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Using a general expression for the spatial dependence of the temperature determined by a steady-state heat flow equation for a cylindrical X-ray target anode with dimensions much larger than the incident electron beam radius, the radius of the melt region on the anode surface has been calculated as a function of the total incident electron beam power. These calculations are shown to be in excellent agreement with experimentally measured values of the melt radius for tungsten, copper, and molybdenum target anode materials which indicates that electron beam melting is well described using the steady-state heat flow equation. A novel method is also presented for the unambiguous determination of the incident electron beam radius, and therefore the X-ray source size, which makes use of the dependence of the onset of target anode melting on the electron beam radius. This approach is shown to yield consistent values for the electron beam radius on tungsten, copper, and molybdenum target anodes.

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