Diatomic gasdynamic lasing molecules as quantum quasi-harmonic oscillators

We investigate the role played by the molecules as quantum oscillators in a diatomic gasdynamic laser by considering quasi-harmonic behaviour within the context of one-dimensional quantum anharmonic oscillators. Vibrational energy levels depending upon a parameter relative to anharmonicity are discussed in terms of the values taken on by this parameter and the values taken on by the vibrational quantum number.     

Dynamical aspects of two-molecule collision process in a diatomic gasdynamic laser

A dynamical analysis on the basic collision process between two molecules is presented within the context of diatomic gasdynamic lasers. In particular, the kinetic energy of the colliding molecules resulting from the process above is considered for quite highly excited bound states from a quasi-classical point of view. In this analysis, the magnitude of molecule velocity is calculated and discussed in terms of the anharmonicity of a given molecule as a quantum anharmonic oscillator.     

Population of molecules as strongly anharmonic oscillators in a diatomic gasdynamic laser

Population distribution is studied quantitatively for a diatomic gasdynamic laser in which the molecules behave as strongly anharmonic oscillators under the action of a Morse internuclear potential. In fact, mathematical relationships concerning the two fundamental parameters associated with anharmonicity are derived.     

Sensitivity to anharmonicity of vibrational energy in a diatomic gasdynamic laser

A parameter for evaluating the sensitivity of quantum vibrational energy to anharmonicity in a diatomic gasdynamic laser is defined and calculated by considering the corresponding diatomic molecules as quantum anharmonic oscillators under an interatomic Morse potential. The variation of the above parameter in terms of the vibrational states and in terms of an involved anharmonic coefficient is discussed. In particular, the parameter in question at the classical limit is examined. Both weak and strong anharmonicities are discussed.     

A generalized formulation for population distribution in a molecular laser

A generalized theoretical model for calculating the population distribution in a molecular laser is proposed. This molecule population is found to be quantized and depending upon temperature. In addition, we show, as a particular case, that population distribution in a diatomic gasdynamic laser arises from our model.     

Excitation of Rydberg states of atoms and diatomic molecules by short laser impulses

Excitation of multilevel Rydberg states (atoms and diatomic molecules) is studied under an intense time-periodic perturbation that is instantaneously turned on and off. For a one-quantum excitation from a lower lying state, general expressions for the Laplace images of the population amplitudes of Rydberg states are obtained with regard to their decay characteristics. It is shown that the problem considered is reduced to the determination of the positions and widths of the energy levels of a quantum system in the field of monochromatic laser radiation of the same frequency and intensity as that in a pulse mode. To determine these quantities, an integral formulation is proposed for the eigenvalue problem for energies that is relatively simply solved with regard to the effect of the ionic core and its complex vibration-rotation structure on diatomic molecules. The specific features of the excitation of Rydberg states and the behavior of Rydberg wave packets are studied depending on the intensity and duration of laser radiation. A quantum phenomenon of rotational orientation of electron-excited diatomic molecules is considered.     

Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.     

Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Pöschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.     

Expansions for the eigenvalues of three-term recurrence relations. Two applications in molecular physics

Approximate expressions for the eigenvalue of a three-term recurrence relation with a general form describing various physical problems are proposed. Their range of availability is examined by comparison with exact values for two different problems: the bound and continuum states of monoelectronic diatomic ions and the Schr?dinger equation describing molecular alignment in intense laser fields. For each case, very good predictions have been obtained, which may be useful as initial values in iterative procedures for deriving exact solutions. Received: 30 January 1998 / Received in final form: 10 April 1998 / Accepted: 25 May 1998     

Mixing gasdynamic laser with nonequilibrium arc excitation

A mixing gasdynamic laser with nonuniform arc excitation is investigated using a model setup. Tentative analysis of the results indicates the appropriateness of using plasmatrons to improve the efficiency of mixing gasdynamic lasers by making carbon dioxide molecules vibrationally more nonuniform. In addition, a plasmatron serves as a preionization source both for a fast-flow gas-discharge laser and for a gasdynamic laser with combined pumping.     

On an integrable deformed affinsphären equation. A reciprocal gasdynamic connection

The integrable affinsphären equation originally arose in a geometric context but has an interesting gasdynamic connection. Here, an integrable deformed version of the affinsphären equation is derived in a novel manner via the action of reciprocal transformations on a related anisentropic gasdynamics system. A linear representation for the deformed affinsphären equation is constructed by means of the reciprocal transformations. The latter are then employed to derive a class of exact solutions in parametric form.     

The effect of the polytropic index γ on the structure of gaseous detonations

The present study aims to clarify the effect of the polytropic index (i.e., the ratio of specific heats in the context of a perfect gas) on the detonation structure. This is addressed by two-dimensional numerical simulations. To ease the clarification of the role of gasdynamics, a simple Arrhenius kinetic law is used for the chemical model. The activation energy, normalized by the shock temperature, is kept constant to obtain the same reaction rate sensitivity to temperature in all considered mixtures. This procedure dissociates the gasdynamic effects from the chemistry effects. The numerical results reveal that in mixtures with low polytropic indicies, the convective mixing is enhanced compared to mixtures with higher polytropic indicies. The mixing is evaluated using Lagrangian tracers. Moreover, mixtures with low polytropic indicies are found to have a shorter reaction length than mixtures with high polytropic indicies. Also, for the range of parameters considered in this study the results indicate that Mach stem bifurcation in detonations due to jetting is primarily a gasdynamic driven mechanism.     

普适性双原子分子解析势能函数的研究

提出了一种构造解析势能函数的新方法,由此得到了一种既适用于中性双原子分子又适用于带电双原子分子离子的解析势能函数。本文用八种基本类型的双原子分子——同核中性基态双原子分子Na₂-X1Σ+_g,同核中性激发态双原子分子C₂-A1Π_u,同核带电基态双原子分子离子He+₂-X2Σ+_u,同核带电激发态双原子分子离子N+₂-B2Σ+_u,异核中性基态双原子分子NaLi-X1Σ+_g,异核中性激发态双原子分子BH-B1Σ+,异核带电基态双原子分子离子(BC)--X3Π,异核带电激发态双原子分子离子(CS)+-A2Π等共21个算例对势能函数进行了验证并与RKR (Rydberg-Klein-Rees)实验数据进行了比较,计算结果与RKR数据符合很好。     

Pulsating optical source appearing under continuous laser energy supply to a hypersonic air flow

The spatio-temporal gasdynamic structures of plasma formations produced in a hypersonic air flow by a focused high-power laser beam are analyzed numerically using the model of inviscid non-heat-conducting equilibrium radiating air. The reasons for the emergence of pulsating gasdynamic nonuniformity in the region between the bow shock wave and the intense laser radiation absorption zone are investigated.     

气动激光器喷管非平衡流2维数值仿真

将Anderson的两振型三温度弛豫模型和严海星整理的弛豫数据相结合,采用2维守恒型方程组对按照最小长度喷管型面设计方法设计的、面积比分别为50和20的气动激光器喷管非平衡流场进行了数值仿真。小信号增益计算结果在每个计算点都和J. S. Vamos等人针对这两种喷管的小信号增益测量试验结果符合很好,解决了传统的准1维非平衡流分析方法不能很好地和试验结果相符的问题,对气动激光器喷管性能设计提供了更精确的评估方法。     

气动激光器喷管非平衡流2维数值仿真

将Anderson的两振型三温度弛豫模型和严海星整理的弛豫数据相结合,采用2维守恒型方程组对按照最小长度喷管型面设计方法设计的、面积比分别为50和20的气动激光器喷管非平衡流场进行了数值仿真。小信号增益计算结果在每个计算点都和J.S.Vamos等人针对这两种喷管的小信号增益测量试验结果符合很好.解决了传统的准1维非平衡流分析方法不能很好地和试验结果相符的问题.对气动激光器喷管性能设计提供了更精确的评估方法。     

Partition functions of atomic and diatomic species in high-temperature atmospheric plasmas

Accurate atomic and diatomic partition functions are required to determine the level populations for the calculations of radiative properties in thermodynamic equilibrium and nonequilibrium plasmas produced by various atmospheric re-entries. In this work, a reliable partition functions database was rebuilt for some atomic and diatomic species from 100 K to 50000 K. The atomic partition functions were obtained by a four-level model, while the diatomic partition functions were predicted based upon a more rigorous approach for the computation of the energy levels. Compared with previous publications, the number of diatomic electronic states considered in our work is as large as possible. Estimates are made for the contributions of each electronic state of the diatomic molecule to the partition function. Moreover, the effect of the number of electronic states on the partition function was also evaluated. Finally, we calculated the specific heat based upon the obtained partition functions. All the results were validated by the available data in recent references and the relative errors were systematically analysed.     

Propagating waves and edge vibrations in anisotropic composite cylinders

The entire dispersive spectra of a cylinder with cylindrical anisotropy are determined from three different algebraic eigenvalue problems deducible from the same finite element formulation. The displacement vector v in this version of the finite element method has the form f(r) exp i(εz + nθ + ωt) with the radial dependence f(r) taken as quadratic interpolation polynomials. Therefore, this discretization procedure allows a cylinder with radially inhomogeneous material properties to be modeled. The three different algebraic eigenvalue problems that emerge depend on whether the axial wave number ε or the natural frequency ω is regarded as the eigenvalue parameter and on the real, purely imaginary or complex nature of ε. For ε specified as real, an eigenvalue problem results for the natural frequencies ω_i for waves propagating along the z-direction of a cylinder of infinite extent. When ε is specified to be purely imaginary, then an algebraic eigenvalue problem governing the edge vibrations (end modes) of a semi-infinite cylinder is obtained. The third eigenvalue problem can be obtained by considering ω to be prescribed and regarding ε as the eigenvalue parameter. The algebraic eigenvalue problem that results is quadratic in the eigenvalue parameter and admits solutions for ε which may be real, purely imaginary or complex. Complex ε's correspond to edge vibrations in a cylinder which are exponentially damped trigonometric wave forms. Moreover, for the case ω = 0, the eigenvalue analysis yields ε as the characteristic inverse decay lengths for systems of elastostatic self-equilibrated edge effects in the context of St. Venant's principle. All the eigenvalue problems are solved by efficient techniques based on subspace iteration. Examples of two four-layer angle-ply cylinders are presented to illustrate this comprehensive finite element analysis.     

Gas dynamics in nuclear-pumped laser and luminescent cells with buffer volumes

A nonstationary gasdynamic model of sealed laser and luminescent cells pumped by uranium fission fragments is developed. This model extends the earlier 1D model of gas dynamics in cells of flat geometry to the case of cells with buffer volumes and allows analysis of gasdynamic processes for the energy deposition step distribution over the laser cell length.