Integral form of the Boltzmann equation for the forced diffusion of charged particles in anisotropically scattering media

Meccanica ◽  
1981 ◽  
Vol 16 (2) ◽  
pp. 67-74 ◽  
Author(s):  
G. Spiga ◽  
S. Succi
Keyword(s):  
Boltzmann Equation ◽  
Charged Particles ◽  
Integral Form ◽  
Scattering Media ◽  
The Boltzmann Equation ◽  
Forced Diffusion

scholarly journals A Thermodynamic Treatment of Anisotropic Diffusion in an Electric Field

1972 ◽  
Vol 25 (6) ◽  
pp. 685 ◽  
Author(s):  
RE Robson
Keyword(s):  
Boltzmann Equation ◽  
Electric Field ◽  
Drift Velocity ◽  
Anisotropic Diffusion ◽  
Diffusion Tensor ◽  
Charged Particles ◽  
Equilibrium Thermodynamics ◽  
Neutral Gas ◽  
The Boltzmann Equation ◽  
Diffusive Processes

Non-equilibrium thermodynamics is used to analyse the diffusive processes associated with a swarm of charged particles (ions or electrons) drifting in a neutral gas under the influence of an electric field. A simple approximate phenomenological relationship connecting components of the diffusion tensor with the drift velocity of the swarm is derived and the utility of the formula is illustrated in several cases where previous analyses have been carried out using the Boltzmann equation.

scholarly journals On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2382
Author(s):  
Andrey Saveliev
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Magnetic Fields ◽  
Kinetic Theory ◽  
Charged Particles ◽  
Kinetic Theory Of Gases ◽  
The Boltzmann Equation ◽  
Ideal Magnetohydrodynamics ◽  
Complex Valued

In this work, we revisit Boltzmann’s distribution function, which, together with the Boltzmann equation, forms the basis for the kinetic theory of gases and solutions to problems in hydrodynamics. We show that magnetic fields may be included as an intrinsic constituent of the distribution function by theoretically motivating, deriving and analyzing its complex-valued version in its most general form. We then validate these considerations by using it to derive the equations of ideal magnetohydrodynamics, thus showing that our method, based on Boltzmann’s formalism, is suitable to describe the dynamics of charged particles in magnetic fields.

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