Guiding-centre Lagrangian and quasi-symmetry

Abstract

A charged particle in a suitably strong magnetic field spirals along the field lines while slowly drifting transversely. This note provides a brief derivation of an effective Lagrangian formulation for the guiding-centre approximation that captures this dynamics without resolving the gyro motion. It also explains how the effective Lagrangian may, for special magnetic fields, admit a 'quasi-symmetry' which can give rise to a conserved quantity helpful for plasma confinement in fields lacking a geometric isometry. The aim of this note is to offer a pedagogical introduction and some perspectives on this well-established subject.

v2: 14 pages, substantially edited for clarity, discussion and references to the literature on quasi-symmetry and its stellarator design applications added, section on existence of flux surfaces added, title spelling changed, published version