scholarly journals An Investigation of the Accuracy of Numerical Solutions of Boltzmann's Equation for Electron Swarms in Gases with Large Inelastic Cross Sections

1979 ◽  
Vol 32 (3) ◽  
pp. 231 ◽  
Author(s):  
Ivan D Reid
Keyword(s):  
Monte Carlo Simulation ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Transport Coefficients ◽  
Distribution Functions ◽  
Monte Carlo Simulation Technique ◽  
Energy Distribution Functions ◽  
Boltzmann's Equation ◽  
Term Approximation ◽  
Boltzmann’S Equation

A Monte Carlo simulation technique has been used to test the accuracy of electron energy distribution functions and transport coefficients calculated using conventional numerical solutions of Boltzmann's equation based on a two-term approximation. The tests have been applied to a number of model gases, some of which have characteristics close to those of real gases, and include cases where the scattering is anisotropic. The results show that, in general, previous application of the numerical solution to real gases has been valid.

scholarly journals Corrigendum: An Investigation of the Accuracy of Numerical Solutions of Boltzmann's Equation for Electron Swarms in Gases with Large Inelastic Cross Sections

1982 ◽  
Vol 35 (4) ◽  
pp. 473 ◽  
Author(s):  
Ivan D Reid
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Computer Codes ◽  
Boltzmann's Equation ◽  
Boltzmann’S Equation

An error has been found in the computer codes used in the Monte Carlo simulations. The correction for this error alters some of the values of Dol by up to several per cent. The conclusions presented in the paper are however not affected.

scholarly journals Comparison between the Boltzmann and Monte Carlo Simulation Methods for the Determination of Electron Swarm Transport Coefficients in Molecular Hydrogen

1979 ◽  
Vol 32 (3) ◽  
pp. 255 ◽  
Author(s):  
Ivan D Reid ◽  
Scott R Hunter
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Solution ◽  
Transport Properties ◽  
Cross Sections ◽  
Molecular Hydrogen ◽  
Transport Coefficients ◽  
Simulation Methods ◽  
Boltzmann's Equation

The transport properties of an electron swarm drifting and diffusing in hydrogen as determined from a numerical solution of Boltzmann's equation are compared with those derived previously from a Monte Carlo simulation. The same set of cross sections has been used with each method to calculate transport coefficients in the range 0�5 .;;; EIN.;;; 200 Td. The comparison shows that the Boltzmann analysis is valid in this case whenever ionization is not significant.

scholarly journals The Cross Sections for Rotational Excitation of H2 And D2 by Low Energy Electrons

1970 ◽  
Vol 23 (5) ◽  
pp. 683 ◽  
Author(s):  
DK Gibson
Keyword(s):  
Cross Sections ◽  
Energy Transport ◽  
Theoretical Calculations ◽  
Transport Coefficients ◽  
Distribution Functions ◽  
Low Energy ◽  
Low Energy Electrons ◽  
A New Technique ◽  
Energy Distribution Functions ◽  
Electron Transport Coefficients

The J = 1 --+ 3 rotational cross section for H2 has been derived from an analysis of electron transport coefficients; A new technique is described for calculating the energy distribution functions taking into account superelastic collisions, since these must be included for an analysis of low energy transport data in D2. Unique rotational cross sections cannot be obtained for this gas from the experimental data available, but two sets of cross sections have been derived which are compatible with the existing data and are also in accord with recent theoretical calculations

scholarly journals Comment on FTI Method and Transport Coefficient Definitions for Charged Particle Swarms in Gases

1995 ◽  
Vol 48 (4) ◽  
pp. 677 ◽  
Author(s):  
RE Robson
Keyword(s):  
Charged Particle ◽  
Path Integral ◽  
Transport Coefficients ◽  
Space Distribution ◽  
Particle Swarms ◽  
Integral Methods ◽  
Time Integral ◽  
Definition Of ◽  
Boltzmann's Equation ◽  
Boltzmann’S Equation

The kinetic theory of charged particle swarms in gases is based upon solution of the space and time dependent Boltzmann's equation for the phase space distribution function f(r, c, t). Hydrodynamic transport coefficients are defined in connection with a density gradient expansion (DGE) of f(r, c, t) and it is believed that these are the quantities measured in experiment. On the other hand, Ikuta and coworkers start with the spatially independent form of the Boltzmann equation, which they solve iteratively as in path-integral methods, and define transport coefficients in terms of the 'starting rate distribution', rather than f itself. Ikuta's procedure has come to be known as the 'flight time integral' (FTI) method and the discrepancies between numerical calculations based upon this and the more commonly known DGE procedure have generated a deal of controversy in recent times. The purpose of this paper is to point out that the respective definitions of the transverse diffusion coefficient DT coincide only for light swarm particles undergoing collisions for which the differential cross section is isotropic, and that the particular technique used for solving Boltzmann's equation, be it a path-integral or a multi-term method, has nothing to do with the numerical discrepancies which are observed when scattering is anisotropic. In particular, it is shown that Ikuta's definition of DT is inconsistent with even the well established result for constant collision frequency.

Transport Parameters of Electrons in N2-O2 Streamer Discharge

2014 ◽  
Vol 575 ◽  
pp. 570-575
Author(s):  
Gulala Muhammad Faraj
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Molecular Nitrogen ◽  
Transport Coefficients ◽  
Chemical Processes ◽  
Plasma Discharges ◽  
Transport Parameters ◽  
Streamer Discharge ◽  
Monte Carlo Simulation Technique ◽  
Physical And Chemical

Electron transport data been calculated numerically in mixture of molecular nitrogen and oxygen, using Monte Carlo simulation technique and a multi-term theory for solving the Boltzmann equation to investigate and obtaining the exact transport coefficients. It may serve the basis for modeling physical and chemical processes in streamer plasma discharges. Transport data influenced by the amount of O2in the mixture. The values of mean energy drift velocity reported.

scholarly journals An Exact Solution of Boltzmann's Equation for a Rigid Sphere Gas

1968 ◽  
Vol 21 (5) ◽  
pp. 543 ◽  
Author(s):  
PI Brooker ◽  
HS Green
Keyword(s):  
Transport Coefficients ◽  
Velocity Distribution Function ◽  
Zero Order ◽  
Rigid Sphere ◽  
Stream Velocity ◽  
Approximation Techniques ◽  
The Third ◽  
Boltzmann's Equation ◽  
Good Agreement ◽  
Boltzmann’S Equation

The second approximation to Boltzmann's equation, in Chapman and Cowling's form, is solved exactly for a rigid sphere gas by using appropriate transformations to reduce the integral equation to a differential equation, which is solved numerically. The values of the transport coefficients, calculated directly from this solution for the velocity distribution function, are in good agreement with those obtained from the usual approximation techniques. A solution for part of the third approximation, with a term of zero order in V, the velocity of a molecule relative to the stream velocity, is also obtained analytically.

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