2012/04/19 by Loïc de Guillebon, Loïc De Guillebon, C. Chandré +1 · 13 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Classical mechanics #Fluid Dynamics and Turbulent Flows #Hamiltonian (control theory) #High-pressure geophysics and materials #Jacobi identity #Kinetic energy #Lie algebra #Mathematical physics #Nonlinear Waves and Solitons #Physics #Plasma #Plasma modeling #Poisson algebra #Poisson bracket #Poisson distribution #Poisson's equation #Quantum mechanics #Vlasov equation #nlin.CD #physics.plasm-ph
paper · pdf · doi:10.1016/j.physleta.2012.07.031
published in Physics Letters A 376(45), 3172-3176 (Elsevier BV)
arxiv created 2012/04/19 · openalex publication_date 2012/08/04 · arxiv updated 2012/10/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.