dorsal/arxiv
View SchemaRigorous approach to the nonlinear saturation of the tearing mode in cylindrical and slab geometry
| Authors | N. Arcis, D. F. Escande, M. Ottaviani |
|---|---|
| Categories | |
| ArXiv ID | physics/0603204 |
| URL | https://arxiv.org/abs/physics/0603204 |
| DOI | 10.1063/1.2199208 |
Abstract
The saturation of the tearing mode instability is described within the standard framework of reduced magnetohydrodynamics (RMHD) in the case of an $r$-dependent or of a uniform resistivity profile. Using the technique of matched asymptotic expansions, where the perturbation parameter is the island width $w$, the problem can be solved in two ways: with the so-called flux coordinate method, which is based on the fact that the current profile is a flux function, and with a new perturbative method that does not use this property. The latter is applicable to more general situations where an external forcing or a sheared velocity profile are involved. The calculation provides a new relationship between the saturated island width and the $\Delta '$ stability parameter that involves a $\ln{w/w_{0}}$ term, where $w_{0}$ is a nonlinear scaling length that was missing in previous work. It also yields the modification of the equilibrium magnetic flux function.
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"abstract": "The saturation of the tearing mode instability is described within the\nstandard framework of reduced magnetohydrodynamics (RMHD) in the case of an\n$r$-dependent or of a uniform resistivity profile. Using the technique of\nmatched asymptotic expansions, where the perturbation parameter is the island\nwidth $w$, the problem can be solved in two ways: with the so-called flux\ncoordinate method, which is based on the fact that the current profile is a\nflux function, and with a new perturbative method that does not use this\nproperty. The latter is applicable to more general situations where an external\nforcing or a sheared velocity profile are involved. The calculation provides a\nnew relationship between the saturated island width and the $\\Delta \u0027$\nstability parameter that involves a $\\ln{w/w_{0}}$ term, where $w_{0}$ is a\nnonlinear scaling length that was missing in previous work. It also yields the\nmodification of the equilibrium magnetic flux function.",
"arxiv_id": "physics/0603204",
"authors": [
"N. Arcis",
"D. F. Escande",
"M. Ottaviani"
],
"categories": [
"physics.plasm-ph"
],
"doi": "10.1063/1.2199208",
"title": "Rigorous approach to the nonlinear saturation of the tearing mode in cylindrical and slab geometry",
"url": "https://arxiv.org/abs/physics/0603204"
},
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