∂ f ∂ t + d r d t ⋅ ∂ f ∂ r + d p d t ⋅ ∂ f ∂ p = 0, over velocity. He starts with the collisionless Boltzmann equation (sometimes called the Vlasov equation, anachronistically in this context), in generalized coordinates: Vlasov suggests that these difficulties originate from the long-range character of Coulomb interaction. Theory of pair collisions cannot explain experiments by Harrison Merrill and Harold Webb on anomalous electron scattering in gaseous plasma.Theory of pair collisions is formally not applicable to Coulomb interaction due to the divergence of the kinetic terms.Theory of pair collisions disagrees with the discovery by Rayleigh, Irving Langmuir and Lewi Tonks of natural vibrations in electron plasma.He mentions the following problems arising when applying the kinetic theory based on pair collisions to plasma dynamics: Difficulties of the standard kinetic approach įirst, 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. The equation was first suggested for description of plasma by Anatoly Vlasov in 1938 and later discussed by him in detail in a monograph. The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction, e.g.
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