on the role of the pre-ionization mechanism in the optical ... · on the role of the pre-ionization...

Phys. Plasmas 26, 062116 (2019); https://doi.org/10.1063/1.5092434 26, 062116

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On the role of the pre-ionization mechanismin the optical breakdown of molecularoxygen induced by CO2 laser: NumericalinvestigationCite as: Phys. Plasmas 26, 062116 (2019); https://doi.org/10.1063/1.5092434Submitted: 11 February 2019 . Accepted: 02 June 2019 . Published Online: 18 June 2019

Yosr E. E.-D. Gamal , O. Aied Nassef, and A. S. Salama

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On the role of the pre-ionization mechanism in theoptical breakdown of molecular oxygen inducedby CO2 laser: Numerical investigation

Cite as: Phys. Plasmas 26, 062116 (2019); doi: 10.1063/1.5092434Submitted: 11 February 2019 . Accepted: 2 June 2019 .Published Online: 18 June 2019

Yosr E. E.-D. Gamal,a) O. Aied Nassef, and A. S. Salama

AFFILIATIONS

Department of Laser Application in Metrology, Photochemistry, and Agriculture, National Institute of Laser Enhanced Sciences,Cairo University, Giza 12613, Egypt

a)Author to whom correspondence should be addressed: [email protected]

ABSTRACT

A numerical study is presented to investigate the threshold intensity dependence on the gas pressure in the breakdown of molecular oxygeninduced by CO2 laser radiation with a wavelength of 10.591lm and a pulse FWHM of 64ns [Camacho et al., J. Phys. D: Appl. Phys. 41, 105201(2008)]. This experiment allowed for a new method of providing an adequate density of the seed electrons required to ignite the breakdownmechanism. The investigations are based on a modification of a previously developed model [Gamal and Omar, Radiat. Phys. Chem. 62(5),361–370 (2001)], which solves a differential equation and designates the time evolution of the electron energy distribution numerically and a set ofrate equations that describe the change of the excited state population. The model considered inverse bremsstrahlung absorption as the mainelectron energy gain process leading to oxygen breakdown. As an interesting finding, in comparing the calculated and measured thresholds as afunction of gas pressure, computations could precisely reveal the densities of the created seed electrons at each value of the tested pressures. Theunsystematic variation of these densities with the gas pressure clarified the origin of the slight oscillations observed in the measured thresholds.Analyzing the electron energy distribution function and its parameters in three gas pressure regions could determine the correlation between thegas pressure and the electron gain and loss processes responsible for oxygen breakdown. This analysis explained the violation from the simple p�1

law observed experimentally in the relation between threshold intensity and gas pressure.

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I. INTRODUCTION

Gaseous breakdown induced by intense laser beams has beeninvestigated both experimentally3–9 and theoretically.10–17 These inves-tigations revealed that breakdown is produced by the sole action of thelaser beam via two main mechanisms: Cascade ionization (CI) orsometimes known as avalanche ionization and multiphoton ionization(MPI). This phenomenon has attracted extensive interest of manyauthors for its application in the development of laser-triggered light-ning which is expected to be a new technique to protect power linesand aircraft.18–21 Accordingly, many researchers are devoted to deter-mining the threshold intensity for air breakdown as the highest inten-sity that can be propagated through the air as a gaseous environmentwithout attenuation. This study is considered as one of the essentialsubjects for lightning control.

Preliminary research on laser-triggered lightning was startedwith a 10.6lm laser (0.12 eV quanta). Breakdown of air caused bysuch far infrared radiation has principally centered on an initiatorymechanism since the small quanta associated with such a long

wavelength is incapable of releasing electrons by multiphoton absorp-tion of the gas atoms or molecules.22,23 In this case, the ionizationgrowth retains a cascade nature.24,25 Smith23 was the first to point outthe need to provide a preionizing mechanism as a source of initiatoryelectrons to ensure reliable and reproducible breakdown with 10.6lmflashes. Early published papers26–29 demonstrated the importance androle of these preionization mechanisms in governing the thresholdintensity for gas breakdown induced by 10.6lm laser radiation. Inthese studies, there has been a measure of uncertainty concerning themechanism by which the first electron in the cascade is liberated.

During the previous decade, Camacho and his co-workers carriedout a series of experimental measurements on laser-induced break-down of different gaseous media using a CO2 laser source operating atwavelengths of 9.621lm and 10.591lm with pulse FWHM of �60 nsand 64ns.1,9,30–33 Their study was directed to obtain threshold inten-sity, Ith, and dependence on gas pressure, p, over a range below theatmosphere. In their measurements, they introduced a previous break-down as a new mechanism for providing the seed electrons in the focal

Phys. Plasmas 26, 062116 (2019); doi: 10.1063/1.5092434 26, 062116-1

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volume before firing on the laser. This method is likely to induce thebreakdown with seed energy in excess and to attenuate the laser untilthe spark disappears. These seed electrons constitute the required ini-tial electron density for igniting the avalanche ionization process.

One of the most interesting results given by Camacho et al. isthat obtained for the breakdown of oxygen where the thresholdintensity dependence on gas pressure showed an unexpected trendwith slope 6¼ �1. The measured threshold intensity is rather insen-sitive to the gas pressure; it almost retained the same value over theexperimentally examined pressure range (4.5 kPa–75 kPa). Thisresult violates the description of the breakdown mechanism usingan extrapolation of the classical microwave breakdown theory tooptical frequencies. Meanwhile, it contradicts the measurementsthat were carried out on the breakdown of oxygen-induced by laserwavelengths extended from vacuum ultraviolet (VUV) to nearinfrared (NIR). In this case, the variation of the measured thresholdintensity as a function of gas pressure showed reasonable consis-tency with the electron cascade theory (Ith a p

�1).4,5,7,8 For all stud-ied gases, this theory found that the threshold intensity decreases asthe pressure increases, over the considered pressure range. The rate ofdecrease with pressure depends on the nature of the tested gas.24

At first glance, the obtained trend of the threshold intensity givenby Camacho et al. was attributed to the experimentally applied newmechanism by which the seed electrons are produced in the focal vol-ume. But a similar result has been obtained in their measurements onthe variation of the threshold intensity over a narrow pressure range(29.218 kPa–62.928 kPa) when this mechanism was absent. No satis-factory experimental evidence illustrating this behavior was given.

Therefore, the goal of this work is to present a theoretical studyfor investigating the origin of the experimentally observed violation ofthe threshold intensity dependence on gas pressure.1 In other words,the analysis is devoted to finding out the reason for the high thresholdsobserved experimentally over the high-pressure regime. Basically, thecalculations aim to evaluate the role played by the new preionizationmechanism (previous breakdown condition) in determining the elec-tron gain and loss processes responsible for oxygen breakdowninduced by a CO2 laser source since these processes can be consideredas an essential factor that controls the relationship between the thresh-old intensity and gas pressure.

To accomplish our goal, for investigating the experimental condi-tions given in Ref. 1, some efficient gain and loss terms other thanthose considered in our previously applied electron cascade model2,34

are taken into account. Accordingly, the utilized model assumed thatgas breakdown proceeds mainly via cascade ionization processes. Thismodel solves the time-dependent energy equation numerically simul-taneously with a set of rate equations describing the population densityof the formed excited states. The computations are performed to pro-vide a relation between the threshold intensity and gas pressure withprofound attention to the role played by the previous breakdown con-dition. In addition, a comparative study of the electron energy distri-bution and its parameters at selected pressures values covering theprobed pressure range is presented. These calculations intended tobenchmark the correlation between the physical processes contribut-ing to oxygen breakdown by far infra-red (FIR) laser radiation andtheir use in plasma generation as a function of both gas pressure andthe initial electron density provided by the experimentally assumedprevious breakdown condition.

II. THEORETICAL FORMULATIONA. Basic equation

The theoretical approach used to describe the electron cascademodel has been explained in detail elsewhere.34 As mentioned above,the utilized model is based on a numerical solution of the time-dependent energy equation and a set of coupled equations describingthe rate of change of the excited state population. To enable the tem-poral variation of the electron energy distribution, this model explicitlyintroduces the time variation of the laser intensity. This, in turn, repre-sents more realistically the conditions found in practice. In this study,this model is applied to investigate the threshold intensity dependenceon the gas pressure in the breakdown of molecular oxygen. The break-down was induced by CO2 laser radiation operating at a wavelength of10.591lm and a pulse FWHM of �64ns.1 Owing to the small valueof the photon energy associated with this far infrared laser wavelength(�0.12 eV), the applied model ignored photoionization of the groundand excited molecules. Accordingly, the model considered inversebremsstrahlung absorption as the major energy gain process responsi-ble for electron growth. Since the occurrence of this process requiresthe presence of seed electrons in the focal volume, this experimentallowed for a previous breakdown condition to substitute the role ofthe photoionization process. This condition leads to the generation ofinitial electron density in the focal volume before firing on the lasersource at each experimentally tested gas pressure value.

The model also allowed for the collisional ionization of theexcited molecules. Such a process is considered to be a two-stage eventso that the rate of ionization growth due to this process is proportionalto the square of the electrons concentration. This would yield a ratefaster than the exponential growth rate since it depends upon theproduct of the electron concentration and the excited state concentra-tion, and the latter is proportional to the electron concentration. Inthis model, the seed electrons present in the focal volume gain energyfrom the electric field associated with the laser beam through theinverse bremsstrahlung absorption process. Then, the electron densitygrowth proceeds via the individual action of the collisional processes.The depletion of this electron density takes place by the processes ofelectron dissociative and three body attachments as well as electrondiffusion. Electrons may also lose their energy by rotational and vibra-tional excitations of ground state oxygen molecules.

In this analysis, we adopted the same structure of the oxygenmolecule given in our previous paper,17,35 namely, a ground state,three excited states, and an ionized state. Consequently, the followinginteractions are taken into account: (i) electron inverse-bremsstrahlung absorption; (ii) rotational excitation; (iii) vibrationalexcitation; (iv) electron impact excitation of the A3

Pþu state by elec-

trons having the energy e > 4.5 eV; (v) electron impact excitation ofthe B3

Pu state by electrons having the energy e > 8.0 eV; (vi)

electron-impact excitation of the E3P�

u state by electrons having theenergy e > 9.7 eV; (vii) electron-impact ionization of ground statemolecules by electrons having energies e > 12.071 eV; (viii) collisionalionization of the three excited states A3

Pþu , B

3Pu, and E

3P�u by

electrons having energies e > 7.571 eV, 4.071 eV, and 2.371 eV, respec-tively; (ix) dissociative attachment, in which an electron interacts withan oxygen molecule forming a negative ion and an oxygen atom. Thisreaction has a threshold at 3.7 eV and peaks at about 6.7 eV;36–38 (x)three-body attachment in which an electron interacts with two oxygenmolecules resulting in a negative molecular ion and an oxygen


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molecule, and the rate of this reaction peaks at low electron energies

A. Determination of the initial electron density overthe tested gas pressure range

Under the previous breakdown condition, despite slight fluctua-tions observed in the experimentally measured threshold intensity (Ith)as a function of gas pressure (p), its trend showed an almost indepen-dence over the tested pressure range. This behavior assured a departurefrom the simple law Ith a p

�1 expected by the electron cascade theory.Consequently, to emphasize this departure, it was necessary to study theinfluence of primary electrons generated in the focal volume by the pre-vious breakdown on the threshold intensity as well as the physical pro-cesses responsible for the gas breakdown over different pressure regions.

In this experiment, no suggestion was given to define the densityof these primary electrons; therefore, computations are performed todetermine the breakdown threshold intensity assuming different val-ues of initial electron density for each gas pressure value. Table I showsthe threshold intensity calculated for initial electron density varyingfrom 1011 cm�3 down to 104 cm�3 at each gas pressure value. Thetable also includes those experimentally measured thresholds.1

B. Threshold intensity dependence on gas pressure:Comparison with experimental results

The underlined threshold intensities represent those thresholdswhich are in reasonable agreement with the measured ones. Thisagreement, in turn, proved the validity of the applied model. For morereliable comparison, these threshold intensities together with the con-sistent initial electron density are displayed graphically in Fig. 1. Inthis figure, curve (1) (solid line) refers to the calculated thresholdintensities and curve (2) (dashed line) represents the consistent valuesof the initial electron density, while the scattered squares denote themeasured thresholds. It is noticed here that the initial electron densityundergoes observable fluctuations at some pressure values as shownby curve (2). This result revealed that they are unsystematically varyingwith the gas pressure. This random variation explained the observedoscillations manifested by the measured and calculated thresholdswhere the drop in the threshold intensity corresponds to an increasein the initial electron density, as presented by the vertical arrows

displayed in Fig. 1. This finding enabled the determination of theexpected value of the electron density generated from the previousbreakdown at each gas pressure value.

Moreover, the almost independent behavior of the thresholdintensity on the gas pressure shown in this experiment (far infraredlaser wavelength) is attributed to two main reasons: first, the influenceof seed electrons from the previous breakdown and second, the effectof collisional loss processes due to electron attachment to an oxygenmolecule which plays an important role in the high-pressure regime.This result indicates that with the previous breakdown condition, thethreshold intensity is controlled by the strong competition betweencollisional ionization and electron loss processes.

The above results gave a strong motivation to study the correla-tion between gas pressure and the physical processes contributing to

TABLE I. Calculated threshold intensities as a function of gas pressure for different values of the initial electron density. The measured thresholds given in Ref. 1 are alsoincluded in this table. The bold threshold intensities represent the closest values to the measured ones.

Gas pressure (kPa)Calculated Ith (W/cm

2)

Exp. Ith (W/cm2)

(Ref. 1)Initial electrondensity (cm�3) 1011 1010 109 108 106 105 104

4.506 1.06 3 109 1.75 � 109 2.50 � 109 3.35 � 109 5.35 � 109 6.71 � 109 7.61 � 109 8.60 � 1087.319 7.90 � 108 1.17 3 109 1.60 � 109 2.1 � 109 3.00 � 109 3.60 � 109 4.20 � 109 1.00 � 10911.279 5.80 � 108 8.40 3 108 1.075 � 109 1.35 � 109 1.90 � 109 2.20 � 109 1.55 � 109 8.80 � 10817.545 4.30 � 108 6.00 � 108 7.60 � 108 9.20 3 108 1.25 � 109 1.41 � 109 1.60 � 109 8.90 � 10822.558 2.75 � 108 5.00 3 108 6.20 � 108 7.40 � 108 1.00 � 109 1.14 � 109 1.26 � 109 4.70 � 10827.264 5.60 � 108 6.80 � 108 8.00 � 108 9.00 � 108 1.12 3 109 1.22 � 109 1.34 � 109 1.10 � 10931.370 5.30 � 108 6.30 � 108 7.40 � 108 8.30 3 108 1.02 � 109 1.12 � 109 1.22 � 109 8.85 � 10841.623 4.90 � 108 5.70 � 108 6.50 3 108 7.20 � 108 8.65 � 108 9.35 � 108 1.00 � 109 6.80 � 10862.954 4.40 � 108 4.99 � 108 5.50 � 108 5.99 � 108 6.99 � 108 8.10 3 108 7.50 � 108 8.40 � 10873.180 4.30 � 108 4.80 � 108 5.25 � 108 5.71 � 108 6.60 � 108 7.005 � 108 7.43 3 108 8.40 � 108

FIG. 1. Comparison between the calculated (solid line) and the measured ones(scattered squares). The dashed line represents the variation of the initial electrondensity with the gas pressure.


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the breakdown mechanism leading eventually to plasma formation.This was done by studying the distribution of the electron energy andits parameters, namely, the temporal variation of electron and excitedmolecule density, the number of ionization and excitation per unittime, the electron mean energy, and the electron energy distribution.To investigate the role of gas pressure in the breakdown mechanism,the calculations are performed for three selected pressure values of theexperimentally tested gas pressure range, namely, (1) 4.506 kPa, (2)41.623 kPa, and (3) 73.180 kPa. These values are deliberately chosensince they represent three different pressure regions.

C. Distribution of the electron energy

A study is carried out to determine the electron energy distribu-tion function (EEDF) at the (A) peak and (B) end of the laser pulse forthe three selected pressure values. These are demonstrated by curves(1)–(3) in Fig. 2.

At the peak of the pulse [Fig. 2(a)], it is clear that the energy dis-tribution varies in a descending manner with the gas pressure asshown by curves (1)–(3). Moreover, the three curves showed a gradualdecrease over the whole electron energy range with their tails directedtoward the high energy region. The behavior presented in this figurereflects the effect of the initial electron density present in the focal vol-ume on the growth rate of the EEDF, where it is shown that at the lowpressures (high initial electron density 1011 e/cm3), fewer collisions(less energy loss) are adequate for the breakdown criterion (7.0� 1012cm�3) to be achieved. For the high pressure region (lower initial elec-tron density 104 e/cm3), the seed electrons can absorb more energyfrom the laser field through the inverse bremsstrahlung absorptionprocess. This absorption becomes more effective at the pulse peak.Once electrons accumulate enough energy (exceeding the excitationand ionization thresholds), they undertake inelastic collisions resultingin excitation followed by ionization as well as direct ionization ofground state molecules. Consequently, this result explains the reduc-tion of the EEDF by about three orders of the magnitude shown bycurve (3) in Fig. 2(a).

In Fig. 2(b) (end of the pulse), although curve (1) showed almostsimilar behavior like that shown at the peak [Fig. 2(a)], but with highervalues, however, different behaviors are observed for the EEDF’sshown by curves (2) and (3). These curves undergo noticeable oscilla-tions over the low energy range. For electrons having energy

their energies in undergoing inelastic collisions, leading to excitationand ionization of the ground state molecules.

Inspection of the obtained result for the low gas pressure value(4.506 kPa (showed that the density of the excited molecules (solidline) starts with a high value, and then it decreases up to 20.0 ns.

Beyond this time, its value showed a gradual increase ending with highvalues at the late stages of the pulse. The decrease in the excited mole-cule density shown during the ascending half of the pulse reflects therapid ionization of the formed excited molecules. Therefore, the conse-quence of this decrease appeared as an increase in the electron densityat the same time interval as shown by the dashed line. The gradualincrease in the density of the excited molecules during the descendinghalf of the pulse shown by the solid line explains the gradual increasein the electron density (dashed line), leading to a state of stability atthe late stages of the laser pulse.

This result indicates that in the low-pressure region, ionization pro-ceeds via two-step collisional ionization of the fast-growing highly excitedmolecules (9.7 eV) by electrons having energy > (12.071–9.7) eV.This high ionization rate may be attributed to the high electronicexcitation cross section corresponding to this state.28 This resultassures the high values of the EEDF shown by curve (1) in Figs. 2(a)and 2(b). So at this low-pressure, electrons possessing energy�3.0 eV are abundant and have a great tendency for ionizing highlyexcited molecules.

In the intermediate gas pressure region (41.623 kPa), a high den-sity of the initial electrons (1.0 � 109 cm�3) is assumed to be allocatedin the focal volume caused by the previous breakdown. In this case,the time evolution of the excited molecules shown by a solid line alsoexhibited a decrease during the early stages of the laser pulse up to5.0 ns. After this time, the density of the excited molecules exposed toa gradual increase, which is continued up to the end of the pulse. Thepresence of high seed electron density enabled fast energy gain fromthe laser field through the inverse bremsstrahlung absorption. Theseelectrons can then undergo inelastic collisions, leading eventually toexcitation followed by immediate ionization (two-step collisional ioni-zation) or direct ionization of ground state molecules. The decrease inthe density of the excited molecules shown by the solid line during theearly stages of the pulse (

rate of these molecules increases with the increase in gas pressure. Thisbehavior is shown from the fast growth of the electron density dis-played by the dashed line in Fig. 3 at this pressure value.

An important feature can be drawn from the shape of the dashedlines obtained in this figure that ionization growth proceeds mainlythrough collisional cascade processes. No evidence indicates the multi-photon ionization process even at the low pressure as one expected.Therefore, the high electron density can easily defeat the possibility ofelectrons loss in the low-pressure region. Increasing the gas pressureincreases the ratio of excitation to the ionization rates. This resultagrees with the calculated EEDF at the peak and end of the laser pulseas shown in Fig. 2 in the low-pressure region since most of the elec-trons are found to possess their high energy even at the end of thepulse.

For better understanding the role of gas pressure in the growth ofthe ionization mechanism, calculations are performed to obtain thechange of the electron evolution at (i) 1.0 ns (early stages), (ii) 32.0 ns(peak), and (iii) 64.0 ns (end of the pulse) for the same three pressurevalues. These are illustrated in Fig. 4: (i) squares (4.506 kPa), (ii) circles(41.623 kPa), and (iii) triangles (73.180 kPa). The results obtained inthis figure strongly confirm the variation of the electron density withthe gas pressure shown in Fig. 3. This is revealed from the increasinggrowth rate of electrons presented by the ratio of the electron densityat the end of the pulse to that obtained at the start of the laser pulse.These ratios are turned out to be 38.5, 3.55 � 105, and 6.85 � 109 forthe three pressure values, respectively. This result explains the roleplayed by the collisional ionization processes in relation to both gaspressure and initial electron density produced from the previousbreakdown in the focal region.

E. Temporal variation of the excitation and ionizationrates

The effect of gas pressure could appear in the enhancement ofthe collisional ionization of the formed excited molecules which are

found to be the highest source of the growth of electrons in gas break-down induced by CO2 laser radiation. Therefore, it was necessary tostudy the correlation between the temporal variation of excitation andionization rates and gas pressure. These are represented in Fig. 5 forthe selected three pressure values: (1) 4.506 kPa, (2) 41.623 kPa, and(3) 73.180 kPa. In this figure, the calculated ionization rates (dashed

FIG. 4. Variation of the number of electrons in the focal volume with the gas pres-sure represented three different time durations of the laser pulse, namely, (i) t ¼1.0 ns, (ii) t ¼ 32.0 ns (pulse peak), and (iii) t ¼ 64.0 ns (pulse end).

FIG. 5. Comparison between the variation of the excitation and ionization rates dur-ing the laser pulse for pressures (1) 4.506 kPa, (2) 41.623 kPa, and (3) 73.180 kPa.


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line) showed similar behavior for the three pressure values where theirtemporal variation follows almost the laser pulse shape (Gaussianshape peaking at 32 ns).

On the contrary, the excitation rate (solid line) showed a differentbehavior with gas pressure. For the low-pressure (4.506 kPa), its valueundergoes a decrease during the first few nanoseconds (5.0ns) fol-lowed by a gradual increase ending with a faster one during the latestages of the pulse. This behavior illustrates the depletion of excitedmolecules through the collisional ionization process, which results inthe abrupt growth of the ionization rate shown by the dashed line.

The results obtained at 41.623kPa (intermediate pressure) showthat over the early stages of the laser pulse, the excitation rate (solid line)showed a well around 5.0ns, followed by a fast increase which is contin-ued during the descending phase of the pulse ending with a fast drop.This could be attributed to the assumed high initial electron density cre-ated from the previous breakdown corresponding to the experimentalconditions under investigation. These electrons can quickly gain energyfrom the laser field through the inverse bremsstrahlung absorption pro-cess to enable them for undergoing inelastic collisions, leading to moreexcitation or ionizing ground and the formed excited molecules.

In the higher pressure region, however, the temporal variation ofthe excitation rate showed a different behavior, where a significantoscillation appeared during the first 10.0 ns ending by a decrease to avalue around �0.06, which is continued over the second half of thepulse. The reduction of the excitation rate shown by the solid line con-firms the high ionization rate around the peak of the pulse. On theother hand, the fast decline of the ionization rate (dashed line) shownduring the descending phase of the pulse gives strong evidence of elec-tron losses due to attachment processes.

Generally speaking, one may conclude that both excitation andionization rates increase with the increase in gas pressure.

F. Time-varying electron mean energy

As further confirmation of the nature of the physical processesthat contribute to the electron density growth, Fig. 6 displays the

behavior of the electron mean energy as a function of time for thesame selected values of the gas. These are shown by curves (1)–(3).

It is noticed from this figure that at the low-pressure value, thecalculated electron mean energy [curve (1)] starts with the assumedelectron mean energy of �4.0 eV,40 corresponding to the initial elec-tron density followed by an increase reaching a peak of 5.5 eV at�10.0 ns. Then, an almost steady state is shown which may be attrib-uted to the flick of the electron energy in and out. This behavior con-tinues to the late stages of the pulse where a gradual decrease isobserved. The result presented by curve (1) illustrates that in the low-pressure regime, collisional processes play a minor role where they aremerely ionizing the highly excited molecules. The breakdown mecha-nism is mainly governed by the high density of the initial electrons.

On the other hand, the variation of the electron mean energyshown at the intermediate and high pressures represented by curves(2) and (3) follows the Gaussian pulse shape, and their values almostcoincide over the whole pulse length. This coincidence may be due tothe high value of the initial seed electrons (�109/cm3) assumed fromthe previous breakdown at 41.623 kPa. The drop appeared during thefirst few nanoseconds for curves (2) and (3) represents the loss of theenergetic electrons in collisional excitation of the highly excited states.These states are immediately ionized by initial electrons carrying amean energy of �4.0 eV generated from the previous breakdown.Beyond this time, the resultant low energy electrons can gain enoughenergy from the laser field through the inverse bremsstrahlung absorp-tion forming the Gaussian shape attained by the electron mean energyshown by curves (2) and (3). This result indicates the effective influ-ence of gas pressure on the enhancement of inelastic collision interac-tions. It is also noticed here that curves (2) and (3) lie below thoseobtained for the lower pressure value [curve (1)]. This result confirmsthe effect of inelastic collision processes on the depletion of the energyof the electrons as the gas pressure increases.

G. Variation of the electron energy distribution duringthe laser pulse

For completeness, calculations are performed to determine thetime variation of the EEDF at the three considered gas pressure values;these are shown in Figs. 7–9. In general, the calculated EEDFs exem-plified the non-Maxwellian behavior. Moreover, the trend of theirtemporal variation is found to depend mainly on the value of the ini-tial electron density produced from the previous breakdown corre-sponding to each gas pressure. For the low-pressure value (initialelectrons of�1011 cm�3), Fig. 7(top), the EEDF represented by a curve(a) started with a high value followed by a slow increase up to t¼ 30nsas shown by curves (b)–(f). Despite the different behavior shown bycurve (m) (at the end of the pulse), the growth of the EEDF illustratedby curves (g)–(l) exhibited an almost negligible increase with its taildirected toward the high energy region. This result reveals the highrate of energy accumulation by the initial electrons and the low lossrate of their energy via inelastic collisional processes. On the contrary,the sharp decrease in EEDF shown by curve (m) indicates the highloss of electron energy due to these inelastic processes.

Figure 7(top) shows that the breakdown condition is verifiedonly near the end of the pulse, and the highest electron density islocated over the energy range (0–5 eV). Therefore, to get deeper infor-mation on the breakdown parameters such as formation time, electrondensity, and amount of energy carried out by the generated electrons,

FIG. 6. Variation of the electron mean energy calculated at the pressures:4.506 kPa [curve (1)], 41.623 kPa [curve (2)], and 73.180 kPa [curve (3)].


Phys. Plasmas 26, 062116 (2019); doi: 10.1063/1.5092434 26, 062116-8



Fig. 7(bottom) displays a contour representation of the EEDF calcu-lated during the late stages of the laser pulse corresponding to elec-trons carrying energy in the range (0–5 eV). For instance, at this low-pressure value, the colored zones showed that the breakdown region(red color) is obtained near the end of the pulse (62.5ns). From thecolor bar shown in this figure, this region is found to possess the high-est density of electrons (7.0 � 1012 cm�3) having an energy of�1.0 eV. This breakdown region is surrounded by ionization zonessignified by the sequence of colors extended from orange to light bluewhich justify the degradation of the electron density through thesesuccessive zones. This result assures that at pressures of few kPa, theloss of energy through inelastic collisional processes is less probable.

At a gas pressure of 41.623 kPa (initial electrons �109 cm�3),similar behavior is observed for the growth of the EEDF as that shownby Fig. 7(top) during the ascending phase of the laser pulse. This corre-sponds to curves (b)–(g) in Fig. 8(top) where the temporal variation ofthe EEDF depicts a progressive increase. Beyond this time, the EEDFshowed a state of coincidence up to the late stages of the pulse wheredifferent behaviors are explained by curves (l) and (m). Both curvesundergo a fast decrease beyond the ionization limit (>12.071 eV) withtheir tails reaching low values of electron density. This behavior ismore evident at the end of the pulse [curve (m)]. Moreover, this curve

suffers perceptible oscillations over the low electron energy region(1.0–10.0 eV). These oscillations are attributed to the unblemishedcompetition between the electron energy loss (rotational, vibrational,and electronic excitations) and the electron growth rate via inelasticcollision processes (ionization of ground and excited molecules). Thegenerated electron density reaches a considerable value during theascending phase of the laser pulse. This value is capable of overcomingthe barrier caused by the attachment losses. The behavior shown bythe EEDF is explained grounding on the fact that around the peak ofthe laser flash, the predicted high initial electron density can accumu-late enough energy from the laser field through the inverse brems-strahlung absorption process. This energy is then expanded inpopulation followed by depopulation of the electronically excited mol-ecules, leading eventually to the enhancement of the electron density.These electrons can easily defeat their loss due to the attachment pro-cesses. To clarify this result, the EEDF is displayed in a contour repre-sentation shown in Fig. 8(bottom). This plot specifies that breakdownoccurs only at the end of the pulse (64 ns) with an electron density of3.57 � 1013 cm�3 and energy around 1.0 eV. The colored sectors sur-rounding the breakdown regions are referred to the ionization zoneswith their electron density shown by the color bar extended from theorange up to the navy blue.

Despite the elevated difference of the assumed initial electrondensity generated from the previous breakdown condition

FIG. 7. Time variation of the EEDF calculated at a pressure of 4.506 kPa (top).Contour development of the EEDF during the laser pulse (bottom).

FIG. 8. The same as in Fig. 7 but for a pressure of 41.623 kPa.


Phys. Plasmas 26, 062116 (2019); doi: 10.1063/1.5092434 26, 062116-9



corresponding to the intermediate and high pressures(109 cm�3–104 cm�3, respectively), on the whole, the trend of theEEDF shown in Fig. 9(top) showed a similar behavior to that displayedin Fig. 8(top). The gradual increase in the EEDF shown during the firststages of the laser pulse [curves (a)–(f)] explains the effect of the lowinitial electron density. This, in turn, reveals that breakdown proceedsmainly via collisional ionization processes. Near the peak, a fasterincrease is observed up to 64ns [curves (g)–(m)] where a sharpdecrease is detected. This decrease reflects the active role played by theinelastic collisional processes during this period (ionization of theground and excited molecules as well as dissociative and three bodyattachments). The contour representation of this relationship is shownin Fig. 9(bottom). Inspection of this plot determines that breakdownalso takes place during the last nanosecond of the laser pulse. The gen-erated electron density is mostly located at 1.0 eV of the extended elec-trons energy range with a density of about 6.84� 1013 cm�3.IV. CONCLUSION

The modified electron cascade model applied in the present workenabled the analysis of the unpredictable dependence of the thresholdintensity as a function of pressure. In addition, the role of previousbreakdown condition as a source of preionization in the study of theoxygen breakdown induced by the CO2 laser beam

1 is presented. The

calculated thresholds are found to be in reasonable agreement with themeasured ones. This agreement proved the validity of the model. Thecalculations performed in this study concluded the following:

• The departure of the Ith vs p characteristic from the expected relationof the electron cascade theory (Ith a p

�1) is shown by calculating theEEDF and its parameters in three selected gas pressure regions. Theresults illustrated the interplay of the density of the initial electronsand loss mechanisms in the determination of the threshold intensity.This finding clarified the observed stability of these intensities.

• The origin of the observed slight fluctuations in the measured thresh-olds is explained by the unsystematic variation of the produced initialfree electron density due to the previous breakdown condition.

• Molecular electronic excitation is found to play an essential role inenhancing the electron density through the two-step collisional ioni-zation process.

• Rotational and vibrational excitations have a significant effect ondepleting the low energy electrons. This, in turn, gives evidence forthe observed increase of the threshold intensity as the pressureincreases.

• Accounting for excitation mechanisms is essential in predicting thethreshold intensity for oxygen breakdown induced by a CO2 lasersource.

• Molecular dissociation is found to have an observable effect on pres-sures� 26.664 kPa, where its contribution appears pronouncedly atelectron energy >10.0 eV. Electrons having such energy more proba-bly undergo inelastic collision to excite ground state molecules to alevel at 9.7 eV. Therefore, this electron energy loss through electronicexcitation acts to offset the rate of molecular dissociation and conse-quently increases the ionization rate.

• The contour representation of the temporal evolution of the EEDF forthe three considered pressure values signifies that the plasma is gener-ated only at the later stages of the laser pulse with an electron density of1012–1013 cm�3 and possessing energy not exceeding 1.0 eV.

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FIG. 9. The same as in Fig. 7 but for a pressure of 73.180 kPa.


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on the role of the pre-ionization mechanism in the optical ... · on the role of the pre-ionization...

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