4. Discussions and conclusions
In this paper, starting from a low electric current in the dipole magnetic field we computed the force-free current path and magnetic field for currents from 0 to 3.5 1011 A. More stable results were obtained when the electric current was represented by more current paths.
We found the shearing and uprising of electric currents. Simultaneously, the surrounding magnetic field was deformed. Moreover, the individual electric current forms a helical structure, which can be searched in observations. Evidently all these features are important for the active region evolution, filament formation and disruption, eruptive prominences, coronal mass ejections and solar flares.
It seems that there is some critical electric current, above which no force-free electric current structures exist. This aspect is interesting from the point of view of mass ejection, but clearly, it needs further verifications.
In our computations we used the constant along the current path. This simplification can be supported by the observation of loops with nearly constant thickness (Klimchuk et al., 1992). Otherwise, needs to depend on the magnetic field.
The present method of current path computations can be used not only for the initially potential magnetic field, but also for the linear force-free magnetic field. In this case the computed currents are considered as additional currents to initial current densities.
The presented model was designed for the electric current path computations. The concept of this model was motivated by the idea that electric currents are not flowing in full plasma volumes, but in current filaments and current sheets. Clearly this model can be used also for a modelling of the 3-D magnetic field. In some respects this model is similar to that of Sakurai (1981, 1989), which was used for the force-free magnetic field calculation with non-constant . Our model is simple and we think that it can be successfully applied mainly in cases with few localized currents. We believe that it is the case of eruptive processes.
© European Southern Observatory (ESO) 1997
Online publication: July 8, 1998