Diffusion limits of the linear boltzmann equation in extended kinetic theory: Weak and strong inelastic collisions

1999 ◽  
Vol 69 (1) ◽  
pp. 51-81
Author(s):  
Lucio Demeio ◽  
Giovanni Frosali
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Inelastic Collisions ◽  
Linear Boltzmann Equation ◽  
Diffusion Limits

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

Run-aways im Neutralgas

1961 ◽  
Vol 16 (3) ◽  
pp. 246-252 ◽  
Author(s):  
G. Ecker ◽  
K. G. Müller
Keyword(s):  
Relaxation Time ◽  
Boltzmann Equation ◽  
Glow Discharge ◽  
Initial Velocity ◽  
Average Velocity ◽  
Electron Beams ◽  
Critical Value ◽  
Inelastic Collisions ◽  
Stopping Power ◽  
Scattering Parameters

The motion of electrons as determined by the field acceleration and the elastic and inelastic collisions with the gas atoms is calculated from the BOLTZMANN equation. We derive the average velocity and the scattering ellipsoid as a function of time. For particles starting from rest there exists always a critical electric field Ec depending on pressure and temperature. Below this critical value electrons approach the stationary drift process. Above the critical value the electrons do not reach a stationary state, they “run away”. For a finite initial velocity ν0 and a field below the critical value Ec the particles are either accelerated to drift, or decelerated to drift, or “run away”, depending on the value ν0. From a calculation of the scattering parameters we find for E > Ec a focussing effect in the velocity space which increases with field strength. Also the relaxation time for the drift process and the stopping power for electron beams can be calculated. Applications to the glow discharge are discussed.

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