Geometrical methods for reduced Hamiltonian models in plasma physics

Strongly magnetized fusion plasmas represent complex multi-scaled systems in space and time. Therefore, reduced models are mandatory for accessing fundamental physical mechanisms in a different regimes (e.g., turbulent, collisional) and geometry configurations. Since more than three decades now, reduced kinetic models like gyrokinetics, resulting from the elimination of the fast scales of motion associated with the particle rotation around magnetic field lines, are in the focus of intense research, both theoretical and numerical. First of all, because the gyrokinetic theory allows to exactly predict turbulent transport responsible for plasma deconfinement and second of all, since it allows a significant reduction of computational time for numerical simulations. Using geometrical methods and in particular Hamiltonian framework for derivation of reduced models allows to control consistency at each order of reduction procedure and to avoid appearance of unphysical terms. In addition to that, using Hamiltonian framework allows identifying exactly conserved quantities associated to the reduced model, which can be used as rigorous code diagnostics for energy consistency. In this talk derivation of the reduced kinetic models issued form the Lagrangian and Hamiltonian formalisms will be presented together with numerical results resuming implementation of exactly conserved properties.

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