Open access peer-reviewed chapter

Calculation of the Metastable Atom Densities in Argon and Neon Abnormal Glow Discharges

Written By

Abdelaziz Bouchikhi

Submitted: November 14th, 2018 Reviewed: January 10th, 2019 Published: May 15th, 2019

DOI: 10.5772/intechopen.84293

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Abstract

In this chapter an investigation of a DC argon and neon abnormal glow discharges with metastable atom density is presented. The values of pressure are between 133.32 and 330 Pa, and the voltage range is from 250 to 400 V in the case of argon gas. In the case of neon gas, the pressure has the value of 399.92 Pa (3 Torr) and the voltage ranges from 300 to 500 V. In the frameworks, an analysis of abnormal glow discharge characteristics is carried out in the case of input data taken from the Boltzmann equation in multi term approximation (BMA), and in the case of input data obtained from BOLISG+ code. As conclusion of these differences of input data in the same gas the output results are different and it appears in the cathodic region. The spatiotemporal distributions of electron and ion densities, the potential and electric field, the mean electron energy and the metastable atom density are shown. A 1D fluid model is used to solve self-consistently the first three moments of the Boltzmann’s equation coupled with the Poisson’s equation. Our results are validated with those obtained by both recent paper and experimental results.

Keywords

  • metastable atom density
  • abnormal glow discharge
  • fluid model
  • input data

1. Introduction

The concern of the amelioration of the plasma reactor is always a domain important in the development technology, among these fields we find glow discharge. A plasma technology in a gas mixture has been studied by several authors. Ono et al. [1] have been studied oxygen-nitrogen gas mixture glow discharge plasma by intervene many chemical reactions in their model. Khomich et al. [2] have been treated the problem of the atomic deposition in the metal surface modification by nitrogen-argon mixture glow discharge in abnormal regime. Ponduri et al. [3] have been analyzed the dissociation of CO2 by dielectric barrier glow discharge, as a consequence of utilization of CO2 gas a lot of kinds of species intervene in the phenomena discharge. Baadj et al. have been [4] investigated Xe-Cl2 gas mixture for the formation of XeCl* exciplex lamp by means of zero-dimensional model. Li et al. [5] have been studied the plasma jet length in Ne, Ar, He and Kr in atmospheric pressure when the excimer molecule formatted from metastable state of the atomic gases, and they have been identified three modes versus of the gas flow rate, its about laminar, transition, and turbulent jet modes.

In this chapter, an research is through concerning the role of neon and argon metastable atoms in the discharge. Metastable atoms have been considered by several authors, both theoretically and experimentally. Metastable densities can experimentally be measured by optical absorption method. In theoretical means, a poise equation, including different production and loss terms is assembled to compute the metastable densities. Experimental measurements were executed, for example, for Neon gas in an RF glow discharge by Eckstein et al. [6], for Ar gas in a microwave boosted glow discharge by Uzelac and Leis [7], and for He gas as a function of discharge conditions by Browne and Dunn [8]. In the research of Smith et al. [9] purely relative absorption signals of Argon metastable atoms as a function of current and pressure were experimented. In the research of Strauss et al. [10] and Ferreira et al. [11] Argon metastable densities were experimented in a afterglow of a pulsed discharge and in the Grimm-type glow discharge, respectively, and some mechanisms for the structure of Argon metastable atoms were recommended. Argon metastable densities have also been experimented by Ferreira et al. [12], and by Ferreira and Ricard [13].

A comparison was complete with Argon metastable densities determined from a coupled-electron-metastable-atom model. Hardy and Sheldon [14] have examined Argon, Helium and Neon gases. A comparison between calculated and measured metastable densities was also realized by Kubota et al. [15] for Helium in a RF and DC glow discharge. Lymberopoulos and Economou [16] have established a combined fluid model for the electrons, Ar metastable atoms, and Ar ions in order to study the effect of metastable atoms in the discharge. In the works [17, 18, 19, 20, 21, 22] rate constants of a number of collision processes in control of the demolition of metastable atoms were got by combining equilibrium equations with the experimented time-dependent variation of the metastable densities or by analyzing the reliance of the decay constants upon pressure. Den Hartog et al. [23, 24] have investigated Helium gas.

Last-mentioned, Fedoseev and Sukhinin [25] have investigated the influence of metastable Ar atoms on gas discharge plasma with dust particles. Shumova et al. [26] have investigated the effect of metastable Ne atoms and dust particles in a positive column of glow discharge.

The aim of this work is to present, influence of the discharge characteristic in the case of input data obtained by BOLSIG+ code, and in the case of input data taken from the Boltzmann equation in multi term approximation (BMA). We note that both these approaches are widely used. For simulations of positive column of glow discharge, Vasilyak et al. [27] used the first approach, while Sukhinin et al. [28] used the second approach. In Section 2, the mathematical model is delineated; it comprises the boundary and initial conditions as well as the numerical method. In Section 3, the results are discussed for Ar discharge. In Section 4, the test scheme is given. In Section 5, Influence of the input data got from BOLSIG+ on the argon discharge has been shown. In Section 6, the characteristics of the Ne discharge with input data taken from BOLSIG+ are presented. Finally, the conclusion of the chapter is given in Section 7.

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2. Discharge modeling

Our mathematical model builds on the first three moments of the Boltzmann equation. The Continuity equations and momentum transfer equations of metastable atom, electrons and positively charged ions. The energy equation is known only for electrons, and to give the effect of the electric field on the particles charged, the Poisson equation is included in the model [29, 30].

The chemical reactions intervene in the discharge are indicated in the Table 1.

Table 1.

Kinetic scheme of processes.

After that, the model in the 1D Cartesian geometry, writes by partial differential equations:

n e t + φ e x = n e n o K o io + n m K m io + n m n m K ci , E1
n + t + φ + x = n e n o K o io + n m K m io + n m n m K ci , E2
n m t + φ m x = n e n o K o m n m K m o n m K m io 2 n m n m K ci n m τ m , E3
ε e n e t + φ x = e φ e E + ε m n e n m K m o + ε ci n m n m K ci n e P ec n e ε m n o K o m + ε io n o K o io + ε io ε m n m K m io , E4
2 V x 2 = e ε o n + n e E5

Here ne, n+, nm, φ m , φ e and φ + are number densities, densities of transport flux of the metastable atoms, electrons and ions, respectively. K o m is the rate coefficient of electron-impact excitation of ground state atoms, ε m = 11.55 eV is the energy loss of excited atoms, no is the constant background gas density, K m io is the rate coefficient of electron-impact ionization of excited atoms with the energy loss ε io ε m , K o io is the rate coefficient of electron-impact ionization of ground state atoms and ε io = 15.76 eV is the energy loss of ionized atoms, K m o is the rate coefficient of de-excitation of excited atoms by electron collisions. E = V / x is the electric field strength. ε o and e are the permittivity of free space and elementary charge, respectively. K ci = 8.1 × 10 10 cm3 s−1 [31] is the rate coefficient of chemo-ionization processes with the energy gain ε ci = 2 ε m ε io . τ m = 1 μs is the metastable lifetime. ε e is the mean electron energy, φ is the electron energy flux. V is the electrostatic potential. P ec is the energy loss per electron due to elastic collision of electrons with the background gas [32].

Momentum transfer equations for metastable atoms, electrons, ions and electron energy [33, 34, 35] are:

φ e = n e μ e E D e n e x , E6
φ + = n + μ + E D + n + x , E7
φ m = D m n m x , E8
φ = n e E μ n e D x E9

Here μ e , μ + , De and D+ are the electron, ion for mobilities and diffusion coefficients, respectively. D and μ are the diffusivity and mobility of electron energy transport. The ion mobility has brought from Phelps and Petrović [36] and their ion diffusivity is computed agree with Einstein’s relation [37]. The coefficients for electrons [38] in argon as dependences on the mean electron energy are got as of INP Greifswald for direct evaluation with the results obtained by Becker et al. [30]. Dm is the metastable atom diffusivity someplace n o D m = 1.7 x 10 18 cm−1 s−1 [19].

2.1 Boundary and initial conditions

The discharge is affected between two parallel plate electrodes and the radius of the electrode is presumed to be higher than the electrode gap and the physical characteristic distributions are approximately uniform along the radial direction. The grounded electrode has been put at x = 1 cm, play the role as the anode ( V anode = 0 ). The powered electrode has been put at x = 0 cm, which initiates the model discretization, play the role as the cathode ( V cathode = V DC ).

At time t = 0 , the metastable atom, electron, and ion densities are supposed constant and equal to 103 cm−3, and the mean electron energy equal to 1 eV.

Presuming disappearance of the metastable atom density, i.e., n m = 0 has been arranged at the cathode, whilst a predominant field-driven flux shut to the cathode the expression D + n + / x = 0 has been used for the positive ion density t > 0. At the anode, the metastable atoms and the electron density are supposed to be zero. The electron flux separating the cathode is calculated by the expression φ e x = 0 t = γφ + x = 0 t t > 0, the mean electron energy is assumed to be 5 eV at the cathode [36] and the gas temperature is equal to 273 K in the discharge.

2.2 Numerical method

For the metastable atom and Poisson equations a finite difference method has been employed. The transport equations of the electron energy, electron and ion are also discretized spatially with the finite difference technique. In this method the exponential scheme has been employed into account [37, 39, 40, 41, 42]. The discretization of the time terms by the right position of the finite difference technique has been used. Consequently, every discretized equation is defined as a tridiagonal matrix, which is solved by Thomas’s algorithm.

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3. Results and discussion of argon discharge

In this part, we will analysis the spatiotemporal evolution of the abnormal glow discharge in the existence of metastable atom density. The gas pressure is 133.32 Pa. The neutral species density is computed from the temperature and gas pressure with the ideal gas law. The constant value for the secondary electron yield is 0.06 [36]. The applied potential at the cathode is −400 V. The uniform subdivision of the space interval in 250 elements and a time step Δt = 10 ps, have been utilized.

Figure 1 shows the temporal progression of the potential (Figure 1(a)), concentration of electrons (Figure 1(b)), concentration of ions (Figure 1(c)), concentration of metastable atoms (Figure 1(d)), the electric field (Figure 1(e)) and the mean electron energy (Figure 1(f)). We remark that the discharge is distinguished by three zones: the first one busied the time simulation amidst in 10−11 and 9 × 10−6 s, the second one took the time simulation inter-time of 9 × 10−6 and 3 × 10−5 s, the final zone busied the time simulation amidst in 3 × 10−5 and 3.6 × 10−5 s.

Figure 1.

Argon spatiotemporal distributions of electric potential (a), electrons volume number (b), ions volume number (c), metastable atom density (d), electric field (e), and mean electron energy (f) at 400 V.

For the first zone, we comment that the metastable atom, electrons and ion concentrations are almost identical. Therefore, the net space charge concentration is unimportant. The electric potential is distinguished by the Laplace form due to the net space charge concentration that is exist. Consequently, the electric field is seemingly constant, besides that the mean electron energy is constant.

In the second zone, we remark a pseudo emergence of the cathodic region, this is characterized by a significance of ion concentration and unimportant of the electron concentration. This is explicated by the velocity of the electron species, which speed a more than the ion species and displaced quickly starting at the cathodic region. Consequently, the amount (ne-n+) is considerable which influence directly the electric potential as consequence the important chute that is present. Inevitably, the electric field is intense. The last earns the electron species an important energy. We comment that the metastable atom concentration is important. This discharge is sustained by the secondary emission coefficient as well as the existence of metastable atom concentration. Sooner than t = 3 × 10−5 s we remark a pseudo emergence of the negative glow region, where it is typified by the similar electron and ion concentrations. Consequently the net space charge concentration is slight. Hence, the electric potential and the electric field are constants. Automatically, the metastable atoms concentration is diminished.

In the last zone, we remark three dissimilar regions: the anode and the plasma regions and the cathode region. The anode region is characterized by the ion concentration that is less important compared to the electron concentration. In this zone we remark that the convergence of each physical characteristics of the discharge are reached at the time 3.6 × 10−5 s.

3.1 Influence of the voltage and gas pressure

In this part, we will study the influence of the voltage and gas pressure on the argon discharge. So, the potential at the cathode is taking of 250 V and we will alter the gas pressure. For the influence of the applied potential on the discharge, we take the gas pressure at 133.32 Pa. bulk.

Figure 2(a) shows the metastable atoms concentration plots depending on the pressure in the study state. The metastable atoms concentration augments with increasing pressure. For elevated pressure the gas density augments, which the electron diffusion coefficient turns out to be fewer and the bulk of the plasma rises which the both sheaths of the anode and cathode turn out to be small. These circumstances of the charged particle manipulate on the metastable atoms behavior in the study stated, i.e., the cathodic region is overflowing with the electron and metastable atom concentrations, which go faster the ion species in the existence of the electric field.

Figure 2.

Metastable atom densities as a function of pressure (a) and as a function of voltage (b) in the stationary state in Argon gas.

Figure 2(b) shows the metastable atoms concentration graphs depending on the potential in the study state. For elevated potential the excitation and ionization processes increase, and the charged particle turns out to be raised in the stationary state. Consequently, the metastable atom concentration graphs become growing.

The greatest of the metastable atom concentration varies amidst in 2.47 × 1010 and 6.63 × 1011 cm−3. We judged these results with calculated values established in the literature [9, 10, 12, 15]. Depending on the discharge circumstances, all these value varies amidst in 2 × 1010 and 5 × 1013 cm−3. Consequently, our calculated values something like in the exact range of the size order. We find that the values of the current densities are 0.137 , 0.508 and 0.843 mA/cm2 related to the pressures of 133.32 , 250.32 and 330.32 Pa, in that order.

Figure 3 represents the current-voltage properties in the stationary state. The results attained beginning of the database of BMA evaluated to those obtained by experimental method [43, 44]. We find that the results get beginning of the database of the BMA are in excellent conformity judgment against to those experimental results [43, 44].

Figure 3.

Comparison between the results obtained by our calculation using a database of BMA for pd = 1 Torr cm and those given by experimental for pd = 0.5 Torr cm in Argon gas.

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4. Validity of the model

Figure 4 demonstrates the comparison amidst in our results and those given by Becker et al. [30] (Figure 4(a)) ion and electron concentrations, (Figure 4(b)) electric field and electric potential, (Figure 4(c)) metastable atom concentration and (Figure 4(d)) mean electron energy. This figure substantiates the validity of our 1D code. The main dissimilarity amidst in those given by Becker et al. and our results are pointing up in the Table 2.

Figure 4.

Comparison between our results and those given by Becker et al.: (a) densities, (b) electric potential and electric field, (c) metastable atom density, and (d) mean electron energy in the stationary state in Argon gas.

Table 2.

The major differences between our results and those given by Becker et al.

We find that the similar discharge has been studied by Fiala et al. [45], where the hybrid model has been employed in two dimensional configurations. We find that the results got by Fiala et al., it was approximately indistinguishable to our results. In exacting, the maximum of particle concentrations is 1.1 × 109 cm−3 and the electric field at the cathode is 675 V/cm for applying voltage that is equal to 126.3 V. Consequently, the hybrid model is equivalent to our fluid model in the presence of the metastable atom concentrations of these discharge circumstances. Besides our model identifier both properties of the discharge, the mean electron energy and the metastable atom concentrations.

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5. Influence for input data of argon abnormal glow discharge

In this part, we will show the properties of the argon plasma discharge in the case of entering data computed by BOLSIG+ software [46]. We remind that the preceding results are obtained with enter data computed by multiterm estimation of the Boltzmann equation. We remind again that the preceding results are identical when are calculated exclusive of the rate coefficients K m o and K m io . The exclusion is the metastable atom concentration, which is prejudiced by these coefficients, i.e., the stepwise ionization processes is insignificant, evaluated to the both ionization of the chemo-ionization and ground state atoms processes. Consequentially, we can calculate the properties of the argon abnormal glow discharge exclusive of K m o and K m io coefficients. The secondary electron emission coefficient is 0.06 . The applied voltage at the cathode is 250 V. The gas pressure is 133.32 Pa.

Figure 5 shows the particle density distributions (Figure 5(a)), metastable atom concentration (Figure 5(b)) and mean electron energy (Figure 5(c)) in the stationary state. When we compare between the results given by Figures 4 and 5, we conclude clearly the influence of entering data of BOLSIG+ on the characteristics of the argon abnormal glow discharge. In exacting the cathodic region illustrated in the Figure 4(a) is totally dissimilar to the cathodic region illustrated in the Figure 5(a). We remind that the similar discharge circumstances (voltage, pressure, etc.) are used in two and multi terms approximations. But, the results are actually dissimilar.

Figure 5.

Argon spatial distributions of (a) particledensities, (b) metastable atom density, and (c) mean electron energy in the stationary state for input data of BOLSIG+.

Table 3 gives the main dissimilarity between entering both data of multiterm approximation and of BOLSIG+.

Table 3.

The major differences between input Data of BOLSIG+ and those given by multiterm approximation.

Figure 6 shows the comparison amidst of the experimental results [47, 48] and our results got beginning database of BOLSIG+ code for pd = 2 Torr cm. We remind that the experimental results [47, 48] are given for the diameter of the electrode equal to 8 cm and the inter-electrodes spacing equal to 1 cm. We remind again that the results obtained by Ref. [47] its approximately dissimilar to the results obtained by Ref. [48] due to the experimental circumstances of the secondary electron emission coefficient. We remark that our results got from database of BOLSIG+ code are in excellent accord with the experimental results [47].

Figure 6.

Comparison between the results obtained by our calculation using database of BOLSIG+ software for pd = 2 Torr cm and those given by experimental for pd = 2 Torr cm in Argon gas.

5.1 Effect of the metastable lifetime on the characteristics of argon abnormal glow discharge

We remind that the preceding computations are effected through the metastable lifetime equal to 1 μs [30], we remind that this value has been proposed by Becker et al. [30]. Figure 7 represents the effect of the metastable lifetime on the curve of the metastable atom concentration in the study state. For this reason we have used a value of metastable lifetime equal to 56 s of the theories [49] and an experimental value equal to 38 s [50]. We remark that the most of the metastable atom concentration augments from 7.76 × 109 to 2.249 × 1011 cm−3. We note that this effect is noticed just for metastable atom concentration and all characteristic of argon abnormal glow discharge rest unmoved in the study stated. As a consequence, the utilization of the experimental or artificial value of the metastable lifetime has an inconsequential of the abnormal glow discharge characteristics.

Figure 7.

Influence of the metastable lifetime on the Argon spatial distribution of metastable atom density in the steady state.

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6. Characteristics of the neon discharge through entering data of the BOLSIG+

In this part, we will investigate the characteristics of the neon abnormal glow discharge through entering data of the BOLSIG+ code. The gas pressure is 3 Torr. The applied voltage is 300 V. The secondary electron emission coefficient is 0.26 [51]. Additional parameters are declared in the Appendix A. Figure 8 shows the curves of ion and electron densities (Figure 8(a)), metastable atom concentration (Figure 8(b)) and current density (Figure 8(c)) depending of the applied voltage in the stationary state. We note that the greatest of the metastable atom concentration is equal to 1.615 × 1011 cm−3. The value of neon current density is 0.1851 mA/cm2. The electric field at the cathode achieves the value of 1696.08 V/cm. We note that the most of the mean electron energy is 46.30 eV in the cathodic region. As a consequence, the fluid model by injecting the metastable atom concentrations is extremely important for investigating the abnormal glow discharge properties of several pure gases and mixed gas.

Figure 8.

Neon spatial distributions of (a) particle densities, (b) metastable atom density, and (c) current density as a function of applied potential in the stationary state.

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7. Conclusion

In order to study the effect of metastable atom density, a second order fluid electric model has been used in the case of a DC low-pressure Ar and Ne abnormal glow discharges. The Poisson equation for the potential and electric field is joined to the first three moments of the Boltzmann’s conservation equations ignoring inertia of the charged particles. In the framework of the local energy approximation, the basic data employed in this chapter are calculated by Becker et al. in the case of multiterm estimation of Boltzmann equation (BMA) [30] and from BOLSIG+ software. The task of metastable atom concentration in the discharge is obvious for study into side of plasma glow discharge for several pure gases and mixed gas. We note that the abnormal glow discharge is sustained by secondary electron emission coefficient and the existence of the metastable atom concentration in this particular discharge.

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Acknowledgments

The authors express their gratitude to Markus M Becker (Greifswald-Germany) for helpful discussions.

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The drift velocity of positive ion neon gas is: w + = 11.27 E / n / 1 + 0.01288 E / n 0.5 (m/s) [52] where E/N is in Td. The metastable lifetime of neon gas is equal to 14.73 s [53]. The diffusion coefficient of metastable atoms is D m = 150 cm2 s−1 Torr [54]. The energy loss of an excited atom is 16.6 eV. The Ionization energy of neon gas is equal to 21.56454 eV. The energy loss (Pec) per electron due to elastic collision of electrons with the background gas is calculated according to [31, 55]. The rate coefficient of chemo-ionization processes is K ci = 3.6 × 10 10 cm3 s−1 for T = 310 K [56]

References

  1. 1. Ono S, Kato H, Tell S. Simulation and experiment of low-pressure oxygen-nitrogen mixture gas glow discharge plasma. Combustion Science and Technology. 1998;133:151
  2. 2. Khomich VA, Ryabtsev AV, Didyk EG, Zhovtyansky VA, Nazarenko VG. Numerical simulation of atomic nitrogen formation in plasma of glow discharge in nitrogen-argon mixture. Technical Physics Letters. 2010;36:918
  3. 3. Ponduri S, Becker MM, Welzel S, van de Sanden MCM, Loffhagen D, Engeln R. Fluid modelling of CO2 dissociation in a dielectric barrier discharge. Journal of Applied Physics. 2016;119:093301
  4. 4. Baadj S, Harrache Z, Belasri A. Electrical and chemical properties of XeCl*(308 nm) exciplex lamp created by a dielectric barrier discharge. Plasma Physics Reports. 2013;39:1043
  5. 5. Li Q, Zhu X, Li J, Pu Y. Role of metastable atoms in the propagation of atmospheric pressure dielectric barrier discharge jets. Journal of Applied Physics. 2010;107:043304
  6. 6. Eckstein EW, Coburn JW, Kay E. Diagnostics of an r.f. sputtering glow discharge - correlation between atomic absorption and mass spectrometry. International Journal of Mass Spectrometry and Ion Physics. 1975;17:129
  7. 7. Uzelac NI, LeisF F. Measurement of gas temperatures and metastable state densities in a microwave boosted glow discharge using a diode laser. Spectrochimica Acta. 1992;47B:877
  8. 8. Browne PG, Dunn MH. Metastable densities and excitation processes in the He-Cd laser discharge. Journal of Physics B. 1973;6:1103
  9. 9. Smith RL, Serxner D, Hess KR. Assessment of the relative role of Penning ionization in low-pressure glow discharges. Analytical Chemistry. 1989;61:1103
  10. 10. Strauss JA, Ferreira NP, Human HGC. An investigation into the role of metastable argon atoms in the afterglow plasma of a low pressure discharge. Spectrochimica Acta. 1982;37B:947
  11. 11. Ferreira NP, Strauss JA, Human HGC. Developments in glow discharge emission spectrometry. Spectrochimica Acta. 1982;37B:273
  12. 12. Ferreira CM, Loureiro J, Ricard A. Populations in the metastable and the resonance levels of argon and stepwise ionization effects in a low-pressure argon positive column. Journal of Applied Physics. 1985;57:82
  13. 13. Ferreira CM, Ricard A. Modelling of the low-pressure argon positive column. Journal of Applied Physics. 1983;54:2261
  14. 14. Hardy KA, Sheldon JW. Metastable atom density in helium, neon, and argon glow discharges. Journal of Applied Physics. 1982;53:8532
  15. 15. Kubota T, Morisaki Y, Ohsawa A, et al. The axial distributions of optical emission and metastable density: comparison between experiments with DC and RF helium glow discharges. Journal of Physics D. 1992;25:613
  16. 16. Lymberopoulos DP, Economou DJ. Fluid simulations of glow discharges: Effect of metastable atoms in argon. Journal of Applied Physics. 1993;73:3668
  17. 17. Phelps AV, Molnar JP. Lifetimes of metastable states of noble gases. Physics Review. 1953;89:1202
  18. 18. Phelps AV. Absorption studies of helium metastable atoms and molecules. Physics Review. 1955;99:1307
  19. 19. Ellis E, Twiddy ND. Time-resolved optical absorption measurements of excited-atom concentrations in the argon afterglow. Journal of Physics B. 1969;2:1366
  20. 20. Copley GH, Lee CS. Electron excitation and deexcitation coefficients for the 3 P 2, 3 P 1, 3 P 0, and 1 P 1 levels of argon. Canadian Journal of Physics. 1975;53:1705
  21. 21. Tachibana K. Excitation of the 1s5,1s4, 1s3, and 1s2 levels of argon by low-energy electrons. Physical Review A. 1986;34:1007
  22. 22. Kolts JH, Setser DW. Decay rates of Ar(4s,3 P 2), Ar(4s′,3 P 0), Kr(5s,3 P 2), and Xe(6s,3 P 2) atoms in argon. The Journal of Chemical Physics. 1978;68:4848
  23. 23. Den Hartog EA, O'Brian TR, Lawler JE. Electron temperature and density diagnostics in a helium glow discharge. Physical Review Letters. 1989;62:1500
  24. 24. Den Hartog EA, Doughty DA, Lawler JE. Laser optogalvanic and fluorescence studies of the cathode region of a glow discharge. Physical Review A. 1988;38:2471
  25. 25. Fedoseev AV, Sukhinin GI. Influence of metastable argon atoms and dust particles on gas discharge plasma. Ukrainian Journal of Physics. 2011;56:1272
  26. 26. Shumova VV, Polyakov DN, Vasilyak LM. Effect of metastable neon atoms in a positive column of glow discharge with dust particles. Plasma Sources Science and Technology. 2014;23:065008
  27. 27. Vasilyak LM, Polyakov DN, Shumova VV. Glow discharge positive column with dust particles in neon. Contributions to Plasma Physics. 2013;53:432
  28. 28. Sukhinin GI, Fedoseev AV, Antipov SN, et al. Dust particle radial confinement in a dc glow discharge. Physical Review E. 2013;87:013101
  29. 29. Alili T, Bouchikhi A, Rizouga M. Investigations of argon and neon abnormal glow discharges in the presence of metastable atom density with fluid model. Canadian Journal of Physics. 2016;94:731
  30. 30. Becker MM, Loffhagen D, Schmidt W. A stabilized finite element method for modeling of gas discharges. Computer Physics Communications. 2009;180:1230
  31. 31. Kolokolov NB, Kudrjavtsev AA, Blagoev AB. Interaction processes with creation of fast electrons in the low temperature plasma. Physica Scripta. 1994;50:371
  32. 32. Sigeneger F, Winkler R. Nonlocal transport and dissipation properties of electrons in inhomogeneous plasmas. IEEE Transactions on Plasma Science. 1999;27:1254
  33. 33. Belenguer P, Boeuf JP. Transition between different regimes of rf glow discharges. Physical Review A. 1990;41:4447
  34. 34. Donkó Z. Hybrid model of a rectangular hollow cathode discharge. Physical Review E. 1998;57:7126
  35. 35. Marié D, Kutasi K, Malovié G, et al. Axial emission profiles and apparent secondary electron yield in abnormal glow discharges in argon. European Physical Journal D: Atomic, Molecular, Optical and Plasma Physics. 2002;21:73
  36. 36. Phelps A, Petrović Z. Cold-cathode discharges and breakdown in argon: Surface and gas phase production of secondary electrons. Plasma Sources Science and Technology. 1999;8:R21
  37. 37. Bouchikhi A. Two-dimensional numerical simulation of the DC glow discharge in the normal mode and with Einstein’s relation of electron diffusivity. Plasma Science and Technology. 2012;14:965
  38. 38. Becker MM, Loffhagen D. Enhanced reliability of drift-diffusion approximation for electrons in fluid models for nonthermal plasmas. AIP Advances. 2013;3:012108
  39. 39. Scharfetter DL, Gummel HK. Large-signal analysis of a silicon read diode oscillator. IEEE Transactions on Electron Devices. 1969;16:64
  40. 40. Bouchikhi A, Hamid A, Flitti A, et al. The application of the 2 order fluid model for the townsend’s discharge study. Acta Electrotehnica. 2008;48:404
  41. 41. Bouchikhi A, Hamid A. 2D DC subnormal glow discharge in argon. Plasma Science and Technology. 2010;12:59
  42. 42. Stankov MN, Petković MD, Marković VL, et al. Numerical modelling of DC argon glow discharge at low pressure without and with Ar (3P2) metastable state. Romanian Journal of Physics. 2014;59:328
  43. 43. Stefanović I, Petrovic´ ZL. Volt ampere characteristics of low current DC discharges in Ar, H2, CH4 and SF6. Japanese Journal of Applied Physics Part 1. 1997;36:4728
  44. 44. Rozsa K, Gallagher A, Donkó Z. Excitation of Ar lines in the cathode region of a DC discharge. Physical Review E. 1995;52:913
  45. 45. Fiala A, Pitchford LC, Boef JP. Two-dimensional, hybrid model of low-pressure glow discharges. Physical Review E. 1994;49:5607
  46. 46. Hagelaar G, Pitchford L. Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models. Plasma Sources Science and Technology. 2005;14:722
  47. 47. Petrović Z, Jelenković B, Phelps A. Communication Privée; 1994
  48. 48. Jelenković B, Rózsa K, Phelps A. Oscillations of low-current electrical discharges between parallel-plane electrodes. II. Pulsed discharges in H2. Physical Review E. 1993;47:2816
  49. 49. Small-Warren NE, Chow-Chiu LY. Lifetime of the metastable 3P2 and 3P0 states of rare-gas atoms. Physical Review A. 1975;11:1777
  50. 50. Katori H, Shimizu F. Lifetime measurement of the 1s5 metastable state of argon and krypton with a magneto-optical trap. Physical Review Letters. 1993;70:3545
  51. 51. Chapman B. Glow Discharge Processes. New York: John Wiley Sons; 1980
  52. 52. Frost LS. Effect of variable ionic on mobility on ambipolar diffusion. Physics Review. 1957;105:354
  53. 53. Zinner M, Spoden P, Kraemer T, et al. Precision measurement of the metastable 3P2 lifetime of neon. Physical Review A. 2003;67:010501(R)
  54. 54. Ricard A. Evolution de la densité des atomes métastables du néon formés dans une décharge à courant continu de faible intensité. JPHS. 1969;30:556
  55. 55. Gaens W, Bogaerts A. Kinetic modelling for an atmospheric pressure argon plasma jet in humid air. Journal of Physics D: Applied Physics. 2014;47:079502
  56. 56. Sheverev VA, Stepaniuk VP, Lister GG. Chemi-ionization in neon plasma. Journal of Applied Physics. 2002;92:3454

Written By

Abdelaziz Bouchikhi

Submitted: November 14th, 2018 Reviewed: January 10th, 2019 Published: May 15th, 2019