Pseudospectral Solution of the Boltzmann Equation: Quantum Cross Sections

2008 ◽  
Author(s):  
Yongbin Chang ◽  
Bernie D. Shizgal ◽  
Takashi Abe
Keyword(s):  
Boltzmann Equation ◽  
Cross Sections ◽  
The Boltzmann Equation

scholarly journals Calculation of Electron Swarm Parameters in Tetrafluoromethane

2020 ◽  
Vol 8 (2) ◽  
pp. 22-28
Author(s):  
Idris H. Salih ◽  
Mohammad M. Othman ◽  
Sherzad A. Taha
Keyword(s):  
Boltzmann Equation ◽  
Field Strength ◽  
Electric Field ◽  
Cross Sections ◽  
Electron Attachment ◽  
High Energy ◽  
Longitudinal Diffusion ◽  
Characteristic Energy ◽  
The Boltzmann Equation ◽  
High Energy Tail

The electron swarm parameters and electron energy distribution function (EEDF) are necessary, especially onunderstanding quantitatively plasma phenomena and ionized gases. The EEDF and electron swarm parameters including the reduce effective ionization coefficient (α-η)/N (α and η are the ionization and attachment coefficient, respectively), electron drift velocity, electron mean energy, characteristic energy, density  normalized longitudinal diffusion coefficient, and density normalized electron mobility in tetrafluoromethane (CF4) which was analyzed and calculated using the two-term approximation of the Boltzmann equation method at room temperature, over a range of the reduced electric field strength (E/N) between 0.1 and 1000 Td(1Td=10-17 V.cm2), where E is the electric field and N is the gas density of the gas. The calculations required cross-sections of the electron beam, thus published momentum transfer, vibration, electronic excitation, ionization, and attachment cross-sections for CF4 were used, the results of the Boltzmann equation in a good agreement with experimental and theoretical values over the entire range of E/N. In all cases, negative differential conductivity regions were found. It is found that the calculated EEDF closes to Maxwellian distribution and decreases sharply at low E/N. The low energy part of EEDF flats and the high-energy tail of EEDF increases with increase E/N. The EEDF found to be non-Maxwellian when the E/N> 10Td, havingenergy variations which reflect electron/molecule energy exchange processes. In addition, limiting field strength (E/N)limit has been calculated from the plots of (α-η)/N, for which the ionization exactlybalances the electron attachment, which is valid for the analysis of insulation characteristics and application to power equipment.

Production of Energetic Atoms by Multiple Collisions

1968 ◽  
Vol 9 (2-3) ◽  
Author(s):  
G. P. Wotzak ◽  
M. D. Kostin
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Energy ◽  
Energy Dependence ◽  
Cross Sections ◽  
Atomic Beam ◽  
High Energy ◽  
Asymptotic Region ◽  
The Boltzmann Equation ◽  
Multiple Collisions ◽  
Collision Density

SummaryThe production of energetic atoms in the epithermal energy region by a high-energy atomic beam is considered by using the Boltzmann equation. Solutions of the Boltzmann equation show that numerous epithermal atoms may be generated as a result of scattering collisions in which an energetic atom transfers kinetic energy to a struck atom. For a system in which all the reactive and non-reactive cross sections have the same energy dependence and in which the thermal motion of the struck atoms can be neglected, numerical results obtained from a stochastic computer program confirm the analytical results for the asymptotic region and give detailed information on the energy dependence of the collision density for the non-asymptotic region near the source. Numerical calculations of reaction yields for a gaseous system containing two atomic species are also presented.

scholarly journals The determination of low energy electron-molecule cross sections via swarm analysis

2008 ◽  
Vol 6 (1) ◽  
pp. 57-69 ◽  
Author(s):  
S. Dujko ◽  
R.D. White ◽  
Z.Lj. Petrovic
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Boltzmann Equation ◽  
Electron Transport ◽  
Cross Sections ◽  
Low Energy ◽  
Energy Electron ◽  
The Boltzmann Equation ◽  
Low Energy Electron

In this paper we discuss the swarm physics based techniques including the Boltzmann equation analysis and Monte Carlo simulation technique for determination of low energy electron-molecule cross sections. A multi term theory for solving the Boltzmann equation and Monte Carlo simulation code have been developed and used to investigate some critical aspects of electron transport in neutral gases under the varying configurations of electric and magnetic fields when non-conservative collisions are operative. These aspects include the validity of the two term approximation and the Legendre polynomial expansion procedure for solving the Boltzmann equation, treatment of non-conservative collisions, the effects of a magnetic field on the electron transport and nature and difference between transport data obtained under various experimental arrangements. It was found that these issues must be carefully considered before unfolding the cross sections from swarms transport data.

scholarly journals Cross Sections for Electron?Carbon Monoxide Collisions in the Range 1?4 eV

1983 ◽  
Vol 36 (4) ◽  
pp. 473 ◽  
Author(s):  
GN Haddad ◽  
HB Milloy
Keyword(s):  
Boltzmann Equation ◽  
Energy Range ◽  
Drift Velocity ◽  
Cross Sections ◽  
Velocity Distribution Function ◽  
Gas Mixtures ◽  
Transport Parameter ◽  
Velocity Data ◽  
The Boltzmann Equation ◽  
Term Approximation

The scattering of electrons from CO molecules has been studied over the energy range from 1 to 4 eV by analysing drift velocity data for pure CO and CO-inert gas mixtures at 294 K. The validity of using the so-called 'two term approximation' for the velocity distribution function in the solution of the Boltzmann equation to analyse drift velocity data for the pure gas (and thus also for the gas mixtures) has been established. The momentum transfer cross section for CO has been determined in the energy range 1-4 eV, and the measurements of the vibrational cross sections by Ehrhardt et al. (1968) have been renormalized. By using a solution of the Boltzmann equation which avoids the two term approximation, these cross sections have been shown to be consistent with previous measurement.s of the transport parameter D 1.1 fl in pure CO.

Solution of the Boltzmann equation for a reacting gas mixture

1993 ◽  
Vol 342 (1665) ◽  
pp. 413-438 ◽  
Keyword(s):  
Activation Energy ◽  
Boltzmann Equation ◽  
Cross Sections ◽  
Bimolecular Reaction ◽  
Model Parameters ◽  
Gas Mixture ◽  
Hard Sphere Model ◽  
Heat Of Reaction ◽  
Exothermic Reactions ◽  
The Boltzmann Equation

A spatially homogeneous gas mixture consisting of structureless molecules of kind A, B, C, D is considered in which the reversible bimolecular reaction A+B ^ C+D occurs. The Boltzmann equation describing this model gas is solved numerically by using the multigroup method. The collision cross sections correspond to the reactive hard sphere model. Parameters are the heat of reaction, the activation energy and the steric factor. Emphasis in the presentation of the results is laid on highly exothermic reactions with large activation energy, in which case the gas undergoes a thermal explosion. It is found that the corrections of the chemical rate constants due to translational non-equilibrium effects are noticeable. The result is a shortening of the reaction period by up to 25%.

Third-order transport coefficients for electrons in N2 and CF4: effects of non-conservative collisions, concurrence with diffusion coefficients and contribution to the spatial profile of the swarm

2021 ◽  
Author(s):  
Ilija Simonovic ◽  
Danko Bošnjaković ◽  
Zoran Lj Petrovic ◽  
Ron D White ◽  
Sasa Dujko
Keyword(s):  
Boltzmann Equation ◽  
Cross Sections ◽  
Diffusion Tensor ◽  
Transport Coefficients ◽  
Electron Attachment ◽  
Third Order ◽  
Spatial Profile ◽  
Monte Carlo Simulation Technique ◽  
The Third ◽  
The Boltzmann Equation

Abstract Using a multi-term solution of the Boltzmann equation and Monte Carlo simulation technique we study behaviour of the third-order transport coefficients for electrons in model gases, including the ionisation model of Lucas and Saelee and modified Ness-Robson model of electron attachment, and in real gases, including N2 and CF4. We observe negative values in the E/n 0-profiles of the longitudinal and transverse third-order transport coefficients for electrons in CF4 (where E is the electric field and n 0 is the gas number density). While negative values of the longitudinal third-order transport coefficients are caused by the presence of rapidly increasing cross sections for vibrational excitations of CF4, the transverse third-order transport coefficient becomes negative over the E/n 0-values after the occurrence of negative differential conductivity. It is found that the accuracy of the two-term approximation for solving the Boltzmann equation is sufficient to investigate the behaviour of the third-order transport coefficients in N2, while for electrons in CF4 it produces large errors and is not even qualitatively correct . The influence of implicit and explicit effects of electron attachment and ionisation on the third-order transport tensor is investigated. In particular, we discuss the effects of attachment heating and attachment cooling on the third-order transport coefficients for electrons in the modified Ness-Robson model, while the effects of ionisation are studied for electrons in the ionisation model of Lucas and Saelee, N2 and CF4. The concurrence between the third-order transport coefficients and the components of the diffusion tensor, and the contribution of the longitudinal component of the third-order transport tensor to the spatial profile of the swarm are also investigated. For electrons in CF4 and CH4, we found that the contribution of the component of the third-order transport tensor to the spatial profile of the swarm between approximately 50 Td and 700 Td, is almost identical to the corresponding contribution for electrons in N2. This suggests that the recent measurements of third-order transport coefficients for electrons in N2 may be extended and generalized to other gases, such as CF4 and CH4.

scholarly journals Cross Sections for Electron Scattering in Nitrogen

1984 ◽  
Vol 37 (5) ◽  
pp. 487 ◽  
Author(s):  
GN Haddad
Keyword(s):  
Boltzmann Equation ◽  
Electron Scattering ◽  
Cross Sections ◽  
Vibrational Excitation ◽  
Electron Drift ◽  
Normalization Factor ◽  
Pure Nitrogen ◽  
The Boltzmann Equation ◽  
Excitation Cross Sections

New measurements of electron drift velocities in mixtures of nitrogen and argon have been analysed to determine the normalization factor for the vibrational excitation cross sections for nitrogen. The validity of applying a two-term solution of the Boltzmann equation in these mixtures is demonstrated. The derived cross sections are shown to be consistent with earlier transport data in pure nitrogen.

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