A field theory approach to the evolution of canonical helicity and energy

TL;DR

This paper introduces a unified field theory framework for plasma and fluid dynamics that links canonical helicity evolution with energy changes across classical and relativistic regimes.

Contribution

It reformulates the governing equations using a generalized Lagrangian that incorporates coupling terms and relativistic effects, unifying single-particle, kinetic, and fluid descriptions.

Findings

Canonical helicity transport applies across regimes

Helicity change is less than energy change under certain conditions

The theory provides a basis for comparing helicity and energy dynamics

Abstract

A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.