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 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.

The 1 s -2 s excitation of hydrogen atoms by electron impact

1960 ◽  
Vol 258 (1293) ◽  
pp. 245-250 ◽  
Keyword(s):  
Electron Impact ◽  
Cross Section ◽  
Cross Sections ◽  
Born Approximation ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Hydrogen Atoms ◽  
Third Order ◽  
The Third ◽  
Intermediate States

The expression for the cross-section obtained from the second Born approximation by including only terms to the third order in the interaction energy is employed to calculate cross-sections for the electron impact excitation of the 2 s level of atomic hydrogen, allow­ance being made for distortion and polarization due to the 1 s , 2 s and 2 p 0.± 1 intermediate states. These cross-sections are compared with the available experimental data.

Nonlinear transport coefficients and plane Couette flow of a viscous, heat-conducting gas between two plates at different temperatures

1987 ◽  
Vol 65 (9) ◽  
pp. 1090-1103 ◽  
Author(s):  
Byung Chan Eu ◽  
Roger E. Khayat ◽  
Gert D. Billing ◽  
Carl Nyeland
Keyword(s):  
Boltzmann Equation ◽  
Couette Flow ◽  
Transport Coefficients ◽  
Heat Conducting ◽  
Hydrodynamic Equations ◽  
Nonlinear Transport ◽  
Plane Couette Flow ◽  
The Boltzmann Equation ◽  
Viscous Heat ◽  
Different Temperatures

By using the example of plane Couette flow between two plates maintained at different temperatures, we present a method of calculating flow profiles for rarefied gases. In the method, generalized hydrodynamic equations are derived from the Boltzmann equation. They are then solved with boundary conditions calculated by taking into consideration the interfacial interaction between the surface and the gas molecule. The nonlinear transport coefficients employed in the generalized hydrodynamic equations are obtained from the Boltzmann equation by means of the modified-moment method. The profiles calculated are in agreement with the Liu–Lees theory as long as the boundary values are in agreement. It is found that the viscous-heating effect has a significant influence on the temperature and velocity profiles. The nonlinearity of transport coefficients also has significant effects on the profiles as the Knudsen and Mach numbers increase.

scholarly journals Is There a Third Integral of Motion?

1975 ◽  
Vol 69 ◽  
pp. 245-245
Author(s):  
P. Pişmiş
Keyword(s):  
Boltzmann Equation ◽  
Phase Space ◽  
Coherent Motion ◽  
Elementary Volume ◽  
Integral Of Motion ◽  
Single Star ◽  
The Third ◽  
The Boltzmann Equation ◽  
The Galaxy ◽  
Plane Orbit

It is argued that in a galaxy like ours a third integral of motion, a third independent argument in the distribution function, should exist if the potential function has to satisfy a third condition imposed on it, namely symmetry with respect to a plane. Orbit computations of single stars in a symmetric potential of the kind (Martinet and Hayli, 1971) indicate that a third integral seems to exist for Population I stars while it ceases to exist for Population II objects. This situation is explained by the author as follows. We state that a third integral should exist for all populations alike if the Boltzmann equation is interpreted within the statistical context for which it is valid. When applied to a complex system like the galaxy the third integral of the Boltzmann equation, which holds for an elementary volume in phase space, will also hold for a single particle if the latter is representative of the behavior of the element of volume as in Population I (coherent motion) whereas it will not necessarily hold for a single star of Population II; in the latter population the elementary volume, containing the same number of stars, does not represent the behavior of the element of volume during the motion of this in phase space.

Third order optical nonlinear studies and its use to estimate thickness of sandwiched films of tetra-phenyl porphyrin derivatives

2016 ◽  
Vol 25 (03) ◽  
pp. 1650039 ◽  
Author(s):  
A.Srinivasa Rao ◽  
Mudasir H. Dar ◽  
N. Venkatramaiah ◽  
R. Venkatesan ◽  
Alok Sharan
Keyword(s):  
Cross Sections ◽  
Optical Nonlinearity ◽  
Index Formula ◽  
Wave Mixing ◽  
Porphyrin Molecule ◽  
Third Order ◽  
Single Beam ◽  
The Third ◽  
Porphyrin Derivatives ◽  
First Time

Third-order nonlinear optical properties of tetra-phenyl porphyrin (H[Formula: see text]TPP) derivatives viz., H[Formula: see text]TPP(OH)[Formula: see text] and Zn(II)TPP doped in boric acid glass thin films were measured using single beam Z-scan and forward degenerate four-wave mixing (DFWM) techniques. Excited state lifetimes and absorption cross-sections were estimated from these experiments. Thickness of the porphyrin doped sandwich glass films were determined using DFWM technique for the first time. The values of nonlinear refractive index ([Formula: see text]) obtained for these systems are are found to be sensitive to the nature of substituents in porphyrin molecule. These results are interpreted in terms of delocalized [Formula: see text] electrons contributing to the third-order optical nonlinearity.

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 Third-Order Nonlinear Optical Behavior of Novel Polythiophene Derivatives Functionalized with Disperse Red 19 Chromophore

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Marilú Chávez-Castillo ◽  
Arelis Ledesma-Juárez ◽  
Marisol Güizado-Rodríguez ◽  
Jesús Castrellón-Uribe ◽  
Gabriel Ramos-Ortiz ◽  
...  
Keyword(s):  
Cross Sections ◽  
Nonlinear Optical ◽  
Oxidative Polymerization ◽  
Cost Effective ◽  
Laser Pulses ◽  
Femtosecond Laser Pulses ◽  
Photon Absorption ◽  
Side Chain ◽  
Third Order ◽  
The Third

Two copolymers of 3-alkylthiophene (alkyl = hexyl, octyl) and a thiophene functionalized with disperse red 19 (TDR19) as chromophore side chain were synthesized by oxidative polymerization. The synthetic procedure was easy to perform, cost-effective, and highly versatile. The molecular structure, molecular weight distribution, film morphology, and optical and thermal properties of these polythiophene derivatives were determined by NMR, FT-IR, UV-Vis GPC, DSC-TGA, and AFM. The third-order nonlinear optical response of these materials was performed with nanosecond and femtosecond laser pulses by using the third-harmonic generation (THG) andZ-scan techniques at infrared wavelengths of 1300 and 800 nm, respectively. From these experiments it was observed that although the TRD19 incorporation into the side chain of the copolymers was lower than 5%, it was sufficient to increase their nonlinear response in solid state. For instance, the third-order nonlinear electric susceptibility (χ3) of solid thin films made of these copolymers exhibited an increment of nearly 60% when TDR19 incorporation increased from 3% to 5%. In solution, the copolymers exhibited similar two-photon absorption cross sectionsσ2PAwith a maximum value of 8545 GM and 233 GM (1 GM = 10−50 cm4 s) per repeated monomeric unit.

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