Influence of laser energy on the electron temperature of a laser-induced Mg plasma

The magnesium plasma induced by a 1064-nm Q-switched Nd:YAG laser in atmospheric air was investigated. The evolution of the plasma was studied by acquiring spectral images at different laser energies and delay times. We observed that the intensities of the spectral lines decrease with larger delay times. The electron temperature was determined using the Boltzmann plot method. At a delay time of 100 ns and laser energy of 350 mJ, the electron temperature attained their highest value at 10164 K and then decreases slowly up to 8833.6 K at 500 ns. We found that the electron temperature of the magnesium plasma increases rapidly with increasing laser energy.


Introduction
In the past decades, there has been an increasing interest in laser-induced breakdown spectroscopy (LIBS) in several research fields such as material processing, space applications and diagnostic techniques [1,2]. LIBS is an essential analytical technique for identification of the elemental composition of a sample [3][4][5][6].
In this technique, a highly energetic laser pulses generated from a Q-switched laser source is focused through a suitable focusing lens to generate a plume of plasma rich in atoms, electrons and ions on the surface of the sample. The focused beam results in the evaporation, atomization and ionization of the sample surface material, and the emitted 1 3 22 Page 2 of 6 a general trend that LIP temperature increases with increasing laser parameters.
In this work, we shall report on laser-induced magnesium plasma with different laser energies and several time delays in order to optimize the spectroscopic performance, and investigate the influence of laser energy on the electron temperature. Section 2 of this work is devoted to the experimental setup and procedure used to obtain the timeresolved emission spectra and the temporal evolution of the electron temperature. The experimental results are presented in Sect. 3. Finally, Sect. 4 gives the conclusion of the results of this work.

Experimental setup
The experimental setup of the laser-induced breakdown spectroscopy is shown in Fig. 1. The setup consists of Nd:YAG laser source for plasma formation and vaporization of the target, monochromator and a time-resolved detector. The 1064-nm beam from a Q-switched Nd:YAG laser, with 10 ns pulse width and 1-Hz pulse repetition rate (PRR), emitting a laser pulse with energy of 150, 250 and 350 mJ, which was measured by a pyrometric detector.
The laser beam was focused horizontally onto the target surface by a means of a quartz lens with 150 mm focal length. The distance from the lens to the target was set to about 14 cm in order to gain a nearly hemispherical plasma plume and a reproducible breakdown. The plasma was generated in air at atmospheric pressure on ~1-mm 2 surface area of the metal target. The content purity of the target was almost 99.99% magnesium plate, which was previously well polished before exposing to the laser beam.
The plasma emission was collected by a fiber bundle, which is coupled to a Mechelle spectrometer built with a gateable intensified charge-coupled device (ICCD) camera with a 1024 × 1024 pixels (istar from Andor Technology). The ICCD detector was synchronized with the trigger of the laser pulse. The synchronization was done using a digital generator (Stanford Research System, model DG645) and the oscilloscope (YOKOGAWA, digital oscilloscope DL9140, Japan). The gate delay was also monitored with the oscilloscope, which was triggered by signals collected by the photodiode. The time delay of the ICCD was varied from 100 to 1000 ns of the different laser energies for the spectra detection. In each measurement, the acquisitions were integrated over a suitable number of accumulations, in order to increase the signal-to-noise ratio. The atomic  emission lines were identified using available atomic spectra data compiled in the national institute for standards and technology database [24].

The spectra of the magnesium-induced plasma
The emission spectrum of the laser-induced magnesium plasma is shown in Fig. 2. The plasma emission was collected by a fiber bundle, which is coupled to a Mechelle spectrometer built with an intensified charge-coupled device (ICCD). The spectra were taken at a delay time of 100 ns and pulse energy of 350 mJ. The characteristic intensity of the Mg emission rapidly decreases with a larger delay time, due to bremsstrahlung emission and radiative recombination between the ions and electrons [25], and this is as a result of plasma quenching. At a delay time of 100 ns, a strong continuum is observed. The MgI 518.4-nm spectral line reaches the highest intensity with laser energy of 350 mJ, and this is fitted into the Lorentz profile in Fig. 3. In order to estimate the electron temperature of the laser-induced magnesium plasma, we study different emission spectra at several delay times. Figure 4 depicts a timeresolved emission spectrum of laser-induced magnesium plasma at different delay times.

The local thermodynamic equilibrium and the optical thinness of the plasma
The determination of the plasma temperature by the Boltzmann plot method requires the plasma to be in the state of thermodynamic equilibrium (LTE) and also must be optically thin. The Mg-induced plasma was optically thin for the line intensities used in the determination of the plasma temperatures [26]. This was observed from the peak intensities of the ratio of the Mg lines used. The experimental data and the stimulation validate that the local thermodynamic equilibrium condition is satisfied with plasmas of longer delay times. This depends on the plasma parameters such as the ambient gas, laser energy and pulse duration used in the experiments [27,28]. The most commonly used method to warrant the existence of LTE is the electron energy distribution function (EEDF) Maxwell distribution, and the McWhirter criterion [23,[29][30][31]. The McWhirter criterion defines the minimum electron number density which must be present in order for LTE to exist, which can be expressed mathematically as [3]: where N e is the electron density (cm −3 ), T is the plasma temperature (K) and E mn is the higher energy difference (eV) between the upper and lower energy states of the Mg lines used.
(1) N e ≥ 1.6 × 10 12 T 1 / 2 (�E mn ) 3 Research recently has revealed that the McWhirter criterion is necessary but insufficient to assess the existence of LTE [32], since it is derived for stationary and homogenous plasmas. From this work, we established that the LTE is satisfied because the electron density deduced from the stark broadening is higher than 10 16 cm −3 .

Theoretical model of the electron temperature
Assuming plasma in LTE, the population of the energy levels of the species obeys the Boltzmann's distribution law [17,23], which can be given by the expression: For experimental systems, we can replace the emissivity by the line intensity, and by taking the natural logarithm of Eq. (4), we obtain the expression in the form: By plotting the magnitude on the left side against the energy of the upper level in Eq. (5), yields a linear fit with a slope of −1/kT. The electron temperature can be calculated from the slope of the Boltzmann's plot without knowing the partition function. The magnesium atomic lines at wavelength of 383.2, 470.3 and 518.4 nm were used to calculate the electron temperature. The spectroscopic data of A mn , E m and g m of the MgI spectral line can be retrieved from the NIST database. The spectroscopic data of the MgI spectra lines are listed in Table 1.
The Boltzmann plot at a delay time of 100 ns and energy of 100 mJ is shown in Fig. 5, and the slope of the plot yielded an electron temperature of 8810 K. The temporal evolution of the electron temperature is shown in Fig. 6, with a delay time varying from 100 to 1000 ns at three   Fig. 7, the electron temperature reaches their highest value at 10164 K, with a delay time of 100 ns and laser energy of 350 mJ, and then decreases slowly up to 8833.6 K at 500 ns. Figure 8 depicts a plot of the electron temperature against the energy of the laser. As evident from the figure, the electron temperature increases with increasing laser energy.

Conclusion
The emission spectroscopy of the laser-induced magnesium plasma in atmospheric air was investigated. The emission spectral lines were resolved at different delay times. From the time-resolved emission spectra of the laser-induced Mg plasma, we observed that the characteristic intensities of the spectral lines rapidly decrease with a larger delay times, this was as a result of bremsstrahlung emission and radiative recombination between the ions and electrons, and this is due to plasma quenching. At a delay time of 100 ns, a strong continuum was observed.