Guiding-centre Lagrangian and quasi-symmetry

Ted Jacobson

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arXiv · 2408.05919

Guiding-centre Lagrangian and quasi-symmetry

Ted Jacobson

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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.

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Ted Jacobson. 2024-08-12. Guiding-centre Lagrangian and quasi-symmetry. https://arxiv.org/abs/2408.05919

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