dorsal/arxiv
View SchemaStatistical characterization of the interchange-instability spectrum of a separable ideal-magnetohydrodynamic model system
| Authors | R. L. Dewar, T. Tatsuno, Z. Yoshida, C. Nuehrenberg, B. F. McMillan |
|---|---|
| Categories | |
| ArXiv ID | physics/0405095 |
| URL | https://arxiv.org/abs/physics/0405095 |
| DOI | 10.1103/PhysRevE.70.066409 |
| Journal | Phys. Rev. E, 70, 066409 (2004) |
Abstract
A Suydam-unstable circular cylinder of plasma with periodic boundary conditions in the axial direction is studied within the approximation of linearized ideal magnetohydrodynamics (MHD). The normal mode equations are completely separable, so both the toroidal Fourier harmonic index n and the poloidal index m are good quantum numbers. The full spectrum of eigenvalues for m in the range 1 to m_max is analyzed quantitatively, using asymptotics for large m, numerics for all m, and graphics for qualitative understanding. The density of eigenvalues scales like the square of m_max for large m_max. Because finite-m corrections scale inversely as the square of m_max, their inclusion is essential in order to obtain the correct statistics for the distribution of eigenvalues. Near the largest growth rate only a single radial eigenmode contributes to the spectrum, so the eigenvalues there depend only on m and n, as in a two-dimensional system. However, unlike the generic separable two-dimensional system, the statistics of the ideal-MHD spectrum departs somewhat from the Poisson distribution, even for arbitrarily large m_max. This departure from Poissonian statistics may be understood qualitatively from the nature of the distribution of rational numbers in the rotational transform profile.
{
"annotation_id": "0e749803-cb73-4619-ab69-8e68ccb76622",
"date_created": "2026-03-02T18:00:49.939000Z",
"date_modified": "2026-03-02T18:00:49.939000Z",
"file_hash": "9493c03ffca3a7532d2ff4e1df516289e44608009be769dfe1d450513ef4bf6a",
"private": false,
"record": {
"abstract": "A Suydam-unstable circular cylinder of plasma with periodic boundary\nconditions in the axial direction is studied within the approximation of\nlinearized ideal magnetohydrodynamics (MHD). The normal mode equations are\ncompletely separable, so both the toroidal Fourier harmonic index n and the\npoloidal index m are good quantum numbers. The full spectrum of eigenvalues for\nm in the range 1 to m_max is analyzed quantitatively, using asymptotics for\nlarge m, numerics for all m, and graphics for qualitative understanding. The\ndensity of eigenvalues scales like the square of m_max for large m_max. Because\nfinite-m corrections scale inversely as the square of m_max, their inclusion is\nessential in order to obtain the correct statistics for the distribution of\neigenvalues. Near the largest growth rate only a single radial eigenmode\ncontributes to the spectrum, so the eigenvalues there depend only on m and n,\nas in a two-dimensional system. However, unlike the generic separable\ntwo-dimensional system, the statistics of the ideal-MHD spectrum departs\nsomewhat from the Poisson distribution, even for arbitrarily large m_max. This\ndeparture from Poissonian statistics may be understood qualitatively from the\nnature of the distribution of rational numbers in the rotational transform\nprofile.",
"arxiv_id": "physics/0405095",
"authors": [
"R. L. Dewar",
"T. Tatsuno",
"Z. Yoshida",
"C. Nuehrenberg",
"B. F. McMillan"
],
"categories": [
"physics.plasm-ph",
"nlin.CD",
"quant-ph"
],
"doi": "10.1103/PhysRevE.70.066409",
"journal_ref": "Phys. Rev. E, 70, 066409 (2004)",
"title": "Statistical characterization of the interchange-instability spectrum of a separable ideal-magnetohydrodynamic model system",
"url": "https://arxiv.org/abs/physics/0405095"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b1d08990-2b72-4047-80f5-74353b56e47f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}