This can be interpreted as the laser pulse duration required to heat up a thickness Ax. While equations (A3) and (A4) 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, thermal conductivity and density are constant there is enough experimental evidence to show that absorptivity increases during the time of irradiation [15, 16]. This means that energy requirements for damage could be less than what is calculated. • The approximation of the generalized Fourier heat flow model by equation (Al), i.e. a one dimensional heat flow model is valid only approximately. This however is not a major problem since with appropriate boundary conditions the general Fourier equation can be solved to get temperature distribution within the object as a function of depth x and time t, i.e. a solution of the form T (x, t) can be found for the general Fourier equation. The absence of convection, radiating and plume absorption effects (arising from the vapour created by laser radiation) is assumed. This also assumes no transverse heat transfer (uniformly heated thin slab transferring heat by conduction with no heat transfer across boundaries). • Further approximation of equation (Al) by equation (2) is valid only for small At and small Ax. Let us consider the melting of a target subjected to laser irradiation. Let the area of the target illuminated be A. Let Cp be specific heat, Tm the temperature of melting, Tj initial temperature. Let the thickness of the target be 3. The heat energy required to raise target to melting temperature is: The laser beam is to supply all this energy. Let I be power intensity of a laser at the surface of the material. Let the pulse duration of the laser be At. Let absorption of surface be a. Energy absorbed by surface is:
RkJQdWJsaXNoZXIy MTU5NjU0Mg==