Analytical modeling of laser ablated sublimators - The heat balance integral method

The purpose of this work is to generate broadly applicable equations of immediate relevance for investigating CW laser-radiation interactions with material targets that vaporize without first melting. The procedure that was adopted is based on the Heat-Balance Integral (HBI) method of Goodman, and emphasizes the use of nondimensional variables. First, it is shown that HBI-based calculations of the vaporization time and the depth of thermal penetration are in essential agreement with exact results, but this does not hold for the backface temperature. This situation is examined in the context of describing ablation in the 'burnthrough mode', which involves two categories of problems: 'high-intensity' situations that may exhibit steady-state features, and 'low-intensity' situations that exhibit perceptible backface-heating in the preablation phase. In conjunction with a key result on steady-state recession rates, the concept of an effective heat of ablation is reexamined and illustrated in the light of data referring to a polycrystalline graphite. The same material is then used to compare calculations based on the HBI approximation with the results of a computer-code analysis that takes the temperature dependence of the thermal properties into account. Finally, it is shown how the inherently one-dimensional HBI approach can be extended to reflect spatial variations in the beam intensity as well as heat losses caused by thermal reradiation and lateral transport.