From liquid crystal models to the guiding-center theory of magnetized plasmas

TL;DR

This paper introduces a novel approach to guiding-center dynamics in magnetized plasmas by integrating liquid crystal theories and a rotation gauge field, simplifying derivations and offering new insights into particle motion.

Contribution

It presents a new perspective on guiding-center theory using a rotation gauge field inspired by liquid crystal models, simplifying the derivation process.

Findings

Derivation of guiding-center equations using a gauge field approach

Identification of a liquid crystal analogue in plasma physics

Simplification of higher-order gyrokinetic methods

Abstract

Upon combining Northrop's picture of charged particle motion with modern liquid crystal theories, this paper provides a new description of guiding center dynamics (to lowest order). This new perspective is based on a rotation gauge field (gyrogauge) that encodes rotations around the magnetic field. In liquid crystal theory, an analogue rotation field is used to encode the rotational state of rod-like molecules. Instead of resorting to sophisticated tools (e.g. Hamiltonian perturbation theory and Lie series expansions) that still remain essential in higher-order gyrokinetics, the present approach combines the WKB method with a simple kinematical ansatz, which is then replaced into the charged particle Lagrangian. The latter is eventually averaged over the gyrophase to produce Littlejohn's guiding-center equations. A crucial role is played by the vector potential for the gyrogauge field. A similar vector potential is related to liquid crystal defects and is known as `wryness tensor' in Eringen's micropolar theory.