We use a fast, efficient method to trace charged particles through realistic magnetospheric electric and magnetic fields, greatly reducing computer simulation times. The method works for particles having arbitrary charge, energy, or pitch angle but which conserve the first two adiabatic invariants. We also apply an efficient method of classifying drift orbits, which greatly simplifies the task of identifying the last closed drift path or other drift boundaries. Finally, we calculate the time-independent evolution of the bounce-averaged phase space density along convective drift orbits. With these three tools, convective evolution of the particle distribution from the tail can now be described quantitatively, an essential step in understanding the production of unstable distributions in the magnetosphere. One can also categorize topologically different drift orbits, which is necessary to understand the unique particle signatures of the convecting plasma such as Alfv¿n layers and plasmapause. These signatures can then be used to extract the electric and magnetic fields or to test the validity of the model fields. The method is particularly appropriate for particles in the energy range 0.01<E<100 keV, which are influenced by both electric and magnetic fields, and for time periods without invariant destroying waves. ¿ American Geophysical Union 1993