Charged particle motion in weakly varying electromagnetic fields: A   multi-scale approach
  The motion of charged particles in weakly varying electromagnetic fields is described using a perturbation method. This provides a systematic and physically transparent description of the particle motion on fast and slow spatio-temporal scales, associated with gyration and drift motions, respectively. A detailed discussion is given of the guiding center concept and the non-inertial frame of reference. An algebraic expression is obtained for the drift motion across the magnetic field, while a differential equation describes the particle motion along the field. The fictitious forces and associated energy transfer between gyration and drift motion parallel and perpendicular to the magnetic field are described. The relation between conservation of magnetic moment and angular momentum is elucidated. 
D. S. Sortland and O. E. Garcia
physics.plasm-ph