We presented a theoretical model for dynamic evolution of emerging magnetic fields.
The core of this model is given by an evolution equation for the height of an emerging field line (loop height evolution equation), and the solution of this equation described how the loop height evolves depending on field-line curvature and
field-strength scale height. Using this model we evaluated evolutionary characteristics of emerging field lines having different shapes. We also quantitatively examined the three-dimensional configuration of emerging field lines to demonstrate that S-shaped field lines underlying the axis of an emerging twisted flux tube do not always have dip structure. Visualization of multiple emerging field lines with their projected shapes (top and side views) suggests that such S-shaped underlying 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).
