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Suppose you have a distribution function $ f_{\alpha}( \vec{r} , \vec{p} , t)$ obtained from Vlasov equations for a certain $\alpha$ species, say some ions.

Is there a rigorous way (in the domain of validity of the model, that is) to estimate a collision density function $ p^{collisions}_{\alpha}( \vec{r} , E_{CM} , t)$ , where $E_{CM}$ is a variable describing collision energy parameters? A link or reference would be great

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I am not sure to understand your question because the vlasov equation is only valid for a collisionless plasma ... The interactions between particles is done through the long range mean electromagnetic field. If you want to include the collision operator you need to work with the Landau's equation or Fokker-Planck one. For an uncharged gas, the Boltzmann's equation gives good results. One of the best author is probably Radu Balescu. He has written many good books on kinetic theory.

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