  Following the method in Ref.(1), this paper introduces a fundamental
Lagrangian 1-form on the particle's coordinates, which determines the dynamics
of all ions and electrons of the magnetized plasma with low-frequency magnetic
perturbations. An Ampere-Vlasov model is utilized to model this fundamental
Lagrangian 1-form based on a kind of coarse-grained scheme. With the
Cary-Littlejohn single-parameter Lie transform method, a new fundamental
Lagrangian 1-form on the gyrocenter coordinates is derived through transforming
the one on particle's coordinates. This new 1-form determines the dynamics of
all ions and electrons on the gyrocenter coordinates. A new Ampere-Vlasov model
totally defined on the gyrocenter coordinates is developed to model the new
Lagrangian 1-form. By incorporating the electrostatic perturbation into the
Lagrangian 1-form, we eventually derived an Ampere-Poisson-Vlasov model defined
on the gyrocenter coordinates.
