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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. The equation was first suggested for description of plasma by Anatoly Vlasov in 1938 (see also ) and later discussed by him in detail in a monograph. ==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 disagrees with the discovery by Rayleigh, Irving Langmuir and Lewi Tonks of natural vibrations in electron plasma. # Theory of pair collisions is 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 called the Vlasov equation, anachronistically in this context), in generalized coordinates: : explicitly a PDE: : and adapted it to the case of a plasma, leading to the systems of equations shown below.〔"Vlasov equation?", M. Hénon, ''Astronomy and Astrophysics'' 114, #1 (October 1982), pp. 211-212, 〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Vlasov equation」の詳細全文を読む スポンサード リンク
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