Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction
- Laboratoire de Physique et Technologie des Plasmas (CNRS UMR 7648), Ecole Polytechnique, 91128 Palaiseau cedex (France)
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, which separates nonzero time-asymptotic wave amplitude states from zero ones, is associated with 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, which can support finite amplitude steady states, and of wave spectra, which cannot.
- OSTI ID:
- 20860426
- Journal Information:
- Physics of Plasmas, Vol. 13, Issue 12; Other Information: DOI: 10.1063/1.2397039; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
AMPLITUDES
BEAM-PLASMA SYSTEMS
BENCHMARKS
COMPARATIVE EVALUATIONS
COUPLING
ELECTRON BEAMS
EQUILIBRIUM
HAMILTONIANS
LANDAU DAMPING
MONTE CARLO METHOD
NONLINEAR PROBLEMS
PHASE TRANSFORMATIONS
PLASMA
PLASMA INSTABILITY
PLASMA SIMULATION
STATISTICAL MECHANICS
STEADY-STATE CONDITIONS
TAIL ELECTRONS
TURBULENCE