Heating effect of an electron beam impinging on a solid surface, allowing for penetration

The heating effect of an electron beam, under the assumption that the entire beam energy is imparted to the target surface (disc heating model), can be calculated fairly readily. At the high voltages and small beam diameters employed in electron-beam machining, however, the problem is complicated by penetration of electrons into the target. This effect is allowed for by a simple model of electron penetration due to Archard,9 by which the spatial distribution of power dissipation in the target is computed. The steady-state heat-flow problem is solved by relaxation. Results obtained on a digital computer, for a range of target materials and beam voltages, are resolved into two curves, from which correction factors for the effects of backscatterand electron-penetration depth can be read and applied to the data given by the disc heating model. Graphs are presented showing the maximum temperatures obtainable, with spots of given sizes, for a range of materials and voltages. The computations are substantially verified by experiment.