The Boltzmann and the Fokker-Planck Equations

  • J. A. Bittencourt


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 /δt) 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.


Boltzmann Equation Neutral Particle Dynamic Friction Binary Collision Collision Term 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • J. A. Bittencourt
    • 1
  1. 1.National Institute for Space Research (INPE)São José dos Campos, SPBrazil

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