Radio bursts originating from the stronger magnetic polar regions of both Uranus and Neptune were detected by the planetary radio astronomy experiment during the Voyager 2 encounters with the planets. It has previously been demonstrated that these bursts are beamed into a broad, hollow emission pattern from their auroral sources. We now show that the bursts at both planets also manifest similar detailed patterns, with the waves beamed into two separate and distinct radiation cones at intermediate wave frequencies. This double-cone emission pattern is predicted by relativistic cyclotron resonance theory, and application of this theory to the observed emission pattern yields the plasma density structure within the radio source region. Calculations indicate that at both Uranus and Neptune the plasma-to-cyclotron frequency ratio can drop well below 0.01 within the active region. Such low values indicate that the southern auroral zones at both planets contain an auroral plasma cavity that is similar to that found in Earth's nightside auroral zone. ¿American Geophysical Union 1991