  A systematic theory of the asymptotic expansion of the magnetohydrodynamic
(MHD) equilibrium in the distance from the magnetic axis is developed to
include arbitrary smooth currents near the magnetic axis. Compared to the
vacuum and the force-free system, an additional magnetic differential equation
must be solved to obtain the pressure-driven currents. It is shown that there
exist variables in which the rest of the MHD system closely mimics the vacuum
system. Thus, a unified treatment of MHD fields is possible. The mathematical
structure of the near-axis expansions to arbitrary order is examined carefully
to show that the double-periodicity of physical quantities in a toroidal domain
can be satisfied order by order. The essential role played by the normal form
in solving the magnetic differential equations is highlighted. Several explicit
examples of vacuum, force-free, and MHD equilibrium in different geometries are
presented.
