  Exact solutions to the static equilibrium magnetohydrodynamic equations are
presented and discussed for both axially and helically reduced systems. For
both symmetries, physical restrictions on the solutions are discussed and it is
seen that there arise two different families of physical solutions
corresponding to two distinct pressure profiles. One is suitable for
atmospherically confined plasma whereas the other is suitable for plasma
residing in a vacuum. For solutions in vacuum, the radial dependence is found
to behave periodically for both axial and helical symmetries. For these
physical solutions, only a truncated solution inside of some chosen domain can
be considered. The magnetic field boundary can than be described by a current
sheet. In the last part of the paper, these static equilibrium solutions are
transformed into solutions with non-zero fluid velocity.
