dorsal/arxiv
View SchemaAxisymmetric equilibria of a gravitating plasma with incompressible flows
| Authors | G. N. Throumoulopoulos, H. Tasso |
|---|---|
| Categories | |
| ArXiv ID | physics/0104072 |
| URL | https://arxiv.org/abs/physics/0104072 |
| DOI | 10.1080/03091920108203409 |
Abstract
It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. {\bf 82}, 2689 (1999)] are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime $\beta_0\approx \gamma_0\approx \delta_0 \approx\epsilon_0\ll 1$, where $\beta_0$, $\gamma_0$, $\delta_0$, and $\epsilon_0$ are related to the thermal, poloidal-current, flow and gravitating energies normalized to the poloidal-magnetic-field energy, respectively, and (b) in the high-energy regime $\beta_0\approx \gamma_0\approx \delta_0 \approx\epsilon_0\gg 1$. It turns out that in the high-energy regime all four forces, pressure-gradient, toroidal-magnetic-field, inertial, and gravitating contribute equally to the formation of magnetic surfaces very extended and localized about the symmetry plane such that the resulting equilibria resemble the accretion disks in astrophysics.
{
"annotation_id": "5abba0ab-0e2a-4516-b894-0f33d073a875",
"date_created": "2026-03-02T18:00:36.120000Z",
"date_modified": "2026-03-02T18:00:36.120000Z",
"file_hash": "928a7c2f190ceecb9fe6c1b20d7fe1347170805cfd50554d9a1a6da130b49e3c",
"private": false,
"record": {
"abstract": "It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric\ngravitating magnetically confined plasma with incompressible flows is governed\nby a second-order elliptic differential equation for the poloidal magnetic flux\nfunction containing five flux functions coupled with a Poisson equation for the\ngravitation potential, and an algebraic relation for the pressure. This set of\nequations is amenable to analytic solutions. As an application, the\nmagnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma\ncurrents derived recently by Krasheninnikov, Catto, and Hazeltine [Phys. Rev.\nLett. {\\bf 82}, 2689 (1999)] are extended to plasmas with finite poloidal\ncurrents, subject to gravitating forces from a massive body (a star or black\nhole) and inertial forces due to incompressible sheared flows. Explicit\nsolutions are obtained in two regimes: (a) in the low-energy regime\n$\\beta_0\\approx \\gamma_0\\approx \\delta_0 \\approx\\epsilon_0\\ll 1$, where\n$\\beta_0$, $\\gamma_0$, $\\delta_0$, and $\\epsilon_0$ are related to the thermal,\npoloidal-current, flow and gravitating energies normalized to the\npoloidal-magnetic-field energy, respectively, and (b) in the high-energy regime\n$\\beta_0\\approx \\gamma_0\\approx \\delta_0 \\approx\\epsilon_0\\gg 1$. It turns out\nthat in the high-energy regime all four forces, pressure-gradient,\ntoroidal-magnetic-field, inertial, and gravitating contribute equally to the\nformation of magnetic surfaces very extended and localized about the symmetry\nplane such that the resulting equilibria resemble the accretion disks in\nastrophysics.",
"arxiv_id": "physics/0104072",
"authors": [
"G. N. Throumoulopoulos",
"H. Tasso"
],
"categories": [
"physics.plasm-ph"
],
"doi": "10.1080/03091920108203409",
"title": "Axisymmetric equilibria of a gravitating plasma with incompressible flows",
"url": "https://arxiv.org/abs/physics/0104072"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "89967302-8b41-487a-9fe7-540b3c999869",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}