Observations of 0.01--10 keV ions at a discrete set of velocities, as expected for ions bouncing repeatedly between hemispheres, have been previously reported both at low altitudes and at geosynchronous orbit. The following two possible models of the ion source have been suggested: for the geosynchronous observations, an equatorial-acceleration model involving temporally confined ion acceleration events and for the low-altitude observations, a model involving a heating wall in the auroral acceleration region from which ions subsequently drift to other latitudes. In the latter case, the spatially bounded source appears temporally bounded from the point of view of one field line drifting over it. We report here Fast Auroral Snapshot (FAST) observations of multienergy events near local noon at several thousand kilometer altitude and show that these events originated in a temporally localized, spatially extended, equatorial source. The dispersion pattern for individual ion bands over latitude is consistent with such a source, and not with the heating wall hypothesis, the observed energy being proportional to the square of the modeled field line length. The latter condition on the dispersion is much more precise than any imposed by a latitudinal drift model. A fit of this model to Akebono and DMSP F8 data previously published by Hirahara et al. (1997) is also shown. The fit to two Akebono events is accurate at lower latitudes, where the magnetic field model is expected to be reliable. The fit to DMSP data corresponding to one of the Akebono events involves additional field-aligned potentials of roughly 100 eV in the auroral zone. Observations of dispersion events of this type are expected to be useful more generally. The nonlocal determination of the magnetic field line length can provide a check on magnetic field models. A match of the observed field line length to the modeled one provides for greatly increased confidence in magnetic mapping. ¿ 1999 American Geophysical Union