Non-axisymmetric magnetostatic equilibrium in cylindrical coordinates and its application to sunspots

Abstract This paper describes a general solution to the 3-dimensional, 2-component mangetostatic equation assuming the total pressure (gas plus magnetic) to be a function of the height only. By adjusting the two arbitrary functions appearing in the general solution one may obtain various particular solutions which are not subject to the assumption of perturbations being small when applied to solar phenomena. One such particular solution qualitatively accounts for the observed asymmetry in the shape of the sunspots and the filimentary structure in them.