Kinetic Theory for Plasmas and Wave-Particle Hamiltonian Dynamics

  • Yves Elskens
Part of the Lecture Notes in Physics book series (LNP, volume 602)


The plasma limit is characterized by the fact that a particle interacts with many partners. The dynamics leads to the Vlasov equation in the mean-field limit. Collective behaviour in the N-body system is naturally described by M \( M{\mathbf{ }} \ll {\mathbf{ }}\mathcal{N} \) N wavelike degrees of freedom, which behave as harmonic oscillator interacting with a population of N \( N{\mathbf{ }} \ll {\mathbf{ }}\mathcal{N} \) N particles. The self-consistent hamiltonian dynamics with M waves is also mean-field for the N particles, and a Vlasov equation applies for N → ∞. The careful understanding of the limit N → ∞ requires taking into account a continuous spectrum of singular excitations of van Kampen-Case type. For M → ∞, the motion of a single particle obeys a Fokker-Planck equation in the strong resonance overlap limit, and the full particle-wave system obeys the quasilinear evolution equations in the weak turbulence regime.


Kinetic Theory Vlasov Equation Langmuir Wave Hamiltonian Dynamic Chaotic Regime 
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© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Yves Elskens
    • 1
  1. 1.Equipe turbulence plasmaUMR 6633 CNRS-Université de ProvenceMarseille cedex 20

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