Ultra-high gradient dielectric wakefield accelerators are a potential option for a linear collider afterburner since they are immune to the ion collapse and electron/positron asymmetry problems implicit in a plasma based afterburner. The first phase of an experiment to study the performance of dielectric Cerenkov wakefield accelerating structures at extremely high gradients in the GV/m range has been completed. The experiment took advantage of the unique SLAC FFTB electron beam and its ultra-short pulse lengths and high currents (e.g., σz = 20 μm at Q = 3 nC). The FFTB electron beam was successfully focused down and sent through short lengths of fused silica capillary tubing (ID = 200 μm / OD = 325 μm). The pulse length of the electron beam was varied to produce a range of electric fields between 2 and 20 GV/m at the inner surface of the dielectric tubes. We observed a sharp increase in optical emissions from the capillaries in the middle part of this surface field range which we believe indicates the transition between sustainable field levels and breakdown. If this initial interpretation is correct, the surfaced fields that were sustained equate to on axis accelerating field of several GV/m. In future experiments being developed for the SLAC SABER and BNL ATF we plan to use the coherent Cerenkov radiation emitted from the capillary tube as a field strength diagnostic and demonstrate GV/m range particle energy gain.