Utilizing the ratio and the summation of two spectral lines for estimation of optical depth: Focus on thick plasmas

In this paper, a study is performed on the spectral lines of plasma radiations created from focusing of the Nd:YAG laser on Al standard alloys at atmospheric air pressure. A new theoretical method is presented to investigate the evolution of the optical depth of the plasma based on the radiative transfer equation, in LTE condition. This work relies on the Boltzmann distribution, lines broadening equations, and as well as the self-absorption relation. Then, an experimental set-up is devised to extract some of plasma parameters such as temperature from modified line ratio analysis, electron density from Stark broadening mechanism, line intensities of two spectral lines in the same order of ionization from similar species, and the plasma length from the shadowgraphy section. In this method, the summation and the ratio of two spectral lines are considered for evaluation of the temporal variations of the plasma parameters in a LIBS homogeneous plasma. The main advantage of this method is that it comprises the both of thin and thick laser induced plasmas without straight calculation of self-absorption coefficient. Moreover, the presented model can also be utilized for evaluation the transition of plasma from the thin condition to the thick one. The results illustrated that by measuring the line intensities of two spectral lines at different evolution times, the plasma cooling and the growth of the optical depth can be followed.