A statistical model of transport in a vacuum

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Abstract
The problem of particle transportinan evacuated pipe is considered. This problem is modeled by treating the distance between pipe wall collisions as a “mean free path”, and using the reciprocal of this as a “cross section” in a transport equation. Such a cross setion is angularly dependent. Thus we are led to the study of a planar geometry linear transport equation with o(μ) = (1-μ2)1/2. Both the Wiener-Hopf method and a singular eigenfunction treatment are used to analyze the semi-infinite pipe problem. Comparisons are made with exact transport calculations, and two refinements are suggested to improve the accuracy of the models presented here.