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Abstract
Stark broadening of spectral lines in laser-produced plasmas is highly sensitive to changes in ambient pressure. This paper presents a novel time-resolved Stark broadening measurements of the OI emission at 777 nm in air plasmas from atmospheric pressure down to 200 Torr. The electron density is calculated from the measured Stark width, varying between 0.11-1.87×1017 m−3; the data demonstrate that decreasing ambient pressure directly decreases the electron density at a given gate delay. NII emissions are used to determine electron temperature via the Boltzmann method, which is found to range from 1.6-3 eV. The calculated temperature is higher in lower pressure air plasmas due to the absence of collisional cooling effects. The tabulated Stark broadening measurements of the OI 777 nm line will be of great use in further studies performing diagnostic calculations in low-pressure, high-temperature environments, such as high-speed aerodynamic flows.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Laser-induced breakdown spectroscopy (LIBS) is a widely used technique implemented for plasma diagnostic characterization and chemical analysis. LIBS efficiently generates a plasma whose optical emissions can be recorded to calculate plasma diagnostic parameters about solid [1,2], liquid [3], gas [4–7], and aerosolized targets [8]. Typically, gaseous LIBS experiments are utilized to characterize plasma properties for high-speed aerodynamic, combustion, and extraterrestrial atmospheric study applications [4,9–15]. Gaseous LIBS is particularly useful for observing changes in electron density and temperature as the laser-produced plasma (LPP) plume evolves dynamically over time [16,17]. LPPs experience a phenomenon called the Stark effect, in which the local electric field caused by the electrons within the plasma splits the degenerate energy states of the electrons and broadens atomic spectral emissions [18,19]. This broadening value can be used to determine the electron density of the plasma [20]. Furthermore, the relative intensities of the spectral emissions of the same species can be used with the Boltzmann equation to determine the electron temperature, assuming partial local thermodynamic equilibrium (pLTE) conditions [19,21].
In typical gaseous LIBS studies involving air or fuel-air mixtures, the hydrogen alpha line at 656 nm is used for quantitative analysis due to its prominence and the abundance of literature quantifying the relationship between H$_{\alpha }$ Stark width and electron density [22,23]. However, air plasmas often present higher-intensity spectral lines for oxygen and nitrogen because of their relative abundance in the atmosphere [24]. Atomic emissions of neutral oxygen, such as O$_I$ at 777 nm, are prominent in the spectrum of air and air mixtures under a wide range of conditions [11,25]. Patnaik et al. reported a much lower background of the O$_I$ 777 nm emission compared to the H$_{\alpha }$ and N emissions in fuel-air plasmas, allowing calculations of the fuel-air ratio with higher fidelity [26]. This line has been used similarly for in situ flame diagnostics to study combustion processes [27]. LIBS measurements are highly dependent on ambient conditions, such as pressure, due to the avalanche breakdown process that generates the laser-produced plasma [28]. Recent studies have extended the use of O atomic emissions to lower-pressure regimes where gaseous breakdown and dynamic plasma processes differ significantly from atomospheric pressure. The O$_I$ 777 nm line has been used to standardize measurements made from LIBS spectra on the Martian surface and enable higher fidelity diagnostic analysis [29–32]. These results indicate that atomic oxygen emissions have the potential to be used for air plasma diagnostic measurements in unique environments, particularly reacting flows in the upper atmosphere. Low-density and low-pressure hypersonic flows contain atomic oxygen, which generates radiative emissions [33,34]; these emissions could potentially be used to perform diagnostic characterization of plasma flows in the hypersonic environment. However, using atomic oxygen spectral emissions as a diagnostic metric for such applications requires a more advanced understanding of how these lines manifest under different pressure conditions.
Stark widths of atomic oxygen emissions have been tabulated to some extent in prior studies at atmospheric pressures [35–37] but probing the behavior of oxygen Stark broadening at lower pressures would greatly benefit future diagnostic applications in this regime. This study presents novel Stark broadening measurements of the O$_I$ 777 nm line in laser-induced air plasmas generated at 200 - 730 Torr over a 1$\mu$s period. Electron density is calculated from the O Stark width and compared to the electron density calculated from H$_{\alpha }$ Stark broadening extracted from the same spectra. electron temperature is then determined from intensities of N$_{II}$ emissions using the Boltzmann method to fully analyze the evolution of diagnostic parameters of the LPP under different pressure conditions. The results of this investigation provide new insight into the dynamic behavior of LPPs at subatmospheric pressures. The tabulation of novel O$_I$ Stark widths at these pressure conditions will help inform future studies performing diagnostic characterization of low-pressure plasmas and reactive flows.
2. Experimental setup
A schematic of the experimental setup used is shown in Fig. 1. An Nd:YAG laser (New Wave GEMINI PIV) with an output wavelength of 1064 nm and a pulse width of 10 ns provided pulses with an energy of 180 mJ/pulse at a repetition frequency of 10 Hz. The pre-focused beam diameter is given nominally as 5mm by the manufacturer. The beam was focused in the center of the vacuum cube of 6 inches x 6 inches x 6 inches using a planoconvex lens with f=+110 mm. Previous literature demonstrates that a shorter focal length lens leads to larger shot-to-shot deviations in signal due to the reductionn in focal volume; using a longer focal length lens to focus the laser radiation onto the target yields better measurement precision [38]. LIBS signals were collected using a second lens with f=+70 mm to direct light to an Ocean Insight HR2 VIS-NIR spectrometer equipped with a 600 grooves/mm grating blazed at 400 nm, a slit width of 10 $\mu$m, $\Delta \lambda$ = 0.231 nm, and a 2098 pixel CCD. The Ocean Insight spectrometer software (Ocean View) performed a non-linearity correction using a calibration file from an Ocean Insight deuterium halogen calibration lamp, enabling automatic correction for spectrometer efficiency during data collection.
Fig. 1. Schematic diagram of main experimental setup components; 1064nm pulsed laser, vacuum chamber, optics, and Ocean Insight HR2 compact spectrometer.
This yielded spectral recordings from 350-800 nm. The pressure in the chamber was regulated using a vacuum pump and a Pirani gauge attached to the chamber, with no gas flow occurring during data acquisition at a given pressure. This experiment recorded breakdown spectra at ambient pressures between 200-730 Torr. A digital delay generator (DDG) was implemented to synchronize timing signals between the laser and spectrometer and achieve time-resolved spectral recordings. The DDG channel connected to the spectrometer was synced to plasma formation by observing traces of the spectrometer gate pulse and plasma signal from a fast photodiode on an oscilloscope. This allowed the value of the spectrometer channel delay on the DDG to be aligned to an effective ’time zero’, after air breakdown and plasma formation. From this point, the channel delay was increased in 100 ns steps out to 1000 ns to record spectral response over a 1 $\mu$s period. The gate width was set to 1 $\mu$s, and 100 recordings were taken at each gate delay for each pressure. This allowed for the capture of time-resolved spectra as the plasma decayed; Fig. 2 shows the monotonic decrease of the O I 777 nm line intensity at 730 Torr over that 1 $\mu$s period observed from the averaged recordings at each gate delay time.
3. Electron temperature determination
3.1 Boltzmann method
The following relation, derived from the Boltzmann equation, is implemented to determine the electron temperature using intensities of various recorded N$_{II}$ emissions [21]:
The left-hand side of Eq. (1) can be plotted against the upper-level energy of the N$_{II}$ line transitions (E$_k$) to generate a Boltzmann plot, where the slope is proportional to the inverse of the electron temperature [39]. The y-intercept term includes $h$, $c$, $N$, and $U(T)$, which represent Planck’s constant, speed of light, total species population, and partition function, respectively. The terms $I^{ki}$, $\lambda$, $g_k$, and $A_{ki}$ refer to the line intensity of the excited $i^{th}$ degenerate $k$ state, the transition wavelength, the degeneracy of the excited energy level, and the transition probability for a given spectral emission line, respectively. The symbols $E_k$, $k_B$, and $T$ refer to the upper-level energy, Boltzmann constant, and excitation temperature, respectively. By plotting the left side of Eq. (1) against the energy corresponding to the excited state of the emission line, the excitation temperature in eV can be determined from the experimental data using a linear fit to calculate the slope. Under partial local thermodynamic equilibrium, discussed in Sect. 3.2, this excitation temperature is equal to the electron temperature. The following N$_{II}$ lines identified in the experimental spectra were used to calculate the electron temperature based on their intensities and the corresponding Boltzmann parameter values tabulated in the NIST ASD [40]: These lines were chosen for temperature analysis because they manifested in the spectra with sufficient resolution and prominence to be effectively used in Eq. (1). Figure 3 displays values from Eq. (1) and the corresponding line fits for spectra captured at 0 ns and 800 ns at 300 Torr, with corresponding T$_e$ from the inverse of the line slope.
3.2 McWhirter criterion
The validity of the Boltzmann temperature method is based on the assumption that the plasma is in a partial local thermodynamic equilibrium (pLTE). To determine whether the laser-induced plasma was in pLTE, the McWhirter criterion [41]
is employed, given by Eq. (2). Here, T$_e$ is the electron temperature (K) and E$_{nm}$ is the maximum energy difference between two consecutive excited states (eV) of the spectral lines used. Note that the Eq. (2) is a necessary but insufficient criterion for the LTE condition [42]. The minimum and maximum electron densities estimated from the Stark broadening of the O$_I$ line are 0.11$\times$10$^{17}$ cm$^{-3}$ and 1.87$\times$10$^{17}$ cm$^{-3}$, respectively. The electron density calculated using H$_{\alpha }$ ranges from 0.49 – 1.85 $\times$10$^{17}$ cm$^{-3}$. Using the electron temperature at each data point and a maximum $\Delta$E$_{nm}$ of 3.1 eV, the right-hand side of Eq. (2) ranges from 6.26 – 8.78$\times$10$^{15}$ cm$^{-3}$. The computed electron density using either chosen emission therefore is always at least one order of magnitude above the calculated McWhirter criterion threshold value for the corresponding electron temperature; Therefore, the pLTE condition is satisfied across all data points in this experiment [42,43].3.3 Temperature analysis
The selected N$_{II}$ emissions listed in Table 1 were implemented with Eq. (1) to calculate the electron temperature at each pressure level and time delay (t$_d$). Time-resolved measurements of electron temperature from 0-1$\mu$s in 100 ns increments between 200 and 730 Torr are shown in Fig. 4. The uncertainty values of the error bars stem from the shot-to-shot standard deviation of the N$_{II}$ lines used for the Boltzmann plot. This standard deviation was propagated through the calculation of temperature using fundamental statistical error propagation rules. The data clearly indicate an inverse relationship between electron temperature at a given time and ambient pressure, which exactly follows the results of [44]. This previous study, conducted at 760-4500 Torr, showed the same increase in temperature as the pressure level decreased toward atmospheric levels. The results of this experiment extend the earlier result to lower pressures and across a wider span of plasma lifetime. The inverse relation between T$_e$ and pressure has been observed in other studies [45–48]; Higher pressures are accompanied by an increase in collisional energy transfer between electrons and the background gas in the chamber, effectively removing energy from the electrons and reducing their temperature. This phenomenon, also called collisional cooling, was observed by Harilal et. al [49] and Hafez et. al. [50] to be more remarkable at increasing gas pressures. Bogaerts et. al. postulated that as the background gas is initially near room temperature, the direct cooling effect is more pronounced with higher amounts of background gas molecules at higher pressures. [51].
Fig. 4. Decay of electron temperature over 1$\mu$s period at varying gas pressures with exponential fit for each pressure.
Table 1. Selected N$_{II}$ emission lines used for temperature determination, along with NIST database parameters for Boltzmann equation fit.
The extension of this trend to subatmospheric pressure air plasmas aligns with these prior theories indicating the lack of background gas inhibits collisional cooling of electrons. More importantly, the time- and pressure-resolved measurements in this study indicate two important conclusions. Firstly, lower pressure gases can facilitate the generation of higher temperature LPPs. Second, lower ambient pressures lead to less cooling of the plasma over its lifetime. The latter determination is made by fitting a single term exponential of the form T = Ae$^{bt}$ to the data and comparing the temperature decay coefficient b, representing a characteristic time with units ns$^{-1}$, at each pressure. Table 2 shows an overall increase in the decay rate with increasing pressure; the most likely explanation for this trend is that the increased presence of a cooler background gas at higher pressures accelerates collisional electron cooling, causing the temperature to decay more rapidly. Therefore, this decay coefficient b can be interpreted as the cooling rate of the plasma. The rise in the decay rate is less drastic as the ambient pressure approaches atmospheric levels, indicating that this effect is more pronounced at lower pressure levels, where there is less cooler ambient gas present to facilitate collisional energy transfer from electrons in the plasma.
Table 2. Exponential fit coefficients quantifying temperature decay over 1 $\mu$s at varying pressure.
4. Electron density determination
4.1 Stark width determination
The Stark effect produces broadening of spectral emission lines; this parameter can be numerically extracted from recorded data and used for plasma diagnostic measurements [20,52]. In this study, Stark broadening of the O$_I$ 777 nm emission is pronounced across all examined pressures and gate delays, as shown above in Fig. 2. Temporal differences in broadening at different gate delays were visually apparent; as expected, the peak full-width at half-max (FWHM) decreases over plasma lifetime. The reduction of this FWHM, and by extension the Stark width, can be used to calculate the decay of electron density over time. Typically, LIBS emissions can be characterized by the convolution of a Gaussian and a Lorentzian profile. The Lorentzian FWHM stems from the Stark effect, which the Gaussian FWHM results from Doppler broadening caused by the velocity distribution of particles in the plasma. In the literature, it has been demonstrated that the Stark effect dominates in LPPs early after plasma formation, and the Gaussian contribution of Doppler broadening is negligible [53–55]. In these cases, the FWHM of a recorded emission peak can be reduced to the sum of the Stark width and instrument broadening [56]. As such, the following relation is used to determine the Stark width $\Delta$w from the measured peak FWHM $\Delta {\lambda }_{total}$ and the instrument broadening $\Delta {\lambda }_{inst}$:
The instrument broadening $\Delta {\lambda }_{inst}$ was obtained by recording the 632 nm emission of a HeNe laser and determining the FWHM of the recorded peak, which was calculated to be 0.464 nm. This process was also repeated for the present hydrogen Balmer alpha (H$_{\alpha }$) emission at 656 nm in order to compare the electron density calculated from Stark broadening of the 777 nm and 656 nm emissions. This benchmark comparison is implemented to evaluate the efficacy of using the more prominent O$_I$ line for plasma diagnostics.
Utilizing the temperatures obtained from the N$_{II}$ lines in Section 3 and the Stark widths obtained from the O$_I$ 777 nm line as per Eq. (3), a methodology developed by Griem using the equation for line broadening and tabulated line parameters was implemented to determine the electron density. Eq. (4) provides a relationship between broadening ($\Delta w$) and density (n$_e$). W and A are the width and shift parameters, respectively, for the emission line chosen tabulated by Griem [52] and listed in Table 3. N$_D$ is the Debye number, given as N$_D$ = 1.72$\times$10$^{9}\frac {T_e^{1.5}}{n_e^{.5}}$.
Figure 5 shows the plotted equations using width and impact parameters for O$_I$ 777 nm at 20000 and 40000K. The yellow dotted line represents the interpolation fit calculated at a temperature of 26948K for a given pressure and gate delay. The intersecting black dashed lines represent where the measured Stark width taken from the spectra of that data point matches an electron density on the interpolated curve. This is repeated for all pressures and gate delay conditions to determine the electron density.
Fig. 5. Example of interpolation fit used to determine electron density from Stark broadening for O$_I$.
Table 3. Impact and width parameters (in Angstroms) for O$_I$ 777 nm line used for interpolation fit to determine electron density.
The Stark width of H$_{\alpha }$ was used with Eq. (5) developed by Surmick and Parriger [54] to determine the electron density for a comparison between the two emissions. The comparative time resolved electron density measurements are shown in Fig. 6. The error represents one standard deviation of the Stark width measured from 100 recordings at each t$_d$; this error was propagated through the electron density calculations using basic rules of uncertainty analysis.
Fig. 6. Temporally resolved electron density calculated from Stark broadening of a) O$_I$ 777 nm and b) H$_{\alpha }$ 656 nm.
4.2 Electron density analysis
A direct relationship between gas pressure and electron density is apparent, in contrast to the observed relationship between temperature and pressure. The electron density value calculated from both emission lines increases for all gate delays as the ambient pressure increases toward atmospheric levels. Once again, this follows from the results of [44]. At early gate delays, the formation of the plasma is largely driven by avalanche ionization due to inverse Brehmsstrahlung processes; the spectra in these regimes typically exhibit increased Stark widths of atomic emissions because of higher electron densities present in the plasma. As ambient pressure is diminished, the intermolecular distance increases, effectively reducing collisional cross sections for the interactions which govern ionization and electron generation in the early plasma. As a result, the early electron densities calculated from the broadening of both emissions are notably higher at atmospheric pressure. Decay of the electron density over the observed 1$\mu s$ period is evident as the plasma cools and recombination occurs; this is quantified by fitting an equation of the form n$_e$=Ce$^{dt}$ to the data, where d represents a characteristic electron density decay time (ns$^{-1}$). Table 4 lists exponential fit parameters for the decay curves at all pressures from the 656 and 777 nm emissions. The decay constant for the fits to n$_e$ determined from the Stark width of H$_{\alpha }$ overall appears to increase as pressure increases, albeit erratically and not monotonically. Including uncertainty, the decay rates for 400 vs. 500 Torr and 600 vs. 730 Torr are not numerically distinguishable. However, a noticeable difference in this parameter exists between the highest and lowest pressure cases. Similar behavior is reflected in the O$_I$ fit curves, with larger and more distinguishable differences in d between pressure levels. This initial comparison of the calculated electron density from the different emission lines indicates that the O$_I$ Stark width could be more sensitive to changes in ambient pressure. The 777 nm line is far more prominent in intensity than H$_{\alpha }$ in air plasmas, and presents with a lower FWHM value. This could partially explain the apparent higher sensitivity to ambient pressure and more drastic change in the decay parameter d reflected by the O$_I$ data in Table 4.
Table 4. Exponential fit parameters for electron density decay curves
Further elucidation of this observed decay behavior can be provided by examining the numerical relationship between plasma parameters and recombination. The electron-ion recombination rate $\alpha _r$ [cm$^3$/s] for hydrogen-like plasmas with $T_e$ < 15 eV is defined as follows [57]:
The $T^{-1/2}$ dependence of Eq. (6) means that the recombination rate decreases as temperature increases. The Boltzmann plot analysis in Sect. 3 supports the trend seen in electron density decay, as lower pressures were characterized by higher electron temperatures due to the lack of collisional cooling. On the basis of the relation above, a higher electron temperature for the plasma at a given pressure and gate delay would then be characterized by a lower recombination rate, effectively slowing the decay of electron density over time. While this equation does not provide a direct numerical correlation between $\alpha _r$ and the fit parameter d, the physics behind the relation between recombination and temperature given by this equation helps to interpret the fit parameters and explain the physical processes that occur in the LPP.
Differences in the electron density calculated from the different emission lines is visually represented in Fig. 7(a), showing the relative difference between n$_e$ calculated from Stark width of both lines at all pressures and gate delays. The values tend to agree with less than 20${\% }$ relative difference when t$_d$ < 200 ns, and then begin to diverge significantly as the plasma cools. This relative difference begins to rise across all pressures as gate delay increases, reaching the 45-80${\% }$ range by 1 $\mu$s. The relative difference in calculated n$_e$ also appears to increase as ambient pressure decreases. As discussed above in the comparison of the decay parameter d, the 777 nm emission Stark width appears more sensitive to changes in pressure and decays faster than H$_{\alpha }$. This could potentially explain the large divergence between the two measured quantities at lower pressures and longer gate delays reflected in Fig. 7, particularly since developed equations relating H$_\alpha$ Stark width to n$_e$ often lack data compiled in lower pressure regimes. Additionally, Fig. 7(b) compares the signal-to-noise ratio (SNR) of the H and O lines at 200, 400, and 730 Torr. SNR is calculated as the difference between peak intensity and mean value of the background, divided by the standard deviation of the background [58]. It should be noted that the SNR of H$_{\alpha }$ does not vary greatly between the three pressures compared to O$_I$. This can largely be attributed to the fact that the intensity of H$_{\alpha }$ was much lower than that of the major N and O lines in this data set, yielding a lower SNR with less variation across temporal and pressure conditions. The SNR of the 777 nm shows some variation in magnitude across pressure, but demonstrates similar behavior across the 1000 ns recording. The plasma formation processes that dominate the early lifetime of an LPP overwhelm the spectrum with continuum emissions and lower the SNR of measured atomic emission lines. Over time, the continuum emission decreases but the atomic emissions remain, lowering the background intensity relative to that of the peaks and increasing measured SNR. This trend manifests clearly in the 777 nm line at 400 and 730 Torr, as the SNR increases till 500 ns and begins to plateau. Overall, this study provides initial evidence demonstrating the prominence and sensitivity of the O$_I$ emission in low pressure regimes, suggesting that it may be more useful for diagnostic purposes in low/dynamic ambient pressure plasmas. All recorded O$_I$ Stark width data, along with corresponding n$_e$ and T$_e$ is tabulated in Table 5.
Fig. 7. a) Relative difference in calculated electron density using O$_I$ vs H$_{\alpha }$ Stark width and b) SNR comparisons of both lines at three different ambient pressures.
Table 5. Tabulated data of O$_I$ Stark widths, computed n$_e$, and T$_e$, and error values for all parameters across experimental conditions.
5. Summary and conclusions
We report the measurement of time-resolved Stark broadening of laser-induced air plasma at 200–730 Torr. The Stark width of the O$_{I}$ 777 nm and H$_{\alpha }$ 656 nm emissions were employed to calculate the time-resolved electron density. The electron temperature calculated from the Boltzmann plots of N$_{II}$ emission line intensities at sub-atmospheric pressures is also reported. Our findings mirror prior studies, which indicate that the electron temperature increases with decreasing ambient pressure, which could be due to the decreasing contributions of collisional energy transfer. The electron density decays quicker at higher pressures, following the inverse temperature dependence of plasma recombination. Finally, novel Stark width measurements of the O$_{I}$ 777 nm line are tabulated, providing an important reference data set to future diagnostic studies characterizing air plasmas at sub-atmospheric pressures. The demonstrated sensitivity and prominence of this O$_I$ emission in air plasmas across a variety of low pressure conditions indicate its potential for use in higher fidelity diagnostic measurements in similar ambient environments.
Funding
Air Force Research Laboratory.
Disclosures
The authors declare that they have no conflicts of interest. This work is Distribution Unlimited; approved for public release under AFRL-2023-5459. The views expressed are those of the author and do not necessarily reflect the official policy or position of the Department of the Air Force, the Department of Defense, or the U.S. government.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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