The standard photoionization-avalanche mechanism, though it presents a basically satisfactory picture of cathode-directed streamer propagation, is shown to contain basic inconsistencies regarding the charge distribution at the streamer tip and the field that it produces. Specifically, the compact unstructured charge distribution postulated in standard theory is incompatible with continuous unidirectional propagation of streamers, especially when the space-charge field is large compared with applied field. A computer-simulation study of streamer-tip behavior is made to resolve these inconsistencies. The program calculates effects of electron drift, electron avalanching, space-charge-generated fields and photoionization in cylindrical coordinates for a matrix of cells extending in both the radial and axial directions. The program is used to compute the evolution in time of trial distributions of the streamer-tip space charge. Beginning with a concentrated spherical charge configuration, the simulation reveals a rapid redistribution of the charge into the form of a thin, hollow, bluntly pointed sheath. The sheath is filled with a conducting neutral plasma and the field within the sheath is nearly zero. When such a sheath configuration is used as the initial distribution, the simulation shows that it propagates forward without essential change of form. The sheath configuration is shown to be free from themore » inconsistencies inherent in the assumption of a compact charge distribution.« less