Beatification: Flattening the Poisson Bracket for Two-Dimensional Fluid and Plasma Theories

Abstract

A perturbative method called beatification is presented for a class of two-dimensional fluid and plasma theories. The Hamiltonian systems considered, namely the Euler, Vlasov-Poisson, Hasegawa-Mima, and modified Hasegawa-Mima equations, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding the correct transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in 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.

16 pages

References in corpus (8)

• GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
• Variational integration for ideal magnetohydrodynamics with built-in advection equations
• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• Hamiltonian derivation of the Charney-Hasegawa-Mima equation
• Semiclassical propagator for SU(n) coherent states
• Derivation of reduced two-dimensional fluid models via Dirac's theory of constrained Hamiltonian systems
• Initial value representation for the SU(n) semiclassical propagator
• A Hamiltonian system for interacting Benjamin-Feir resonances

Cited by in corpus (2)

• Structure and structure-preserving algorithms for plasma physics
• Extended phase-space symplectic integration for electron dynamics