# Variational formulation of the Gardner's restacking algorithm

## Abstract

The incompressibility of the phase flow of Hamiltonian wave-plasma interactions restrains the class of realizable wave-driven transformations of the particle distribution. After the interaction, the distribution remains composed of the original phase-space elements, or local densities, which are only rearranged (''restacked'') by the wave. A variational formalism is developed to study the corresponding limitations on the energy and momentum transfer. A case of particular interest is a toroidal plasma immersed in a dc magnetic field. The restacking algorithm by Gardner [Phys. Fluids 6, 839 (1963)] is formulated precisely. The minimum energy state for a plasma with a given current is determined

- Authors:

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab., Princeton, NJ (US)

- Sponsoring Org.:
- USDOE Office of Science (SC) (US)

- OSTI Identifier:
- 827920

- Report Number(s):
- PPPL-3946

TRN: US0403734

- DOE Contract Number:
- AC02-76CH03073

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 26 Apr 2004

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALGORITHMS; DISTRIBUTION; HAMILTONIANS; MAGNETIC FIELDS; MOMENTUM TRANSFER; PHASE SPACE; PLASMA; TRANSFORMATIONS; HAMILTONIAN; MAPPING; MATHEMATICAL PHYSICS

### Citation Formats

```
I.Y. Dodin, and N.J. Fisch.
```*Variational formulation of the Gardner's restacking algorithm*. United States: N. p., 2004.
Web. doi:10.2172/827920.

```
I.Y. Dodin, & N.J. Fisch.
```*Variational formulation of the Gardner's restacking algorithm*. United States. doi:10.2172/827920.

```
I.Y. Dodin, and N.J. Fisch. Mon .
"Variational formulation of the Gardner's restacking algorithm". United States. doi:10.2172/827920. https://www.osti.gov/servlets/purl/827920.
```

```
@article{osti_827920,
```

title = {Variational formulation of the Gardner's restacking algorithm},

author = {I.Y. Dodin and N.J. Fisch},

abstractNote = {The incompressibility of the phase flow of Hamiltonian wave-plasma interactions restrains the class of realizable wave-driven transformations of the particle distribution. After the interaction, the distribution remains composed of the original phase-space elements, or local densities, which are only rearranged (''restacked'') by the wave. A variational formalism is developed to study the corresponding limitations on the energy and momentum transfer. A case of particular interest is a toroidal plasma immersed in a dc magnetic field. The restacking algorithm by Gardner [Phys. Fluids 6, 839 (1963)] is formulated precisely. The minimum energy state for a plasma with a given current is determined},

doi = {10.2172/827920},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Apr 26 00:00:00 EDT 2004},

month = {Mon Apr 26 00:00:00 EDT 2004}

}

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