MAGNETIC ENERGY BUILDUP IN A QUADRUPOLE FIELD BY PHOTOSPHERIC SHEAR MOTION

Using a two-dimensional, dissipative magnetohydrodynamic model, this p aper presents a numerical simulation of the magnetic energy buildup in a quadrupolar field by photospheric shear motion. When electric curre nt density is larger than a certain critical value, an anomalous resis tivity is introduced in order to account for the dissipation caused by instabilities in high current regions. It is shown that like a bipola r field, a quadrupolar field can efficiently store magnetic free energ y through photospheric shear motion. Electric current formed by shear concentrates on the separatrix and magnetic loops rooted in areas wher e the shear velocity gradient is large. The atmosphere is heated by an omalous resistive dissipation during the shear. Both magnetic and ther mal energy increases nonlinearly with shearing displacement. When the anomalous resistivity increases or the critical current density decrea ses, the growth rate reduces for magnetic energy but goes up for therm al energy.