Hamiltonian structure of reduced fluid models for plasmas obtained from a kinetic description

Loïc de Guillebon (1, 2) , Cristel Chandre (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - Ex E8 Dynamique non linéaire

We consider the Hamiltonian structure of reduced fluid models obtained from a kinetic description of collisionless plasmas by Vlasov-Maxwell equations. We investigate the possibility of finding Poisson subalgebras associated with fluid models starting from the Vlasov-Maxwell Poisson algebra. In this way, we show that the only possible Poisson subalgebra involves the moments of zeroth and first order of the Vlasov distribution, meaning the fluid density and the fluid velocity. We find that the bracket derived in [Phys. Rev. Lett. 93, 175002 (2004)] which involves moments of order 2 is not a Poisson bracket since it does not satisfy the Jacobi identity.

Keywords: Hamiltonian systems; plasma physics; fluid reduction; Jacobi identity

Domains: Plasma Physics [physics.plasm-ph]; Chaotic Dynamics [nlin.CD]; Dynamical Systems [math.DS]

Loïc de Guillebon, Cristel Chandre. Hamiltonian structure of reduced fluid models for plasmas obtained from a kinetic description. Physics Letters A, 2012, 376 (45), pp.3172. ⟨10.1016/j.physleta.2012.07.031⟩. ⟨hal-00689111⟩