The Boltzmann collision model

Owing to the presence of the pair correlation function, the collision model in Eq. (6.2) is unclosed. Thus, in order to close the kinetic equation (Eq. 6.1), we must provide a closure for written in terms of /. The simplest closure is the Boltzmann Stofizahlansatz (Boltzmann, 1872)  

The elastic Boltzmann collision model has a unique equilibrium solution defined by C = 0. This Maxwellian distribution is given by 

Note that the transport term on the left-hand side of Eq. (6.1) can be larger or smaller in magnitude than the collision term. For cases in which the collision term is much more important than the transport term, the solution to Eq. (6.1) with the Boltzmann collision model is a local Maxwellian wherein ap. Up, and p depend on space and time but / is well approximated by Eq. (6.10). In this limit, the particles behave as an ideal gas and the mean velocity obeys the Euler equation. 

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We shall start with the Boltzmann collision model, which belongs to the last group. The Boltzmann-induced distribution FB. established at the instant t = 0 of the strong collision, in the case of an isotropic medium, is given by... 

Starting from the Boltzmann collision model, we write down the formula for the Boltzmann orientational distribution FB pertaining to weak electromagnetic... 

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