## Hamiltonian structure of the guiding center plasma model

## Abstract

The guiding center plasma model (also known as kinetic MHD) is a rigorous sub-cyclotron-frequency closure of the Vlasov-Maxwell system. While the model has been known for decades and it plays a fundamental role in describing the physics of strongly magnetized collisionless plasmas, its Hamiltonian structure has never been found. We provide explicit expressions for the model's Poisson bracket and Hamiltonian and thereby prove that the model is an infinite-dimensional Hamiltonian system. The bracket is derived in a manner which ensures that it satisfies the Jacobi identity. We also report on several previously unknown circulation theorems satisfied by the guiding center plasma model. Without knowledge of the Hamiltonian structure, these circulation theorems would be difficult to guess.

- Authors:

- Courant Institute of Mathematical Sciences, New York, New York 10012, USA

- Publication Date:

- Research Org.:
- New York Univ. (NYU), NY (United States); Oak Ridge Associated Univ., Oak Ridge, TN (United States)

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

- OSTI Identifier:
- 1540153

- Grant/Contract Number:
- FG02-86ER53223; AC05-06OR23100

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 2; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Physics

### Citation Formats

```
Burby, J. W., and Sengupta, W. Hamiltonian structure of the guiding center plasma model. United States: N. p., 2018.
Web. doi:10.1063/1.5016453.
```

```
Burby, J. W., & Sengupta, W. Hamiltonian structure of the guiding center plasma model. United States. doi:10.1063/1.5016453.
```

```
Burby, J. W., and Sengupta, W. Thu .
"Hamiltonian structure of the guiding center plasma model". United States. doi:10.1063/1.5016453. https://www.osti.gov/servlets/purl/1540153.
```

```
@article{osti_1540153,
```

title = {Hamiltonian structure of the guiding center plasma model},

author = {Burby, J. W. and Sengupta, W.},

abstractNote = {The guiding center plasma model (also known as kinetic MHD) is a rigorous sub-cyclotron-frequency closure of the Vlasov-Maxwell system. While the model has been known for decades and it plays a fundamental role in describing the physics of strongly magnetized collisionless plasmas, its Hamiltonian structure has never been found. We provide explicit expressions for the model's Poisson bracket and Hamiltonian and thereby prove that the model is an infinite-dimensional Hamiltonian system. The bracket is derived in a manner which ensures that it satisfies the Jacobi identity. We also report on several previously unknown circulation theorems satisfied by the guiding center plasma model. Without knowledge of the Hamiltonian structure, these circulation theorems would be difficult to guess.},

doi = {10.1063/1.5016453},

journal = {Physics of Plasmas},

number = 2,

volume = 25,

place = {United States},

year = {2018},

month = {2}

}

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