dorsal/arxiv
View SchemaA comparison of incompressible limits for resistive plasmas
| Authors | B. F. McMillan, R. L. Dewar, R. G. Storer |
|---|---|
| Categories | |
| ArXiv ID | physics/0405002 |
| URL | https://arxiv.org/abs/physics/0405002 |
| DOI | 10.1088/0741-3335/46/7/003 |
| Journal | J. Plasma Fusion Res. SERIES 6, 40-44 (2004) |
Abstract
The constraint of incompressibility is often used to simplify the magnetohydrodynamic (MHD) description of linearized plasma dynamics because it does not affect the ideal MHD marginal stability point. In this paper two methods for introducing incompressibility are compared in a cylindrical plasma model: In the first method, the limit $\gamma \to \infty$ is taken, where $\gamma$ is the ratio of specific heats; in the second, an anisotropic mass tensor $\mathbf{\rho}$ is used, with the component parallel to the magnetic field taken to vanish, $\rho_{\parallel} \to 0$. Use of resistive MHD reveals the nature of these two limits because the Alfv\'en and slow magnetosonic continua of ideal MHD are converted to point spectra and moved into the complex plane. Both limits profoundly change the slow-magnetosonic spectrum, but only the second limit faithfully reproduces the resistive Alfv\'en spectrum and its wavemodes. In ideal MHD, the slow magnetosonic continuum degenerates to the Alfv\'en continuum in the first method, while it is moved to infinity by the second. The degeneracy in the first is broken by finite resistivity. For numerical and semi-analytical study of these models, we choose plasma equilibria which cast light on puzzling aspects of results found in earlier literature.
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"abstract": "The constraint of incompressibility is often used to simplify the\nmagnetohydrodynamic (MHD) description of linearized plasma dynamics because it\ndoes not affect the ideal MHD marginal stability point. In this paper two\nmethods for introducing incompressibility are compared in a cylindrical plasma\nmodel: In the first method, the limit $\\gamma \\to \\infty$ is taken, where\n$\\gamma$ is the ratio of specific heats; in the second, an anisotropic mass\ntensor $\\mathbf{\\rho}$ is used, with the component parallel to the magnetic\nfield taken to vanish, $\\rho_{\\parallel} \\to 0$. Use of resistive MHD reveals\nthe nature of these two limits because the Alfv\\\u0027en and slow magnetosonic\ncontinua of ideal MHD are converted to point spectra and moved into the complex\nplane. Both limits profoundly change the slow-magnetosonic spectrum, but only\nthe second limit faithfully reproduces the resistive Alfv\\\u0027en spectrum and its\nwavemodes. In ideal MHD, the slow magnetosonic continuum degenerates to the\nAlfv\\\u0027en continuum in the first method, while it is moved to infinity by the\nsecond. The degeneracy in the first is broken by finite resistivity. For\nnumerical and semi-analytical study of these models, we choose plasma\nequilibria which cast light on puzzling aspects of results found in earlier\nliterature.",
"arxiv_id": "physics/0405002",
"authors": [
"B. F. McMillan",
"R. L. Dewar",
"R. G. Storer"
],
"categories": [
"physics.plasm-ph"
],
"doi": "10.1088/0741-3335/46/7/003",
"journal_ref": "J. Plasma Fusion Res. SERIES 6, 40-44 (2004)",
"title": "A comparison of incompressible limits for resistive plasmas",
"url": "https://arxiv.org/abs/physics/0405002"
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