Abstract
Translational symmetric ideal magnetohydrodynamic plasma with steady incompressible flow is considered. The domain then is of cylindrical shape with arbitrary cross section. Several exact solution classes for nonlinear cases are obtained. The obtained solutions are bounded at infinity, in which they are physically acceptable and have applications in astrophysics as well as solar magnetic fields. Some of the solutions are examined to describe low and high β-plasma equilibria in terms of elementary functions. They can be employed to describe plasma in the solar corona, the photosphere, and the upper corona.
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