  Equilibrium equations for magnetically confined, axisymmetric plasmas are
derived by means of the energy-Casimir variational principle in the context of
Hall magnetohydrodynamics (MHD). This approach stems from the noncanonical
Hamiltonian structure of Hall MHD, the simplest, quasineutral two-fluid model
that incorporates contributions due to ion Hall drifts. The axisymmetric
Casimir invariants are used, along with the Hamiltonian functional to apply the
energy-Casimir variational principle for axisymmetric two-fluid plasmas with
incompressible ion flows. This results in a system of equations of the
Grad-Shafranov-Bernoulli (GSB) type with four free functions. Two families of
analytic solutions to the GSB system are then calculated, based on specific
choices for the free functions. These solutions are subsequently applied to
Tokamak-relevant configurations using proper boundary shaping methods. The Hall
MHD model predicts a departure of the ion velocity surfaces from the magnetic
surfaces which are frozen in the electron fluid. This separation of the
characteristic surfaces is corroborated by the analytic solutions calculated in
this study. The equilibria constructed by these solutions exhibit favorable
characteristics for plasma confinement, for example they possess closed and
nested magnetic and flow surfaces with pressure profiles peaked at the plasma
core. The relevance of these solutions to laboratory and astrophysical plasmas
is finally discussed, with particular focus on systems that involve length
scales on the order of the ion skin depth.
