Geometric Considerations of the Evolution of Magnetic Flux Ropes
D.B., Berdichevsky
Abstract: We use flux conservation and magnetohydrodynamics (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 t0 the flux tube B-field is the force-free magnetostatic 
Lundquist solution, which energetically corresponds to the most 
stable state for any flux tube structure. 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.