Self-consistent modelling of X-ray preionized XeCl-laser discharges

In this theoretical work a 0-D model for a self-sustained X-ray preionized XeCl-laser discharge is presented. The model is self-consistent in the sense that it simultaneously solves, contrarily to the usual decoupling procedure, the Boltzmann equation for electrons, the kinetic equations for excited and ionic species, the equations for the electrical circuit and the laser photon density. It includes a rather complete kinetics of HCl(v) vibrational excitation, dissociation and dissociative attachment. The influence of electron collisions with excited species and of e-e Coulomb collisions on the plasma parameters and transport coefficients is discussed. Some evidence of the non-stationary equilibrium between the electron distribution and the reduced electric field E/N is given. Results of the model are compared with experimental ones corresponding to a XeCl-laser discharge driven by a L-C inversion circuit. The model predicts well the main trends for the variation of the laser energy in a large range of experimental conditions. The discrepancy between experiment and model for absolute values of the laser energy is discussed.     

An experimental study of angular distribution of fast secondaries in 50 GeV/cπ −-Em collisions

The pseudo-rapidity distribution has been studied for 50 GeV/cπ ⁻-colliding with various groups of target nuclei in emulsion. These data are compared with the published data onp-A collisions. It is observed that leading component multiplicity inπ ⁻-Em collisions decreases withN _h in highη-region. It is also observed that nearly 20% of the interactions proceed via single cluster formation at this projectile energy.     

A Confined <Emphasis Type="Italic">N</Emphasis>-Dimensional Harmonic Oscillator

We compute the energy eigenvalues for the N-dimensional harmonic oscillator confined in an impenetrable spherical cavity. The results show their dependence on the size of the cavity and the space dimension N. The obtained results are compared with those for the free N-dimensional harmonic oscillator, and as a result, the notion of fractional dimensions is pointed out. Finally, we examine the correlation between eigenenergies for confined oscillators in different dimensions.     

Resonance model study of strangeness production in pp collisions

Results for the energy dependence of the elementary kaon production cross sections in proton-proton collisions are reported. Calculations are performed within an extended version of the resonance model which was used for the previous studies of elementary kaon production in pion-nucleon and pion-Δ collisions. Although the model treatment is within theempirical tree level (observed widths for the resonances are used), it is fully relativistic, and includes all relevant baryon resonances up to 2 GeV. One of the purposes of this study is to provide the results for the simulation codes of subthreshold kaon production in heavy ion collisions. This is the first, consistent study of the elementary kaon production reactions including both πB and BB (B = N,Δ) collisions on the same footing. Comparisons are made between the calculated results and the existing semi-empirical parametrizations which are widely used for the simulation codes, as well as the experimental data.     

Kinetic parameters,collision rates,energy exchanges and transport coefficients of non-thermal electrons in premixed flames at sub-breakdown electric field strengths

The effects of an electric field on the collision rates, energy exchanges and transport properties of electrons in premixed flames are investigated via solutions to the Boltzmann kinetic equation. The case of high electric field strength, which results in high-energy, non-thermal electrons, is analysed in detail at sub-breakdown conditions. The rates of inelastic collisions and the energy exchange between electrons and neutrals in the reaction zone of the flame are characterised quantitatively. The analysis includes attachment, ionisation, impact dissociation, and vibrational and electronic excitation processes. Our results suggest that Townsend breakdown occurs for E/N = 140 Td. Vibrational excitation is the dominant process up to breakdown, despite important rates of electronic excitation of CO, CO₂ and N₂ as well as impact dissociation of O₂ being apparent from 50 Td onwards. Ohmic heating in the reaction zone is found to be negligible (less than 2% of peak heat release rate) up to breakdown field strengths for realistic electron densities equal to 10¹⁰ cm^?3. The observed trends are largely independent of equivalence ratio. In the non-thermal regime, electron transport coefficients are insensitive to mixture composition and approximately constant across the flame, but are highly dependent on the electric field strength. In the thermal limit, kinetic parameters and transport coefficients vary substantially across the flame due to the spatially inhomogeneous concentration of water vapour. A practical approach for identifying the plasma regime (thermal versus non-thermal) in studies of electric field effects on flames is proposed.     

Proton impact charge exchange and excitation cross sections for liquid Sn divertor studies

The quantum dynamics of charge exchange (electron capture) and excitation processes in proton collisions with Sn atoms is studied for the first time by using the two-centre atomic orbital close coupling method. The expansion basis includes the lowest nine states of singlet and triplet symmetry of Sn and all the states with n ≤ 8 of the H atom. The spin-resolved state-selective charge exchange (up to n = 5) and excitation cross sections are calculated in the energy range of 0.5 − 100 keV . Strong coupling between the electron capture and excitation channels is observed in the low-energy (E ≤ 10 keV) region associated with the energy quasi-resonance of some projectile and target states. The intensities of some strong Sn spectral lines are also calculated for a number of typical tokamak edge plasma temperatures.     

Quantum qualitative dynamics

We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH ₄SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion.     

Vibrational Excitation of N2(B,C) and N+2(B) States in N2 and N2 – H2 Flowing Microwave Discharges

The ro‐vibrational spectra of N₂ microwave discharges have been analysed by emission spectroscopy. It is deduced the rotational and vibrational temperatures of N₂ states. The characteristic of vibrational temperature Θ₁ of the N₂ (X, v) ground state has been specifically determined.It has been found that the N₂ (C, B, v') and N⁺₂ (B, v') radiative states are directly excited by electron collisions on the N₂ (X,v) ground state at a N₂ gas pressure of 0.1 Torr (discharge tube of 5 mm I.D, microwave power 100 Watt) with a Θ₁ value near 10⁴ K. At higher gas pressure up to 5 Torr, the N₂ (C, v') states remain alone to be mainly excited by electron collisions on N₂ (X, v). It is considered the excitations of the N₂ (B, v') states by collisions of electrons and N₂ (X,v > 4) vibrational molecules on the N₂ (A) metastable states.With x < 9% H₂ into N₂, it is observed an increase of N₂, 2^nd pos intensity, resulting of an increase of high energy electrons. Inversely, the N₂, 1^st pos intensity decreased, partly following the decrease of low energy electrons (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Systems of oscillators with statistical energy exchange in collisions

Classical transition probabilities are derived for the exchange of energy between sets of weakly coupled harmonic oscillators, subject to the assumption that energy is ‘statistically redistributed’ in all collisions. In the case of single oscillators the result is particularly simple and an explicit solution of the relaxation equation for such a system is derived. A ‘mean first passage time’ for the dissociation of truncated harmonic oscillators is also obtained using Widom's theory and the limiting case of equilibrium reaction is discussed.

The same approach is sketched briefly for the case of quantized systems in which statistical redistribution of energy is allowed.

Within the general scope of the model, these transition probabilities represent the most efficient conceivable coupling between system and heat bath.     

Analysis of multiparticle production data on proton-nucleus collisions using a new variable

Multiparticle production data on proton-nucleus collisions have been analyzed taking the number of ‘created’ charged particles instead of the observed number of shower particles as the variable. The mean normalized multiplicity,R _A , has been found to be independent of energy in the energy range (7–8000) GeV and its mass number dependence has been obtained. The modified analysis introduces some more regularities in the experimental results onp-nucleus collisions like the invariance with respect to energy of the relationshipR _A = α + βN _h and the KNO-like scaling of the multiplicity distributions of the created charged particles. The functional form of the scaling function has been calculated.     

Line coupling in the temperature and frequency dependences of absorption in the microwindows of the 4.3 μm CO2 band

The shapes of the self- and N₂-broadened ν₃CO₂ fundamental vibration-rotation band in the microwindows (troughs between the lines) have been measured at various temperatures. Important deviations with respect to the superposition of Lorentzian profiles are observed. These deviations are interpreted in terms of line coupling, which redistributes the intensity in the whole band. In order to take into account this line coupling, two models are considered within the frame of the impact theory. The first model uses the strong-collision approximation to describe the rotational energy transferred by collisions. It leads to a simple analytical expression for the band profile. The second model is based on the exponential-gap law. These two models account well for the frequency dependence of the measured absorption in the microwindows and for the temperature dependence in the case of the N₂-broadened CO₂ band but not in the self-broadened case. The influence of the line-coupling rotational distribution, which differs significantly in the two models, is discussed. The possible role of the finite duration of collision in rotational energy transfer is examined.     

Effect of molecular nitrogen on the electron mobility in a mixture of argon and optically excited sodium vapor

A parametric study of the electron energy distribution function (EEDF) and the electron mobility in the mixture Na + Ar + N₂ is carried out. An analysis is made of the conditions that obtain in a photoplasma when the detachment of the mean electron energy from the neutral gas temperature is due to superelastic collisions (collisions of the second kind) with excited sodium atoms. The case of low ionization of the medium at low vibrational temperatures of the ground state of the nitrogen molecules is considered. To find the EEDF a numerical solution of the Boltzmann transport equation is carried out. It is found that in the indicated mixture the presence of nitrogen leads to a depletion of the EEDF in the region of efficient vibrational excitation of the molecules and promotes the formation of inversion in the EEDF ∂f(ɛ)/∂ɛ>0 in the energy range corresponding to the Ramsauer minimum in the cross section of elastic collisions of electrons with the argon atoms. It is shown that the nonequilibrium character of the EEDF leads to a complicated dependence of the electron mobility on the partial ratios of the components of the mixture, the degree of ionization of the medium, and the population of the resonantly excited sodium atoms. Zh. Tekh. Fiz. 69, 14–19 (April 1999)     

Vibrational and rotational energy transfer of CH+ in collisions with 4He and 3He

A quantum mechanical investigation of vibrational and rotational energy transfer in cold and ultra cold collisions of CH⁺ with ³He and ⁴He atoms is presented. Ab initio potential energy calculations are carried out at the BCCD(T) level and a global 3D potential energy surface is obtained using the Reproducing Kernel Hilbert Space (RKHS) method. Close coupling scattering calculations using this surface are performed at collision energy ranging from 10^-6 to 2000 cm^-1. In the very low collision energy limit, the vibrational and rotational quenching cross sections of CH⁺ in collisions with He are found to be of the same order of magnitude. This unusual result is attributed to the large angular anisotropy of the intermolecular potential and to the unusually small equilibrium value of the Jacobi R coordinate of the He–CH⁺ complex. As for the He–N₂ ⁺ collision, we also find a strong isotope effect in the very low collision energy range which is analyzed in terms of scattering length and the differences between these two collisions are also discussed.     

基于幂次相互作用的二维磁性团簇耦合能研究

在扩散限制凝聚模型基础上,采用Monte Carlo方法模拟了磁耦合作用随粒子间距离幂次变化的磁性粒子动力学凝聚过程.重点研究了在不同幂指数α值下团簇在生长过程中,即随着粒子数N的增加,团簇平均耦合能E_c(N)的演化过程.模拟结果表明:对于α≥5时,E_c(N)随着粒子数N的增加变化较小;当α=2时,E关键词： 扩散限制凝聚模型 幂次相互作用 耦合能     

A generalization of Rayleigh's theorem for the infinite harmonic crystal

We show that if one replacesN masses in an infinite harmonic, perfect-dimensional crystal byN ₁ lighter andN ₂ heavier ones such thatN ₁+ N₂ =N is finite, then one introduces at most vN₁ (isolated) bound states. This can be considered as an extension of the results of Romerio and Wreszinski.Supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).     

Classical gravitational radiation from quasi-elastic particle scattering in models with extra dimensions

An equation for the emission of classical gravitational waves due to quasi-elastic N → N particle scattering is derived in a model with compactified extra dimensions. In addition to previous classical studies, additional terms that are suppressed by factors of one over the frequency time compactification radius are also calculated. From this, a single formula is given which predicts the energy loss into the gravitational radiation from elastic collisions as well in the low-and high-energy limit. The text was submitted by the authors in English.     

Species segregation in one-dimensional granular-system simulations

We present one-dimensional molecular dynamics simulations of a two-species, initially uniform, freely evolving granular system. Colliding particles swap their relative position with a 50% probability allowing for the initial spatial ordering of the particles to evolve in time and frictional forces to operate. Unlike one-dimensional systems of identical particles, two-species one-dimensional systems of quasi-elastic particles are ergodic and the particles' velocity distributions tend to evolve towards Maxwell-Boltzmann distributions. Under such conditions, standard fluid equations with merely an additional sink term in the energy equation, reflecting the non-elasticity of the interparticle collisions, provide an excellent means to investigate the system's evolution. According to the predictions of fluid theory we find that the clustering instability is dominated by a non-propagating mode at a wavelength of the order 10πL/Nɛ , where N is the total number of particles, L the spatial extent of the system and ɛ the inelasticity coefficient. The typical fluid velocities at the time of inelastic collapse are seen to be supersonic, unless Nɛ ≲ 10π . Species segregation, driven by the frictional force occurs as a result of the strong temperature gradients within clusters which pushes the light particles towards the clusters' edges and the heavy particles towards the center. Segregation within clusters is complete at the time of inelastic collapse.     

Violation of ensemble equivalence in the antiferromagnetic mean-field XY model

It is well known that long-range interactions pose serious problems for the formulation of statistical mechanics. We show in this paper that ensemble equivalence is violated in a simple mean-field model of N fully coupled classical rotators with repulsive interaction (antiferromagnetic XY model). While in the canonical ensemble the rotators are randomly dispersed over all angles, in the microcanonical ensemble a bi-cluster of rotators separated by angle , forms in the low energy limit. We attribute this behavior to the extreme degeneracy of the ground state. We obtain empirically an analytical formula for the probability density function for the angle made by the rotator, which compares extremely well with numerical data and should become exact in the zero energy limit. At low energy, in the presence of the bi-cluster, an extensive amount of energy is located in the single harmonic mode, with the result that the energy temperature relation is modified. Although still linear, , it has the slope , instead of the canonical value . Received 1 February 2000     

Beam-energy and system-size dependence of dynamical net charge fluctuations

We present measurements of net charge fluctuations in Au + Au collisions at ?{s_NN }\sqrt {s_{NN} } = 19.6, 62.4, 130, and 200 GeV, Cu + Cu collisions at ?{s_NN }\sqrt {s_{NN} } = 62.4, 200 GeV, and p + p collisions at ?s\sqrt s = 200 GeV using the net charge dynamical fluctuations measure ν+ −,dyn. The dynamical fluctuations are non-zero at all energies and exhibit a rather modest dependence on beam energy. We find that at a given energy and collision system, net charge dynamical fluctuations violate 1/N _ch scaling, but display approximate 1/N _part scaling. We observe strong dependence of dynamical fluctuations on the azimuthal angular range and pseudorapidity widths.