2013/01/31 by J. Squire, H. Qin, W. M. Tang +1
Mathematics · Physics and Astronomy · #Casimir effect #Eulerian path #Gas Dynamics and Kinetic Theory #Hamiltonian (control theory) #Hamiltonian mechanics #Lagrangian #Legendre polynomials #Legendre transformation #Magnetic confinement fusion research #Nonlinear Waves and Solitons #Phase space #Principle of least action #Variational principle #math-ph #math.MP #physics.plasm-ph
paper · pdf · doi:10.1063/1.4791664
published as Phys. Plasmas 20, 022501 (2013) · 36 pages, 1 figure
openalex publication_date 2013/02/01 · arxiv created 2013/02/06 · arxiv updated 2013/02/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in H. Cendra et al., [J. Math. Phys. 39, 3138 (1998)]. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincaré theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.