Guiding-centre Lagrangian and quasi-symmetry

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...

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Bibliographic Details
Published inJournal of plasma physics Vol. 91; no. 2
Main Author Jacobson, Ted
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 31.03.2025
Subjects
Approximation
Charged particles
Energy
Magnetic fields
Plasma control
Symmetry
Tutorial
Velocity
plasma confinement
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ISSN0022-3778
1469-7807
1469-7807
DOI10.1017/S0022377825000133

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Summary: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.
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ISSN:0022-3778
1469-7807
1469-7807
DOI:10.1017/S0022377825000133