A gyro-gauge independent minimal guiding-center reduction by Lie-transforming the velocity vector field

Loïc de Guillebon (1, 2) , Michel Vittot (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - Ex E8 Dynamique non linéaire

We introduce a gyro-gauge independent formulation of a simplified guiding-center reduction, which removes the fast time-scale from particle dynamics by Lie-transforming the velocity vector field. This is close to Krylov-Bogoliubov method of averaging the equations of motion, although more geometric. At leading order, the Lie-transform consists in the generator of Larmor gyration, which can be explicitly inverted, while working with gauge-independent coordinates and operators, by using the physical gyro-angle as a (constrained) coordinate. This brings both the change of coordinates and the reduced dynamics of the minimal guiding-center reduction order by order in a Larmor radius expansion. The procedure is algorithmic and the reduction is systematically derived up to full second order, in a more straightforward way than when Lie-transforming the phase-space Lagrangian or averaging the equations of motion. The results write up some structures in the guiding-center expansion. Extensions and limitations of the method are considered.

Mots clés: guiding-center; Lie-transform; averaging; fast time-scale; Larmor radius expansion; gauge-independent coordinates

Domaines: Physique des plasmas [physics.plasm-ph]

Loïc de Guillebon, Michel Vittot. A gyro-gauge independent minimal guiding-center reduction by Lie-transforming the velocity vector field. Physics of Plasmas, 2013, 20, pp.082505. ⟨hal-00756763v2⟩