  We formulate a finite-size particle numerical model of strongly magnetized
plasmas in the drift-kinetic approximation. We use the phase space action as an
alternative to previous variational formulations based on Low's Lagrangian or
on a Hamiltonian with a non-canonical Poisson bracket. The useful property of
this variational principle is that it allows independent transformations of
particle coordinates and velocities, i.e., transformations in particle phase
space. With such transformations, a finite degree-of-freedom drift-kinetic
action is obtained through time-averaging of the finite degree-of-freedom
fully-kinetic action. Variation of the drift-kinetic Lagrangian density leads
to a self-consistent, macro-particles and fields numerical model. Since the
computational particles utilize only guiding center coordinates and velocities,
there is a large computational advantage in the time integration part of the
algorithm. Numerical comparison between the time-averaged fully-kinetic and
drift-kinetic charge and current, deposited on a computational grid, offers
insight into the range of validity of the model. Being based on a variational
principle, the algorithm respects the energy conserving property of the
underlying continuous system. The development in this paper serves to further
emphasize the advantages of using variational approaches in plasma particle
simulations.
