Canonical Hamiltonian Model of Reduced MHD and its Comparison with the Two-Dimensional Euler System

While expressing the ideal fluid/plasma equations in terms of Eulerian variables, we encounter a noncanonical Hamiltonian structure. In other words, Poisson operators determining symplectic geometry have nontrivial kernels that foliate phase spaces. There are several different recipes for “canonicalizing” such Hamiltonian formalisms by either reducing or extending phase spaces. Clebsch parametrization is a well-known method for reducing phase spaces. Here we introduce a new scheme that generalizes the Clebsch parametrization. Using the new set of variables, we delineate a fundamental difference between the reduced magnetohydrodynamic equations and the two-dimensional Euler equations. c