A guiding-center Fokker-Planck collision operator for nonuniform   magnetic fields
  A new formulation for collisional kinetic theory is presented based on the use of Lie-transform methods to eliminate fast orbital time scales from a general bilinear collision operator. As an application of this new formalism, a general guiding-center bilinear Fokker-Planck (FP) collision operator is derived following the elimination of the fast gyromotion time scale of a charged particle moving in a nonuniform magnetic field. It is expected that classical transport processes in a strongly magnetized nonuniform plasma can, thus, be described in terms of this reduced guiding-center FP kinetic theory. The present paper introduces the reduced-collision formalism only while its applications are left to future work. 
Alain J. Brizard