the influence of electron density on the formation of streamers in electrical discharges triggered...

688 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 27, NO. 3, JUNE 1999

The Influence of Electron Density on theFormation of Streamers in Electrical Discharges

Triggered with Ultrashort Laser PulsesBruno La Fontaine, Fran¸cois Vidal, Daniel Comtois, Ching-Yuan Chien, Alain Desparois, Tudor Wyatt Johnston,

Jean-Claude Kieffer, Hubert P. Mercure,Member, IEEE, Henri Pepin, and Farouk A. M. Rizk,Fellow, IEEE

Abstract—In an ongoing program using ultrashort laser pulsesto provoke discharges in air over considerable distances at electricfields below breakdown threshold, we have studied the conditionsfor the onset of streamers in such laser-produced plasmas, bothexperimentally and through numerical simulations. The resultsdemonstrate the importance of the electron density and of itsgradient on the generation of streamers. Also, a significant re-duction of the breakdown voltage for a 30-cm plane–plane gapin air was observed with a laser pulse energy of 15 mJ. Finally,a direct comparison of laser-induced breakdown in air and innitrogen shows the influence of electron attachment to oxygen onthe discharge process.

Index Terms—Laser, lightning, streamer, ultrashort.

I. INTRODUCTION

T HE study of electrical discharges is central to many fieldsof applied science, such as lightning protection and high-

voltage engineering [1]. The use of lasers to trigger dischargeshas been studied for many years [2]–[4]. This technique ispotentially very interesting because the natural breakdownvoltage can be significantly reduced, the discharge can beprecisely located in space and time, and it can be initiatedfrom a distance. Such control is important both for practicalconsiderations such as the operation of devices, e.g., high-voltage switches, or for more fundamental studies of thedischarge process.

Extending the ability of controlling discharges to longgaps, and eventually to lightning, offers enormous scientificand economic value and it constitutes an area of intenseresearch [5]–[12]. Japanese researchers in Osaka have reportedtriggering lightning, using 2-kJ laser pulses [13]. Other groupswere able to trigger large-scale electrical discharges with high-energy CO lasers [10], [14]. These schemes are clearly notefficient and they require large laser systems. Other approachesusing UV lasers [9], [11] or ultra-short laser pulses [15], [16](subpicosecond) have been proposed but further investigations

Manuscript received June 2, 1998; revised March 24, 1999. This work wassupported in part by the Natural Science and Engineering Council of Canada.

B. La Fontaine, F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, T.W. Johnston, J.-C. Kieffer, H. P´epin, and F. A. M. Rizk are with theInstitut National de la Recherche Scientifique, (INRS)-Energie et Materiaux,Universite du Quebec, Varennes, Que., J3X 1S2 Canada.

H. P. Mercure is with the Institut de Recherche d’Hydro-Quebec (IREQ),Varennes, Que., J3X 1S1 Canada.

Publisher Item Identifier S 0093-3813(99)05500-9.

are required to validate these concepts. It is in the latter classthat this work falls. The main challenge is to use the laserenergy efficiently in order to trigger and guide the dischargeover considerable distances, well beyond normal laboratoryscales. Ultrashort laser pulses offer unique advantages in thissense. Because of their very high intensity, it is possibleto ionize the air completely with relatively low energy perpulse. In addition, because of their nonlinear propagation inair and their ability to form extremely long filaments, they offerthe possibility to obtain continuous, ionized channels that areseveral hundred meters long [17].

The work presented here is the first step of a feasibilityassessment of the technique. The approach we have adoptedrelies on a systematic small-scale study (30-cm gap), throughexperiments and theoretical modeling, of the mechanisms thatlead to triggering of the discharge by an ultrashort laser pulse.We believe this will allow us to identify the most promisingconfiguration for triggering long gap discharges at low externalelectric field. The first step toward this goal is to understandthe development of streamers from the plasmas created by asubpicosecond laser pulse in the presence of an external fieldbelow the natural breakdown threshold.

The work presented in this paper constitutes one of thefirst attempts at a physical understanding of the production ofthe streamers, which are prerequisites to breakdown. First, theexperimental conditions are here so as to simplify the problemas much as possible, not so as to optimize the triggering effectat this small scale. By choosing to create the plasma with thelaser pulse before the electric field is applied, we rely on thenatural decay mechanisms such as electron recombination tohomogenize the plasma and to decouple the plasma creationproblem from the initial conditions for streamer inception.Secondly, the configuration is designed to simulate, on a smallscale, a lightning-interception scheme. In this scheme, the laseris fired some time before the electric field has reached a levelwhich is critical for self-breakdown or lightning propagation.This implies the need to study how the laser-produced plasmaevolves before and after an external electric field is applied.The principal aspect of this work consists in investigating theinfluence of free electrons and their temporal evolution on thedischarge dynamics.

In the following we consider specifically the triggering ofdischarges by an ultrashort laser pulse focused at a pointbetween two plane electrodes. The many different factors that

0093–3813/99$10.00 1999 IEEE

LA FONTAINE et al.: ELECTRON DENSITY ON THE FORMATION OF STREAMERS IN ELECTRICAL DISCHARGES 689

are important for triggering discharges with this laser beamwill manifest themselves at different stages of the dischargewe investigate. We define here five stages as follows. First, amore-or-less cylindrical plasma is produced as the laser pulseis focused between the electrodes and ionizes the air overa distance of several centimeters. (Unlike a long-pulse laser,which produces an electron avalanche in the oscillatory laserfield, the ionization here comes directly from the multiphotonor tunneling processes.) Second, the plasma density decreasesand becomes more uniform as it evolves freely until theelectric field is applied. Then ionization waves (streamers)grow from the end of the plasma channel toward the electrodes,as the electric field is applied. The positive streamer, the onedirected toward the negative electrode, will propagate first asit requires an ambient electric field that is lower than thatrequired by a negative streamer [18]. Next, these relativelycold plasma streamers make connections to the electrodes and,as the current starts to flow, the temperature and conductivityof the plasma increase. At this point, the plasma, whichcan now be considered a conductive channel, has essentiallybecome a “space leader” that starts to propagate toward theelectrodes. Finally, the leader bridges the whole gap, leadingto an arc.

It is clear from this description that the creation of stream-ers is a necessary condition for electrical breakdown sincethey produce a conductive channel connecting the electrodes,although it is well known that it is not always sufficient.For this study, we have chosen experimental conditions forwhich the observation of streamers almost always led toelectrical breakdown. This allows us to simplify the problemof modeling by restricting it to the first three phases, namely,the plasma creation, its evolution, and the generation of thefirst positive streamer.

Further simplifications are brought about by using as littlelaser energy as possible while maintaining a triggering ability,so that the plasma heating is kept to a minimum. Thus webelieve that for the conditions studied here, complex thermody-namics and hydrodynamics effects that would arise if the initialplasma were hot can be neglected. (Of course, experimentswere performed at higher values of laser energy but theresults of these investigations involving more complicatedmechanisms will be reported in a future communication.) Inthe present conditions, the electron density spatial distributionis the main characteristic of the plasma. The maximum electrondensity can be adjusted experimentally by varying the timedelay between the creation of the plasma and the application ofthe electric field. It is determined entirely by the recombinationof the electrons in the case of pure nitrogen and by thecombined effect of recombination and attachment in the caseof air.

II. EXPERIMENTAL SETUP

The experiments are performed at INRS–Energie etMateriaux. The experimental setup comprises three maincomponents: the laser system, the high-voltage dischargefacility, and the diagnostics. The laser is a chirped-pulseamplified, ultrashort pulse Nd:Glass laser, operating at awavelength of 1053 nm, or 526.5 nm after frequency doubling.

The width of the pulse is 500 fs and its energy can be as largeas 800 mJ. For the experiments described here, the laserenergy is set to (15 5) mJ, the wavelength is 526.5 nm, andthe full beam diameter is 6 mm. The high-voltage dischargecell and the diagnostics are depicted schematically in Fig. 1.The volume enclosed between the two plane electrodes ofthe cell can be evacuated and back-filled with a selected gasmixture, at a desired pressure. For the present experiments,because of the limit on our high-voltage supply, we use eithernitrogen (N ) or dry air at a pressure of 350 torr. This isthe highest pressure that still allows us to generate reducedfields of about 13 kVcm atm , which seems necessaryfor laser breakdown at this level of laser energy. This cellis located inside a Faraday cage (not shown) to preventelectromagnetic interference with the control electronics andwith the diagnostics. High-voltage impulses of up to about280 kV can be applied to the cell, using a two-stage impulsegenerator. The value of the front resistance in this circuit isused to set the pulse front to 0.6s, while the time-to-halfvalue is about 50 s. The application of this high-voltageimpulse can be synchronized with the time of arrival ofthe laser pulse to about 100 ns. Different diagnostics areused to monitor the evolution of the discharge. A calibrated,capacitive voltage divider is used to measure the appliedvoltage. A flush-plate, capacitive probe monitors the temporalvariation of the electric field at the ground electrode.Its sensitivity is 0.048 kVcm mV s . These signalsare recorded on a digital oscilloscope (Tektronix, modelTDS784A) having a bandwidth of 1 GHz and can be storedon a microcomputer, using a LabView interface. The imageof the discharge is analyzed with an image converter camera(Thomson TSN506N) that can be operated in streak mode,framing mode, or static mode. The image produced by thisinstrument is read out with a 16-bit Peltier-cooled charge-coupled device (CCD) camera (Photometrics). The spatialresolution of the imaging system is defined both by thenumerical aperture of the lens used to produce the imageas well as by the magnification and pixel size of the CCDcamera. With a Nikon lens, a magnification factor of

and a CCD pixel size of 20 m, the observed spatialresolution is about 6 mm. The temporal resolution is typicallyaround 10 ns for the conditions of this experiment. Thissystem allows time-resolved low-light level detection ofimages, which is essential to study streamers. High-resolutionimages of the plasma are also recorded with the CCD in theabsence of an electric field, with a resolution of about 100

m.

III. CREATION AND EVOLUTION OF THE PLASMA

A. Experimental Conditions

A plasma is created between the two planar electrodes byfocusing the laser beam through 2-cm-diameter holes, with an

50 cm lens. The geometrical focal spot (i.e., in vacuum)is located 19 cm from the ground electrode. A high-resolutionimage of a plasma in the absence of an external electric fieldis presented in Fig. 2, to illustrate the nonuniformity of the


Fig. 1. Schematic of the experimental setup. The high-voltage circuit comprises two capacitors that are charged in parallel up to 140 kV and then dischargedin series to provide pulses of up to 280 kV, with a rise time of 0.6�s and a fall time of 50�s. The high-voltage discharge cell is composed oftwo parallel electrodes separated by 30 cm. The laser beam is focused between these plates, through small holes, with anf = 50 cm lens. A streakcamera records the image of the electrical discharge.

Fig. 2. Light intensity profile of the plasma, around focus. The laser isfocused in air, at a pressure of 760 torr, with anf = 50 cm lens. Theposition of the geometrical focus is 0 cm.

light emitted near the focus of the beam. Its spectral contentis mainly due to emission lines from nitrogen and oxygenions. This image was taken in conditions similar to thoseconsidered in the streamer study, except that the air pressureis here 760 torr. Since the image recorded on the CCD is

integrated over the whole duration of the plasma, it is difficultto relate it directly to electron density. However, because thedensity decays extremely rapidly and the emission should bestrongest when the density is still high, we believe that thedata indicate a nonuniformity at the initial instant, when theplasma is created. The plasma emission is characterized bya peak near the geometrical focus of the beam and a tail oflower intensity that is 4–5 cm long, in the region before thefocus, closer to the lens. Very little light or no light at all isobserved past focus.

For the values of electron density of interest here (10cm ), any nonuniformity should be smoothed away veryrapidly via electron–ion volume recombination, which occurson a time scale much shorter than a microsecond. To illustratethis effect, the time evolution of electron density in nitrogen(dotted line) and in dry air (solid line) is plotted in Fig. 3,for two different initial values of density: 10 cm and10 cm . We only consider electron–ion recombination andattachment in the evaluation of the density decay, as they arethe dominant mechanisms. After a few hundred nanoseconds,the curves for initial density values between 10cm to10 cm all merge together, so that the distribution willbe fairly uniform over a length of at least 4–5 cm. The


Fig. 3. Temporal evolution of the electron density in air and in nitrogen ata pressure of 350 torr. The density decay is calculated by taking into accountrecombination and attachment for initial plasma densities of a 1018 cm�3

and b 1014 cm�3.

subsequent temporal evolution will then mainly affect theamplitude of this distribution, which should then, because ofvolume recombination, decay inversely with time in nitrogen.However, in the case of dry air, electron attachment to oxygenwill result in a faster decay than in the case of pure nitrogenand the electron density will drop abruptly.

From the foregoing it is clear that, by varying the delaybetween the laser pulse and the high-voltage pulse, the initialdensity conditions can be varied by large factors while keepingother parameters fairly constant.

B. Modeling the Laser-Created Plasma

We attempt here to model the plasma creation and to identifythe physical factors that affect the spatial distribution of theelectron density, in order to provide initial plasma conditionsfor modeling the streamer formation in Section IV-B. Thisinvolves describing the propagation of the laser beam aswell as the ionization process. As a first step, we use aversion of the nonlinear Schrodinger equation assuming anideal Gaussian beam and considering multiphoton ionization.This model shows the classical self-focusing of the beamas a whole and predicts laser intensity, beam radius, andtime evolution of the electron density around the region offocus. This is a very idealistic case since a real beam hasa structure which is much more complex and, in additionto whole beam self-focusing, filaments will develop as aresult of small-scale self-focusing when the power exceedslocally the critical power. Since a more realistic and completedescription would depend very much on the details of theinitial beam characteristics (amplitude and phase distribution)and on complex refraction effects near the focal region, itwould be extremely difficult to implement. As a consequence,we choose to introduce, in a second step, a simple geometricalmodel, linked to experimental observations, that describes theasymptotic propagation of the beam.

In order to fully describe the propagation of the beam inair or nitrogen, it would be necessary to solve Maxwell’sequations together with the laws describing the interactionwith the medium. We will restrict ourselves here to calculating

the beam propagation using the paraxial approximation incylindrical coordinates and in the retarded time frame of [19]

(1)

where is the envelope of the electric field of thelaser pulse, is the radial coordinate, is the longitudinalcoordinate, and is retarded time coordinate ,which describes the temporal structure of the laser pulse.Dispersion can be neglected at the wavelength consideredhere. The calculations are made for a converging beam thatis focused with an 50 cm lens.

The nonlinear refraction index of the medium is given as

(2)

where is the laser intensity,is the plasma critical density, is the electron

density, and the imaginary part represents the attenuationof the pulse due to the absorption of the light by the medium.The first term of this equation describes the gas self-focusingeffect and the second term represents the defocusing effect ofthe plasma that was created by the pulse itself. The value ofthe nonlinear index , for ultrashort pulses and wavelengthsof a few hundred nanometers, is around 510 cm Wat 760 torr, both for air and nitrogen [20].

The electron production rate, via photo-ionization, is givenby

(3)

where is the initial neutral molecule density and is theionization probability per unit time. For the wavelength used inthis study (526.5 nm), the main mechanism to be considered,at laser intensities below 210 W/cm , is multiphotonionization [21]. This is the case here, except perhaps close tofocus, where the intensity may be high enough to induce tunnelionization. The following power law describes multiphotonionization [21]:

(4)

where

(5)

is the ionization potential of the oxygen or nitrogen andis the number of photons required to ionize the

gas.We consider the point which corresponds initially to

the center of the pulse, and assume that the pulse shape doesnot change considerably as it propagates. This assumption isjustified, except very close to the focal point. After separatingthe variables, we can evaluate only the radial componentsof the laser electric field envelope (being the independentvariable)

(6)


where and is a function describingthe temporal structure of the pulse. The electron density isobtained from (3)

(7)

where and

For a Gaussian function , where isthe pulse duration, one obtains . We solvedapproximately (1) for using the variational approachof Anderson and Bonnedal [22] where a Gaussian trial functionis assumed. We neglect the attenuation of the pulse in thecalculations. The validity of this assumption has been verifieda posteriori: we found that, considering only the energy lossesdue to photoionization and to inverse bremsstrahlung [23],only a few percents of the laser energy is absorbed. This factjustifies neglecting the rise of the gas temperature at the focalspot.

The calculated axial distribution of the laser intensity aswell as the beam radius in the vicinity of the geometricalfocus is shown in Fig. 4(a), for a laser beam of 15-mJ propagating in air at atmospheric pressure. A similar plotof the axial density distribution and plasma radius appears inFig. 4(b). One should notice the shift of the peak toward thelaser from the geometrical focus by about 4 cm. This is causedin part by the nonlinear self-focusing of the beam that makesit collapse faster and by the strong defocusing effect of theplasma then refracting the light away. The maximum electrondensity obtained is around 610 cm , which represents anionization fraction of about 15% at the focus.

A comparison with the experimental result presented inFig. 2 reveals significant differences in the shape of thedensity profiles and in the position of the peak of experimentalemission, which appears less than a centimeter before thegeometrical focus, whereas the model indicate a larger focusshift of about 4 cm. Since the calculation is made assuming anideal Gaussian beam, it is reasonable to think that the origin ofthe discrepancies lies in the lower quality of the experimentalbeam profile whose details are difficult to quantify.

A very important aspect to consider is the nonlinear propa-gation of the laser beam. With a pulsewidth of 500 fs and anenergy of 15 mJ, the laser beam possesses a power of about30 GW, which is well above the minimum or critical powerfor self-focusing of about 0.9 GW [24]

(8)

In this equation, 526.5 nm is the laser wavelength and5 10 cm /W is the nonlinear index of the medium.

With a laser power roughly 30 times greater than the criticalpower, it is possible for the beam to self-focus and to formseveral filamentary structures as it propagates if fluctuationsare present on the initial beam profile.

(a)

(b)

Fig. 4. (a) Calculated laser intensity and beam radius around the region offocus. The profiles indicate a shift of focus of about 4 cm from the geometricalfocus located atz = 0 cm. (b) Electron density profile and plasma radius at theinstant of creation. The axial electron density shows a high peak atz = �4cm, with a radius of�25 �m.

For a perfectly smooth beam, no beam breakup is observedin the calculation but the model indicates a 4-cm shift of thefocal point due to whole beam self-focusing. However, thereal beam profile is initially characterized by a relatively widespectrum of amplitude and phase modulations. Sufficientlylarge local fluctuation will tend to grow individually becauseof the nonlinear Kerr effect and may form filaments. For adistribution of the lateral scale lengths of these filamentarystructures, one would expect them to overlap at a distancefrom the geometrical focus that depends on their size, withthe smaller ones being closer to . One can then seethat for a realistic beam, the energy will be concentrated overa region distributed between the geometrical focus and somedistance before it. This is consistent with a simple evaluationof the conditions for beam breakup using the-integral

(9)

It is usually accepted that for , the beam starts to break


Fig. 5. Calculated electron density 0.5�s after the creation of the plasma,considering only electron–ion recombination (no attachment). The axial dis-tribution is flat, with a much reduced amplitude compared to Fig. 4(b). Theplasma radius has also increased significantly to about 80�m. In the figure,the geometrical focus lies atz = 0 cm.

up and the intensity in the “hot spots” becomes very high [25].This condition is satisfied here for the region starting about 4cm before the geometrical focus.

As mentioned above, the electron distribution initially cre-ated by the laser is going to be smoothed by recombinationand attachment. The electron density profile 0.5s after itscreation is illustrated in Fig. 5, using the initial electrondensity distribution presented in Fig. 4(b) and considering onlyrecombination for simplicity. Notice the significant amplitudedecay to roughly 6 10 cm , accompanied by an increaseof the plasma dimensions. Its length is approximately 10 cmand its diameter is about 80m. Dimensions of the plasmaincrease because recombination is nonlinear and is fasterfor the higher densities. The same shape is obtained whenattachment is taken into account (except that the density valuesare smaller) since it depends linearly on the density, and it isslower than recombination at high densities (see Fig. 3).

From the above analysis, it appears that the detailed model-ing of the plasma created by the focused laser pulse is a verydifficult task. It would require a complete knowledge of theinitial beam characteristics, which is practically impossible ex-cept perhaps for a beam with a diffraction-limited wavefront. Athorough treatment of the ionization and defocusing effects inthe plasma would also be essential. It proves more convenientto use a simpler, geometrical description of the laser pulsepropagation. This simpler model, which incorporates more ofthe experimental observations but involves a free parameter, isused to define the initial conditions to be used in the modelingof the streamer inception (see Section IV-B).

In this simplified model, we consider a beam that convergestoward focus with an angle determined by the numericalaperture of the focusing lens. In the region near focus, a plasmais created that refracts the beam so that the angle atwhich the beam emerges from the focal point is larger than,which is in agreement with experimental observations. Fromthese arguments, we can describe the asymptotic propagationof the beam, away from the focal region, thus avoiding any

Fig. 6. Calculated electron density profiles at different times after thecreation of the plasma (t = 0.1, 0.2, and 2�s) using a model with a simplifiedtreatment of the refraction effects in the plasma. The density gradient is muchsteeper past focus, as the laser light is expelled by the plasma. The lengthof the plasma channel stays fairly constant as the density decays with time.(Geometrical focus is atz = 0 cm.)

complex, nonlinear effects occurring at very high intensities.Setting the lens position as , where is the focallength, and assuming conservation of energy (which seems tobe a good first-degree approximation, as mentioned above),the laser intensity of a Gaussian beam, along the propagationaxis, can be expressed as

(10)

where for and for .From this intensity distribution, we can calculate the densityprofile using (7). The only free parameter is the assumed exitangle . (In the conditions of the experiment, this exit anglewas not readily measurable.)

This treatment allows a good qualitative description of theplasma behavior, as observed after a several hundreds ofnanoseconds. As mentioned above, the image of the plasmashows very little or no light emitted past the focal point,which means that the exit angle is large compared to

. A profile obtained with is shownin Fig. 6, for different delays after the creation of the plasma(0.1, 0.5, and 2 s) in nitrogen. The same figure holds forair except that the densities are lower due to attachment. Wewould like to point out that the maximum gradient on thepositive side is directly proportional to the angle . Thusa steeper gradient is associated with and reflectsthe strong refraction of the laser beam in the plasma. We notealso that the plasma length obtained does not vary much withthe delay.

The steep gradients play an important role in the onset ofstreamers. When an external electric field is applied and thecharges separate, a steep gradient will result in a strong localfield. Since a threshold value of the electric field (24 kV/cm)is required to generate electron avalanches in air, one canappreciate the importance of the field enhancement mechanismat the end of the plasma channel in order to generate streamersin low external fields. This effect is discussed below.


Fig. 7. Snapshot images of the laser-initiated discharge in air, at a pressure of 350 torr, with a laser pulse energy of 15 mJ. (a) Image of the plasma createdbetween the electrodes with a delay�t = �1.4 �s with respect to the peak of the high-voltage impulse. The picture is integrated over 0.5�s. The plasmais the bright line in the center of the gap and extends approximately over 6 cm. (b) Image of the streamer coronas extending from the plasma channel.This picture is taken with an integration time fromt0 = �0.3 �s to 0.2�s, and the laser created the plasma at a delay�t = �0.4 �s. The peak of theapplied voltage is 180 kV, which corresponds to a reduced electric field of� 13 kV�cm�1

� atm�1.

IV. STREAMER GENERATION

AND THE ELECTRICAL DISCHARGE

A. Experimental Observations

The development of the system after the high-voltage im-pulse is applied between the two planar electrodes can best beobserved with the images recorded in streak and framing mode.The main time coordinateuses the time of plasma creation asits origin. We also define the time delay between the creationof the plasma by the laser and the peak of the high-voltageimpulse as . For negative values of , the plasma is createdbefore the peak of the high-voltage impulse. In addition, wewill use the alternate time coordinate whose origincorresponds to the peak of the high-voltage pulse.

Snapshots of the laser beam producing the plasma in airat 350 torr between the electrodes and of the two streamerenvelopes (coronas) arching out from the ends of the plasmachannel are presented in Fig. 7(a) and (b), respectively, fora case where the laser is fired close to the voltage peak.These images are representative of the different events thatwere recorded. The negative electrode appears at the top ofthe image, while the ground electrode is at the bottom. We setthe origin of the laser propagation axis to be the geometricalfocal spot of the laser, which lies about 19 cm above theground electrode. The laser beam propagates from bottom totop. The gap length is 30 cm and the integration time for thispicture is 0.5 s.

One can clearly see in Fig. 7(a) the plasma emission whichdefines a 6-cm channel between the electrodes, from 6cm to 0 cm, for a case when the time delay between thecreation of the plasma by the laser and the peak of the high-

voltage impulse is 1.4 s. A fair amount of straylight is seen on this image, due to the high sensitivity ofthe detector and to scattering of the laser light off surfacesclose by. The location of the plasma light is indicated withan arrow on the schematic diagram of the focusing geometryin Fig. 7. The axial position of the plasma emission on thispicture is in good agreement with the discussion on the plasmaformation presented in the previous section (see Figs. 5 and 6).After the electric field is applied, we observe the developmentof streamer coronas from the ends of the plasma channel,toward the electrodes. This is illustrated in Fig. 7(b), whichrepresents the light from the discharge recorded as the electricfield reaches its maximum, at . (In this case, the laserpulse created the plasma at a delay 0.4 s). Thestreamers on the top of Fig. 7(b) are positive (since theyextend toward the cathode), while the streamers on the bottom(extending toward the anode) are negative. The images of thetwo coronas differ noticeably. The positive corona usually hasmore branches and exhibits more graininess. In addition, thelateral extent of the negative corona is greater than that ofthe positive one. This can partly be explained, we believe,by the fact that the negative streamers start after the positivestreamers have made a connection to the cathode and thatthere is a significant field enhancement at the negative end ofthe plasma at that time. This is made clear as one examinesthe streak picture ( versus ) shown in Fig. 8(b). In thisfigure, the same vertical spatial coordinate as in Fig. 7 is used,but now the horizontal axis represents timeincreasing fromleft to right. For comparison, the time-varying high-voltagepulse is also plotted on the same time scale in Fig. 8(a) toillustrate the synchronization of the positive streamer with the


Fig. 8. Streak image of the laser-initiated discharge in air, at a pressure of 350 torr, with a laser pulse energy of 15 mJ. (a) External electric field appliedto the gap. (b) Image of the streamer coronas taken in streak mode. One can observe the onset of the positive streamers first, followed by the inceptionof the negative ones. In this case, the plasma was created at�t = �1.7 �s.

peak of the applied voltage. One can clearly observe the firstpositive streamer starting from the end of the plasma channeland propagating upwards toward the cathode at an initial speedof several times 10m s, accelerating to 106 ms. As soon asthis first streamer arrives at the electrode, another streamer, thisone negative, starts from the other end of the plasma channel,toward the anode at a slower speed of about 510 m s orless. This is consistent with the well-known fact that negativestreamers require a stronger electric field to propagate [18].We have observed experimentally that the field at one end ofthe plasma channel is reinforced when a streamer (positive ornegative) starting from the opposite end bridges the gap. Asthe streamer makes a connection, the capacitive probe recordsa sudden reinforcement or drop of the electric field at theground electrode, associated respectively to a connection onthe cathode or on the anode side. This is illustrated in Fig. 9,where a typical record of the variation of the electric field atthe ground electrode, as measured with a capacitive probe, ispresented. This signal was recorded in conditions similar tothose of Fig. 8. The peaks around 0.8 s (as indicatedwith arrows) correspond to connections of the positive andnegative streamers to the electrodes. These results mean that asthe positive streamer establishes a connection with the cathode,the field at the negative end of the plasma channel is reinforcedas a negative streamer starts to propagate. Since the field isenhanced, the extent of the negative corona is greater than thatof the first positive streamer corona.

One can also observe a re-illumination of the positivestreamer channel that coincides with the onset of the first neg-ative streamer. We think that this re-illumination is the results

Fig. 9. Typical record of the variation of the electric field at the groundelectrode as measured with a capacitive probe. This signal was recorded for adischarge initiated by laser, in conditions similar to those of Fig. 8. The peaksaroundt0 = �0.8�s (as indicated with arrows) correspond to connections ofthe positive and negative streamers to the electrodes. The dashed line indicatesthe high-voltage waveform and the dotted line corresponds to the laser pulsemonitor.

of a secondary streamer process, as described by Marode [28].An increase of the length of the central plasma channel, whichwas termed “space leader” in the introduction, follows until thecurrent grows sufficiently to allow an arc to bridge the gap.

It is important here to repeat that, for the conditions studied,the onset of the first positive streamer corona is usually a suffi-cient condition for the complete discharge to happen, i.e., veryseldom are streamers observed without electrical breakdown.We would also like to point out that the characteristics of thelaser-initiated discharge were fairly independent of the timedelay between the plasma creation and the application of thefield, for the conditions studied here.


Fig. 10. Probability of triggering a discharge in air (solid circles) andnitrogen (open circles) for a 30-cm gap, at 350 torr and with an externalelectric field impulse of at its peak. Parabolic fits to the data are also plottedto guide the eye.

We define the probability of electrical breakdown as thenumber of events for which an arc occurs divided by thetotal number of events recorded, for a standard delay window(0.5 s wide) and at a fixed external field. We have observeda high probability of triggering the discharge, using relativelylittle laser energy ( 15 mJ), and a voltage significantly lowerthan the natural breakdown voltage of this cell. In this case,the laser-induced breakdown voltage is 170 kV, which corre-sponds to an average electric field of 12.2 kVcm atm inthe gap. The natural breakdown field is measured to be about25 kV cm atm in dry air.

The effect of the plasma electron density on the dischargeis evaluated by varying the delay between the laser and high-voltage pulses, changing the background gas and changing thepressure. As was mentioned, the electron density in the plasmachannel can be adjusted by varying the delay between theplasma creation and the instant of applying the electric field.This delay, therefore, has a direct effect on the intensity of thelocal field produced by charge separation. The probability ofbreakdown at a pressure of 350 torr as a function of the delay,in the case of nitrogen and dry air is presented in Fig. 10 andillustrates this effect. The general upward slope of the curvesindicates (as one would expect) that the longer the delay beforeapplying the electric field, and so the lower the electron densityat the instant the field is applied, the harder it is to trigger thedischarge. The fact that the discharge can be triggered at longernegative delays in nitrogen than in dry air indicates that theattachment of electrons to oxygen has a strong influence indry air, as was expected (see Fig. 3).

In order to further investigate the effects of electron attach-ment in air, we have attempted to suppress the influence ofelectron attachment for delays of up to1 s by performingsome experiments at a reduced pressure of 75 torr. Since

Fig. 11. Temporal evolution of the electron density in air and in nitrogen ata pressure of 75 torr. The density decay is calculated by taking into accountrecombination and attachment for initial plasma densities of a: 1018 cm�3

and b: 1014 cm�3.

the attachment rate scales as the square of the pressure formoderate values of electric field [15] while recombinationdoes not vary with gas pressure, the temporal evolution ofthe electron density for dry air and nitrogen, at a pressure of75 torr, should be almost identical up to several hundreds ofnanoseconds after the plasma creation, as presented in Fig. 11.At 75 torr, we observe experimentally that it is in generaleasier to trigger the air gap than the nitrogen gap and that thevalues of delay that allow triggering in air are usually slightlylonger than those found for nitrogen. This behavior, which isin contrast to that observed at 350 torr, can be explained bythe fact that the attachment is much less important at lowerpressure and that the oxygen content of air (20%) makes iteasier to ionize than pure nitrogen (the ionization potentialsare 12.1 and 15.6 eV for molecular oxygen and nitrogen,respectively). This results in a slightly larger plasma radius andstronger refraction of the laser pulse past the focal point in thecase of air. Both these effects tend to increase the local electricfield at the end of the plasma channel, which is important forthe initiation of streamers as we will see in the next section.

B. Modeling the Onset of Positive Streamers

We start from the results obtained with the simple geomet-rical model for the beam propagation and plasma creationdescribed in the previous section. We would like to remindthe reader that the angle of the laser light exiting the plasma

(see Fig. 6) is proportional to the maximum electrondensity gradient and is used as a free parameter to describethe refraction effects of the plasma on the laser beam. We willshow here that it is possible to simulate the start of a streamerfor a reasonable value of for a given delay between thelaser pulse and the peak of the electric field and for the currentexperimental conditions, i.e., nitrogen or air pressure of 350torr and an electric field impulse of 6 kV/cm at its peak. Thetime-varying electric field applied to the gap, for 0.5 s,is described as follows:

(11)


and for 0.5 s. Here is expressed inkilovolts per centimeter (kV/cm) and timein microseconds.This pulse grows over 0.5 s, has a peak of 6 kV/cm (at

0 s), and then decays over the next 100s.We utilize here a so-called 1.5-dimensional (1.5-D) streamer

model, where the axial coordinateis described in detail andthe radius of the plasma is uniform and constant during thesimulation. This model is likely to describe reasonably wellthe initial stage of the streamer formation. At later stages,two-dimensional (2-D) simulations made on shorter scalesshow that the streamer radius can increase considerably [26],[27]. Unfortunately, 2-D simulations would be extremely time-consuming on the spatial scales studied here. The equationsunderlying the 1.5-D model are specified next.

The equation of continuity for the electrons and the ions is

(12)

where the index applies to electrons , positive ions ,or negative ions . The source terms are

(13)

In this expression, is the ionization rate, the attach-ment rate, the electron–ion recombination coefficient, and

the ion–ion recombination coefficient. representsphotoionization induced by molecular de-excitation [29].

In the drift-diffusion approximation, the average velocity ofspecies in the axial direction is given by

(14)

where the and signs apply, respectively, to positively andnegatively charged species; is the axial electric field, whichis the sum of the externally applied electric field and ofthe field generated by the charge separation within the plasma

. We used 10 cm /s and 2.2 10cm /s [30]. All the other coefficients for air and pure nitrogenthat we used were found in the appendices of [15] and [29],respectively. For both gases we used an electron diffusioncoefficient of (cm s) 1.52 10 (atm) [31]. Iondiffusion has been neglected.

The contribution of the charge separation to the axialcomponent of the electric field is obtained from Poisson’sequation. In the framework of the 1.5-D model, only the valueof the field on the axis matters. Its distribution is written as

(15)

Fig. 12. Charge separation at the ends of the plasma channel. Presented arethe electron density at� 300 ns with respect to the peak of the high-voltagepulse, using the simplified plasma creation model and the resulting electricfield, for three different values of the exit angle�out. a: �out = 0.17�, b:�out = 0.5�, and c:�out = 1.7�.

where is the plasma radius. The integration limits in thislast equation may extend past the electrodes if we take intoaccount their mirror effect. We have not, however, consideredthis effect here because we are mainly interested in the onsetof the streamers, which takes place far from the electrodes.

Equation (12) has been solved by means of the LCPFCTalgorithm [32] on a fixed nonuniform grid with a constantspacing of typically 25 m for (i.e., toward the cathode).The time step was typically 0.01 ns. Electron diffusion hasbeen performed as a separate step within an implicit numericalscheme.

Experimentally, the delay between the laser and the peak ofthe high-voltage pulse corresponding to a 50–60% dischargeprobability in nitrogen at a pressure of 350 torr, with a laserpulse energy of 15 mJ, is about 1s. These are the conditionsused for the simulations presented here.

The only missing input parameters for the model are theexit angle and the radius of the plasma. The regionsof particular interest here are the ends of the channel wherethe charge separation occurs and the streamers form. FromFig. 4(a), the radius of the laser pulse is about 200–300min this region. Since we have supposed a Gaussian profile, theradius of the plasma is going to be reduced by a factor of

because of multiphoton ionization (the number of photonsrequired to ionize nitrogen is 7). The radius of the plasmaobtained is therefore about 100m, which is also what wasobtained in Fig. 5.

In order to simulate the experiment, we had to estimatethe exit angle, calculate the initial electron density profile forthat angle, and then perform several computer runs in orderto find the least value for that led to streamer inception.We have found that an exit angle greater than about 1.7was necessary in order to observe the formation of a streamerin nitrogen, for a delay of 1 s with respect to the peakof the high-voltage pulse. The point is that the exit angle

has to be large enough to produce a sufficiently steepdensity gradient to allow the rapid onset of a strong localelectric field. This is illustrated in Fig. 12, where the local


electric field corresponding to density profiles obtained at threedifferent exit angles is plotted, 200 ns after the beginning of thehigh-voltage pulse (i.e., 300 ns before the peak). The anglesconsidered are 0.17, which corresponds to the numericalangle of the lens, 0.5, and 1.7. The electron density is plottedas a solid line and the electric field appears as a dotted line.Here the conditions leading to the formation of a positivestreamer (which happens about 100 ns later) are reached inthe last case only.

The exit angle 1.7 has been determined from theexperimental data showing a probability of about 50% for trig-gering the discharge in nitrogen, for a delay of approximately

1 s (see Fig. 10). Everything else being kept constant, wehave verified that no streamer could grow at longer negativedelays and that they could be observed at shorter delays,in agreement with the experimental results. This procedureis repeated for the case of air, keeping the same exit angleand the same plasma radius. The simulation results indicate amaximum delay of about 600 ns with respect to the peak ofthe high-voltage pulse, which is in good agreement with theexperiment (see Fig. 10). We also verified that the procedurecan reproduce results obtained at a slightly higher voltage,keeping the same exit angle and plasma radius.

The electron density evolution is depicted in Fig. 13(a),for hundreds of nanoseconds after the application of the highvoltage. At about 100 ns one observes the development ofan ionization wave for , i.e., a positive streamer, thatpropagates toward the cathode. The density of the streamerinitially grows steadily with time and its speed is initially sev-eral times 10 m s and increases further later. This is typicalof positive streamer velocities under the present experimentalconditions and fits the experimental data presented in Fig. 8.

The detailed behavior of the positive streamer formation canbe described as follows. First, a local electrical field is createdthrough charge separation at the position of the steep densitygradient, immediately after the application of the externalelectric field. When the local field is high enough, the electronslying in this region (present in the background plasma orcoming from photoionization) start to multiply through anavalanche process. The threshold field for avalanche in thepresent case is higher than for a uniform field since electronsare rapidly expelled from the high-field region. At a laterstage, the avalanche starts to progress toward the cathode, asseen in Fig. 13(b). The growth of the electron density on thecathode side is in contrast with a density decay in the plasmachannel itself, where the field is weak and recombination andattachment dominate.

On the anode side, the conditions are not so favorablefor the formation of negative streamers as for the positivestreamers since the density gradient is softer, and thus thefield enhancement is much less important, as can be seen inFig. 12. As a matter of fact, no negative streamer is seeninitially, both in the simulation and in the experiment (seeFig. 8). It is reasonable to think that the negative streamers inthe experiment form at a later stage because the distribution ofthe potential around the negative tip of the conductive plasmachannel is increased after positive streamers have made aconnection to the cathode. Following this view, the formation

(a)

(b)

Fig. 13. Evolution of the streamer for a plasma created with a�t = �1�s.(a) The density profiles calculated at different times after the application ofthe electric field are plotted here. One can clearly see the development of theionization wave. (The timet0 indicated in the figure is relative to the peakof the high voltage pulse.) (b) The electric field enhancement associated withthe ionization wave is plotted here.

of the negative streamers would be a consequence of the localfield enhancement due the combined effect of charge sepa-ration (as for the positive streamers) and of the conductivityof the channel. Unfortunately, our simple 1.5-D model is notable to simulate this phenomenon: the conductivity of thesingle positive streamer produced is far too small to increasethe field at the negative end of the channel significantly.Possible improvements of the model would consist of takinginto account several simultaneous positive streamers as wellas some temperature effects due to Joule heating, which wouldincrease the conductivity of the channel and would lead to alarger enhancement of the field. However, these improvementsare beyond the scope of the present work.

V. CONCLUSION

In this paper we have studied, both from an experimentaland a theoretical point of view, two essential stages of thelaser triggered discharge: the creation of the plasma by afocused ultrashort laser pulse and the onset of the first positivestreamers as the external field is applied.


The creation of the plasma is a complicated process in-volving numerous effects and depending on the small-scaledetails of the initial beam. Despite these complications, therelatively simple models developed here seem to describe themain features of the plasma observed after a certain delay,such as its position and its longitudinal size, mainly becauseof the smoothing effect of electron–ion recombination.

The effect of the electron density on the generation ofstreamers and on the triggering ability of the laser pulse,as well as the importance of electron attachment in air havebeen clearly demonstrated by varying the delay between theplasma creation and the application of the high voltage to theelectrodes, in air and in nitrogen, at 350 and 75 torr. Our modelfor the generation of the first positive streamer can describethe general experimental behavior reasonably well, providingthat we adjust one free parameter (the exit angle of the laserpulse). Having calibrated this free parameter for nitrogen atthe 50–60% discharge probability time delay, the correct timedelay for the 50% discharge probability in air was obtained.

Another significant result of the streamer model is theimportance of the electron density profile on the onset of thefirst positive streamer. A steep gradient in the axial directionof the electron density profile produces a strong local electricfield due to the separation of the electrons and ions as theexternal electric field is applied, which allows the onset of anavalanche and the formation of a streamer.

In order to further validate this model and give it betterpredictive value, it would be desirable to measure the exactdistribution of the electron density and temperature at thetime when the external electric field is applied. This task is,however, quite challenging since the model predicts such lowvalues of the electron density and temperature that any effectwould be likely buried in noise.

The modeling of the later stages of the discharge, i.e., theonset of the negative streamer, the heating of the plasma“leader,” and the final jump, represent major challenges thatneed be addressed in the future. This is important in orderto be able to extrapolate these results to a very large gap orto lightning discharges and to find the configurations that aremost efficient.

More work is under way to evaluate the importance oftemperature in the triggering process. It is obvious that theseeffects will dominate after the first streamer makes a connec-tion to the electrode and current starts to flow and heat thechannel. It is also important to note that an increase of theenergy deposited within the plasma channel at the time ofits creation will induce thermal effects which should help toreduce further the external electric field required to inducethe formation of streamers and a gap breakdown. Studiesusing higher laser energy, different laser wavelengths andpulselengths would be valuable in order to address these pointsand these topics will also be pursued at a larger scale in thefuture.

ACKNOWLEDGMENT

The authors wish to thank F. Poitras for his invaluabletechnical assistance throughout the course of this work. Theywould also like to acknowledge many useful discussions with

Z. Jiang, R. Marchand, F. Martin of INRS and with P.Couture and J. L. Lachambre of Hydro-Quebec. The authorsare also grateful for enlightening discussions with A. Bondiou-Clergerie of ONERA as well as for her recommendations.

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[31] C. Wu and E. E. Kunhardt, “Formation and propagation of streamers inN2-SF6 mixtures,”Phys. Rev. A, vol. 37, no. 11, pp. 4396–4406, 1988.

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Bruno La Fontaine received the Ph.D. degree in 1992 from Institut Nationalde la Recherche Scientifique (INRS), Universite du Quebec.

After post-doctoral studies at AT&T Bell Laboratories, he joined theAdvanced Microtechnology Program at the Lawrence Livermore NationalLaboratory in 1995. He is now Professor at INRS-Energie et Materiaux,which he joined in 1997. He has been involved in the study of laser–plasmainteractions related to Inertial Confinement Fusion as well as in appliedresearch such as X-ray lasers and EUV lithography. His current researchinvolves control of electrical discharges with high-power ultrashort pulselasers as well as laser-based inspection techniques for nanotechnology.

Francois Vidal was born in Windsor, Que., Canada.He received the Ph.D. degree from the Universityof Montreal in 1988.

He has been working as a Computational Physi-cist at the Institut National de la Recherche Scien-tifique, Quebec, Canada, since 1991. Besides mag-netoplasmas, his latest fields of research includelaser-induced plasma spectroscopy, laser-triggereddischarges in long gaps, laser propagation in plas-mas and in air, and kinetic modeling of hot plasmas.

Daniel Comtois was born in Montreal, Que., Canada. He received the B.Sc.degree in physics from the University of Montreal in 1997.

He joined INRS-Energie et Matériaux, where he is now working on laser-triggered electrical discharges, toward the Ph.D. degree.

Ching-Yuan Chien, photogrsph and biography not available at the time ofpublication.

Alain Desparois was born in Montreal, Que., Canada, on August 7, 1975.He received the B.Sc. degree in physics from the University of Montréal in1997.

He completed the M.Sc. degree on the study of electrical dischargestriggered with ultra-short laser pulses in 1998 and is currently working towardsthe Ph.D. degree in laser ultrasonics.

Tudor Wyatt Johnston was born in Montreal, Que.,Canada. He received the B.Eng. degree in physicsin 1953 from McGill University, Montreal, and thePh.D. degree from the University of Cambridge,U.K., in 1958.

From 1958 to 1969, he was a Research Sci-entist at the RCA Victor Research Laboratoriesin Montreal, where he worked on a wide varietyof topics involving plasma physics related to thevarious aerospace programs. After a short stint at thePhysics Department of the University of Houston,

Houston, TX, he returned in 1973 to the Montreal area to INRS-Energie etMateriaux as a Full Professor and began to work on various plasma topicsarising in the study of laser–plasma interactions. His current research interestsinclude the relativistic electron effects in plasmas due to high-intensity lasers.

Jean-Claude Kieffer is a Professor at INRS-Energie et Matériaux. His currentresearch interests include the physics of ultrafast laser-induced plasmas, theapplications of ultrafast X-ray sources, and femtosecond technology andmetrology.

Hubert P. Mercure (M’81) received the Bachelor of Physics degree in 1970from Universite de Montreal and the Ph.D. degree from the University ofToronto, Toronto, Ont., Canada in 1976.

He joined IREQ in 1978 and has worked as a Research Scientist in thedepartments of High Voltage and High Power. His mainstream researchactivities are in the field of lightning protection and of the mechanisms ofsurface discharges on insulators. He has worked on high-voltage switches,using SF6 as an insulating medium and a laser-triggered ingitor (750 kV, 20-ns switch-on time). He initiated the experimental study of triggered lightningat Hydro-Quebec, in 1976. He is currently Manager, Power Lines Division,in the Transmission and Distribution Technologies Group at IREQ.

Henri Pepin received the B.Sc.Eng. degree in 1963 from INSA-Lyon, France,and the D.Sc. degree in physics in 1968 from the University of Paris, France.

From 1969 to 1971, he was an Assistant Professor at the Physics Departmentof the University of Montreal. Since 1971 he has been Professor at the InstitutNational de la Recherche Scientifique–Universite du Quebec (INRS-Energieet Materiaux). His current research interests include various applications oflaser–plasma interactions such as control of electrical discharges with high-power ultrashort pulse lasers with application to laser-triggered lightning, laserablation deposition for application to microelectronics, as well as ultrahighintensity laser–matter interaction in the context of laser fusion.

Farouk A. M. Rizk (SM’75–F’82) was born in Egypt on July 6, 1934. Hereceived the B.Sc.Eng. degree in 1955 and the M.Sc. degree in 1958 fromCairo University, Cairo Egipt, a Licentiate of Technology degree in 1960from the Royal Institute of Technology, Stockholm, Sweden, and the Doctorof Technology degree in 1963 from Chalmers University of Technology,Gothenburg, Sweden.

He worked as a Research Engineer at ASEA, Sweden, in the High PowerLaboratory, Ludvika, (1960–1963) and in the Computer Department, Vasteras(1963). He worked for the Egyptian Electricity Authority (1964–1971),becoming Manager, High Voltage, in 1968. He joined the Institut de Recherched’Hydro-Quebec (IREQ) as a Senior Research Scientist in 1972, becomingProgram Manager in 1975, Scientific Director (1976), Director Power Trans-mission (1980), and Vice-President (1986). Since January 1987, he holds thetitle of Fellow Research Scientist at IREQ.

Dr. Rizk was awarded the Egyptian National Prize of Engineering Sciencefor 1971 and decorated by the Order of Worthiness (Third Class) in 1972 andthe Order of Science (First Class) in 1973. He is a Registered ProfessionalEngineer in the Province of Quebec and has been, since 1984, InternationalChairman of Technical Committee 28: Insulation Coordination, of the In-ternational Electrotechnical Commission (IEC) and since 1988, Convener ofCIGRe Working Group on Insulator Pollution.

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