Hamiltonian formulation of the modified Hasegawa–Mima equation

• Derivation of a Hamiltonian formulation of the modified Hasegawa–Mima equation.
• Application of Dirac's theory of constrained Hamiltonian systems.
• Discussion on the Jacobi identity and Casimir invariants.

We derive the Hamiltonian structure of the modified Hasegawa–Mima equation from the ion fluid equations applying Dirac's theory of constraints. We discuss the Casimirs obtained from the corresponding Poisson structure.