@inbook {2604,
	title = {Relaxation Behavior for the Lorentz Fokker Planck Equation: Model Cross Sections and Nonextensive Entropy},
	booktitle = {Rarefied Gas Dynamics},
	series = {Aip Conference Proceedings},
	volume = {1084},
	year = {2009},
	note = {ISI Document Delivery No.: BJF97Times Cited: 0Cited Reference Count: 19Shizgal, Bernie D.Proceedings Paper26th International Symposium on Rarefied Gas Dynmaics (RGD26)JUN 20-JUL 25, 2008Kyoto, JAPANJapan Soc Promot Sci, Japan Aerpspace Explorat Agcy, Soc Promot Space Sci, Iwantani Naoji Fdn, Inoue Fdn Sci, Casio Sci Promot Fdn, Kaijma Fdn, IHI Corp, IHI Aerospac Engn Co Ltd, Osaka Vaccuun Ltd, Nissin Inc2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA},
	pages = {39-44},
	publisher = {Amer Inst Physics},
	organization = {Amer Inst Physics},
	address = {Melville},
	abstract = {The relaxation behavior of a test particle in a background gas at equilibrium for which the test particle background particle mass ratio, m(t)/m(b) tends to zero, that is the Lorentz limit, is studied with the Lorentz-Fokker-Planck equation. This is the situation for electrons in inert gases. If there is also an applied electric field the stationary distribution is not the equilibrium Maxwellian. In the present paper, the evolution of the isotropic distribution function is studied with both a finite difference solution and one based on the expansion of the distribution function in the eigenfunctions of the Fokker-Planck operator. The eigenvalue spectrum depends strongly on the velocity dependence of the momentum transfer cross section in the Fokker-Planck equation. In particular, the spectrum is composed of a discrete spectrum and a continuum, and the continuum can dominate the spectrum. The role of the eigenvalue spectrum of this operator on the time evolution of the distribution function is studied. In particular, the time dependence of the entropy is determined and we show that the Kullback-Leibler entropy rationalizes the approach to a stationary distribution. The Tsallis non-extensive entropy is not required to explain the evolution of the distributions.},
	keywords = {Boltzmann equation, DEGRADATION, electron, Maxwell molecules, METHOD QDM, NONCLASSICAL BASIS FUNCTIONS, pseudospectral method, QUADRATURE DISCRETIZATION METHOD, quantum cross section, RARE-GAS MODERATORS, SUPRATHERMAL PARTICLE DISTRIBUTIONS, THERMALIZATION},
	isbn = {0094-243X978-0-7354-0615-5},
	url = {<Go to ISI>://000265564800005},
	author = {Shizgal, B. D.},
	editor = {Abe, T.}
}
@article {3725,
	title = {On the existence of a steady electron distribution for systems with electron attachment: Ar-CCl4 mixtures},
	journal = {Chemical Physics Letters},
	volume = {260},
	number = {3-4},
	year = {1996},
	note = {ISI Document Delivery No.: VJ539Times Cited: 1Cited Reference Count: 18},
	month = {Sep},
	pages = {365-370},
	type = {Article},
	abstract = {The relaxation of a nonequilibrium distribution of electrons in a mixture of Ar and CCl4 is studied. In a previous paper [J. Phys. B 34 (1991) 2909], Shizgal demonstrated that with the neglect of vibrationally inelastic collisions, a nonequilibrium steady electron distribution does occur even with the loss of electrons. The rate of disappearance of electrons due to attachment is rapid for high concentrations of CCl4. In this Letter, we extend the previous analysis to include inelastic collisions and find that for CCl4 and Ar mixtures there is no steady electron distribution function with increasing molecular gas concentrations.},
	keywords = {ARGON, CROSS-SECTIONS, DEGRADATION, GAS, SF6, THERMALIZATION},
	isbn = {0009-2614},
	url = {<Go to ISI>://A1996VJ53900008},
	author = {Kowari, K. and Shizgal, B.}
}
@article {2780,
	title = {A UNIFORM WENTZEL-KRAMERS-BRILLOUIN APPROACH TO ELECTRON-TRANSPORT IN MOLECULAR GASES},
	journal = {Journal of Chemical Physics},
	volume = {99},
	number = {10},
	year = {1993},
	note = {ISI Document Delivery No.: MH744Times Cited: 4Cited Reference Count: 46},
	month = {Nov},
	pages = {7638-7651},
	type = {Article},
	abstract = {The relaxation of a nonequilibrium distribution of electrons in molecular gases, and the transient and steady electron transport properties are studied with the Boltzmann equation, which accurately accounts for elastic and inelastic electron-moderator collisions. The elastic collision operator is a self-adjoint Fokker-Planck operator, whereas the-inelastic collision term is a difference operator. We consider a discretization of the inelastic collision operator which is motivated by the discrete energy losses that occur. For small energy losses, a continuous approximation is introduced such that the inelastic collision term is approximated by a Fokker-Planck operator similar to the elastic collision operator. The transient electron transport properties are studied for an initial electron distribution function in terms of the eigenvalue spectrum of both the elastic and inelastic collision operators. The Fokker-Planck eigenvalue problem is transformed into a Schrodinger equation and the nature of the spectrum is studied in terms of the Wentzel-Kramers-Brillouin and supersymmetric Wentzel-Kramers-Brillouin approximations. The methodology is applied to model systems and the transport of electrons in methane.},
	keywords = {BOLTZMANN-EQUATION ANALYSIS, COEFFICIENTS, DIFFUSION, FIELD DEPENDENCE, MODERATORS, NEUTRAL GASES, PARAMETERS, SWARM, THERMALIZATION, VELOCITY DISTRIBUTION FUNCTION, WKB},
	isbn = {0021-9606},
	url = {<Go to ISI>://A1993MH74400037},
	author = {Demeio, L. and Shizgal, B.}
}
@article {7058,
	title = {TIME-DEPENDENT ELECTRON-DISTRIBUTION FUNCTIONS AND DEGRADATION SPECTRA - A COMPARISON OF THE SPENCER-FANO EQUATION AND THE BOLTZMANN-EQUATION},
	journal = {Applied Radiation and Isotopes},
	volume = {42},
	number = {10},
	year = {1991},
	note = {ISI Document Delivery No.: GL858Times Cited: 8Cited Reference Count: 43SYMP ON THE PHYSICS OF ELECTRON TRANSPORTAPR 02-03, 1990GAITHERSBURG, MDUS DOE, OFF HLTH \& ENVIRONM RES},
	pages = {985-994},
	type = {Proceedings Paper},
	abstract = {The thermalization of electrons in gaseous moderators for initial nonequilibrium distributions not far removed from thermal energies has been studied previously with a Fokker-Planck equation for electron distribution. For electron energies in the keV to eV energy range an approach based on the Spencer-Fano equation has also been used. The present paper considers a detailed comparison of the two approaches to electron thermalization. The Spencer-Fano equation is analogous to the Fokker-Planck equation but with the moderator temperature set to zero, that is, with the cold gas approximation. The effect of the cold gas approximation on the time evolution of the nonequilibrium distributions and on the calculation of thermalization times is discussed in detail. The cold gas approximation is shown to be the basis for most of the concepts used in radiation chemistry and physics to study electron degradation. Applications to the thermalization of electrons in the inert gases are considered. The analysis is restricted to elastic electron-moderator collisions.},
	keywords = {ARGON, HELIUM, HOT-ATOM REACTIONS, INITIAL PRODUCTS, NITROGEN, RARE-GAS MODERATORS, SUBEXCITATION ELECTRONS, THERMALIZATION, TRANSPORT, YIELDS},
	isbn = {0969-8043},
	url = {<Go to ISI>://A1991GL85800010},
	author = {Kowari, K. and Shizgal, B.}
}
