Field-aligned currents and polar cap electric fields

An equation is derived which describes the relation between the field-aligned current, the electric field, and the density inhomogeneity in the polar cap region. Self-consistent electric field patterns are obtained for the case when a pair of field-aligned currents (downward on the dawn side and upward on the dusk side) and an enhancement of the electron concentration in the auroral belt are present. It is found that the field pattern agrees with Heppner's basic pattern if there is an electric field component along the auroral belt which directs from the noon sector toward the midnight sector.