A family of quantitative magnetospheric models is used to determine the cusp position in the ionosphere and to analyze the field topology around the outer cusp. It is demonstrated that the ''cusp proper'' (~1¿¿2 hours), observed in particle precipitation patterns, can be defined as the footprint of the magnetopause current layer with field lines connected to the interplanetary medium via a normal magnetic field component. A wider magnetic local time extent of the cleft (~8--16 hours MLT) can be associated with field lines connected to the low-latitude boundary layer between XGSM=0 and 20 RE downtail and extending 1--2 RE inward from the magnetopause layer. It is suggested that the finite-sized physical cusp originates as a result of gyroviscous erosion at the magnetopause current layer that enlarges the topologically singular magnetic cusp. The model-predicted magnetic latitude (MLAT) of the ionospheric footprint of the cusp is 79¿ during quiet conditions and 74¿ during active periods.

The latitude of the cusp varies also with universal time and with season, due to variation of the dipole tilt angle. The corrected magnetic coordinates are found to exhibit the smallest amplitude of diurnal variation of the cusp position and are recommended for mapping of auroral phenomena. Other coordinate systems produce artificial diurnal variations of the cusp position. These artificial effects have an amplitude of ¿2.5 (¿1) hours MLT and ¿4¿ (¿2¿) MLAT for dipole (eccentric dipole) coordinates, respectively. An interplanetary magnetic field (IMF) By component linearly superposed with the magnetospheric field can shift the magnetic local time of the cusp by a maximum of 0.07--0.15 hour/nT. A negative (positive) IMF Bz component can shift equatorward (poleward) the position of the cusp by a maximum of 0.1¿--0.2¿/nT. A similar effect is obtained with a positive (negative) Bz component. These results imply that the instantaneous effect of a negative Bz component on the equatowrard shift of the cusp is smaller than an indirect effect due to increased magnetic activity. Some of the model predictions are compared with cusp observations made on board the Swedish Viking satellite. Both the Viking and other observations can be quantitatively explained by the model predictions. ¿ American Geophysical Union 1991