HR: 0830h
AN: SM21B-0215    [PDF]
TI: Plasma Weak Turbulence Theory: From Bi-fluid To Hall-MHD, Hamiltonian Canonical Formulations
AU: Belmont, g
EM: gerard.belmont@cetp.ipsl.fr
AF: CETP/CNRS-IPSL, 10-12 avenue de l'Europe, Velizy, 78140 France
AU: * Sahraoui, F
EM: fouad.sahraoui@cetp.ipsl.fr
AF: CETP/CNRS-IPSL, 10-12 avenue de l'Europe, Velizy, 78140 France
AU: Rezeau, L
EM: laurence.rezeau@cetp.ipsl.fr
AF: CETP/CNRS-IPSL, 10-12 avenue de l'Europe, Velizy, 78140 France
AB: The different levels of description of fluid media (e.g. MHD, Hall-MHD, bi-fluid,...) are commonly known under the form of Newtonian systems of equations. Nevertheless, this form proves to be in general inconvenient for applying some general mathematical treatments such as deriving the so-called "weak (or wave) turbulence theories" of these media. We show that the Hamiltonian formalism is the most powerful mathematical frame for such studies. We therefore look for Hamiltonian formulations for the different levels of the fluid description of a plasma, using the variational principle with the appropriate Lagrangian invariants. Starting from the bi-fluid system, we show that such a formulation can be obtained by combining the Lagrangians already used for describing: i) the motion of a charged particle in an electromagnetic field; ii) the evolution of an electromagnetic field in presence of sources; iii) the motion of a neutral fluid (Clebsch variables). The result is obtained in terms of generalized-Clebsch variables. Reducing this bi-fluid Hamiltonian formulation to lower orders of the fluid approximations is then shown to be mandatory to obtain analytical results for linear waves and non linear wave-wave couplings. We show how this goal can be reached in two steps, leading to: i) a "Reduced Bi-Fluid" system, with the displacement current neglected and ii) the Hall-MHD system, with the electron mass neglected. We show that the only generalized Clebsch variables of each species are sufficient to describe the full Hall-MHD dynamics. Some future applications of such a powerful formalism are outlined.
DE: 2728 Magnetosheath
DE: 2752 MHD waves and instabilities
DE: 3220 Nonlinear dynamics
DE: 7839 Nonlinear phenomena
DE: 7863 Turbulence
SC: SPA - Magnetospheric Physics [SM]
MN: 2003 Fall Meeting