Energy versus time dispersion of precipitating ion bursts was observed during two rocket flights in the morning auroral oval. Individual bursts lasted about 20 seconds and repeated on a time scale of 100 seconds. The dispersion is interpreted as energy-dependent time-of-flight delay which provides identification of ion charge-to-mass ratio as well as injection source distance. The data are consistent with injections of magnetosheath ions with injection distances ranging from 7 to 19 earth radii. Individual events extended over a region of a least several degrees of magnetic longitude and 0.3 degrees of invariant latitude. It is suggested that these events are associated with turbulent plasma entry into the magnetospheric entry layer.