Cross-section variations of coronal magnetic loops

Axisymmetric nonlinear force-free field models were employed to study the variation of the cross-section of coronal loops. In order to simulate these loops, we placed the point source of the fields under the photosphere and made the symmetric axis parallel to the photospheric surface. Based upon qualitative theoretical analyses and numerical simulations on the dipoles in these models, we compared the simulated magnetic loops with similar arclength and symmetric distributions of magnetic strength, and obtained the following results: The cross-section expansion of the current-free loops is fairly large and nearly isotropic, and that of highly sheared force-free loops is small and anisotropic. The anisotropy of the cross-section expansion, however, tends to vanish in extremely sheared loops. Magnetic loops with constant thickness, as an extreme case in the dipole nonlinear force-free fields, can be reached asymptotically when the magnetic shear increases. They tend to appear in the vicinity of the plane, vertically intersecting the symmetric axis at the point source, and their footpoints are not exactly located in the peak sites of vertical electric current density on the photospheric surface.