Beatification: Flattening Poisson brackets for plasma theory and computation

A perturbative method called beatification$^{\dagger}$ is presented for producing nonlinear Hamiltonian fluid and plasma theories. Plasma Hamiltonian theories, fluid and kinetic, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding a transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in the phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables. Examples will be given. \\ $\dagger$ P.~J.~Morrison and J.~Vanneste, Ann.~Phys.~{\bf 368}, 117 (2016); T.~F.~Viscondi, I.~L.~Caldas, and P.~J.~Morrison, Phys.~Plasmas {\bf24}, 032102 (2017); J.\ Phys.~A {\bf49}, 165501 (2016).