dorsal/arxiv
View SchemaIdeal magnetohydrodynamic equilibria with helical symmetry and incompressible flows
| Authors | G. N. Throumoulopoulos, H. Tasso |
|---|---|
| Categories | |
| ArXiv ID | physics/9907004 |
| URL | https://arxiv.org/abs/physics/9907004 |
| DOI | 10.1017/S0022377899008041 |
Abstract
A recent study on axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas {\bf 5}, 2378 (1998)] is extended to the generic case of helically symmetric equilibria with incompressible flows. It is shown that the equilibrium states of the system under consideration are governed by an elliptic partial differential equation for the helical magnetic flux function $\psi$ containing five surface quantities along with a relation for the pressure. The above mentioned equation can be transformed to one possessing differential part identical in form to the corresponding static equilibrium equation, which is amenable to several classes of analytic solutions. In particular, equilibria with electric fields perpendicular to the magnetic surfaces and non-constant-Mach-number flows are constructed. Unlike the case in axisymmetric equilibria with isothermal magnetic surfaces, helically symmetric $T=T(\psi)$ equilibria are over-determined, i.e., in this case the equilibrium equations reduce to a set of eight ordinary differential equations with seven surface quantities. In addition, it is proved the non-existence of incompressible helically symmetric equilibria with (a) purely helical flows (b) non-parallel flows with isothermal magnetic surfaces and the magnetic field modulus being a surface quantity (omnigenous equilibria).
{
"annotation_id": "cc53307e-c53f-46fb-b98b-6a147436525e",
"date_created": "2026-03-02T18:01:24.586000Z",
"date_modified": "2026-03-02T18:01:24.586000Z",
"file_hash": "8f5d5da8bbb877dc23c9dcc66a9438decb7cab258a768dab7312091087dd159a",
"private": false,
"record": {
"abstract": "A recent study on axisymmetric ideal magnetohydrodynamic equilibria with\nincompressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas {\\bf\n5}, 2378 (1998)] is extended to the generic case of helically symmetric\nequilibria with incompressible flows. It is shown that the equilibrium states\nof the system under consideration are governed by an elliptic partial\ndifferential equation for the helical magnetic flux function $\\psi$ containing\nfive surface quantities along with a relation for the pressure. The above\nmentioned equation can be transformed to one possessing differential part\nidentical in form to the corresponding static equilibrium equation, which is\namenable to several classes of analytic solutions. In particular, equilibria\nwith electric fields perpendicular to the magnetic surfaces and\nnon-constant-Mach-number flows are constructed. Unlike the case in axisymmetric\nequilibria with isothermal magnetic surfaces, helically symmetric $T=T(\\psi)$\nequilibria are over-determined, i.e., in this case the equilibrium equations\nreduce to a set of eight ordinary differential equations with seven surface\nquantities. In addition, it is proved the non-existence of incompressible\nhelically symmetric equilibria with (a) purely helical flows (b) non-parallel\nflows with isothermal magnetic surfaces and the magnetic field modulus being a\nsurface quantity (omnigenous equilibria).",
"arxiv_id": "physics/9907004",
"authors": [
"G. N. Throumoulopoulos",
"H. Tasso"
],
"categories": [
"physics.plasm-ph"
],
"doi": "10.1017/S0022377899008041",
"title": "Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows",
"url": "https://arxiv.org/abs/physics/9907004"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "36147ae2-a86e-47d6-b0c1-fe72954455b7",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}