The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range (for example, Coulomb) interaction.
•
# Theory of pair collisions disagrees with the discovery by Rayleigh, Irving Langmuir and Lewi Tonks of natural vibrations in electron plasma.
•
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.
Schrödinger equation | Nernst equation | Monge–Ampère equation | Boltzmann equation | Diophantine equation | Andrey Vlasov | Ordinary differential equation | ordinary differential equation | Young–Laplace equation | Wave equation | wave equation | Vlasov equation | Tait equation | Smoluchowski coagulation equation | Sauerbrey equation | Redlich–Kwong equation of state | Ramanujan–Nagell equation | Quadratic equation | Prony equation | Pell's equation | Mathieu's equation | Marchenko equation | Majorana's equation | Linear equation | linear equation | Liénard equation | Kepler's equation | Kaup–Kupershmidt equation | Ishimori equation | Hyperbolic partial differential equation |
A kinetic description is achieved by solving the Boltzmann equation or, when the correct description of long-range Coulomb interaction is necessary, by the Vlasov equation which contains self-consistent collective electromagnetic field, or by the Fokker-Planck equation, in which approximations have been used to derive manageable collision terms.