In this paper we present simulation results and observational data from the Geotail comprehensive plasma instrument of an ion distribution function signature which arises due to nonlinear particle dynamics in the quiet time magnetotail. The signature manifests itself as peaks and valleys in the ion distribution function whose separation scales as the fourth root of the particle energy. The Geotail observations represent the first independent corroboration of this signature since it was seen in ISEE 1 data by Chen et al. [1990>. The simulations demonstrate that the signature is present in the pitch-angle-resolved distribution even in the case of perfectly symmetric particle sources in the northern and southern hemispheres. When combined with magnetometer data, we show how the peaks and valleys may be used to determine the current sheet thickness using a single satellite. The current sheet thickness determined in this fashion is less than but consistent with other measurements of the current sheet. ¿ 1999 American Geophysical Union