Mean Free Paths, Ion Drift Velocities, and the Poisson Distribution

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Abstract
In elementary kinetic theory of gases, the topic of free paths is usually limited to the simplest case of finding the probability of zero collisions in a travel distance x . This leads to a mean free path and it also discloses that the greatest probability of collision in a distance Δx occurs for x = 0 . The most probable free path then does not coincide with the mean free path. This paper carries on the analysis to evaluation of the probability of exactly one collision in a distance x and still further to the probability of exactly n collisions in x . All of these probabilities, for which the number of collisions n is greater than zero, are bell-shaped curves with the most probable value of x coinciding with n times the mean free path. The results are applied to analyze the sharpness of the observed drift velocity of ions moving through a gas in an electric field.

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