The Maxwell-Boltzmann approximation for ion kinetic modeling
  This paper aims to justify the Maxwell-Boltzmann approximation for electrons, preserving the dynamics of ions at the kinetic level. Under sufficient regularity assumption, we provide a precise scaling where the Maxwell-Boltzmann approximation is obtained. In addition, we prove that the reduced ions problem is well-posed globally in time. 
Claude Bardos and Fran\c{c}ois Golse and Toan T. Nguyen and R\'emi   Sentis
math.AP math-ph math.MP