Electron kinetics of molecular nitrogen dc discharge

Boltzmann equation for the electron gas in a DC discharge was solved simultaneously with the system of balance equations governing the populations of the vibrational levels in the ground state of molecular nitrogen. The calculation was performed for a stationary discharge in which the vibrational dissociation mechanism (ladder) is compensated by the wall recombination of nitrogen atoms. The results include the electron and molecular vibrational distributions together with the dissociation degree calculated over a wide range of the discharge parameters.     

Non-equilibrium vibrational,attachment and dissociation kinetics of HCl in XeCl selfsustained laser discharges

The vibrational kinetics of HCl in a Ne-buffered XeCl selfsustained laser discharge is self-consistently calculated by coupling the vibrational master equation with the chemical one, the Boltzmann equation for electron transport and the circuit equations. The results show the limits of the classical simplified schemes of HCl vibrational kinetics used in the literature. Problems connected with the neglection of HCl depletion instabilities in the calculations are discussed using a parallel resistor network model.     

含振动能激发Boltzmann模型方程气体动理论统一算法验证与分析

为模拟研究高温高马赫数下多原子气体内能激发对跨流域非平衡流动的影响,将转动能、振动能分别作为气体分子速度分布函数的自变量,把转动能和振动能处理为连续分布的能量模式,将Boltzmann方程的碰撞项分解成弹性碰撞项和非弹性碰撞项,同时将非弹性碰撞按一定松弛速率分解为平动-转动能松弛过程和平动-转动-振动能松弛过程,构造了一类考虑振动能激发的Boltzmann模型方程,并证明了其守恒性和H定理.基于内部能量变量对分布函数无穷积分,引入三个约化速度分布函数,得到一组考虑振动能激发的约化速度分布函数控制方程组,使用离散速度坐标法,基于LU-SGS隐式格式和有限体积法求解离散速度分布函数,建立含振动能激发的气体动理论统一算法.通过开展高稀薄流到连续流圆柱绕流问题统一算法与直接模拟蒙特卡罗法模拟结果对比分析,特别是过渡流区平动、转动、振动非平衡效应对绕流流场与物面力热特性的影响机制,证实了所建立的含振动能激发的Boltzmann模型方程及气体动理论统一算法的准确可靠性.     

Gear's method in vibrational kinetics

Gear's predictor-corrector multistep method is applied to a rigid system of nonlinear ordinary differential equations, describing vibrational kinetic processes in molecular (diatomic) gas. The applicability of Naidis's formulas, for the linear problem is studied. The evolution of the starting Boltzmann distribution to the quasiequilibrium Trinor distribution is studied. The vibrational relaxation curves are calculated taking into account VV and VT processes and the possibilities of a more complicated starting physical model are examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 57–62, March, 1985.     

Response signal in a femtosecond pump-probe experiment in a condensed medium with account of the memory induced by the relaxation medium

For a model molecular system with one vibrational degree of freedom and three electronic states coupled by pump and probe laser pulses in a condensed medium, the response signal in a femtosecond pump-probe experiment is calculated. The potential curves of all three states are described by the Morse potential. Calculations are performed using two qualitatively different approaches to describing the medium-induced relaxation: with memory of the relaxation process and without memory (Markovian approximation). The temporal evolution of the vibrational wave packet in the intermediate electronically excited state is described using a master equation for the density matrix of the molecular system, which is derived within the framework of the Nakajima-Zwanzig formalism. It is demonstrated that, at short delay times, when the proposed approach is applicable, taking into account memory effects can substantially change the form of the pump-probe experiment signal in comparison with the signal calculated in the Markovian approximation.     

Superradiance and energy transfer within a system of atoms

We investigate cooperative effects in energy relaxation and energy transfer for N atoms in a thermal radiation field with superradiance master equations as well as a closed set of coupled moment equations. Both spatially large and spatially small systems are considered. For small systems nonlinear rate equations for the energy are related to the moment equations. Symmetry of the small system to interchanging atoms is used to incorporate off-diagonal solutions of the superradiance master equation in expressions for the probability of the transfer of energy from one group of atoms to another. The long time excitation probability for initially unexcited atoms is large and strongly correlated. Cooperative processes in a large system which fall off with the distance between a cooperating pair of atoms include energy loss and transfer terms in the master equation. The energy transfer is oscillatory in time. Energy relaxation is shown by numerical solution to become cooperative in a very sudden manner as the scale of the atomic system is decreased through the resonant wavelength.     

Quantum Boltzmann equations for binary interactions between identical particles

The inhomogeneous master equation obtained in a previous paper (by Van Vliet) is employed to obtain as first-moment equation two quantum mechanical Boltzmann equations (diagonal) for systems of weakly interacting identical particles. The interactions considered are of a binary nature: fermion-fermion or boson-boson. The resulting equations have the same structure as before. The total Boltzmann equation (diagonal and nondiagonal part) is also derived.     

Global Existence of Classical Solutions to the Vlasov-Poisson-Boltzmann System

The time evolution of the distribution function for the charged particles in a dilute gas is governed by the Vlasov–Poisson–Boltzmann system when the force is self-induced and its potential function satisfies the Poisson equation. In this paper, we give a satisfactory global existence theory of classical solutions to this system when the initial data is a small perturbation of a global Maxwellian. Moreover, the convergence rate in time to the global Maxwellian is also obtained through the energy method. The proof is based on the theory of compressible Navier–Stokes equations with forcing and the decomposition of the solutions to the Boltzmann equation with respect to the local Maxwellian introduced in [23] and elaborated in [31].     

A new hierarchy system on the basis of a “Master” Boltzmann equation for microscopic density

It is shown that Boltzmann's equation written in terms of microscopic density (namely the unaveraged Boltzmann function) has a wider range of validity as well as finer resolvability for fluctuations than the conventional Boltzmann equation governing Boltzmann's function. In fact the new Boltzmann equation for ideal gases has implications as a microscopically exact continuity equation like Klimontovich's equation for plasmas, and can be derived without invoking any statistical concepts, e.g., distribution functions, or molecular chaos. The Boltzmann equation in the older formalism is obtained by averaging this equation only under a restricted condition of the molecular chaos. The new Boltzmann equation is seen to contain information comparable with Liouville's equation, and serves as a master kinetic equation. A new hierarchy system is formulated in a certain parallelism to the BBGKY hierarchy. They are shown to yield an identical one-particle equation. The difference between the two hierarchy systems first appears in the two-particle equation. The difference is twofold. First, the present formalism includes thermal fluctuations that are missing in the BBGKY formalism. Second, the former allows us to formulate multi-time correlations as well, whereas the latter is restricted to simultaneous correlation. These two features are favorably utilized in deriving the Landau-Lifshitz fluctuation law in a most straightforward manner. Also, equations describing the nonequilibrium interaction between thermal and fluid-dynamical fluctuations are derived.     

Rate processes in condensed media: Basic equations

A general theory of rate processes is developed. Starting from the first principles, the non-Markovian and Markovian type equations governing relaxation processes are derived. Under certain conditions (which are specified) these equations may be approximately reduced to master equations.The theory is applied to two specific models. In one of them the electron-nuclear system is represented by two intersecting electronic energy hyper-surfaces with a continuum of degrees of freedom plus a small perturbation causing transitions between these electronic states. The equations determining the time behaviour of the electronic subsystem in the general case do not coincide with master equations and the time evolution of the system has mixed oscillatory decaying behaviour.Another model takes into account a possible competition between electronic and vibrational relaxations. The corresponding kinetic equations are derived.     

Collisionless Boltzmann equations and integrable moment equations

A collisionless Boltzmann equation, describing long waves in a dense gas of particles interacting via short-range forces, is shown to be equivalent to the Benney equations, which describe long waves in a perfect two-dimensional fluid with a free surface. These equations also describe, in a random phase approximation, the evolution, on long space and time scales, of multiply periodic solutions of the nonlinear Schrödinger equation. The derivative nonlinear Schrödinger equation is likewise shown to be related to an integrable system of moment equations.     

Time-correlation function for macroscopic observables in a classical gas

The state of a gas is characterized by occupation numbers of cells in-space. The mean values and fluctuations of these numbers are studied with the help of a master equation. The results are discussed within the framework of the theory of random forces. An equation of motion of the time-correlation function (TCF) is derived and it is shown that the temporal development of the TCF can be described by a linearized Boltzmann equation.The support of the Deutsche Forschungs-Gemeinschaft (DFG) is gratefully acknowledged.     

Investigation of the glow and contracted discharge plasmas in nitrogen by coherent anti-Stokes Raman spectroscopy,optical interferometry,and numerical simulation

The translational temperature in the plasma of glow and contracted discharges is measured using the methods of coherent anti-Stokes Raman spectroscopy and optical interferometry. The current density in the discharge is determined by measuring the electron concentration with optical interferometry and emission spectroscopy. The distribution of nitrogen molecules over vibrational and rotational levels in the ground state, the electron energy distribution, and the time dependence of the gas temperature are numerically found based on a model including the homogeneous Boltzmann equation and balance equations for the concentrations of charged and excited particles and for the gas temperature. The dynamics of transition to the quasi-steady-state distribution of nitrogen molecules over vibrational levels is studied.     

重复频率脉冲大气放电中氮气的振动温度

氮气分子的振动自由度在大气放电低温等离子体中会被高度激发。从振动能级的简谐振子模型和Boltzmann分布近似出发,研究重复频率脉冲放电中振动温度的变化行为。结果表明,决定重频条件下振动温度的主要过程是电子碰撞振动激发和振动-平动弛豫,而在振动能级高度激发的情形下其与氧原子的化学反应也会产生影响。对于振动激发过程,通过跃迁反比相似率推导出的特征弛豫时间与动理学模型符合较好。在振动-平动弛豫中占主导贡献的为干燥大气中的氧原子或潮湿大气中的水分子。当氧原子数密度为1014 cm-3时,若初始振动温度在5000 K,在化学反应过程中振动能量的特征弛豫时间在0.1~1 s量级。     

Non Equilibrium Vibrational Population and Dissociation Rates of Oxygen in Electrical Discharges: The Role of Atoms and of the Recombination Process

The influence of oxygen atoms on the population densities of vibrational levels of molecular oxygen has been studied for discharge conditions in which the atoms come 1) from electronic transitions to Herzberg and Schumann systems 2) from the pure vibrational mechanism (PVM) discussed in Chem. Phys. 30 (1978) 95. In the first case the atoms deactivate the first vibrational levels of O₂, thus reducing the vibrational temperature and the propagation of the introduced vibrational quanta by V — V exchanges. Under these conditions PVM disappears. An assisted recombination dissociation mechanism, however, holds in these conditions, due to the recombination process which induces a strong disequilibrium on the levels near to the dissociation continuum. These levels can redissociate by collisions with heavy particles. The results of pure vibrational mechanism in the presence of atoms are very similar to those discussed in our previous work. The production of oxygen atoms self adjusts to small values due to the increased importance of V — T deactivation by oxygen atoms.     

Statistical Ionization Equilibrium in Partially Degenerate Plasmas

The thermal ionization equilibrium in plasmas is considered at pressures for which the electron gas is partially to considerably degenerate. An ionization equation is derived which takes into account that i) the electron energies are distributed according to Fermi statistics and ii) the (heavy) ions and atoms obey Boltzmann statistics which is valid up to pressures at which the wave functions of the atoms begin to overlap. A comparison of the quantum statistical and Saha ionization equations indicates that the degeneracy effects in the electron gas suppress somewhat the ionization. It is remarkable that the Saha equation describes, approximately, the thermal ionization equilibrium up to the critical pressure at which the wave functions of the atoms begin to overlap (e.g., up to P ~ 103 Bar and P ~ 106 Bar in the cases of Cs and H plasmas, respectively), although the electrons are noticeably degenerate.     

A stochastic approach to the kinetic theory of gases

A theory of fluctuations in non-equilibrium diluted gases is presented. The velocity distribution function is treated as a stochastic variable and a master equation for its probability is derived. This evolution equation is based on two processes: binary hard sphere collisions and free flow. A mean-field approximation leads to a non-linear master equation containing explicitly a parameter which represents the spatial correlation length of the fluctuations. An infinite hierarchy of equations for the successive moments is found. If the correlation length is sufficiently short a truncation after the first equation is possible and this leads to the Boltzmann kinetic equation. The associated probability distribution is Poissonian. As to the fluctuation of the macroscopic quantities, an approximation scheme permits to recover the Langevin approach of fluctuating hydrodynamics near equilibrium and its fluctuation-dissipation relations.