  The Generalized Hasegawa-Mima (GHM) equation, which generalizes the standard
Hasegawa-Mima (HM) equation, is a nonlinear equation describing the evolution
of drift wave turbulence in curved magnetic fields. The GHM equation can be
obtained from a drift wave turbulence ordering that does not involve ordering
conditions on spatial derivatives of the magnetic field or the plasma density,
and it is therefore appropriate to describe the evolution of electrostatic
turbulence in strongly inhomogeneous magnetized plasmas. In this work, we
discuss the noncanonical Hamiltonian structure of the GHM equation, and obtain
conditions for the nonlinear stability of steady solutions through the
energy-Casimir stability criterion. These results are then applied to describe
drift waves and infer the existence of stable toroidal zonal flows with radial
shear in dipole magnetic fields.
