Difficulties of The Standard Kinetic Approach
First, Vlasov argues that the standard kinetic approach based on the Boltzmann equation has difficulties when applied to a description of the plasma with long-range Coulomb interaction. He mentions the following problems arising when applying the kinetic theory based on pair collisions to plasma dynamics:
- Theory of pair collisions disagree with the discovery by Rayleigh, Irving Langmuir and Lewi Tonks of natural vibrations in electron plasma.
- Theory of pair collisions formally not applicable to Coulomb interaction due to the divergence of the kinetic terms.
- Theory of pair collisions cannot explain experiments by Harrison Merrill and Harold Webb on anomalous electron scattering in gaseous plasma.
Vlasov suggests that these difficulties originate from the long-range character of Coulomb interaction. He starts with the collisionless Boltzmann equation (sometimes anachronistically called the Vlasov equation in this context),
and adapted it to the case of a plasma, leading to the systems of equations shown below.
Read more about this topic: Vlasov Equation
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