Non-axisymmetric Magnetostatic Equilibrium in Cylindrical Coordinates and Its Application to Sunspots

The present paper describes a general solution to the three-dimensional, two-con-ponent magnetostaitic equations in cylindrical coordinates, assuming the total pressure (sum of gas pressure and magnetic pressure) is a function of the altitude only. By adjusting the two arbitrary functions appearing in the general solution one may produce various patieular solutions which are not subjected to any limitation of perturbation conditions while applied to solar phenomena. Moreover, it is found that a particular solution as to qualitatively elucidate the asymmetry of sunspots in shape in addition to the filamentary structure in sunspots.