# Hamiltonian description of closed configurations of the vacuum magnetic field

## Abstract

Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov’ev, and V.D. Shafranov.

- Authors:

- National Research Centre Kurchatov Institute (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22472339

- Resource Type:
- Journal Article

- Journal Name:
- Plasma Physics Reports

- Additional Journal Information:
- Journal Volume: 41; Journal Issue: 5; Other Information: Copyright (c) 2015 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-780X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CLOSED CONFIGURATIONS; EV RANGE; HAMILTONIANS; MAGNETIC FIELD CONFIGURATIONS; MAGNETIC FIELDS; REVIEWS

### Citation Formats

```
Skovoroda, A. A., E-mail: skovoroda-aa@nrcki.ru.
```*Hamiltonian description of closed configurations of the vacuum magnetic field*. United States: N. p., 2015.
Web. doi:10.1134/S1063780X15050062.

```
Skovoroda, A. A., E-mail: skovoroda-aa@nrcki.ru.
```*Hamiltonian description of closed configurations of the vacuum magnetic field*. United States. doi:10.1134/S1063780X15050062.

```
Skovoroda, A. A., E-mail: skovoroda-aa@nrcki.ru. Fri .
"Hamiltonian description of closed configurations of the vacuum magnetic field". United States. doi:10.1134/S1063780X15050062.
```

```
@article{osti_22472339,
```

title = {Hamiltonian description of closed configurations of the vacuum magnetic field},

author = {Skovoroda, A. A., E-mail: skovoroda-aa@nrcki.ru},

abstractNote = {Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov’ev, and V.D. Shafranov.},

doi = {10.1134/S1063780X15050062},

journal = {Plasma Physics Reports},

issn = {1063-780X},

number = 5,

volume = 41,

place = {United States},

year = {2015},

month = {5}

}

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