scholarly journals Influence of Excited Molecules on Electron Swarm Transport Coefficients and Gas Discharge Kinetics

1997 ◽  
Vol 50 (3) ◽  
pp. 591 ◽  
Author(s):  
Zoran Lj. Petrovi ◽  
Slobodan B. Vrhovac ◽  
Jasmina V. Jovanovi ◽  
Zoran M. Raspopovi ◽  
Svetlan A. Bzeni
Keyword(s):  
Vibrational Excitation ◽  
Transport Coefficients ◽  
Kinetic Scheme ◽  
Gas Discharge ◽  
Distribution Functions ◽  
Molecular Collision ◽  
Gas Discharges ◽  
Section Data ◽  
Excited Molecules ◽  
State Densities

In this paper we study different effects of excited molecules on swarm parameters, electron energy distribution functions and gas discharge modeling. First we discuss a possible experiment in parahydrogen to resolve the discrepancy in hydrogen vibrational excitation cross section data. Negative differential conductivity (NDC) is a kinetic phenomenon which manifests itself in a particular dependence of the drift velocity on E/N and it is affected by superelastic collisions with excited states. A complete kinetic scheme for argon required to model excited state densities in gas discharges is also described. These results are used to explain experiments in capacitively and inductively coupled RF plasmas used for processing. The paper illustrates the application of atomic and molecular collision data, swarm data and the theoretical techniques in modeling of gas discharges with large abundances of excited molecules. It is pointed out that swarm experiments with excited molecules are lacking and that there is a shortage of reliable data, while the numerical procedures are sufficiently developed to include all the important effects.

A GENERALIZED VARIATIONAL PRINCIPLE FOR TRANSPORT PHENOMENA

1958 ◽  
Vol 36 (10) ◽  
pp. 1308-1318 ◽  
Author(s):  
G. E. Tauber
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Ritz Method ◽  
Transport Coefficients ◽  
Distribution Functions ◽  
Generalized Variational Principle ◽  
Lattice Vibrations ◽  
Arbitrary Direction ◽  
Energy Surfaces ◽  
Thermomagnetic Phenomena

A generalized variational principle has been formulated which takes the phonon distribution functions and the external magnetic field into account, is valid for an arbitrary direction of the electric field and polarization of the lattice vibrations, and does not depend on any special form of the energy surfaces. The various transport coefficients, for both thermoelectric and thermomagnetic phenomena, are obtained by the Ritz method in terms of infinite determinants without requiring an explicit solution of the transport equations.

scholarly journals Electron Transport in Argon - Hydrogen Mixtures

1980 ◽  
Vol 33 (6) ◽  
pp. 975 ◽  
Author(s):  
GN Haddad ◽  
RW Crompton
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Cross Section ◽  
Transport Coefficients ◽  
Velocity Distribution Function ◽  
Significant Error ◽  
Cross Section Data ◽  
Section Data ◽  
Hydrogen Mixtures ◽  
Legendre Expansion

The transport coefficients υdr and D⊥/μ have been measured in mixtures of 0.5 % and 4 % hydrogen in argon. All measurements were made at 293 K. It is shown that for these mixtures the use of the solution of the Boltzmann equation based on the two-term Legendre expansion of the velocity distribution function introduces no significant error in the analysis of the transport data. All the experimental data have been predicted to within � 3.5 % using previously published cross section data.

scholarly journals Device for calibration of low pressure gauges development

2002 ◽  
Vol 2 (4) ◽  
pp. 189-195
Author(s):  
Z.D. Nikitovic
Keyword(s):  
High Vacuum ◽  
Low Pressure ◽  
Calibration Procedure ◽  
Vacuum System ◽  
Molecular Collision ◽  
Gas Discharges ◽  
Dry Air ◽  
Vacuum Region ◽  
Set Up ◽  
Made In

Vacuum system set-up is presented and used for calibration of pressure gauges in the region of rough vacuum, from 103 mbar to 10-1 mbar, with dry air. The capacitance manometer is used for the calibration of piezoresistant manometer, oil, mercury and mercury micrometers U manometers. The applicability of the experimental set-up and obtained results for the low pressure gauges calibration in the medium and high vacuum region is approved. It was shown how calibration of some cheaper pressure gauges might be performed and reliable measurements of the pressure may be made in the region that is of interest for atomic and molecular collision physics and low-pressure gas discharges. It was also shown that mentioned calibration procedure could be used for calibration of different U manometer types in order to renormalize older atomic and molecular collision data.

scholarly journals Low-Energy Molecular Collision Processes in Space

1987 ◽  
Vol 120 ◽  
pp. 31-41
Author(s):  
Kazuo Takayanagi
Keyword(s):  
Cross Sections ◽  
Reaction Rates ◽  
Intermolecular Forces ◽  
Low Energy ◽  
Collision System ◽  
Molecular Collision ◽  
Section Data ◽  
Collision Partner ◽  
Collision Processes ◽  
Chemical Reaction Rates

Among the low-energy nonreactive molecular collisions, the rotational and vibrational transitions are the most important inelastic processes. the collision partner is an electron, an ion, or a neutral particle. Depending on the process and the collision system concerned, the magnitude and the energy dependence of the relevant cross sections are widely different. the present status of our knowledge is briefly summarized and some sample cross section data for H2and CO are shown. Useful relations among the rotational cross sections are indicated. the importance of the long-range intermolecular forces in determining some chemical reaction rates is also pointed out.

Improved Rate Laws and Population Balance Simulation Methods; CRE Applications, Including the Combustion Synthesis of Valuable Nano-Particles

2006 ◽  
Vol 4 (1) ◽  
Author(s):  
Daniel E. Rosner
Keyword(s):  
Cfd Simulation ◽  
Transport Coefficients ◽  
Population Balance ◽  
Distribution Functions ◽  
Nano Particles ◽  
Simulation Methods ◽  
Next Generation ◽  
Brownian Coagulation ◽  
Rate Laws ◽  
Al2o3 Nps

Using ‘flame-synthesized’ nanoparticles (nps) as one prototypical application, we illustrate our recent progress in two broad areas of current CRE-interest, viz., the development of: 1. Improved rate laws/transport coefficients for next-generation Eulerian, multi-(state) variable population-balance formulations, and 2. Quadrature-based multi-variate moment methods (hereafter QMOM) suitable for articulation with evolving Eulerian CFD simulation methods Admittedly, in previous work much insight was obtained by introducing deliberately (over-) simplified rate laws (for nucleation, Brownian coagulation, vapor growth/evaporation, sintering, thermophoresis,…) into the generally nonlinear integro-partial differential equation called the ‘population balance’ equation (PBE). However, despite the complexity of this equation, and the need to satisfy it along with many other local PDE-balance principles in multi-dimensional CRE environments, in our view current requirements for reactor design, as well as the frequent need to infer meaningful physico-chemical parameters based on laboratory measurements on populations rather than individual ‘particles’, make the introduction of more accurate rate/transport laws essential for next-generation particle synthesis reactor models. Our present examples are motivated both by measurements/calculations of the structure of laminar counterflow flames synthesizing Al2O3 nps and/or the predicted performance of well-mixed steady-flow devices in which sintering or sublimation occurs. Corresponding illustrative results, which focus on the rate laws for sphere dissolution or aggregate Brownian coagulation support our contentions that: i) systematic introduction of more accurate rate laws (including nucleation, sintering, growth, …)/transport coefficients will be essential to meet the quantitative demands of next-generation PBE-based CRE-simulation models for high-value particulate synthesis equipment, and, ii) QMOM is able to incorporate realistic rate laws and faithfully generate their effects on important ‘moments’ characterizing the product joint distribution functions.

HIGH FREQUENCY GAS DISCHARGE BREAKDOWN IN NEON

1952 ◽  
Vol 30 (5) ◽  
pp. 565-576 ◽  
Author(s):  
A. D. MacDonald ◽  
D. D. Betts
Keyword(s):  
Kinetic Theory ◽  
Electric Fields ◽  
Cross Sections ◽  
Electrical Breakdown ◽  
Ionization Rate ◽  
Gas Discharge ◽  
Distribution Functions ◽  
Boltzmann Transport ◽  
Discharge Data ◽  
Confluent Hypergeometric Functions

Electrical breakdown of neon at high frequencies has been treated theoretically on the basis of the Boltzmann transport equation. Exciting and ionizing collisions are accounted for as energy loss terms in the Boltzmann equation and measured values of the ionization efficiency are used in the integral determining the ionization rate. Electrons are lost to the discharge by diffusion. The equations are treated separately for the cases in which the collision frequency is much less than or much greater than the radian frequency of the applied field. The electron energy distribution functions are expressed in terms of Bessel functions, confluent hypergeometric functions, and simple exponentials. The ionization rate and the diffusion coefficient are calculated using these distribution functions in kinetic theory formulas, and combined with the diffusion equation to predict breakdown fields. The theoretically predicted fields are compared with experiment at 3000 Mc. per sec. The breakdown equations, calculated from kinetic theory and using no gas discharge data other than collision cross sections, predict breakdown electric fields within the limits of accuracy determined by these cross sections over a large range of experimental variables.

scholarly journals Calculations for deep inelastic scattering using fast interpolation grid techniques at NNLO in QCD and the extraction of $$\alpha _{\mathrm {s}}$$ from HERA data

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
D. Britzger ◽  
J. Currie ◽  
A. Gehrmann-De Ridder ◽  
T. Gehrmann ◽  
E. W. N. Glover ◽  
...  
Keyword(s):  
Inelastic Scattering ◽  
Deep Inelastic Scattering ◽  
Strong Coupling ◽  
Distribution Functions ◽  
Strong Coupling Constant ◽  
Model Parameters ◽  
Coupling Constant ◽  
Section Data ◽  
Inclusive Jet ◽  
Interpolation Grid

Abstract The extension of interpolation-grid frameworks for perturbative QCD calculations at next-to-next-to-leading order (NNLO) is presented for deep inelastic scattering (DIS) processes. A fast and flexible evaluation of higher-order predictions for any a posteriori choice of parton distribution functions (PDFs) or value of the strong coupling constant is essential in iterative fitting procedures to extract PDFs and Standard Model parameters as well as for a detailed study of the scale dependence. The APPLfast project, described here, provides a generic interface between the parton-level Monte Carlo program NNLOjet and both the APPLgrid and fastNLO libraries for the production of interpolation grids at NNLO accuracy. Details of the interface for DIS processes are presented together with the required interpolation grids at NNLO, which are made available. They cover numerous inclusive jet measurements by the H1 and ZEUS experiments at HERA. An extraction of the strong coupling constant is performed as an application of the use of such grids and a best-fit value of $$\alpha _{\mathrm {s}} (M_{{\mathrm {Z}}}) = 0.1170\,(15)_\text {exp}\,(25)_\text {th}$$αs(MZ)=0.1170(15)exp(25)th is obtained using the HERA inclusive jet cross section data.

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