dorsal/arxiv
View SchemaEuler potentials for the MHD Kamchatnov-Hopf soliton solution
| Authors | Vladimir S. Semenov, Daniil B. Korovinski, Helfried K. Biernat |
|---|---|
| Categories | |
| ArXiv ID | physics/0111212 |
| URL | https://arxiv.org/abs/physics/0111212 |
| DOI | 10.5194/npg-9-347-2002 |
Abstract
In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invariant of the mapping of a 3D sphere into a 2D sphere; it can have arbitrary helicity depending on control parameters. It is shown how to define Euler potentials globally. The singular curve of the Euler potential plays the key role in computing helicity. With the introduction of Euler potentials, the helicity can be calculated as an integral over the surface bounded by this singular curve. A special programme for visualization is worked out. Helicity coordinates are introduced which can be useful for numerical simulations where helicity control is needed.
{
"annotation_id": "468e038b-9107-4db5-b158-5b5098f22519",
"date_created": "2026-03-02T18:00:39.550000Z",
"date_modified": "2026-03-02T18:00:39.550000Z",
"file_hash": "986c945a376425b63a8dafb97d811274cea624f737180e2054ccbec6ecac04c4",
"private": false,
"record": {
"abstract": "In the MHD description of plasma phenomena the concept of magnetic helicity\nturns out to be very useful. We present here an example of introducing Euler\npotentials into a topological MHD soliton which has non-trivial helicity. The\nMHD soliton solution (Kamchatnov, 1982) is based on the Hopf invariant of the\nmapping of a 3D sphere into a 2D sphere; it can have arbitrary helicity\ndepending on control parameters. It is shown how to define Euler potentials\nglobally. The singular curve of the Euler potential plays the key role in\ncomputing helicity. With the introduction of Euler potentials, the helicity can\nbe calculated as an integral over the surface bounded by this singular curve. A\nspecial programme for visualization is worked out. Helicity coordinates are\nintroduced which can be useful for numerical simulations where helicity control\nis needed.",
"arxiv_id": "physics/0111212",
"authors": [
"Vladimir S. Semenov",
"Daniil B. Korovinski",
"Helfried K. Biernat"
],
"categories": [
"physics.plasm-ph",
"physics.space-ph"
],
"doi": "10.5194/npg-9-347-2002",
"title": "Euler potentials for the MHD Kamchatnov-Hopf soliton solution",
"url": "https://arxiv.org/abs/physics/0111212"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "9cb6bb52-d4ef-42d4-b501-eddc8aa1934a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}