Discrete auroral arcs are caused by precipitating accelerated electrons, and there is a lot of observational evidence for the associated potential structure being U-shaped below about 15000 km altitude. However, according to our studies using Polar data at higher altitude, there is a lack of convergent electric field signatures at similar to 20000-35000 km and consequently we suggest that the U-shaped potential contours close below this altitude range. To explain this finding, an O-shaped potential model is proposed, together with a maintenance mechanism which involves parallel energisation of middle-energy electrons by waves in the 15000-30000 km altitude range. Test particle simulations show that the presence of waves brings this "cooperative" model in quantitative agreement with both Polar and low-altitude observations. We also discuss our statistical Freja satellite studies of the observational relationship between the peak energy (voltage) and the current density in inverted-V regions. The result is that the current and voltage are sometimes correlated in the evening sector events, but almost always anticorrelated in the morning sector. This result, which is very interesting in its own right, may also have some relationship to the potential structure question, (C) 2001 Elsevier Science Ltd. All rights reserved.