We presented a theoretical model for dynamic evolution of emerging magnetic fields.
The core of this model is an evolution equation that determines how the height of an emerging magnetic field line (loop) changes with time under the force of gravity, magnetic pressure, and magnetic tension (loop height evolution equation). A solution of this equation tells that the temporal change of loop height depends on field-line curvature κ and
field-strength scale height H, which led us to evolutionary characteristics of emerging field lines having different shapes. We also quantitatively examined three-dimensional configurations of these field lines, showing that S-shaped inner field lines underlying the axis of an emerging twisted flux tube do not always have dip structure. Coloring multiple emerging field lines in 3D space depending on the squared value of current density at their chromospheric footpoints demonstrated that these S-shaped field lines tend to have high current density at their chromospheric footpoints.
Reference
Magara, T.
2004, ApJ, 605, 480
Dynamic evolution of emerging field lines that compose a twisted flux tube. The thick black field line represents flux-tube axis.
Loop height evolution equation (solution).
