Magnetic energy injection mechanism via flux emergence
Flux emergence is a dynamic process involving interactions between plasma flows and magnetic fields, which injects magnetic energy into the solar atmosphere. To describe the energy injection via this process we introduced emergence velocity, a physical quantity determined by spatial relationship
between velocity field vector and magnetic field vector. A key feature of this quantity is that it represents net effect of flux emergence on the energy injection conducted via a combination of vertical flow and horizontal flow. Using the emergence velocity, we demonstrated that geometric
shape of an emerging field line plays an important role in the energy injection.
Reference
Magara, T. 2011 ApJ, 731, 122
(net effect of flux emergence on energy injection conducted via combination of vertical flow and horizontal flow)

(net injection of magnetic energy)

net emergence (left panel; v_emg > 0) and net submergence (right panel; v_emg < 0)

Energy injection at early and late phases of flux emergence
