Rigorous derivation of the Landau equation in the weak coupling limit

Pages: 1895 - 1916, Volume 8, Issue 6, November 2009

doi:10.3934/cpaa.2009.8.1895       Abstract        Full Text (282.6K)       Related Articles

Kay Kirkpatrick - Massachusetts Institute of Technology, 77 Mass. Ave., Cambridge, MA 02139, United States (email)

Abstract: We examine a family of microscopic models of plasmas, with a parameter $\alpha$ 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 $\alpha$ 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.

Keywords:  Kinetic theory, particle systems, plasma models.
Mathematics Subject Classification:  Primary: 82B40, 82D10; Secondary: 60K35.

Received: August 2008;      Revised: April 2009;      Published: August 2009.