Convection electric field patterns at high latitudes appropriate to periods of low geomagnetic activity are presented. The postulate that the global Joule dissipation rate is a minimum is employed to derive characteristic field distributions for the situation when ring current ohmic losses are negligible and the auroral oval enhancement of height-integrated Hall conductivity is small. The fast Fourier transform is introduced to compute Fourier coefficients of discrete field-aligned current data, and the method is shown to be quite useful in this context as a least squares fitting routine. The model calculations demonstrate the approach of the high-latitude ionosphere toward the perfect shielding configuration predicted by the theory for quiet times.