beam input signal to be amplified by the apparatus.

9. · Apparatus according to claim 7» wherein a fully reflective mirror and a partially reflective mirror are provided in the working chamber to cause the apparatus to function as a generator or oscillator.

10. Apparatus according to any of claims 7 to 9, wherein the means for supplying the fuel and supporting medium to the combustion chamber includes regulators by which the temperature and pressure of the hot gaseous equilibrium mixture can be controlled.

11. The method of providing a population inversion of <3>2> substantially as herein described. 12· Apparatus for providing a population inversion of COgj constructed and arranged substantially as herein described with reference to the accompanying drawings. - 34 *