The Gyro-Kinetic Approximation : an attempt at explaining the method based on Darboux Algorithm and Lie Transform

Emmanuel Frenod (1, 2) , Mathieu Lutz (1, 3)

1 CALVI - Scientific computation and visualization
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
3 IRMA - Institut de Recherche Mathématique Avancée

This Proceeding presents the method that allows us to get the Gyro-Kinetic Approximation of the Dynamical System satisfied by the trajectory of a particle submitted to a Strong Magnetic Field. The goal of the method is to build a change of coordinates in order to make the dynamic of two components of the trajectory to disappear. This change of coordinates is based on a Darboux mathematical Algorithm and on a Lie Transform

Domaines: Analyse fonctionnelle [math.FA]; Géométrie symplectique [math.SG]; Physique mathématique [math-ph]; Physique des plasmas [physics.plasm-ph]

Emmanuel Frenod, Mathieu Lutz. The Gyro-Kinetic Approximation : an attempt at explaining the method based on Darboux Algorithm and Lie Transform. 2011. ⟨hal-00638657⟩