Stationary model of laser-induced plasma: Critical evaluation and applications

Abstract

We present an algorithm for both laser-induced plasma emission spectra simulation and rapid peak-identification suitable for selection of analytical lines (free of spectral interferences, minimally self-absorbed, most intense lines). Calculations of plasma composition and radiation transport are based on the model of a uniform plasma under local thermodynamic equilibrium (LTE) requiring 3 + (K − 1) parameters – temperature T, electron density ne, plasma mass m and array of K mass fractions of chemical elements {c}. A simple cost function based on Pearson's r with a sole maximum in T–ne space is proposed to achieve the best convergence between the experimental and model spectra. We have found the best fitted T, ne, m for spatially integrated experimental spectra of standard samples of high- and low-alloy steels at delays of 1–10 μs (gate 0.4 μs) after a laser pulse within three spectral ranges (255.1–276.4, 392.6–412.2, 529.3–547.0 nm) by a brute force technique. The instrumental function of the Czerny–Turner spectrometer equipped with an intensified charge coupled device (ICCD) detector has been accurately accounted for which has been notably improved the model and experimental spectra similarity. Several optimizations including a fast Fourier transform (FFT) convolution and a polynomial approximation of Voigt profile allowed acceleration of computing to several milliseconds per spectrum.We observed a discrepancy between the best-fitted values of T obtained in the ultraviolet (UV) and visible ranges, while the ne values were close to each other in these ranges. The UV range is dominated by the ionic Fe II lines but most of the lines in the visible range are atomic Fe I lines. Thus, a possible explanation of the T difference is an inhomogeneity of the plasma (different temperatures for the “hot” plasma core and the “cold” periphery). As a spectacular example for line identification, we demonstrate that 275 emission lines are ascribed to 106 peaks within the UV range out of a total of ~12,000 lines found in spectral databases. Selection of analytical lines to determine chromium in cast iron and carbon in steels is discussed. Applicability of the algorithm to reveal analytical lines for silver, lanthanum and yttrium determination in soils and ores is mentioned. The developed algorithms are useful for choice of the best analytical line under certain plasma and spectrometer parameters in terms of: (i) spectral interferences, (ii) transmittance and (iii) intensity, for estimation of detection limits of trace elements in a known sample matrix, for detection of erroneous entries in databases, including transition probabilities and Stark parameters.