Fundamentals of Plasma Physics pp 589-627 | Cite as

# The Boltzmann and the Fokker-Planck Equations

## Abstract

When the Boltzmann equation was first introduced in Chapter 5, the collisional effects were incorporated in its right-hand side [see equation (5.5.27)] through a general collision term (*δ* *f*_{ α }
/*δ**t*)_{ coll } still to be specified. We present now a derivation of the Boltzmann collision term, which takes into account only *binary collisions*. This collision term involves integrals over the particle velocities, so that the Boltzmann equation turns out to be an *integro-differential equation*. The fact that the Boltzmann collision integral takes into account only binary collisions limits considerably its applicability for a plasma, where each charged particle interacts simultaneously with a large number of neighboring charged particles. Although these multiple coulomb collisions are very important for a plasma, there are some cases (as in weakly ionized plasmas) where the binary charge-neutral collisions play a dominant role.

## Keywords

Boltzmann Equation Neutral Particle Dynamic Friction Binary Collision Collision Term## Preview

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