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Plasma modelling and numerical simulations

1. Modelling of hot plasmas:

  • Relativistic plasma model: single particle vs. collective effects; N body problem; Scaling laws in plasmas.
  • Magnetohydrodynamics (MHD) cold plasma models; Link between hydrodynamic model and the Vlasov model: The Water-Bag model; MHD model and scaling laws.
  • Solving Vlasov-Poisson equations (electrostatic case); particular or Lagrangian methods, Particles-In-Cell(PIC) codes; direct method or development of Vlasov codes; Time-splitting Technique; Advection and Semi-Lagrangian codes; problem of filamentation of the distribution function in phase space, and conservation of the entropy.
  • Vlasov-Maxwell Model: Treatment of the relativistic Vlasov equation; Invariance of the transverse canonical moments; Application to 'laser-plasma interaction, stimulated Raman scattering; comparison with the fluids methods, multiple time scale; Manley-Rowe Invariants

2. Modelling of cold plasmas:

  • Introduction;
  • Collisions in the BBGKY hierarchy, Boltzmann equation and the microscopic approach, Equations of moments and the macroscopic approach, particle methods (PIC and FPM);
  • Plasma-surface interactions phenomena; examples for models of reactive plasmas.
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Université de Lorraine, Nancy, France