An extended analytical solution of the Boltzmann equation for non-homogeneous fusion and astrophysical plasmas

1988 ◽  
Vol 40 (3) ◽  
pp. 441-453 ◽  
Author(s):  
S. Cuperman ◽  
D. Zoler
Keyword(s):  
Boltzmann Equation ◽  
Analytical Solution ◽  
Free Path ◽  
Density Gradient ◽  
Transport Coefficients ◽  
Spherical Geometry ◽  
Mean Free Path ◽  
Astrophysical Plasmas ◽  
Electron Plasmas ◽  
Gravitational Fields

The perturbative Chapman-Enskog procedure for solving Boltzmann's equation, holding when f1 ≪ f0 (f = f0 + f1 + …), is replaced by a method that is free of such a limitation. This work represents an extension to the case of strongly anisotropic plasma systems and the spherical geometry of that of Campbell (1984, 1986). The solution obtained here is expressed in terms of prescribed ratios of mean free path for collisions, as well as electric and gravitational fields, to the temperature- and density-gradient lengths. This solution is also used to discuss the limitation of the conduction transport coefficients in electron plasmas.

Anisotropic mean free path in simulations of fluids traveling down a density gradient

2010 ◽  
Vol 132 (22) ◽  
pp. 224302 ◽  
Author(s):  
Jessica R. Whitman ◽  
Gregory L. Aranovich ◽  
Marc D. Donohue
Keyword(s):  
Free Path ◽  
Density Gradient ◽  
Mean Free Path

scholarly journals Theory and applications of the relativistic Boltzmann equation

2014 ◽  
Vol 11 (02) ◽  
pp. 1460005 ◽  
Author(s):  
Gilberto M. Kremer
Keyword(s):  
Thermal Conductivity ◽  
Boltzmann Equation ◽  
Gravitational Potential ◽  
Transport Coefficients ◽  
Potential Gradient ◽  
The Other ◽  
Gravitational Fields ◽  
Relativistic Boltzmann Equation ◽  
Coefficient Of Thermal Conductivity ◽  
External Electromagnetic Fields

In this work, two systems are analyzed within the framework of the relativistic Boltzmann equation. One of them refers to a description of binary mixtures of electrons and protons and of electrons and photons subjected to external electromagnetic fields in special relativity. In this case the Fourier and Ohm laws are derived and the corresponding transport coefficients are obtained. In the other a relativistic gas under the influence of the Schwarzschild metric is studied. It is shown that the heat flux in Fourier's law in the presence of gravitational fields has three contributions, the usual dependence on the temperature gradient, and two relativistic contributions, one of them associated with an acceleration and another to a gravitational potential gradient. Furthermore, it is shown that the transport coefficient of thermal conductivity decreases in the presence of a gravitational field. The dependence of the temperature field in the presence of a gravitational potential is also discussed.

scholarly journals Landauer-Datta-Lundstrom Generalized Transport Model for Nanoelectronics

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Yuriy Kruglyak
Keyword(s):  
Electron Transport ◽  
Band Structure ◽  
Free Path ◽  
Power Law ◽  
Linear Response ◽  
Transport Model ◽  
Transport Coefficients ◽  
Mean Free Path ◽  
Linear Dispersion ◽  
Thermoelectric Transport

The Landauer-Datta-Lundstrom electron transport model is briefly summarized. If a band structure is given, the number of conduction modes can be evaluated and if a model for a mean-free-path for backscattering can be established, then the near-equilibrium thermoelectric transport coefficients can be calculated using the final expressions listed below for 1D, 2D, and 3D resistors in ballistic, quasiballistic, and diffusive linear response regimes when there are differences in both voltage and temperature across the device. The final expressions of thermoelectric transport coefficients through the Fermi-Dirac integrals are collected for 1D, 2D, and 3D semiconductors with parabolic band structure and for 2D graphene linear dispersion in ballistic and diffusive regimes with the power law scattering.

THE TEMPERATURE DISTRIBUTION PRODUCED BY ACOUSTIC ABSORPTION: II. BOLTZMANN EQUATION APPROACH

1966 ◽  
Vol 44 (12) ◽  
pp. 3013-3023 ◽  
Author(s):  
S. Simons
Keyword(s):  
Boltzmann Equation ◽  
Temperature Distribution ◽  
Free Path ◽  
Low Temperatures ◽  
Mean Free Path ◽  
Collision Term ◽  
Acoustic Absorption ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
The Mean

A calculation is given of the time-independent temperature distribution produced by the absorption of an acoustic wave under conditions in which the mean free path of the thermal particles is of the order of the specimen dimensions. Results are obtained for plane geometry by solving the relevant Boltzmann equation with a relaxation time approximation for the collision term. The results suggest an experimental method for obtaining the mean free path of electrons in metals at low temperatures, similar in some respects to the method of conduction in thin films.

On Nonlocal Constitutive Relations, Continued Fraction Expansion for the Wave Vector Dependent Diffusion Coefficient

1977 ◽  
Vol 32 (7) ◽  
pp. 678-684 ◽  
Author(s):  
Siegfried Hess
Keyword(s):  
Diffusion Coefficient ◽  
Boltzmann Equation ◽  
Wave Vector ◽  
Continued Fraction ◽  
Constitutive Relations ◽  
Transport Coefficients ◽  
Mean Free Path ◽  
Upper And Lower Bounds ◽  
Continued Fraction Expansion ◽  
The Boltzmann Equation

Abstract Nonlocal constitutive relations which involve wave vector dependent transport coefficients can be derived from the Boltzmann equation. Diffusion of a Lorentzian gas is treated as an illustrative example. Transport-relaxation equations obtained from the Boltzmann equation with the help of the moment method lead to a continued fraction expansion for the wave vector dependent diffusion coefficient D(k). Rapidly converging upper and lower bounds on D(k)/D(0) are found which are meaningful for all values of lk where l is a mean free path and k is the magnitude of the wave vektor k. Also some remarks on a frequency and wave vector dependent diffusion coefficient are made.

Inelastic mean free path and phase-shift determinations in NiO, using EXELFS

1993 ◽  
Vol 3 (7) ◽  
pp. 1649-1659
Author(s):  
Mohammad A. Tafreshi ◽  
Stefan Csillag ◽  
Zou Wei Yuan ◽  
Christian Bohm ◽  
Elisabeth Lefèvre ◽  
...  
Keyword(s):  
Phase Shift ◽  
Free Path ◽  
Mean Free Path ◽  
Inelastic Mean Free Path
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