# Modelling the Lagrangian of magnetized plasmas with low-frequency magnetic perturbations by a gyrokinetic Ampere-Poisson model

## TL;DR

This paper develops a gyrokinetic Ampere-Poisson model for magnetized plasmas with low-frequency magnetic perturbations, using a Lagrangian formalism and Lie transform methods to accurately describe plasma dynamics.

## Contribution

It introduces a novel gyrocenter Lagrangian framework and derives an Ampere-Poisson-Vlasov model incorporating electrostatic perturbations for magnetized plasmas.

## Key findings

- Derived a new gyrocenter Lagrangian 1-form.
- Developed an Ampere-Vlasov model on gyrocenter coordinates.
- Incorporated electrostatic perturbations into the model.

## Abstract

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.