Equations of plasma physics ultimately derive their Hamiltonian and action principle forms from those of Maxwell's equations self-consistently coupled to charged particle dynamics. The forms vary depending on the model (e.g. kinetic or fluid) and the variables (e.g. Eulerian, Lagrangian, or Clebsch) used for plasma description, and this has been a source of confusion and rediscovery (see e.g. [1,2] for review). In the past 25 years there has been extensive research on the Hamiltonian and action principle formulations of plasma equations. The various formulations will be reviewed and their interconnections explored. Recent advances in the use of these formulations for describing a variety of plasma phenomena will be discussed. Topics may include: a) Reduced Fluid Models, their derivation and classification for tokamak models with gyroviscosity, ITG, ETG, etc; b) Hamiltonian Closure Theory, obtaining exact and inexact fluid models from kinetic theory; c) Fluctuation Spectra, their derivation by statistical mechanics principles for fluid and Vlasov turbulence; d) Hamiltonian Simulated Annealing, the use of Poisson brackets in a numerical relaxation method for calculating coherent structures; and e) Single and Multi-wave Models, their derivation and application to beam-plasma interaction.
[1] P. J. Morrison, Rev. Mod. Phys., vol. 70 , 467 (1998)
[2] H. Ye and P. J. Morrison, Phys. Fluids B, vol. 4, 771 (1992).