Rigorous derivation of the landau equation in the weak coupling limit

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Abstract

We examine a family of microscopic models of plasmas, with a parameter α comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak coupling limit, to a velocity diffusion described by the linear Landau equation (also known as the Fokker-Planck equation). The present work extends and unifies previous results that handled the extremes of the parameter α to the whole range (0, 1/2], by showing that clusters of overlapping obstacles are negligible in the limit. Additionally, we study the diffusion coefficient of the Landau equation and show it to be independent of the parameter.

Original languageEnglish (US)
Pages (from-to)1895-1916
Number of pages22
JournalCommunications on Pure and Applied Analysis
Volume8
Issue number6
DOIs
StatePublished - Nov 2009
Externally publishedYes

Keywords

  • Kinetic theory
  • Particle systems
  • Plasma models

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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