Vibrational Kinetics Research Articles

Conditions for applicability of a diffusion description for vibrational-translational relaxation of diatomic molecules

The description of relaxation by the methods of classical statistics and mechanics has a number of advantages, the chief one of which is obviously the opportunity of using in place of a large number of balance equations for individual levels a single transport equation for a distribution function over vibrational energy and, in a number of cases, the additional opportunity for more general and clearer consideration of the various factors characterizing intra- and intermolecular interactions. A version of the classical theory for vibrational relaxation during weak interaction of molecules with a gas is diffusion theory in which a Fokker-Planck diffusion equation serves as the transport equation. In particular, a detailed study of the influence of anharmonicity at various values of the adiabaticity parameter ξo on the kinetic characteristics of the process was carried out [2] within the limits of this theory on the basis of a solution of the diffusion equation from [1]; earlier [3], vibrational relaxation in a light inert-gas medium was considered in the diffusion approximation (for harmonic and anharmonic oscillators) which coresponds to relaxation for nonadiabatic interaction in a uniform temperature field (ξo → 0) as shown in [1]. The possibility of describing vibrational kinetics within the framework of diffusion theory involves two basic problems: 1) the possibility of approximating the transport equation for classical oscillators with a Fokker-Planck equation, and 2) the possibility of describing the relaxation of quantum oscillators by classical methods or the correspondence of classical and quantum theory of relaxation for weak interaction of molecules with a medium. The first of these problems is considered here.

Comparison of rigorous and simple vibrational models for the CO2 gasdynamic laser

The accuracy of a simple vibrational model for computing the gain in a CO2 gasdynamic laser is assessed by comparing results computed from it with results computed from a rigorous vibrational model. The simple model is that of Anderson et al. (1971), in which the vibrational kinetics are modeled by grouping the nonequilibrium vibrational degrees of freedom into two modes, to each of which there corresponds an equation describing vibrational relaxation. The two models agree fairly well in the computed gain at low temperatures, but the simple model predicts too high a gain at the higher temperatures of current interest. The sources of error contributing to the overestimation given by the simple model are determined by examining the simplified relaxation equations.

Vibrational nonequilibrium in gases

The stationary and quasistationary distribution functions of the vibrational energy considered in this survey include all the basic types of vibrational distributions and have a sufficiently general nature. This generality is determined primarily by the fact that the stationary or quasistationary modes are, as a rule, compulsory of any nonequilibrium process. The clarification of the governing role of the quasistationary stage during a nonequilibrium process is the main result in the area of vibrational kinetics in recent years, which discloses extensive possibilities for controlling nonequilibrium processes.

Effect of laser radiation on the vibrational distribution of CO2

In connection with progress in the field of CO2 lasers, questions of the vibrational kinetics of molecules of CO2 have been discussed in many communications. In a majority of cases of practical importance, the distribution of CO2 is due to processes of vibrational exchange (V-V) on which is based the well-known thermodynamic model [1]. In other cases, the V-V exchange does not determine the vibrational distribution, since the perturbation is small; therefore, it is found sufficient to consider a small number of levels of CO2 (usually three), whose populations satisfy the linear equations of the balance [2]. There is the possibility of conditions where the vibrations are strongly excited and, at the same time, V-V processes are insignificant (a very small CO2 impurity in the inert gas, with a high degree of ionization). Then the number of equations becomes large. The present article discusses one such case: the excitation of a steady-state vibrational distribution in a glow discharge by laser radiation, whose solution is rather graphic.

Calculation of the energy characteristics of an electricdischarge CO2laser

A model is proposed for the calculation of the output power of a fast-flow electric-discharge CO2 laser. The model can be applied to various laser systems (with self-sustaining and non-self-sustaining discharges, with addition of CO2 after passing through the discharge zone and without such addition). Quasi-onedimensional equations of gasdynamics are solved numerically together with equations of vibrational kinetics and allowance is made for the electrical excitation and stimulated transitions. An example of a calculation dealing with a CO2+N2+He laser is given.

Kinetics of vibrational exchange in two-component gaseous mixtures in the presence of a resonant laser radiation field

The kinetics of nonresonant vibration-vibrational (v-v) exchange in binary mixtures is considered in the presence of a laser field using the harmonic oscillator model and the approximation of single-quantum transitions. An integral representation is obtained for the distributions over the vibrational levels of each component making allowance for the v-v exchange, vibration-translational (v-T) relaxation, and influence of an infrared radiation source. A closed system of equations for the relaxation of the vibrational energy in the modes is derived ignoring the decay processes. The nonequilibrium distribution functions are obtained for the steady-state and quasisteady-state conditions. It is shown that if v1>v2 (v1 is the frequency of the mode excited by the laser field and v2 is the frequency of the mode to which the energy is transferred), the vibrational kinetics of a binary mixture may differ considerably from the kinetics of a single-component medium provided that the strong laser, field acts on the first component and the rate of exchange of the quanta between the modes under consideration is sufficiently rapid. This circumstance makes it possible to utilize a directional v-v exchange for the purpose of efficient heating of a mode with a lower vibrational energy. The conditions under which this occurs are determined.

Laser polymerization in gases

Theoretical estimates are obtained of the possibility of using infrared laser radiation in the initiation of polymerization reactions in gases. A numerical solution of a system of vibrational and chemical kinetics equations shows that if the vibration-translational relaxation is sufficiently slow, it should be possible to polymerize such substances as acetylene, ethylene, etc.

Cascade mechanism of the excitation of molecular vibrations by resonant laser radiation

A theoretical analysis is made of the vibrational kinetics of molecules under nonequilibrium conditions of the cascade excitation of molecules by resonant laser radiation. The exact solutions of the kinetic equation are obtained in the harmonic oscillator model. An expression is derived for the time dependence of the average vibrational energy accumulated in a specific vibrational mode. The analysis shows that the cascade mechanism has the following advantages: It provides means for an effective control of the rate of excitation of the molecular vibrations and it increases the average energy stored in the vibrational modes. Two methods for combined pumping of a specific vibrational mode are suggested: One is the combined action of a discharge and laser radiation and the other is a combined chemical and laser pumping.

Cascade mechanism of the excitation of molecular vibrations by resonant laser radiation. Multicomponent media

A theoretical analysis is made of the vibrational kinetics in multicomponent gaseous media under nonequilibrium conditions of the cascade excitation by resonant laser radiation. The harmonic oscillator model is used to derive the exact solutions of the kinetic equations. It is shown that all the components of the distribution function retain their Boltzmann form if initially the system is in equilibrium. A system of equations for the vibrational energies is solved. The solutions are obtained for different rates of the vibration-translational relaxation in both modes of a two-component medium. A study is made of the steady-state conditions in a binary mixture. The analysis shows that the neglect of the vibration-vibrational exchange between different modes in polyatomic molecules may result in considerable deviations from the real kinetics in the whole system.

VIBRATIONAL RELAXATION IN GASES AND MOLECULAR LASERS

This article reviews the current status of the theory of vibrational relaxation in gases and its applications to the theory of molecular lasers. We discuss relaxation of the vibrational energy of diatomic and polyatomic molecules as represented by harmonic-oscillator models. The vibrational kinetics in a system of anharmonic oscillators is analyzed in detail. We treat quasi-steady-state population distributions of vibrational levels that arise under substantially non-equilibrium conditions, both in a singlecomponent molecular system and in gas mixtures. We discuss relaxation that proceeds in the presence of sources of vibrationally-excited molecules: infrared resonance radiation, recombination, and dissociation; in particular, we analyze the process of non-equilibrium dissociation at low gas temperatures. We discuss from a unified standpoint based on vibrational kinetics the working mechanisms of lasers using vibrational-rotational transitions in diatomic and polyatomic molecules with various means of excitation (electrical, chemical, and gas-dynamic).

Performance comparison of pulsed discharge and E-beam controlled CO2 lasers

A pulsed CO2 laser model for axial pulse and TEA lasers is developed based on combining electric excitation with vibrational energy level kinetics and a laser cavity intensity model. The model is applied to electron-beam-controlled lasers by adding an electron-beam plasma generation component. Calculated results show the electron-beam laser has a maximum output energy efficiency approaching 20% if the input energy is sufficient to rapidly heat the gas to the self-terminating temperature, about 600 °K. Efficiencies higher than 20% have been achieved with pulsed discharge lasers but with a consequent penalty in output energy, because the state-of-the-art limits the amount of electrical energy input to less than that necessary to reach the self-terminating temperature in axial pulsed or TEA lasers. Results of kinetics studies suggested several approximations that permit analysis of laser performance for the self-terminating temperature condition. These approximations lead to a set of transcendental but closed form coupled expressions which yield solutions in good agreement with those obtained by exact kinetics treatment. Contour plots for a 1 mA/cm2 electron-beam laser, obtained from the closed form treatment, make it possible to determine the maximum laser energy output and efficiency for any given gas mixture. The upper bound on laser energy output was found to be 100 J/liter atmosphere.

Gasdynamic lasers and photon machines

The basic operational highlights of CO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> gas-dynamic lasers (GDL's) are described. Features common to powerful gas lasers are indicated. A simplified model of the vibrational kinetics of the system is presented, and the importance of rapid expansion nozzles is shown from analytic solutions of the equations. A high-power pulsed GDL is described, along with estimations of power extraction. A closed-cycle laser is suggested, leading to a description of a photon generator/engine. Thermodynamic analysis of the closed-cycle laser illustrates in principle the possibility of direct conversion of laser energy to work.

Gain Kinetics of CO2 Gasdynamic Laser Mixtures at High Pressure

A combined analytical and experimental investigation of rapidly expanded CO2 laser mixtures is described. Study of the vibrational kinetics indicates that population inversions with high vibrational energy density can be produced at high pressures by utilizing low (starved) concentrations of CO2. Scaling laws for predicting the gain of starved systems are developed. A description is given of gain measurements carried out using a CO2 laser to probe the flow in a nozzle at the point where the Mach number is approximately four. Population inversions at static pressures as high as about 1 atm have been observed and found to be in reasonable agreement with predictions.

Mexico City, Mexico 6–10 November 1966 8th International Congress of Audiology

The ultrasonic absorption in the liquid furan - 2,5-dihydrofuran, furan - 2,3-dihydrofuran and furan - tetrahydrofuran mixtures have been measured in the frequency range from 10 MHz to 2 GHz at temperatures varying from 273 K to 293 K. The method based on the Herzfeld - Litovitz theory for description of experimental data over the frequency and concentration region is proposed. The results of calculations have been interpreted in terms of VV-, VV′- and VT-processes which determine the vibrational kinetics in liquid mixtures. The observed temperature dependence of the kinetic parameters is also discussed. It is shown that proposed method may be used for the estimation of relaxation times of molecules which have a very short vibrational lifetimes.

Laser transition with predissociation lower state in the no molecule

Vibrational relaxation of NO molecules excited by a pulsed e-beam sustained discharge (EBSD) with the use of CO laser probing was studied. We developed numerical model of vibrational kinetics in ensemble of NO molecules due to comparing the experimental and calculated data on absorption dynamics of vibrational excited NO molecules.