Depending on the surface of interest and material properties one or several of these mechanisms may be important for calculating threshold values. Central to the question of the interaction of lasers with materials is the issue of laser heating. The equation governing this heat transfer for unit area can be simply written as: This is a special one dimensional steady state case of the Fourier law of heat conduction, where Q is energy at the surface, t is time, T is temperature at surface, x is direction of heat flow. It is of course possible to solve the generalised Fourier law of heat conduction [23] and a variety of approaches exist [12, 13, 14, 15, 16]. For a laser with a pulse duration of At and AQ energy absorbed by the material, the above equation can be approximated to: Where Ax is the layer heated by the laser pulse. For unit area of the material it can be shown (see Appendix-A) that the thickness of the heated layer is Equation 3 gives the thickness of layer heated up, given a laser pulse of duration At. This depends only on material properties of specific heat Cp thermal conductivity K, and density P. For a given At the thickness of the heated layer depends on the factor This can be interpreted as the laser pulse duration required to heat up a thickness Ax. While equations (3) and (4) represent approximations they will be used in our calculations. Some specific assumptions made in our approach need to be emphasized. These are: • the energy absorbed depends on the surface absorptivity, specific heat, thermal conductivity and density. These are assumed to be constant. While it is not too inaccurate to assume that specific heat,1 thermal conductivity1 and density are ^Editor's note: These do vary substantially over the temperature range of interest for many materials, but assuming their constancy is adequate to show the means of arriving at constraints.
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