An axisymmetric distribution of electrons incident on a carbon target causes heating of the target. The thermal conductivity of the various carbon polymorphs varies rapidly with temperature. We have solved the nonlinear steady‐state heat‐flow problem. We show that type IIb diamond would be an ideal source for carbonKradiation and that such a static target will sustain a power input of 6.5 kW on an area whose diameter is 1 mm and might, with proper design, operate at an even higher power input on the same area. We show that a power input of 6.5 kW at 6.0 kV on the above area would produce carbonKradiation of sufficient intensity so that the exposure time for PMMA (polymethylmethacrylate, an x‐ray resist of extremely high resolution but relatively low sensitivity) is only 1 min for a source‐to‐substrate distance of 2.54 cm.