# Comprehensive Analysis of Copper Plasma: A Laser-Induced Breakdown Spectroscopic Approach

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## Abstract

**:**

_{e}), electron density (N

_{e}), number of particles in the Debye sphere, plasma frequency, inverse bremsstrahlung absorption coefficient, electron thermal velocity, electron–ion collision frequency and in the decrease of Debye length (λ

_{D}) and plasma skin depth (PSD). The experimental techniques and the theoretical explanations for the variation of plasma parameters and their applications are also detailed. As the ambient pressure increases, the motion of plasma species becomes restricted, resulting in the increase of T

_{e}, calculated using the Boltzmann plot. From the values of λ

_{D}, PSD, and N

_{e}, it is understood that the copper plasma under investigation is thermally non-relativistic and satisfies McWhirter’s criterion, thus, revealing the local thermodynamic equilibrium condition of plasma. The effects of Debye shielding and stark broadening on the spectral lines are also investigated. Thus, the study helps bring newfangled dimensions to the application of plasma by exploring the possibility of tailoring plasma parameters.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Instrumentation

#### 2.2. Plasma Parameters

_{e}is the plasma electron temperature, k

_{B}is Boltzmann’s constant, and g

_{i}and g

_{j}are the degeneracy of excited i and ground j state. The minimum electron density (N

_{e}) necessary for the LTE between two states separated in energy by ΔE (in eV) is a function of T

_{e}(K) and is given by the McWhirter criterion (Equation (2)) [24]. Under the LTE condition, the T

_{e}is calculated from the intensities (Equation (3)) of spectral lines using the Boltzmann plot method [22,25,26].

_{ij}—transition probability, E

_{i}—excited level energy of the upper state i, F—experimental factor, and C—the species concentration. From the slope of the plot of $ln\frac{I\lambda}{{A}_{ij}{g}_{i}}$ vs. E

_{i}, the electron temperature T

_{e}can be deduced.

_{1/2}, of the spectral lines, N

_{e}can be calculated using Equation (5) [27,28,29]. The Δλ

_{1/2}of a well-isolated Stark-broadened line arises due to the contribution from electron impact and ion impact (first and second term of the Equation (5), respectively) [30].

_{I}is the ion-broadening parameter, and N

_{D}is the number of particles in Debye Length. By neglecting the contribution of ion impact broadening, being small, Equation (5) can be expressed as [22,31]

_{e}and T

_{e}) can be used to calculate the other essential plasma parameters. To reduce the effect of the local electric field and to maintain the quasi-neutrality characteristics inside the plasma, the charged particles respond to give a shielding called Debye Shielding. The shielding length is referred to as the Debye length (λ

_{D}), also called the Debye radius. The λ

_{D}and the number of particles inside it, N

_{D,}can be obtained from Equations (7) and (8) [32].

_{b}). The value of f

_{b}that depends only on N

_{e}can be calculated using Equation (9) [33].

_{p}, the depth to which electromagnetic radiation can penetrate is called plasma skin depth (PSD) and is given by Equation (10), where c = 3 × 10

^{8}m/s.

_{e}, the electron of mass m

_{e}attains an average velocity called electron thermal velocity $\left({v}_{{T}_{e}}\right)$, given by Equation (12). In dense plasma, the electron–ion collision rate is high, and the rate of collision is given by Equation (13).

## 3. Results and Discussion

_{e}) is calculated, and its variation with P is shown in Figure 4b. It is observed that the value of T

_{e}is less at low chamber pressure and increases with the pressure for a given laser fluence (80 mJ), which is reflected as a decrease in the slope of the Boltzmann plot. When the chamber pressure is increased to 100 mbar, the value of T

_{e}is 11,273.46 K. This temperature is not included in Figure 4b as there is a greater difference in the values of pressure. The observation justifies the analysis of Figure 2 that the increase of P restricts the plume expansion and enhances the collision of energetic plasma species. Knowledge of plasma temperature is essential in magnetically confined plasma, to obtain fusion continuity for a long time in nuclear power plants [39].

_{e}, which can be estimated from the average FWHM of the Stark-broadened profile of the non-overlapped peaks in a spectrum. For example, at pressure 0.2 mbar, the peaks corresponding to Cu I—402.67, 406.52, 454.02, 459.63, 466.04, 510.42, 515.07, and 521.48 nm—are considered for the calculation of N

_{e}using the value of ω from the literature [40,41] in Equation (6). The representative peak at 515.07 nm at a pressure of 0.2 mbar for Cu I, showing stark broadening, is displayed in Figure 5a. Out of the three broadening mechanisms—Doppler broadening, collision broadening, and stark broadening—the third is the dominant broadening mechanism in the laser plasma, which influences the spectral linewidth more. The local electric field greatly influences the spectral emission from the densest region of the plasma, leading to a stark broadening and shift in the atomic and ionic emission line. The pressure dependence of N

_{e}in the range of 0.01 mbar to 1 mbar is shown in Figure 5b. The study reveals that irrespective of the chamber pressure, the value of N

_{e}is greater than the critical value set by McWhirter’s criterion, indicating the LTE condition. It can also be understood from Figure 5b that N

_{e}increases, with P reaching a value of 2.24 × 10

^{16}cm

^{−3}at 100 mbar, which agrees well with the explanation given for plasma plume and T

_{e}. The greater the chamber pressure, the greater the number of air molecules in contact with the target surface, which plays a significant role in the energy exchange between them. The higher P reduces the mean free path of the species in the plasma, producing denser plasma with higher temperatures [42].

_{e}and the field refracts and reduces the laser energy density at the target. This accounts for the reduced rate of increase of T

_{e}and N

_{e}beyond 0.4 mbar. Another factor that comes into play is the inverse bremsstrahlung arising due to the increased collision frequency of plasma species. Knowledge of the plasma temperature and density is needed to realize the dissociation, atomization, ionization, and excitation processes in plasma that play a vital role in the quantitative analysis of materials using LIBS.

_{D}), calculated using Equation (7). Thus, λ

_{D}can be regarded as one of the fundamental properties of plasma, a function of N

_{e}and T

_{e}. The significance of investigating λ

_{D}is that it gives information about the quasi-neutrality of the plasma, as λ

_{D}is the characteristic distance of separation between electrons and ions in the plasma. The difference between the electron density (N

_{e}) and ion density (N

_{i}) ΔN = $\left|{N}_{e}-{N}_{i}\right|$, tells about the quasi-neutrality of the plasma system of length L. The variation of λ

_{D}and the total number of particles in the Debye sphere (N

_{D}—calculated using Equation (8)) with P is shown in Figure 6a,b. Figure 6a shows the decrease of λ

_{D}with ambient pressure. A comparison of λ

_{D}with plume size (L) reveals that λ

_{D}<< L, which agrees with the literature [43]. The quasi-neutrality condition demands ΔN << N

_{e}and N

_{i}or L >> λ

_{D}, which suggests that the plasma plume shown in Figure 2 is in a quasi-neutral state. The quasi-neutrality of a plasma can be defined on a macroscopic scale, while there may be deviations in the microscopic scale. From Figure 6b, it can be seen that N

_{D}increases with P. From Figure 5b and Figure 6b, it can be inferred that as the chamber pressure increases, the number density of charged species dominates in N

_{D}.

_{p}, the oscillating nature of the plasma is also investigated. The pressure dependence of f

_{p}, the characteristic plasma frequency, is shown in Figure 7a, which shows an increase with P due to the rise in T

_{e}and N

_{e}. The plasma electrons oscillate at high frequencies due to thermal distress. At larger f

_{p}(overdense plasma) the electromagnetic waves will get reflected from the plasma, and at smaller f

_{p}(underdense plasma) it will get refracted through the plasma. The decreasing nature of PSD, as evident from Figure 7b, is due to its inverse dependence on f

_{p}. From Equations (7) and (10) it is evident that the λ

_{D}and PSD are inversely proportional to the square root of N

_{e}. PSD can give information on the relativistic nature of the plasma in comparison with λ

_{D}, i.e., when λ

_{D}< PSD this means that the plasma is thermally non-relativistic (kT

_{e}<< m

_{e}c

^{2}= 0.5 MeV), and when λ

_{D}≥ PSD, plasma is said to be thermally relativistic [44]. Knowledge of the relativistic nature of plasma is highly essential in the applications such as ion propulsion, fast ignitor fusion, proton therapy, astrophysics, time-resolved radio-biological studies, and radio-chemistry experiments [45]. From Figure 6a and Figure 7b, it is evident that for the copper plasma in the present investigation, λ

_{D}< PSD, revealing that the plasma is thermally non-relativistic.

_{e}and N

_{D}increase with P. The variation of IB co-efficient, α

_{IB}, with P from 0.01 mbar to 1 mbar is shown in Figure 8a. The value of α

_{IB}at 100 mbar is 9.78 × 10

^{−15}cm

^{−1}. As the increase of P increases N

_{e}and N

_{D}, the probability of interaction of a photon with an electron in the plasma becomes high, which accounts for the increased absorption leading to the IB. As IB changes the electron momentum, the electron thermal velocity (${v}_{{T}_{e}}$) also changes. The variation of average velocity ${v}_{{T}_{e}}$, calculated using Equation (11), with P is shown in Figure 8b. The increase of T

_{e}, N

_{e}, N

_{D}, and ${v}_{{T}_{e}}$ with P enhances the electron–ion collision frequency (V

_{ei}), as shown in Figure 8c. The increase of ${v}_{{T}_{e}}$ with T

_{e}which in turn with P increases the electron momentum and, hence, lowers the electron de Broglie wavelength (λ

_{th,e}), is shown in Figure 8d.

## 4. Conclusions

_{e}is greater than the critical value set by McWhirter’s criterion. Thus, the increase of plasma density with pressure causes a shielding effect, decreasing the Debye length and increasing the total number of particles in the Debye sphere. The analysis of copper plasma also revealed that it fulfills the condition for quasi-neutrality, ΔN ˂˂ N

_{e}and N

_{i}or L >> λ

_{D}, which also agrees well with the plasma plume analysis. Since the plasma electrons oscillate at high frequency due to thermal distress, as T

_{e}and N

_{e}increase, the value of f

_{p}also increases with P. The variation of PSD with P throws light into the relativistic nature of plasma, which is highly significant for applications in astrophysics, proton therapy, and radiochemistry. In the present work, as λ

_{D}< PSD, the copper plasma is said to be thermally non-relativistic. Information regarding the highly dominant absorption mechanism, IB, in plasma is also studied. The variation of IB co-efficient, α

_{IB}, shows an increase with P, which is attributed to the enhanced interaction of photons with electrons in the plasma accounting for the increased IB absorption. This results in increased electron momentum, increasing electron thermal velocity, electron–ion collision frequency, and electron de Broglie wavelength with ambient pressure. Thus, the comprehensive analysis of the laser-induced copper plasma opens up the potential of LIBS in panoramic fields of science, where the plasma parameters play a significant role.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Cremers, D.A.; Radziemski, L.J. History and Fundamentals of LIBS. In Laser-Induced Breakdown Spectroscopy (LIBS); Miziolek, A.W., Palleschi, V., Schechter, I., Eds.; Cambridge University Press: Cambridge, UK, 2006; Volume 9780521852, pp. 1–39. ISBN 9780511541261. [Google Scholar]
- Noll, R. Laser-Induced Breakdown Spectroscopy; Springer Berlin Heidelberg: Berlin, Heidelberg, 2012; ISBN 978-3-642-20667-2. [Google Scholar]
- Kanyinda Jean-Noëla, M.; Tshamala Arthurb, K.; Jean-Marcc, B. LIBS Technology and Its Application: Overview of the Different Research Areas. J. Environ. Sci. Public Heal.
**2020**, 04, 134–149. [Google Scholar] [CrossRef] - Zhang, Q.; Liu, Y.; Chen, Y.; Zhangcheng, Y.; Zhuo, Z.; Li, L. Online Detection of Halogen Atoms in Atmospheric VOCs by the LIBS-SPAMS Technique. Opt. Express
**2020**, 28, 22844. [Google Scholar] [CrossRef] - Zhou, Z.; Ge, Y.; Liu, Y. Real-Time Monitoring of Carbon Concentration Using Laser-Induced Breakdown Spectroscopy and Machine Learning. Opt. Express
**2021**, 29, 39811. [Google Scholar] [CrossRef] - Ye, Y.; Wan, E.; Sun, Z.; Zhang, X.; Zhang, Z.; Liu, Y. Online Detection and Source Tracing of Crop Straw Burning. J. Laser Appl.
**2022**, 34, 042049. [Google Scholar] [CrossRef] - Kochuev, D.A.; Voznesenskaya, A.A.; Galkin, A.F.; Khorkov, K.S.; Chernikov, A.S.; Chkalov, R. V Influence of Laser-Induced Plasma Parameters on the Formation of Laser-Induced Surface-Periodic Structures. J. Phys. Conf. Ser.
**2021**, 2077, 012009. [Google Scholar] [CrossRef] - Lachko, I.M.; Volkov, R.V.; Golishnikov, D.M.; Gordienko, V.M.; Dzhidzhoev, M.S.; Mar’in, B.V.; Mikheev, P.M.; Savel’ev, A.B.; Uryupina, D.S.; Shashkov, A.A. Control of Femtosecond Laser Plasma Parameters by Surface Contaminants Cleaning with Preceding Laser Pulse. In Proceedings of the Volume 5482, Laser Optics 2003: Superintense Light Fields and Ultrafast Processes, St. Petersburg, Russia, 30 June–4 July 2003; pp. 102–111. [Google Scholar]
- Ojeda-G-P, A.; Döbeli, M.; Lippert, T. Influence of Plume Properties on Thin Film Composition in Pulsed Laser Deposition. Adv. Mater. Interfaces
**2018**, 5, 1701062. [Google Scholar] [CrossRef] - Escobar-Alarcón, L.; Arrieta, A.; Camps, E.; Romero, S.; Fernandez, M.; Haro-Poniatowski, E. Influence of the Plasma Parameters on the Properties of Aluminum Oxide Thin Films Deposited by Laser Ablation. Appl. Phys. A
**2008**, 93, 605–609. [Google Scholar] [CrossRef] - Radziemski, L.J.; Cremers, D.A. Laser-Induced Plasmas and Applications; Marcel Dekker: New York, NY, USA, 1989; ISBN 9780511541261. [Google Scholar]
- Diwakar, P.K.; Hahn, D.W. Study of Early Laser-Induced Plasma Dynamics: Transient Electron Density Gradients via Thomson Scattering and Stark Broadening, and the Implications on Laser-Induced Breakdown Spectroscopy Measurements. Spectrochim. Acta Part B At. Spectrosc.
**2008**, 63, 1038–1046. [Google Scholar] [CrossRef] - Irimiciuc, S.A.; Gurlui, S.; Bulai, G.; Nica, P.; Agop, M.; Focsa, C. Langmuir Probe Investigation of Transient Plasmas Generated by Femtosecond Laser Ablation of Several Metals: Influence of the Target Physical Properties on the Plume Dynamics. Appl. Surf. Sci.
**2017**, 417, 108–118. [Google Scholar] [CrossRef] - Krebs, H.-U.; Weisheit, M.; Faupel, J.; Süske, E.; Scharf, T.; Fuhse, C.; Störmer, M.; Sturm, K.; Seibt, M.; Kijewski, H.; et al. Pulsed Laser Deposition (PLD)—A Versatile Thin Film Technique. In Advances in Solid State Physics; Springer: Berlin, Germany, 2003; pp. 505–518. [Google Scholar]
- Richter, A. Characteristic Features of Laser-Produced Plasmas for Thin Film Deposition. Thin Solid Films
**1990**, 188, 275–292. [Google Scholar] [CrossRef] - Kumar, N.; Dash, S.; Tyagi, A.K.; Raj, B. Dynamics of Plasma Expansion in the Pulsed Laser Material Interaction. Sadhana
**2010**, 35, 493–511. [Google Scholar] [CrossRef] - Sarkar, A.; Shah, R.V.; Alamelu, D.; Aggarwal, S.K. Studies on the Ns-IR-Laser-Induced Plasma Parameters in the Vanadium Oxide. J. At. Mol. Opt. Phys.
**2011**, 2011, 1–7. [Google Scholar] [CrossRef] - Harilal, S.S.; Bindhu, C.V.; Issac, R.C.; Nampoori, V.P.N.; Vallabhan, C.P.G. Electron Density and Temperature Measurements in a Laser Produced Carbon Plasma. J. Appl. Phys.
**1997**, 82, 2140–2146. [Google Scholar] [CrossRef] - Harilal, S.S.; Phillips, M.C.; Froula, D.H.; Anoop, K.K.; Issac, R.C.; Beg, F.N. Optical Diagnostics of Laser-Produced Plasmas. arXiv
**2022**, arXiv:2201.08783. [Google Scholar] - Hussain Shah, S.K.; Iqbal, J.; Ahmad, P.; Khandaker, M.U.; Haq, S.; Naeem, M. Laser Induced Breakdown Spectroscopy Methods and Applications: A Comprehensive Review. Radiat. Phys. Chem.
**2020**, 170, 108666. [Google Scholar] [CrossRef] - Pasquini, C.; Cortez, J.; Silva, L.M.C.; Gonzaga, F.B. Laser Induced Breakdown Spectroscopy. J. Braz. Chem. Soc.
**2007**, 18, 463–512. [Google Scholar] [CrossRef] - Hafez, M.A.; Khedr, M.A.; Elaksher, F.F.; Gamal, Y.E. Characteristics of Cu Plasma Produced by a Laser Interaction with a Solid Target. Plasma Sources Sci. Technol.
**2003**, 12, 185–198. [Google Scholar] [CrossRef] - Griem, H.R. Principles of Plasma Spectroscopy; Cambridge University Press: Cambridge, UK, 1997; ISBN 9780521455046. [Google Scholar]
- McWhirter, R.W.P.; Richard, H. Plasma Diagnostic Techniques; Huddlestone, R.H., Leonard, S.L., Eds.; Academic Press: New York, NY, USA, 1965. [Google Scholar]
- Liu, H.C.; Mao, X.L.; Yoo, J.H.; Russo, R.E.U. Early Phase Laser Induced Plasma Diagnostics and Mass Removal during Single-Pulse Laser Ablation of Silicon. Spectrochim. Acta Part B At. Spectrosc.
**1999**, 54, 1607–1624. [Google Scholar] [CrossRef] - Fikry, M.; Tawfik, W.; Omar, M.M. Investigation on the Effects of Laser Parameters on the Plasma Profile of Copper Using Picosecond Laser Induced Plasma Spectroscopy. Opt. Quantum Electron.
**2020**, 52, 249. [Google Scholar] [CrossRef] - Gornushkin, I.B.; King, L.A.; Smith, B.W.; Omenetto, N.; Winefordner, J.D. Line Broadening Mechanisms in the Low Pressure Laser-Induced Plasma. Spectrochim. Acta Part B At. Spectrosc.
**1999**, 54, 1207–1217. [Google Scholar] [CrossRef] - Colón, C.; Alonso-Medina, A.; Herrán-Martínez, C. Spectroscopic Study of a Laser-Produced Lead Plasma: Experimental Atomic Transition Probabilities for Pb III Lines. J. Phys. B At. Mol. Opt. Phys.
**1999**, 32, 3887–3897. [Google Scholar] [CrossRef] - Shaikh, N.M.; Rashid, B.; Hafeez, S.; Jamil, Y.; Baig, M.A. Measurement of Electron Density and Temperature of a Laser-Induced Zinc Plasma. J. Phys. D. Appl. Phys.
**2006**, 39, 1384–1391. [Google Scholar] [CrossRef] - Sarkar, A.; Singh, M. Laser-Induced Plasma Electron Number Density: Stark Broadening Method versus the Saha–Boltzmann Equation. Plasma Sci. Technol.
**2017**, 19, 025403. [Google Scholar] [CrossRef] - Search, H.; Journals, C.; Contact, A.; Iopscience, M.; Address, I.P. Characteristics of Excimer Laser Induced Plasma from an Aluminum Target by Spectroscopic Study Characteristics of Excimer Laser Induced Plasma from an Aluminum Target by Spectroscopic Study. Jpn. J. Appl. Phys.
**1999**, 2958, 18–24. [Google Scholar] - Gibbon, P. Introduction to Plasma Physics. In Proceedings of the 2014 CAS-CERN Accelerator School: Plasma Wake Acceleration, Geneva, Switzerland, 23–29 November 2014; pp. 51–65. [Google Scholar] [CrossRef]
- Chen, F.F. Introduction to Plasma Physics and Controlled Fusion; Springer International Publishing: Cham, Switzerland, 2016; ISBN 978-3-319-22308-7. [Google Scholar]
- Haq, S.U.; Ahmat, L.; Mumtaz, M.; Shakeel, H.; Mahmood, S.; Nadeem, A. Spectroscopic Studies of Magnesium Plasma Produced by Fundamental and Second Harmonics of Nd:YAG Laser. Phys. Plasmas
**2015**, 22, 083504. [Google Scholar] [CrossRef] - Hahn, D.W.; Lunden, M.M. Detection and Analysis of Aerosol Particles by Laser-Induced Breakdown Spectroscopy. Aerosol Sci. Technol.
**2000**, 33, 30–48. [Google Scholar] [CrossRef] - Jaspers, R.J.E. Plasma Spectroscopy. Fusion Sci. Technol.
**2012**, 61, 384–393. [Google Scholar] [CrossRef] - Unnikrishnan, V.K.; Alti, K.; Kartha, V.B.; Santhosh, C.; Gupta, G.P.; Suri, B.M. Measurements of Plasma Temperature and Electron Density in Laser-Induced Copper Plasma by Time-Resolved Spectroscopy of Neutral Atom and Ion Emissions. Pramana
**2010**, 74, 983–993. [Google Scholar] [CrossRef] - NIST Atomic Spectra Database. Available online: http://physics.nist.gov (accessed on 1 January 2021).
- National Academies of Sciences, Engineering, and Medicine. Plasma Science:Enabling Technology, Sustainability, Security, and Exploration; The National Academies Press: Washington, DC, USA, 2021; ISBN 9780309677639. [Google Scholar]
- Konjević, N.; Wiese, W.L. Experimental Stark Widths and Shifts for Spectral Lines of Neutral and Ionized Atoms. J. Phys. Chem. Ref. Data
**1990**, 19, 1307–1385. [Google Scholar] [CrossRef] - Konjević, N.; Lesage, A.; Fuhr, J.R.; Wiese, W.L. Experimental Stark Widths and Shifts for Spectral Lines of Neutral and Ionized Atoms (A Critical Review of Selected Data for the Period 1989 Through 2000). J. Phys. Chem. Ref. Data
**2002**, 31, 819–927. [Google Scholar] [CrossRef] - Farid, N.; Bashir, S.; Mahmood, K. Effect of Ambient Gas Conditions on Laser-Induced Copper Plasma and Surface Morphology. Phys. Scr.
**2012**, 85, 015702. [Google Scholar] [CrossRef] - Wiesemann, K. A Short Introduction to Plasma Physics. arXiv
**2014**, arXiv:1404.0509. [Google Scholar] - Stenson, E.V.; Horn-Stanja, J.; Stoneking, M.R.; Pedersen, T.S. Debye Length and Plasma Skin Depth: Two Length Scales of Interest in the Creation and Diagnosis of Laboratory Pair Plasmas. J. Plasma Phys.
**2017**, 83, 595830106. [Google Scholar] [CrossRef] - Umstadter, D. Review of Physics and Applications of Relativistic Plasmas Driven by Ultra-Intense Lasers. Phys. Plasmas
**2001**, 8, 1774. [Google Scholar] [CrossRef] [Green Version]

**Figure 3.**(

**a**) Copper plasma emission spectrum at different ambient air pressure and (

**b**) the enlarged portion of the spectrum in the range 320 to 500 nm.

**Figure 4.**(

**a**) Boltzmann plot for Cu I emission lines and (

**b**) variation of electron plasma temperature, T

_{e}, (R

^{2}= 0.9957) at different ambient air pressure.

**Figure 5.**(

**a**) FWHM measurement of a Stark broadened peak at Cu I 515.07 nm and (

**b**) variation of density, N

_{e}(R

^{2}= 0.9580) with ambient air pressure.

**Figure 6.**Variation of (

**a**) Debye length, λ

_{D}(R

^{2}= 0.9288)

_{,}and (

**b**) number of particles in the Debye sphere, N

_{D}(R

^{2}= 0.9570)

_{,}with ambient air pressure.

**Figure 7.**Variations in (

**a**) electron plasma frequency, f

_{p}, (R

^{2}= 0.9613) and (

**b**) plasma skin depth, PSD, (R

^{2}= 0.9718) with ambient air pressure.

**Figure 8.**Variation of (

**a**) IB coefficient—α

_{IB}(R

^{2}= 0.9319) and (

**b**) electron-thermal velocity—${v}_{{T}_{e}}$ (R

^{2}= 0.9967), (

**c**) electron-ion collision frequency—V

_{ei}(R

^{2}= 0.8068) and (

**d**) electron thermal de Broglie wavelength—λ

_{th,e}(R

^{2}= 0.9957)with varying ambient air pressure.

Atom/Ion | Observed λ (nm) | A_{ij} (s^{−1}) | E_{i} (eV) | g_{i} | Transitions |
---|---|---|---|---|---|

Lower Level ➔ Upper Level | |||||

Cu I | 324.81 | 1.395 × 10^{8} | 3.816692 | 4 | 3d^{10}4p ➔ 3d^{10}4s |

Cu I | 327.21 | 1.376 × 10^{8} | 3.785898 | 2 | 3d^{10}4p ➔ 3d^{10}4s |

Cu I | 402.51 | 1.90 × 10^{7} | 6.867196 | 4 | 3d^{10}5d ➔ 3d^{10}4p |

Cu I | 406.6 | 2.10 × 10^{7} | 6.867646 | 6 | 3d^{10}5d ➔ 3d^{10}4p |

Cu I | 427.27 | 3.45 × 10^{7} | 7.737027 | 8 | 3d^{9}4s(^{3}D)5s ➔ 3d^{9}(^{2}D)4s4p(^{3}P°) |

Cu I | 453.38 | 2.12 × 10^{7} | 7.883492 | 4 | 3d^{9}4s(^{3}D)5s ➔3d^{9}(^{2}D)4s4p(^{3}P°) |

Cu I | 465.96 | 3.80 × 10^{7} | 7.737027 | 8 | 3d^{9}4s(^{3}D)5s ➔ 3d^{9}(^{2}D)4s4p(^{3}P°) |

Cu I | 471.33 | 5.5 × 10^{6} | 7.737027 | 8 | 3d^{9}4s(^{3}D)5s ➔ 3d^{9}(^{2}D)4s4p(^{3}P°) |

Cu I | 510.42 | 2.0 × 10^{6} | 3.816692 | 4 | 3d^{10}4p ➔ 3d^{9}4s^{2} |

Cu I | 515.07 | 6.0 × 10^{7} | 6.191175 | 4 | 3d^{10}4p ➔ 3d^{10}4d |

Cu I | 521.48 | 7.5 × 10^{7} | 6.192025 | 6 | 3d^{10}4p ➔ 3d^{10}4d |

Cu I | 522.36 | 1.50 × 10^{7} | 6.191175 | 4 | 3d^{10}4p ➔ 3d^{10}4d |

Cu I | 578.92 | 1.65 × 10^{6} | 3.785898 | 2 | 3d^{10}4p ➔ 3d^{9}4s^{2} |

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**MDPI and ACS Style**

Ajith, A.; Swapna, M.N.S.; Cabrera, H.; Sankararaman, S.I.
Comprehensive Analysis of Copper Plasma: A Laser-Induced Breakdown Spectroscopic Approach. *Photonics* **2023**, *10*, 199.
https://doi.org/10.3390/photonics10020199

**AMA Style**

Ajith A, Swapna MNS, Cabrera H, Sankararaman SI.
Comprehensive Analysis of Copper Plasma: A Laser-Induced Breakdown Spectroscopic Approach. *Photonics*. 2023; 10(2):199.
https://doi.org/10.3390/photonics10020199

**Chicago/Turabian Style**

Ajith, Asokan, Mohanachandran Nair Sindhu Swapna, Humberto Cabrera, and Sankaranarayana Iyer Sankararaman.
2023. "Comprehensive Analysis of Copper Plasma: A Laser-Induced Breakdown Spectroscopic Approach" *Photonics* 10, no. 2: 199.
https://doi.org/10.3390/photonics10020199