Plasma Weak Turbulence Theory: From Bi-fluid To Hall-MHD, Hamiltonian Canonical Formulations

Details Plasma Weak Turbulence Theory: From Bi-fluid To Hall-MHD, Hamiltonian Canonical Formulations Plasma Weak Turbulence Theory: From Bi-fluid To Hall-MHD, Hamiltonian Canonical Formulations

Dec 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003agufmsm21b0215b&link_type=abstract

American Geophysical Union, Fall Meeting 2003, abstract #SM21B-0215

Statistics

Applications

2728 Magnetosheath, 2752 Mhd Waves And Instabilities, 3220 Nonlinear Dynamics, 7839 Nonlinear Phenomena, 7863 Turbulence

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Plasma Weak Turbulence Theory: From Bi-fluid To Hall-MHD, Hamiltonian Canonical Formulations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Plasma Weak Turbulence Theory: From Bi-fluid To Hall-MHD, Hamiltonian Canonical Formulations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Plasma Weak Turbulence Theory: From Bi-fluid To Hall-MHD, Hamiltonian Canonical Formulations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1648403