  Recent results will be presented on steady states of magnetically confined
plasmas obtained by conventional and Hamiltonian methods. The presentation
consists of three parts. The first one concerns the derivation of a generalized
Grad-Shafranov equation describing helically symmetric equilibria with pressure
anisotropy and incompressible plasma flow of arbitrary direction with
application to straight-stellarator configurations [1]. The impact of pressure
anisotropy and flow on the equilibrium characteristics is also examined. In the
second part the axisymmetric equilibrium code HELENA is extended for pressure
anisotropy and flow parallel to the magnetic field and ITER-pertinent
equilibria are constructed. In the third part the Hamiltonian formulation of
helically symmetric plasmas is established within the framework of extended
MHD, a simplified two-fluid model including Hall-ion and electron-inertia
contributions [2,3]. Four families of Casimir invariants are obtained and they
are used to construct Energy-Casimir variational principles for deriving
generalized extended MHD equilibrium equations with arbitrary flow. The system
is then cast into the form of Grad-Shafranov-Bernoulli equations. In addition,
an example of an incompressible double-Beltrami equilibrium will be presented
in connection with a straight-stellarator configuration.
