Abstract
Two families of analytical solutions are presented that describe isothermal magnetostatic atmospheres in uniform gravity and varying in two Cartesian dimensions. The solutions in each family share a common set of magnetic flux surfaces but have different profiles of field intensity, magnetic shear, and plasma distribution across these flux surfaces such that force balance is satisfied. A family of solutions with this mathematical degree of freedom had previously been found by Dungey. The construction and properties of the new solutions are described. The hydromagnetic stability of these solutions is discussed by using the sufficiency criteria of Hu to determine those profiles of magnetic field and plasma that assure stability for the whole system. Among the stable equilibria found are examples of sheared magnetic structures intruding into a uniformly magnetized, isothermal atmosphere. One of the two families of solutions is extended to equilibrium states that vary fully with all three Cartesian coordinates. These extended solutions allow the possibility of constructing complex structures by juxtapositioning discrete three-dimensional magnetic structures built separately. These two-dimensional and three-dimensional magnetostatic states may be useful as initial states for numerical simulation of time-dependent magnetohydrodynamic processes in the solar atmosphere.
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