Hamiltonian canonical formulation of Hall-magnetohydrodynamics: Toward an application to weak turbulence theory

Hamiltonian formulations for the different levels of the fluid description of a plasma using the variational principle were presented. The equivalence of the obtained description in terms of the generalized-Clebsch variables to the familiar Newtonian formulation was also discussed. Results showed that each solution of the hamiltonian system was also a solution for the Newtonian one.