| Abstract: | This paper deals with mathematical fundamentals of the foregoing one on the treatment of spherical dynamo models. A representation of arbitrary vector fields in the three-dimensional euclidian space as a sum of a poloidal and a toroidal part is founded. In this way well-known representations of axisymmetric or not necessarily axisymmetric but solenoidal fields are generalized. The mentioned parts of a field show some remarkable properties allowing far-reaching consequences in special problems. As an example equations governing a class of force-free magnetic fields are solved. Then possibilities of further generalization are investigated. |
