The Boltzmann Equation and Transport Equa- tions of Charged Particles

2014 ◽  
pp. 183-216 ◽  
Keyword(s):  
Boltzmann Equation ◽  
Charged Particles ◽  
Equa Tions ◽  
The Boltzmann Equation

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.

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

Approach to Equilibrium, the H-Theorem and Irreversibility

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Detailed Knowledge ◽  
Approach To Equilibrium ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

Like most of the greatest equations in science, the Boltzmann equation is not only beautiful but also generous. Indeed, it delivers a great deal of information without imposing a detailed knowledge of its solutions. In fact, Boltzmann himself derived most if not all of his main results without ever showing that his equation did admit rigorous solutions. This Chapter illustrates one of the most profound contributions of Boltzmann, namely the famous H-theorem, providing the first quantitative bridge between the irreversible evolution of the macroscopic world and the reversible laws of the underlying microdynamics.

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