  The purpose of this paper is to develop a simplified model as the modeling of
the magnetized plasmas. The starting point is an assumption that the
distribution of the ensemble of charged particles in the same species is
homogeneous over gyrophase. The particles in this ensemble are located at the
same guiding-cneter position $(\mathbf{X},\mu,U)$. Then, a fundamental
Lagrangian differential 1-form is developed. It contains all particles in the
magnetized plasma system as well as the Coulomb pair force between particles
instead of field-particle interaction used in conventional gyrokinetic models.
By transforming the Lagrangian 1-form to the new one on guiding-center
coordinate with the ensemble summation over gyrophase, the new fundamental
1-form is naturally independent of gyrophase of each particle based on the
homogeneous distribution over gyrophase, and it determines the dynamics of all
particles on the new coordinates. By using a coarse-grained scheme, this new
1-form can be modeled by the guiding-center kinetic model.
