On solar faculae heating by electric currents

A solar facula model is considered describing the facula as a magnetic tube with the radius of 100-200 km magnetic field strengths of 1500-2000 Gs and solenoid-type configuration of magnetic field. The circle electric currents related to the magnetic field are located at the boundary of the tube in a thin transition layer. The heating of a facula is due to Joule dissipation. Corresponding conduction equation is solved. It is shown that the Ohmic heating is significant, and may essentially contribute to the increase of the facula effective temperature when the magnetic field gradient in a transition layer is dB/dr approximately (3-7) Gs/cm