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Theoretical investigation of streamer characteristics in Ne–Xe–HCl pulsed high-pressure

discharges

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2014 Phys. Scr. 89 085603

(http://iopscience.iop.org/1402-4896/89/8/085603)

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Theoretical investigation of streamercharacteristics in Ne–Xe–HCl pulsedhigh-pressure discharges

D Amir-Aid, Z Harrache and A Belasri

Laboratoire de Physique des Plasmas, Matériaux Conducteurs et leurs Applications, Université desSciences et de la Technologie d’Oran, USTO-MB, Oran, Algérie

E-mail: drisseto@yahoo.fr, harrache@gmail.com and ahmed_belasri@yahoo.fr

Received 19 September 2013, revised 10 May 2014Accepted for publication 27 May 2014Published 2 July 2014

AbstractThe aim of this work is to highlight some quantities characterizing the anode-directed streamergenerated in the Ne/Xe/HCl gas mixture plasma at high pressure and under non-uniformpreionization conditions. This mixture is used as excitation medium for XeCl excimer lasers. Acomprehensive model of discharge is presented. This model gives the space-time evolution ofelectron density and electric field, streamer appearance time, streamer expansion distance andvelocity. The effect of HCl concentration in the gas mixture, as well as gas pressure and gapdistance on streamer characteristics, have been investigated and discussed. Calculations suggestthat the streamer velocity is patently affected by the gap distance with a significant dependenceon the HCl concentration in the gas mixture.

Keywords: preionized electrical discharge, streamer instability, expansion distance

1. Introduction

The electrical breakdown of gases has received a great deal ofinterest for many years [1, 2]. It is well accepted that electricalbreakdown at high pressures often proceeds via the creationand propagation of streamers [3–6]. These are needle-shapedregions of free ionization embedded within relatively union-ized gas that can grow even in average applied fields, wellbelow those required for significant electron impact ioniza-tion. Field enhancement at the sharp tip of streamers allowsthe creation of substantial free ionization, even in low averagefields [7, 8].

The XeCl laser has a number of important applicationsrelated to its high power and the fact that it produces UVradiation [9–13]. Despite these remarkable proprieties, XeCllaser suffers from some limitations; when sustained by high-pressure discharges, it is subject to instabilities. Theinstability mechanism is assumed to result from the followingcircumstances: (a) streamers can appear near each electrodeand lead to arcing during the formation of the plasma [14]; (b)once the plasma is formed, chemical kinetic instabilities can

lead to plasma filamentation due to volume instability knownas halogen depletion instability [15–18]. Experimentalinvestigations of XeCl lasers have proved that the instabilitiesoccur before the end of laser emission [19–21]. In [22], weshow that there is a strong distortion of the electric field dueto a strong growth of the density of the streamer in the sheathduring the formation of plasma. In another work [23], weused an analytical model to study the formation of the cath-ode-directed streamer in high pressure electrical discharge.The obtained results show clearly that the velocity and theradius of the channel vary during the propagation of thestreamer. The present work focuses on the effect of somedischarge parameters, such as HCl concentration in the gasmixture, as well as gas pressure and gap distance, on theanode-directed streamer characteristics in plasma for XeClexcimer laser at high pressure.

The outline of this paper is as follows: the discussion insection 2 passes quickly over the computational and mathe-matical details of the present model. In section 3, the com-putational results are presented and discussed. Finally weconclude in section 4 with a summary.

| Royal Swedish Academy of Sciences Physica Scripta

Phys. Scr. 89 (2014) 085603 (9pp) doi:10.1088/0031-8949/89/8/085603

0031-8949/14/085603+09$33.00 © 2014 The Royal Swedish Academy of Sciences Printed in the UK1

2. Numerical model

The numerical model used to capture the physics with theavalanche and streamer discharges consists of the chargedparticle continuity equations coupled to the Poisson equation[24]. The gas mixture used in the simulations is Ne–Xe–HClat room temperature. It is based on a longitudinal mono-dimensional model of the cathode region coupled to the zero-dimensional model of the positive column [22]. In this model,two parallel-plate electrodes separated by a distance d areconsidered. The preionization at the cathode creates a spot ofinitially quasi-neutral plasma. Then, a constant high voltageV0 is applied to the electrodes at the instant t= 0. The profileof the non-uniform preionization considered in this work isthat the electron and ion densities are zero for a distance lessthan 40 μm. However, these densities are equal to 107 cm−3

for a distance superior or equal to 40 μm [22]. The scheme ofthe discharge and external circuit is the same than that usedin [22].

The continuity equations for electrons and ions are asfollows:

α Ε Ν∂∂

+∂

∂= = =

n

t

n v

xS n v x t

( )[ ( , ) ], (1)e e e

e e

∂∂

+∂

∂=

n

t

n v

xS

( ), (2)

p p p

where the indices e and p refer to the electrons and the ions,respectively; ne and np are the electron and ion densities; veand

vp are the mean velocities (directed along the discharge axis);

and α denotes the coefficient of ionization and S the sourceterm. E and N are respectively the electric field and back-ground gas density. Note that the ionization coefficientdepends on the reduced electric field E/N.

The Poisson equation is as follows:

ε

= − −Ve

n n( ), (3)p e2

0

where V is the electric potential.

The simplified transport equations of momentum transferof the charged particles are as follows:

μ Ε= − ∂∂ ( )n v nx

n D , (4)e e e e e e

Table 1. List of discharge parameters used in this work.

Discharge parameters Our data

Gas mixtureconcentrations

Ne/Xe/HCl with 0.5% of xenon anddifferent concentrations of HCl

Gas pressure (bar) 0.5, 1, 2, 2.5, 3, 5Applied voltageV0 (kV)

20

Gap distance (cm) 2, 2.5, 3, 3.5, 4Discharge areaA (cm2)

100

Kind of electriccircuit

CL with C= 150 nF and L= 5 nH

Preionizationdensity ne0

0 for x< 40 μm, 107 cm−3 for x ⩾ 40 μm

Figure 1. Space-time evolution in the cathode region of the electrondensity (a) and the electric field (b). Ne/Xe/HCl (99.37%, 0.5%,0.13%), V0 = 20 kV, p = 2.5 bar, d= 3 cm.

Table 2. Values of the streamer appearance time versus the HClpercentage, the total pressure, and the interelectrode distance.

Streamerappearancetime (ns)

HCl percentage(%) p= 2.5 bar,d= 3 cm

Total pressure(bar) [HCl] =0.13%, d= 3 cm

Gap distance(cm) p= 2.5 bar[HCl] = 0.13%

27.5 — — 1.535.4 — — 241.01 — 0.5 —

43.55 — — 2.544.68 — 1 —

47.14 0.044 — —

48.62 — 2 —

51.95 0.13 — —

51.95 — 2.5 —

51.95 — — 359.85 0.26 — —

63.8 — 3 —

66.71 0.36 — —

67.75 — — 3.577.42 0.5 — —

78 — 5 —

91.7 — — 4

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Phys. Scr. 89 (2014) 085603 D Amir-Aid et al

μ Ε= − ∂∂ ( )n v nx

n D , (5)p p p p p p

where μ and D are the mobility and the diffusion coefficientof the species (electron or ion) in neon. This mobility isnegative for electrons and positive for ions. The local electricfield approximation is used for the present model. It has beensupposed that the transport coefficients at a given time dependonly on the value of the local electric field in this point and atthis instant. The system of equations (1)–(5) governs thedynamics of streamer.

The electronic current density on the cathode is related tothe ionic current density by the relation:

γ=j t j t(0, ) (0, ), (6)e p

j t(0, )e

is the electronic current density on the cathode at time

t, j t(0, )p

is the ionic current density and γ is the secondary

electron emission due to the cathode bombardment by thepositive ions. In this paper, we use for γ the value of 0.01.

The applied voltage through the discharge is given by

= +V t V t V t( ) ( ) ( ), (7)ap cr plas

where V t( )plas and = ( )V t V d t( ) ,cr cr are the voltage across

the positive column and the cathode region, respectively, for agiven time t. The relation between the current Icr and the

voltage Vcr in the cathode region is described by the currentequation:

∫

ε= −∂∂

+ +⎡⎣ ⎤⎦

IA

d

V

t

A

dj x t j x t x( , ) ( , ) d , (8)

d

e p

cr 0cr

cr

cr 0

cr

where A represents the electrode area, and j x t( , )e

and

j x t( , )p

are, the electron and ion current densities respec-

tively for a given position x and time t.The zero-dimensional model consists of three main

modules: a plasma chemistry module, a circuit module and aBoltzmann equation module. The plasma chemistry moduleconstructs differential equations for the evolution of thedensity of species. The system of equations describing thepositive column and the cathode region are solved in twosteps as follows: for a given voltage Vcr across the cathoderegion at a time t, the plasma kinetic equations coupled withthe circuit equations are solved with the classical GEARmethod [25] between the instants t and +t dt. Taking Icr inequation (8) from the above calculation ( =I Icr plas) at time

+t dt( ), where Iplas is the plasma current calculated in thepositive column, the one-dimensional fluid equations are

500

400

300

200

100

00 50 100 150 200 250 300

Time (ms)

2.5 bar, d=3cm, [HC1]=0.044%

2.5 bar, d=3cm, [HC1]=0.13%

2.5 bar, d=3cm, [HC1]=0.26%

2.5 bar, d=3cm, [HC1]=0.5%

2 bar, d=3cm, [HC1]=0.13%

3 bar, d=3cm, [HC1]=0.13%

2.5 bar, d=2.5cm, [HC1]=0.13%

2.5 bar, d=3.5cm, [HC1]=0.13%

2.5 bar, d=4cm, [HC1]=0.13%

2.5 bar, d=3cm, [HC1]=0.044%

2.5 bar, d=3cm, [HC1]=0.13%

2.5 bar, d=3cm, [HC1]=0.26%

2.5 bar, d=3cm, [HC1]=0.5%

2 bar, d=3cm, [HC1]=0.13%

3 bar, d=3cm, [HC1]=0.13%

2.5 bar, d=2.5cm, [HC1]=0.13%

2.5 bar, d=3.5cm, [HC1]=0.13%

2.5 bar, d=4cm, [HC1]=0.13%

3.0x109

2.5x109

2.0x109

1.5x109

1.0x109

5.0x108

0.0

Dep

osite

d po

wer

(W)

Time (ns)0 50 100 150 200 250 300

Dis

char

ge c

urre

nt (k

A)

(a)

(b)

Figure 2. Time variation of the discharge current (a) and the electrondissipated power (b) for different values of HCl percentage, gaspressure and interelectrode distance. Figure 3.Variation of the streamer’s velocity (a) and electron density

(b) as a function of the head position and for different values of HClconcentration.

3

Phys. Scr. 89 (2014) 085603 D Amir-Aid et al

Figure 4. Temporal evolution of the streamer velocity for different values of HCl concentration.

Figure 5. Temporal evolution of the streamer’s expansion distance for different values of HCl concentration.

4

Phys. Scr. 89 (2014) 085603 D Amir-Aid et al

integrated in space ( < <x d0 cr) and time between t and+t dt( ).For the kinetic scheme and the employed cross-sections,

we consider the Ne–Xe–HCl mixture used in [9, 10]. Thetransport coefficients and the electronic collision frequencies,which depend on the reduced electric field (E/N), are pre-calculated and tabulated by solving the steady state, homo-geneous electron Boltzmann equation, using BOLSIG solver[26]. It is worth noting that the bibliographic research on theelectronic reaction rates shows that most of references arelong-established, but they constitute the basis of the set ofmodels used for description of plasma display panels [27],excimer lamps and lasers [10, 14, 16, 28–30].

3. Results and discussion

We discuss in this paper results obtained from the self-sus-tained model previously described to modeling the anode-directed streamer propagation in an excimer laser mixture andfor different discharge parameters (see table 1). We

investigate the outcome of varying the halogen percentage,the gas pressure and the gap distance on the streamer’sproperties.

The space-time evolutions of the electron density and theelectric field are plotted on figures 1(a) and (b). We note that,for the first instants, the electron density increases rapidly toreach a maximum of about 1013 cm−3 at the instant 52.40 ns(figure 1(a)). The electric field increases with time to reach itsmaximum of about 105 V cm−1 at the vicinity of the cathode(figure 1(b)). As the electron density grows, a considerablespace charge is generated that distorts the electric field at theinstant 52.38 ns (figure 1(b)). This effect becomes strong asthe electron density increases.

The balance of electron production and loss, in preionizeddischarges for excimer lamps and lasers, is strongly influencedby the halogen concentration in the mixture due to the domi-nant electron loss process, which is the dissociative attachmentof electrons to halogen molecule [5, 10, 14, 15, 18, 30–34]. Toknow the effect of the gas mixture composition on the strea-mer’s characteristics, we performed calculations for five con-centrations of halogen HCl: 0.044, 0.13, 0.26, 0.36, and 0.5%.The xenon concentration is fixed at 0.5%. In table 2, weindicate the values of the streamer appearance time versus thehalogen concentration in the Ne/Xe/HCl gas mixture, thegas pressure and the gap distance. This time is defined asthe necessary time for ions to arrive on the cathode andthe streamer triggers. It is seen that the appearance time of thestreamer increases with HCl percentage, gas pressure and gapdistance increasing.

The effects of the HCl percentage, the total gas pressureand the gap distance on the electric characteristics of thedischarge during the pulse are shown on figures 2(a) and (b).A high current (figure 2(a)) and a large deposition of powerby electrons (figure 2(b)) are observed for a low HCl con-centration (0.044%). The current and deposited power peaksdecrease with gas pressure and gap distance increasing. Also,we note a breakdown delay of the laser pulse at higherhalogen concentration (0.5%), higher pressure (3 bar) andlonger gap (4 cm). When the streamer takes form, its densityincreases rapidly during a short time. Then, the streamer joinsthe plasma already formed, which induces an abrupt increasein the electron density and consequently in the current and theelectron deposited power.

3.1. Effect of HCl concentration on streamer properties

The propagation velocity of streamer is deduced from thefollowing relation:

=−−

vx x

t t,0

0

where x is the position of the streamer head at the instant t,corresponding to the maximum of net charge density.Figure 3 shows the variation of the streamer’s velocity andelectron density as a function of the head position. Note thatthe growth of the streamer velocity (figure 3(a)), dependingon the position, is greater than the pourcentage of HCl islower; it reaches a maximum value of 3 × 108 cm s−1 for a

Figure 6.Variation of the streamer’s velocity (a) and electron density(b) as a function of the head position and for different values of totalgas pressure.

5

Phys. Scr. 89 (2014) 085603 D Amir-Aid et al

Figure 7. Temporal evolution of the streamer velocity for different values of total gas pressure.

Figure 8. Temporal evolution of the streamer’s expansion distance for different values of total gas pressure.

6

Phys. Scr. 89 (2014) 085603 D Amir-Aid et al

HCl concentration of 0.044%, however, it is of about 108

for a HCl concentration of 0.5%. The growth of the HClconcentration at fixed xenon concentration leads to thereduction of the electron density due to the increase of theattachment to HCl (figure 3(b)). The streamer velocityincreases exponentially with time and its value decreases byincreasing HCl concentration (figure 4). On figure 5, weobserve that the streamer expansion distance reaches amaximum value of about 0.21 cm. We define here thisdistance as the distance of propagation of the streamer alongthe discharge gap. The expansion time (streamer propaga-tion time) varies from 0.5 ns for HCl concentration of0.044% to 2 ns for HCl concentration of 0.5%. This is dueto the fact that when the attachment increases, the electrondensity decreases and consequently the streamer takes moretime to be formed and then propagates towards the plasmamedium. It is worth to note that the drift of these streamerstowards the plasma induces the halogen depletion instabilityshown in [14, 16]. The authors found that the plasma uni-formity is strongly sensitive to this instability.

3.2. Effect of gas pressure on streamer properties

The dependence of the streamer’s velocity and electron den-sity on the head position, for various gas pressures is reportedin figures 6(a) and (b). The velocity varies linearly with thehead position. Its value decreases with increasing in pressure(figure 6(a)). The electron density follows the same evolutionas the streamer velocity (figure 6(b)). It increases to reach aconstant value. It seems clearly that the electron density isaffected when the gas pressure grows. This is due to theionization increase in the cathode region [10, 22]. Figures 7and 8 represent the time variations of the streamer’s velocityand expansion distance for various total gas pressures. Thevelocity of the streamer increases during the discharge and itsvalue decreases slightly with pressure increasing (figure 7).We can say in figure 8 that the expansion distance is notaffected greatly by the gas pressure.

3.3. Effect of interelectrode distance on streamer properties

This part of calculations is carried out for an applied voltageof 20 kV, a gas mixture composition of Ne–Xe–HCl(99.37%–0.5%–0.13%) with a total gas pressure of 2.5 bar.Figures 9(a) and (b) represent the dependence of the strea-mer’s velocity and electron density on the head position, forvarious interelectrode distances (2, 2.5, and 4 cm). Thevelocity varies linearly with the head position. Its valuedecreases as the distance between electrodes increases(figure 9(a)). The electron density follows the same evolutionas the streamer velocity (figure 9(b)). It increases to reach aconstant value. When the interelectrode distance increases,the applied field will be decreased, which affects significantlythe streamer’s electron density. Figures 10 and 11 representthe time variations of the streamer’s velocity and expansiondistance for various interelectrode distances. The velocity ofthe streamer increases during the discharge and its valuedecreases with gap distance increasing (figure 10). It is seenin figure 11 that the expansion distance reaches a maximumvalue of about 0.16 cm. The propagation time of the streamerpasses from the value 0.3 ns for a distance of 2 cm to thevalue 1.7 ns for a distance of 4 cm.

4. Summary

This work represents a contribution to understand the anode-directed streamer propagation in a Ne–Xe–HCl pulsed high-pressure discharge for excimer lasers. It is based on a long-itudinal mono-dimensional fluid model. Cathode region,plasma, and external circuit are included in this model. Itgives the space-time evolution of electron density and electricfield, streamer appearance time, and streamer’s expansiondistance and velocity. The present study shows that thebehavior of discharge streamers depends on many parameterssuch as the environment in which the discharge propagates(gas mixture), the total gas pressure, and the distance betweenelectrodes.

Figure 9.Variation of the streamer’s velocity (a) and electron density(b) as a function of the head position and for different values ofinterelectrode distance.

7

Phys. Scr. 89 (2014) 085603 D Amir-Aid et al

Figure 10. Temporal evolution of the streamer velocity for different values of interelectrode distance.

Figure 11. Temporal evolution of the streamer’s expansion distance for different values of interelectrode distance.

8

Phys. Scr. 89 (2014) 085603 D Amir-Aid et al

The obtained results allow us to draw the followingconclusions.

(a) For low HCl concentrations, the physical quantities(streamer’s velocity and electron density, dischargecurrent and electron deposited power) have the highestvalues. The appearance time of the streamer increaseslinearly with the HCl concentration. The growth of theHCl concentration at fixed xenon concentration leads tothe reduction of the electron density due to the increaseof the attachment to HCl.

(b) The electron density is affected when the gas pressuregrows. The velocity of the streamer increases during thedischarge and its value decreases slightly with pressureincreasing. The expansion distance is not affected greatlyby the gas pressure.

(c) For large values of interelectrode distance, the physicalquantities mentioned above, decrease significantly. Thepropagation time of the streamer passes from the value0.3 ns for a distance of 2 cm to the value 1.7 ns for adistance of 4 cm.

Acknowledgments

This work has been supported by Agence Nationale pour leDéveloppement de la Recherche Universitaire (Algeria) in theframe of project PNR (Ref.13/0/91). One of the authors, ZH,acknowledges fruitful discussions with Dr A Alia.

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