In this paper, the unsteady state heat transfer equations with time dependent boundary conditions are coupled with a two-dimensional finite element method to predict the work-roll temperature distribution during the continuous hot slab rolling process. To achieve an accurate temperature field, the effects of various factors including the thermal relationship of the work-roll and the metal slab, the idling work-roll revolutions, the rolling speed, the slab/roll interfacial heat transfer coefficient, and the magnitude of the thickness reduction of the slab at each deformation pass are taken into account. Comparisons between the predicted and published experimental results are used to illustrate the validity of the mathematical model.

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A compact laser-produced plasma x-ray source radiates 1 nm x rays with an average power of 24 W in 2π steradians. The x-ray conversion efficiency is 9% of the laser power delivered on target. The 300 W laser power is generated by a compact diode-pumped, solid-state Nd:YAG laser system. The point source x-ray radiation is collimated with a polycapillary optic to a parallel x-ray beam. The collimated plasma source (CPS) is used to demonstrate proximity x-ray lithography of 100 nm lines with a 16 μm gap between the mask and wafer. The CPS is optimized for integration with an x-ray stepper to provide a complete collimated plasma lithography exposure tool for the manufacture of high-speed GaAs devices.

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