Geometric considerations of the evolution of magnetic flux ropes

Summary form only given. We use flux conservation and magnetohydro-dynamics (MHD) theory to discuss essential differences in the nature of the evolution of two analytical solutions describing magnetic flux tubes evolving in time. The first of these maintains the elongation of the tube, while the second maintains a constant angular extension with respect to a possible point-like source. In the first case, free-expansion of the plasma (density N) occurs only in a direction perpendicular to the flux tube axis. In the second case, isotropic evolution is considered. In both cases it is assumed that at initial time to the flux tube B-field is a force-free solution. We show that for each case conservation of magnetic flux is enough to establish the scaling with time of the B-field. Further it is shown that in the free, isotropic expansion of the plasma the magnetic force-free nature of the B-field is preserved for all time. Possible examples, in the heliosphere, of these two types of evolution are presented.