# 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 also 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:

- Univ. of Washington, Seattle, WA (United States). William E. Boeing Dept. of Aeronautics and Astronautics

- Publication Date:

- Research Org.:
- Univ. of Washington, Seattle, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1467837

- Alternate Identifier(s):
- OSTI ID: 1261217

- Grant/Contract Number:
- SC0010340

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 7; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; self organized systems; Maxwell equations; Lagrangian mechanics; equations of motion; magnetic fluids; vortex dynamics; enthalpy; fluid equations; magnetohydrodynamic equations; magnetic fields

### 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. Mon .
"A field theory approach to the evolution of canonical helicity and energy". United States.
doi:10.1063/1.4956465. https://www.osti.gov/servlets/purl/1467837.
```

```
@article{osti_1467837,
```

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 also 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 = {Mon Jul 11 00:00:00 EDT 2016},

month = {Mon Jul 11 00:00:00 EDT 2016}

}

*Citation information provided by*

Web of Science

Web of Science