dorsal/arxiv
View SchemaOn resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow
| Authors | G. N. Throumoulopoulos, H. Tasso |
|---|---|
| Categories | |
| ArXiv ID | physics/0009081 |
| URL | https://arxiv.org/abs/physics/0009081 |
| DOI | 10.1017/S0022377800008849 |
Abstract
It is shown that the magnetohydrodynamic equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal magnetic flux function $\psi$ coupled with a Bernoulli type equation for the plasma density (which are identical in form to the corresponding ideal MHD equilibrium equations) along with the relation $\Delta^\star \psi=V_c \sigma$. (Here, $\Delta^\star$ is the Grad-Schl\"{u}ter-Shafranov operator, $\sigma$ is the conductivity and $V_c$ is the constant toroidal-loop voltage divided by $2 \pi $). In particular, for incompressible flows the above mentioned partial differential equation becomes elliptic and decouples from the Bernoulli equation [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas {\bf 5}, 2378 (1998)]. For a conductivity of the form $\sigma=\sigma(R, \psi)$ ($R$ is the distance from the axis of symmetry) several classes of analytic equilibria with incompressible flows can be constructed having qualitatively plausible $\sigma$ profiles, i.e. profiles with $\sigma$ taking a maximum value close to the magnetic axis and a minimum value on the plasma surface. For $\sigma=\sigma(\psi)$ consideration of the relation $\Delta^\star\psi = V_c \sigma(\psi)$ in the vicinity of the magnetic axis leads therein to a proof of the non-existence of either compressible or incompressible equilibria. This result can be extended to the more general case of non-parallel flows lying within the magnetic surfaces.
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"abstract": "It is shown that the magnetohydrodynamic equilibrium states of an\naxisymmetric toroidal plasma with finite resistivity and flows parallel to the\nmagnetic field are governed by a second-order partial differential equation for\nthe poloidal magnetic flux function $\\psi$ coupled with a Bernoulli type\nequation for the plasma density (which are identical in form to the\ncorresponding ideal MHD equilibrium equations) along with the relation\n$\\Delta^\\star \\psi=V_c \\sigma$. (Here, $\\Delta^\\star$ is the\nGrad-Schl\\\"{u}ter-Shafranov operator, $\\sigma$ is the conductivity and $V_c$ is\nthe constant toroidal-loop voltage divided by $2 \\pi $). In particular, for\nincompressible flows the above mentioned partial differential equation becomes\nelliptic and decouples from the Bernoulli equation [H. Tasso and G. N.\nThroumoulopoulos, Phys. Plasmas {\\bf 5}, 2378 (1998)]. For a conductivity of\nthe form $\\sigma=\\sigma(R, \\psi)$ ($R$ is the distance from the axis of\nsymmetry) several classes of analytic equilibria with incompressible flows can\nbe constructed having qualitatively plausible $\\sigma$ profiles, i.e. profiles\nwith $\\sigma$ taking a maximum value close to the magnetic axis and a minimum\nvalue on the plasma surface. For $\\sigma=\\sigma(\\psi)$ consideration of the\nrelation $\\Delta^\\star\\psi = V_c \\sigma(\\psi)$ in the vicinity of the magnetic\naxis leads therein to a proof of the non-existence of either compressible or\nincompressible equilibria. This result can be extended to the more general case\nof non-parallel flows lying within the magnetic surfaces.",
"arxiv_id": "physics/0009081",
"authors": [
"G. N. Throumoulopoulos",
"H. Tasso"
],
"categories": [
"physics.plasm-ph"
],
"doi": "10.1017/S0022377800008849",
"title": "On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow",
"url": "https://arxiv.org/abs/physics/0009081"
},
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