dorsal/arxiv
View SchemaEquilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction
| Authors | M. -C. Firpo, F. Leyvraz, G. Attuel |
|---|---|
| Categories | |
| ArXiv ID | physics/0611082 |
| URL | https://arxiv.org/abs/physics/0611082 |
| DOI | 10.1063/1.2397039 |
Abstract
Under the conditions of weak Langmuir turbulence, a self-consistent wave-particle Hamiltonian models the effective nonlinear interaction of a spectrum of M waves with N resonant out-of-equilibrium tail electrons. In order to address its intrinsically nonlinear time-asymptotic behavior, a Monte Carlo code was built to estimate its equilibrium statistical mechanics in both the canonical and microcanonical ensembles. First the single wave model is considered in the cold beam/plasma instability and in the O'Neil setting for nonlinear Landau damping. O'Neil's threshold, that separates nonzero time-asymptotic wave amplitude states from zero ones, is associated to a second order phase transition. These two studies provide both a testbed for the Monte Carlo canonical and microcanonical codes, with the comparison with exact canonical results, and an opportunity to propose quantitative results to longstanding issues in basic nonlinear plasma physics. Then the properly speaking weak turbulence framework is considered through the case of a large spectrum of waves. Focusing on the small coupling limit, as a benchmark for the statistical mechanics of weak Langmuir turbulence, it is shown that Monte Carlo microcanonical results fully agree with an exact microcanonical derivation. The wave spectrum is predicted to collapse towards small wavelengths together with the escape of initially resonant particles towards low bulk plasma thermal speeds. This study reveals the fundamental discrepancy between the long-time dynamics of single waves, that can support finite amplitude steady states, and of wave spectra, that cannot.
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"abstract": "Under the conditions of weak Langmuir turbulence, a self-consistent\nwave-particle Hamiltonian models the effective nonlinear interaction of a\nspectrum of M waves with N resonant out-of-equilibrium tail electrons. In order\nto address its intrinsically nonlinear time-asymptotic behavior, a Monte Carlo\ncode was built to estimate its equilibrium statistical mechanics in both the\ncanonical and microcanonical ensembles. First the single wave model is\nconsidered in the cold beam/plasma instability and in the O\u0027Neil setting for\nnonlinear Landau damping. O\u0027Neil\u0027s threshold, that separates nonzero\ntime-asymptotic wave amplitude states from zero ones, is associated to a second\norder phase transition. These two studies provide both a testbed for the Monte\nCarlo canonical and microcanonical codes, with the comparison with exact\ncanonical results, and an opportunity to propose quantitative results to\nlongstanding issues in basic nonlinear plasma physics. Then the properly\nspeaking weak turbulence framework is considered through the case of a large\nspectrum of waves. Focusing on the small coupling limit, as a benchmark for the\nstatistical mechanics of weak Langmuir turbulence, it is shown that Monte Carlo\nmicrocanonical results fully agree with an exact microcanonical derivation. The\nwave spectrum is predicted to collapse towards small wavelengths together with\nthe escape of initially resonant particles towards low bulk plasma thermal\nspeeds. This study reveals the fundamental discrepancy between the long-time\ndynamics of single waves, that can support finite amplitude steady states, and\nof wave spectra, that cannot.",
"arxiv_id": "physics/0611082",
"authors": [
"M. -C. Firpo",
"F. Leyvraz",
"G. Attuel"
],
"categories": [
"physics.plasm-ph",
"physics.gen-ph"
],
"doi": "10.1063/1.2397039",
"title": "Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction",
"url": "https://arxiv.org/abs/physics/0611082"
},
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