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Kinetic Theory of the Lorentz Gas
Author(s) -
Chen Qun,
Bernstein Ira B.
Publication year - 1994
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.2150340211
Subject(s) - physics , iterated function , lorentz transformation , kinetic energy , work (physics) , kinetic theory , mean free path , diffusion , brownian motion , diffusion equation , steady state (chemistry) , lorentz force , classical mechanics , statistical physics , mathematical analysis , quantum mechanics , thermodynamics , magnetic field , mathematics , electron , chemistry , economy , economics , service (business)
The steady state kinetic equation for the Lorentz gas, where μ=e x · v/v, has been solved numerically. Analytic approximations have been developed for f ( z , v, 0) in the limits of mean‐free‐path long and short compared with the system size. These have been shown to be good, and to provide a useful starting point for the numerical procedure employed, which iterates on f ( x , v, 0). Their success suggests that counterpart approximations may work well for more complicated steady state kinetic problems of interest in the physics of the edge in proposed controlled fusion reactors, the diffusion of neutrons, the Brownian motion of heavy molecules, and the structure of shocks. It has also been demonstrated that the determination of f ( z , v, 0) can be reduced to the solution of a one dimensional integral equation.