Generation of magnetic fields : various multipolar seed fieldsGeneration of magnetic fields : various multipolar seed fields
Faculty of Sciences. Physics
Department of Physics
Cambridge :Electromagnetics Academy, 2007[*]2007
Engineering sciences. Technology
Progress in Electromagnetics Research Symposium (PIERS 2007), March 26-30, 2007, Beijing, Peoples Republic of China
University of Antwerp
The exact solution for the kinematic dynamo in spherical coordinates (r, theta, phi) is given by Callebaut  when the azimuthal velocity is supposed to be a given, but axbitraxy, function of r and 79 only. Using a bipolar seed field yielded a qualitative agreement with the sunspot butterfly diagram and the polar faculae butterfly diagram. Next we have investigated the case that a quadrupolar seed field resides in the Sun (Callebaut and Khater, 2006) as some observations reveal a quadrupolar and even an octupolax contribution to some surface and interplanetary phenomena. A combination of a bipolar, a quadrupolar and an octupolar field may yield a fairer agreement with observations. However, the ratio of the various components is still a problem: determination from the solar surface or from interplanetary space gives approximate values. The separation between the sunspot region and the polar faculae, although both are generated by the same mechanism, is manifest: the region where the radial variation of the angular frequency of the rotation vanishes. One serious drawback: as for other models the agreement near the poles is poor, although it was improved much in comparison with a bipolar field alone by realizing that the coefficients of bipolar and quadrupolar field have opposite signs.