We investigate the use of electron data to probe the structure of parallel electrostatic fields. Low-energy electrons can be trapped between their magnetic mirror points below an observer and the upward directed electric field above. The shape of the trapping region in phase space gives information about the field structure. We use equivalent potential diagrams and plots of phase space boundaries in (&mgr;, E) space both to explain our results and to demonstrate the utility of these formalisms for studying particle motion in time-independent electric fields. A comparison of theoretical boundaries in (v∥, v⊥) space with S3-3 data shows that it is difficult to determine the shape of the low-energy trapping boundary with present particle experiments. We discuss the instrumentation required to measure the low-energy electron population with sufficient detail to resolve these boundaries.