1301.6066 (J. Squire et al.)

The Hamiltonian structure and Euler-Poincaré formulation of the
Vlasov-Maxwell and gyrokinetic systems    [PDF]

J. Squire, H. Qin, W. M. Tang, C. Chandre

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. 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-Poincar\'{e} theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. [1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)

View original: http://arxiv.org/abs/1301.6066