dorsal/arxiv
View SchemaThe Breakdown of Alfven's Theorem in Ideal Plasma Flows
| Authors | Gregory L. Eyink, Hussein Aluie |
|---|---|
| Categories | |
| ArXiv ID | physics/0607073 |
| URL | https://arxiv.org/abs/physics/0607073 |
| DOI | 10.1016/j.physd.2006.08.009 |
Abstract
This paper presents both rigorous results and physical theory on the breakdown of magnetic flux conservation for ideal plasmas, by nonlinear effects. Our analysis is based upon an effective equation for magnetohydrodynamic (MHD) modes at length-scales $>\ell,$ with smaller scales eliminated, as in renormalization-group methodology. We prove that flux-conservation can be violated for an arbitrarily small length-scale $\ell,$ and in the absence of any non-ideality, but only if singular current sheets and vortex sheets both exist and intersect in sets of large enough dimension. This result gives analytical support to and rigorous constraints on theories of fast turbulent reconnection. Mathematically, our theorem is analogous to Onsager's result on energy dissipation anomaly in hydrodynamic turbulence. As a physical phenomenon, the breakdown of magnetic-flux conservation in ideal MHD is similar to the decay of magnetic flux through a narrow superconducting ring, by phase-slip of quantized flux lines. The effect should be observable both in numerical MHD simulations and in laboratory plasma experiments at moderately high magnetic Reynolds numbers.
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"abstract": "This paper presents both rigorous results and physical theory on the\nbreakdown of magnetic flux conservation for ideal plasmas, by nonlinear\neffects. Our analysis is based upon an effective equation for\nmagnetohydrodynamic (MHD) modes at length-scales $\u003e\\ell,$ with smaller scales\neliminated, as in renormalization-group methodology. We prove that\nflux-conservation can be violated for an arbitrarily small length-scale $\\ell,$\nand in the absence of any non-ideality, but only if singular current sheets and\nvortex sheets both exist and intersect in sets of large enough dimension. This\nresult gives analytical support to and rigorous constraints on theories of fast\nturbulent reconnection. Mathematically, our theorem is analogous to Onsager\u0027s\nresult on energy dissipation anomaly in hydrodynamic turbulence. As a physical\nphenomenon, the breakdown of magnetic-flux conservation in ideal MHD is similar\nto the decay of magnetic flux through a narrow superconducting ring, by\nphase-slip of quantized flux lines. The effect should be observable both in\nnumerical MHD simulations and in laboratory plasma experiments at moderately\nhigh magnetic Reynolds numbers.",
"arxiv_id": "physics/0607073",
"authors": [
"Gregory L. Eyink",
"Hussein Aluie"
],
"categories": [
"physics.plasm-ph",
"astro-ph",
"cond-mat.supr-con",
"physics.space-ph"
],
"doi": "10.1016/j.physd.2006.08.009",
"title": "The Breakdown of Alfven\u0027s Theorem in Ideal Plasma Flows",
"url": "https://arxiv.org/abs/physics/0607073"
},
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