Kinetic theory of the Lorentz gas

The steady state kinetic equation μv ∂f(z,v,μ)/∂z = ∂/∂μ [1-μ2/τ(v) ∂f(z,v,μ)/∂μ] for the Lorentz gas, where μ ez.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. (orig.)