A numerical modeling investigation of the spectral emission of laserinduced plasma in MgCl_{2}NaCl aqueous solution has been presented. A model based on equilibrium equations has been developed for the computation of the plasma composition and excited levels population. Physical interpretation is presented to comment on firstly the evolution of atomic species number densities, and secondly on the population of the excited species emitting MgII and NaI resonant lines for temperatures ranging from 3000 K to 20 000 K. It is shown that MgII line reach a maximum of population on the issuing level, at norm temperature of 13800 K. Whereas, NaI line presents two norm temperatures, evaluated at 3300 K and 11700 K. This splitting of the NaI norm temperature is explained by the lowionization potential and weak concentration of the sodium atom in this aqueous solution. Thus, the proposed model can be useful to predict the optimal plasma temperature for the detection of given chemical element, which is not easy to reveal experimentally.
LaserInduced Breakdown Spectroscopy (LIBS) is identified as the optical emission spectroscopy of the laserinduced plasma [
Several studies have been reported on the correlation between the LIBS emission spectra from a water target and LIBS system parameters [
Samek et al. [
However, relatively few works have been concerned with theoretical approach of the dependence of line intensities emitted from water plasma on the LIBS system parameters; for example, Ahmed and Jaïdane [
The work described in this paper is motivated by the desire to gain fundamental knowledge concerning the effect of plasma temperature on LaserInduced Plasma Spectral Emission (LIPSE), and ultimately to determine the suitable plasma temperature for the detection of a given chemical element.
The first part of this work is devoted to a brief description of assumptions used for the LIPSE study. The second part presents the calculation of the number densities of species considered in the MgCl_{2}NaCl aqueous solution. In the last part of the paper, results concerning the densities of species emitting MgII and NaI lines are presented as a function of plasma temperature.
The interpretation of LIPSE is a complex task with many unsolved problems. The most important questions concern the ablation mechanisms [
Nevertheless, the description of LIPSE phenomenon can be simplified by making certain hypothesis [
Conventionally, LIBS measurements are made in the microsecond time scale, that is, when the LIBS plasma is under recombination conditions. In the microsecond regime of the plasma lifetime, typical values of electron number density
The reported
For the temperature range considered in this study. the plasma induced in MgCl_{2}NaCl solution, is supposed to be composed of the following species: electrons (e^{}), H, H^{+}, O, O^{+}, Na, Na^{+}, Mg, Mg^{+}, Mg^{++}, Cl, Cl^{+}, H_{2}O, O_{2}, OH, and H_{2}. Species with elevated ionization energy (
The laserinduced plasma is supposed to be homogeneous. It is well known that plasmas present a spatial distribution of their parameters. This plasma inhomogeneity yields to a self absorption of resonant spectral lines. Solving a model for those inhomogeneous plasmas could be very complicated. However for a waterplasma at the end of its cooling process and within a short observation window, spatial gradients have a lower influence on the plasma parameters. Thus the homogeneity of the plasma and optical thinness are assumed, that is, the reabsorption effect is neglected for the plasma induced on the liquid surface.
The laserinduced plasma is treated as a closed system, where matter conservation and electrical neutrality are assumed. Of course this assumption is suspect but it is made in this work to simplify the problem.
Considering the above assumptions, the intensity
As the laserinduced plasma satisfied the local thermodynamic equilibrium (LTE), levels populations obey the Boltzmann statistic, that is, the population
In this work, the partition functions have been computed using NIST energy level data [
It should be noted that the relevant partition functions are those calculated by using only observed levels. This is a crude approximation because it neglects the existence of many other levels. However, in general, partition function varied slightly over lowtemperature range.
According to (
However, assuming the LTE state of the laserinduced plasma, a system of equations with species densities as unknowns could be formed by Dalton, matter conservation, and Saha and GuldbergWaage equations. This equilibrium model based on the LTE assumption is referred to, as the LTEmodel.
Adopting the LTEmodel, a code is written in Maple language for the numerical computation of the plasma composition. The “solve” Maple command is used for solving the system of equations.
The system is initialized by an approached value of the electron density at the starting calculation point, then equations system is solved and a new value for
This code has been adapted to calculate the composition of equilibrium plasma of 50 mg/L MgCl_{2}NaCl aqueous solution at atmospheric pressure, for given temperature.
To corroborate our calculation, species number densities calculated with this numerical code for wateralkaline salt plasma are compared with previous published data in [
Results presented in Figure
Species densities as function of temperature, for plasma of MgCl_{2}NaCl solution concentrated at 50 mg/L, at atmospheric pressure under thermal equilibrium
Figure
After reaching maximal values, charged species densities follow a slight decrease, for example, H^{+} density stays nearly constant around 17 000 K, with
Concerning the electrons density
Figure
The spectroscopic analysis of LIBS spectrum obtained from water sample shows that only resonance emission lines, corresponding with lower energy excited states, exhibit wellresolved lines [
The most intense resonance lines, recorded in the LIBS spectrum of the MgCl_{2}NaCl aqueous solution, are MgII (279 nm) and NaI (588 nm) lines [
Atomic data of MgII and NaI lines [
Element 

Transition 






Mg  279.55  3s ^{2}S3p ^{2}P  0  4.43  2.68  2  4 
Na  588.99  3s ^{2}S3p ^{2}P  0  2.104  6.28  2  4 
Table
Applying the Boltzmann law equation (
Figure
Population of excited level Mg(3p), as function of temperature, in the equilibrium plasma of MgCl_{2}NaCl solution concentrated at 50 mg/L.
This figure shows that MgII spectral line reaches a maximum of upperlevel population, at socalled norm temperature,
A more detailed explanation is given by Boltzmann equation Equation (
Figure
Population of excited level Na(3p), as function of temperature, in the equilibrium plasma of MgCl_{2}NaCl solution concentrated at 50 mg/L.
Unlike the MgII spectral line, NaI line presents two maxima of upperlevel population, at norm temperatures of 3300 and 11700 K. It should be noted that NaI norm temperatures are both lower than that of MgII.
The curve of number density of Na(3p)excited atoms as a function of temperature (Figure
At low temperature (
Summing up, it seems that, the appearance of two norm temperatures for the NaI line is due, on the one hand to the near to the ground correspondent NaI emitting level and the lowionization potential of the sodium atom and on the other hand to the low concentration of this species in the aqueous solution.
To make in evidence the effect of sodium concentration on the NaI norm temperatures, the density of excited sodium at Na(3p) state, as function of temperature is represented in Figure
Density of sodium at Na(3p)excited states, as function of temperature, in equilibrium plasma induced on MgCl_{2}NaCl aqueous solution, for different sodium concentration (shown in g
This figure displays a disappearance of the splitting of NaI norm temperature for higher concentration of sodium. As Na concentration increase, the first maximum of NaI upper level population approaches the second one till both overlap forming only one maximum. The second norm temperature is approximately the same for all aqueous solutions. In fact the second peak of the density of excited sodium is related to the ionization of major species in the aqueous solution, such as hydrogen and oxygen atoms.
This work presents a theoretical interpretation for the understanding of the plasma temperature effect on the spectral emission of plasma induced in MgCl_{2}NaCl aqueous solution. LTE model is carried out to compute the plasma composition and it allowed the estimation of atoms, ions, and electron densities in the laserinduced plasma in the water sample at atmospheric pressure, for temperature ranging from 3000 K to 20 000 K. The populations of excited species emitting MgII and NaI lines are also calculated.
The obtained results reveal that MgII line presented a maximum of population on the issuing level, at norm temperature of 13800 K; However, NaI line presents two norm temperatures both lower than the MgII norm temperature. Considering the optically thinness assumption of the laserinduced plasma, the intensity of given spectral line is proportional to the number density of atoms on the upper excited level. Therefore, for better sensibility of the LIBS technique, comparing to the Mg II line, it is recommended to record NaI signal at relatively cold plasma, either by lowering the laser pulse energy, or by detecting the spectral emission at late stage of the plasma lifetime. Moreover, when using common broadband spectrometer systems that measure both lines at once it is suggested that spectrometers should collect light from early in the plasma when it is hot and stay open until it is cold to maximize signal from these two elements.
It should be noted that the numerical model built in this study is not restricted to magnesium and sodium aqueous solutions; it could be applied to any other wateralkaline salt mixture. As seen for magnesium and sodium species, for any other alkaline species such as lithium, calcium, and potassium, the corresponding norm temperature will depend essentially on the ionization potential, upper energy level, and dominance of the considered alkaline species in the aqueous solution.
In this work, it is assumed that the laserinduced plasma is ideal, that is, spatially homogeneous, electrically neutral, optically thin, in local thermodynamic equilibrium (LTE). In reality, not all these conditions may be fulfilled; the effect of departures from plasma ideality is planned for future investigations.