  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.
