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

## 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.

- Authors:

- William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States)

- Publication Date:

- OSTI Identifier:
- 22600039

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COMPARATIVE EVALUATIONS; DENSITY; DISTRIBUTION; DISTRIBUTION FUNCTIONS; ELECTROMAGNETIC FIELDS; EQUATIONS; FIELD THEORIES; FLUID MECHANICS; HELICITY; LAGRANGIAN FUNCTION; PARTICLES; PLASMA; RELATIVISTIC RANGE; TRANSPORT THEORY

### Citation Formats

```
You, S.
```*A field theory approach to the evolution of canonical helicity and energy*. United States: N. p., 2016.
Web. doi:10.1063/1.4956465.

```
You, S.
```*A field theory approach to the evolution of canonical helicity and energy*. United States. doi:10.1063/1.4956465.

```
You, S. Fri .
"A field theory approach to the evolution of canonical helicity and energy". United States.
doi:10.1063/1.4956465.
```

```
@article{osti_22600039,
```

title = {A field theory approach to the evolution of canonical helicity and energy},

author = {You, S.},

abstractNote = {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.},

doi = {10.1063/1.4956465},

journal = {Physics of Plasmas},

number = 7,

volume = 23,

place = {United States},

year = {Fri Jul 15 00:00:00 EDT 2016},

month = {Fri Jul 15 00:00:00 EDT 2016}

}