Guiding-centre Lagrangian and quasi-symmetry

TL;DR

This paper derives an effective Lagrangian for guiding-centre motion in magnetic fields, highlighting quasi-symmetries that can lead to conserved quantities, aiding plasma confinement in complex magnetic geometries.

Contribution

It provides a pedagogical derivation of the guiding-centre Lagrangian and discusses quasi-symmetries that can exist without geometric isometries.

Findings

Effective Lagrangian captures guiding-centre dynamics.

Quasi-symmetries can produce conserved quantities.

Insights into plasma confinement in complex fields.

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.