AD-A263 212

PL-TR-92-2266

DISCHARGE OF ELECTI CALLY CHARGED CLOUDS

Jean-Claude DielsXin Mlao ZhaoChao Yung VehCal YI Wang

University of New MexicoDepartment of Physics and AstronomyAlbuquerque, NM 87131 DTII

26 October 1M S PR 19

Final ReportSeptember 1990 - September 1992

Approved for public release; distribution unlimited

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IE VNCY USE ONLY (408vt blank) 2. REOT DATE 3. REPORT TYPE AND DAT[S COVERED26 October 199.2 Final Report, Sept 1990Sept 192

4. TITLE AND ISUTITLE -IS. FUNDING NUMBERSDiseharge of Flectrically Charged Clouds PE 62101F

PR ILIR TA OB 1I.J AA

6. AUTHOR(S) Contract F196218-90-K-005(-Jean-Claude Dieis, Xin Miao Zhao, Chao-yucn Yeh andCai Yi Wang

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*Department of physics and AstronomyUniiversity of Now MexicoAlbuquerque, NMl 87131

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13. ABSTRACT (M-aximum200lwords)

In a one year program, we have established a new mechanism for triggering lightningusing low energy (less than 1 mJ) ultrashort (subpicosecond) pulses. A pre-ionizedof needle-shaped" path is created by three to four photon ionization of oxygen orapplied field results in a local enhancement of the field, sufficient to reachavalanche breakdown. Measurement of multiphoton ionization cross secti n have estab--lish ed 3that a few mj/cm2 in 200 fs at 248nm are sufficient to create 10' electronsper cm3 . Laser induced discharge of 90 KV over 25cm have been d emonstrated with npulses at 248nm, at pressure of 1/7 atm.This result and the theory indicate that less than I mJ in less than 1 ps durationpulses at 248nm should induce the discharge at atmospheric pressure. A fs laseroscillator-amplifier has been assembled to perform such testsn

WISDOMTHAI1I. NUMBER OF PAGESLighning30

Laser 16. PRICE CODETriSggred Lightning__________

17, 5ECURITY CLASSIFICATION 16. SECURITY CLASSIFICATION 19. SECURITY CLASSIICTION' 20. LIMIVATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassi-Oied SARNIN 7S40-01-250-SSOO Standard Form ý98 (Rey 2-89)

Contents

1 Objective I

2 Motivation I

'3 - Background I

4 Highlights of the method 2

5 Theory 25.1 F's pulse propagation and mOtpression ............. :35.2 FAvolution towards a streamer.. ................. (

6 Experimental work 76.1 f[he oscillator . ...............................6.2 YAG laser Amplifier ...... ....................... 86.3 Frequency trippling assembly ., * *................... 106.4 KrF laser UV (248nm) pulse amplifier ................ It6.5 Synclhronizor. ................................. 126.6 iiulse meatsureueitt without nuoliinear )roCss. ........... 13(6.7 loizat ioti cross sect ions ........................... I I6.8 High Voltage ('ell ............................... !56.9 Inducing 100 kV discharge in air ........................ 17

7 Conclusion 19

Reference 20

A Pulse propagation/compression 22

B Evolution towards a streamer COD 23

4: IMls QRAI•:• t~anoComo

0TIC ?AD

Lkianfnou~ncedJu-sti 01tato

-•~Di lbUti1on/_--' .Availability Codes

Dist Se aA-'a

1 Objective

To develop a safe and reliable method to discharge thunderclouds. The targetfield at which we aim to trigger the lightning is 1/10 of the self breakdownfield in air.

2 Motivation

'I'The ability to continuously discharge t hunderclouds over rocket launch pad,,and airl)orts would prevent tlhe delays and hazards associated with lightning.Lightning strikes have damaged the radar cone of aircralt's, and destroyedrockets [1] through tlhv electromagiwtitc pulse affecting the navigationa Cul -puter. This development will also have an impact on storin research. Asudden change in the electromagnetic forces present in a cumulonimbus mayaffect its development. It has been thought in the past that a shock wavesuch as caused by thunder at an early stage of a storm development maycause rain, preventing hail [2] that would occur at a later stage. The abilityto trigger lightning in and to the cloud would lead to a better modeling andunderstanding of the storms, and even the prospect of having a limited actionon them.

3 Background

A commonly used method to trigger lightning is to fire a rocket trailed by agrounding wire [3. 4] through the 100 in height space charge layer shieldingthe ground. As (coml)ared to the t(ethod proposed here. this method has thewfollowing disadv'ant ages:

9 The space charges accumulate around the rocket fast enough to shieldit. Obviously, this could not occur with a conductive volume createdat the speed of light.

"* While there is a preferential path created for the lightning, there is notthe ten-fold field enhancement that is required to ensure that no otherelement (airplane. rocket can trigger the lightning).

S2.- i

W1

9 The rockets cannot be launched on a continuous bases. The repetitionrate of the laser trigger can easily exceed 10 Hz.

Another method that has been considered in the past and is still beinginvestigated by a Japanese group [5] is lightning triggering with a powerfulC02 laser. The main disadvantage of the latter method is that it requiresa laser field exceeding the avalanche breakdown field. The laser producedplasma is thus opaque to the radiation. a fact that limits the range overwhich an ionized path can be created.

4 Highlights of the methodCharge seeding A pencil shaped volume of free electrons is created by3- and 4- photon ionization of oxygen and nitrogen in a region of high field.using a fs pulse at 248 nm.

Pulse propagation The fs pulse is given a negative frequency sweep (downchirp)such that pulse compression in air occurs. The resulting peak amplificationcompensates the depletion due to multiphoton ionization, and linear absorp-tion.

Photodetachment A long pulse of visible light (530 ini) is launched si-multaneously. to maintain the conductive path (by photodetaching the 0-and 0- ions).

Field enhancement The motion of the charges in the external field issuch that an internal field is created, with a ten fold local enhancenientl atthe "tip" of the pencil. When the enhanced local field reaches lhe thresholdfor avalanche breakdown, the discharge is initiated.

5 Theory

We have established a theoretical model for the fs triggering of lightning.and performed numerical calculations. The theoretical work detailed in thefollowing subsections include:

e Calculation of pulse propagat iou, compression and niulti phot on ioniza-Slion

* Prediction of conditions of chirp and focusing that lead to optimumS11ifoirii "seeding" of electroiis

* (alchulatioll of hlie charge evoh'luthio ald restill-ilig field eiihalin'ueilt

* Prediction of the optimui rafto of diameter to height for the ioniwedcolumn.

5.1 Fs pulse propagation and compression

The procedure for calculating the p)ulse propagation and compression is out-lined in Appendix A and in ref. [6. 7] WVe will present, here only a briefsummary of the main results.

Fig. I shows the ionized volume created by focusing the beam to a Imm beam waist at 50 m from groutd. A fairly localized and narrow pencilof charges is created, with a density in excess of 2 x 1013 - 'm- when adownchirped Gaussian beam is used. For larger pulse energies. the ioni:,atioiivolume is ahead of the beam waist. as illustrated in Fig. 2. It may beadvantageous to focus tle beam at higher altitules, uSC 111111ch higher pi lseelielgies, iII order to crlate a iotiizal ioii volume of largelr diaitoer. 'Thre' isa compromise to be reached:

e For a given pulse energy, the density of photoelect rons increases propor-tionally to 1/w 6 (oxygen) or 1/u.8 (nitrogen). where tv is the transversedimension of the beam

* For a cylinder of radius r ionized at 10'em-3 . the local enhancementof the field is fastest for r _> 5cm

The second condition results from the computer simulations of the evolutionof the charges under the applied field presented in the following section.[he optimum diameter of the ionization volume will have to be deterinimied

*experiment ally, as it is a function of the size of the fs laser source availablhfor triggering the lightning. Another important consideration is the location(altituide) of the peak field. Our calculations as well as the preliminarydischarge tests show that it is preferable to locate the ionized volume in the

T3

, '.• •• • •"° ,. ....... A..-....•

"i - ,-t• i - •• i ..• i '

O. e.e t es 3.0 a... 4eo e.e ug .e g vs.. seoe seeo iOS~eZ(meters)

Figure I:Electron density versus distance (height above ground) for a 200 fs ,i1ll widt ihalf maximum (FWHM) Gaussian beam of 5 mJ energy focti.ed to a heaniwaist of wo = lmm at 50 m. The pulse temporal shape is £(t) = &,exp{ -- (1 +if)(•-)2 } with values for the chirp coefficient c = 0. 0.15. 1.0, 1.3. and 2.corresponding to solid. dotted, dashed, long-dash and dalIi-dot,, lite ,s, and

= -200 .v4, I ti.

4

IiiI.

I.4t

0.0 10.0 o 0.0 $0.0 40.6 56.0 40.0 6.o0 80.0 60.0 100.0Z(metere)

Figure 2:Electron density versus height, for a 10 mJ 200 fs (FWHM) Gaussian beamfocused to a waist of w0 = 2 mm at 50 m. The pulse shape is the same as inFig. 1 with the chirp coefficients 0, 0.5, 1, 1.5 and 2 corresponding to solid.dotted. dashed. long-dash and dash-dotted lines.

region of highest field. Near the earth, the fields do not generally exceed50 kV/m [81, while fields as high as :3 MV/m have been measured at high.altitude.

5.2 Evolution towards a streamer

This subsection summarizes our theoretical results, which are outlined inmore details in Appendix B and in refs. [7, 9, 10].

The purpose of the theory is to determine whether the charge seedingproduced by fs photoionization will lead to the formation of a st reamer, andtrigger the lightning.

We approximate the results of the preceeding section by a cylinder of ra-dius r containing a Gaussian distribution of electrons N'(:) and ions Ni(z).Under influence of the external field. the electrons and ions will separate, cre-ating a local field that opposes the applied field. WVe establish in AppendixB the equations of motion for the electrons and fields. taking into accountcylindrical symmetry in treating this three-dimensional problem. WVe solvesimultaneously Poisson's equation (three dimensional), the system of con-servation equation for the electrons and various ions. taking nito accountphotoionization (creation of the initial charge densities). attachment of theelectrons by oxygen to create 0- and 02 , photoionization of these nega-tive ions by an auxiliary laser pulse (long laser pulse in the visible range).electron-ion and ion-ion recombinations, and finally elastic and ionizing col-lisions.

The calculations were applied to the model atmosphere. as well as to thelaboratory testing cell. A typical resuilt for the cell is shown in Figs. :3. wherethe field "on axis" (of the beam) is shown as a function of height, for varioustime increments.

In Fig. 3, successive plots of electric field versus height (in in) are shown.taken at 147 ns interval, following the creation of a "pencil" of pholoion-ization with peak density in the center of 2 x 1012 c'-/cn#:. and a (iaussian(vertical) distribution of 0.25 in width (FWHM). The radius of the pencilof electrons and positive ions created by fs UV photoionization is 100 pin.The applied electric field is assumed to be uniform and equal to 7.50 kV/m.Separation of charges result in a decrease of the field in the middle of thevertical distribution of charges. A very steep increase of t he local field - andof charge density - occurs at the upper and lower boundaries of the ionized

6i

zf

U

10.0000 0.625 0. i250 0. 187S 0.0= 0.3125 0.3750 0. 43V5 0.500X

Figure 3:Electric field in the laboratory cell versus height coordinate, for 5 successivetime increments of 14-7 ns following fs photoionization of a cylinldrical volumeof 400 jim radius. The charge distribution is assumed to be uniform alongthe radial coordinate, and Gaussian along the axis of the cylinder, with aFWHM of 0.25 m. The applied field is uniform, equal to 750 kV/m.

volume, as shown in Fig. 3. The combined enhancement of the number ofelectrons and of the field leads to avalanche multiplication. initiating thedischarge.

Numerous computer simulations show that the same qualitative pictureemerges for the atmospheric situation.

6 Experimental work

In parallel to the theoretical work, la? oratory tests have been performed, anda facility to study laser induced discharge in air has been constructed. The"following tasks have veti coCmplohteld:

* Construction of a fs source of m.) pulses at 248 nm, consisting in a mode-locked dye laser at 744 ni. a 3 stage amplifier, a frequency tripler, and

7

an excimer laser amplifier.

* Construction of a 100 kV discharge chamber with profiled electrodf s

e Measurement of the multiphoton ionization cross-sect ions of 02 and N2

* Observation of 100 kV discharge induced in dry air by 248 nm pulses

6.1 The oscillator

The oscillator is a dye laser (antiresonant ring) hybridly mode-locked, pumpedby a mode-locked argon laser. The (100 %) pulse to pulse fluctuations of thedye laser oscillator makes the output of the chain an uncontrolled statisti-cal event. The problem is illustrated by the oscilloscope recording of Fig. 4showing a single sweep snapshot of the pulse train. It is only for the largestpulse, which occur with a probability of less than 10 (. that the amplifiedspontaneous emission can be suppressed in the amplifier chain. Consider-

7: ing that the high voltage discharge chamber cannot be fired at more than Ishot/3 minutes, it is imperative to use an oscillator with a better duty cycle.

We have converted the dye oscillator into E. Ti:sapphire mode-locked laser.-The conversion is essential to have a reliable source of fs pulses for the lab-oratory analysis of the discharge. This laser provide self-mode Iocked pulseswhich reduced the number of optics inside the cavity and provides a stableuniform fs pulse train as shown in Fig. (5).

We expect 300 mlW output beam from the laser consisting in a train of200fs pulses at 744 nm with a repetition rate of 80 Aill:. A t uning wedge willbe inserted ior wavelength selection and two SF14 prisnis inside the cavityallows us to adjust the chirp of the pulses.

6.2 Y"AG laser Amplifier"These 25 nJ, 200 fs pulses will be amplified to 1 mJ by a amplifier (LI)$751as gain medium) pumped at 8 H: by a frequency doubled Nd:YAG [11].

=i Initially designed with three stages, the amplifier has been recent ly upgradedwith a fourth (last) stage using a "Bethune cell" to provide utwiform pumpingto the source pulse. The four stage amplifier provided 107 times amplificationfor the input pulstes. The amplifier is shown in Fig. 6.

8

h( t ii 1 , I 1 dII I'tl til t I1c oI ( Sc I Iw al I III

Output coupler

26 cm 8Cal

13 cmBrewter rism

8Hz, IOns

SI'--,,,+Mods Locked Nd:YR6

532nm S.... r -X .....~~~.. .............. ..........................--X l lmJ/pulse

744nm++ 9OM'1Hz

200nJ/pulse ................................................................................... %

Figure 6: 8Hz YAG second harmonic pumped fs pulse amplifier

As usual, eliminating ASE and timing control between the pump andseeding pulses will be an important issue for the amplifier. Improved qualityof the seeding pulse train, spatial filter inside the amplifier and the fineelectronics time control should enhance the performance of the amplifier.

6.3 Frequency trippling assembly

The amplified pulses are focused into a 1 mm thickness KH2P0 4 (KDP) togenerate second harmonic and subsequently a 3 mm thickness KDP for thethird harmonic generation. The setup is presented in Fig. 7

Frequency trippling from 744 nm to 248 nm is performed with a sequenceof two KDP crytals, cut for type I second harmonic generation (of 744 nm)and sum frequency (372 nm + 744 nm), respectively. A -"dichroic" half waveplate (half wave at 372 nm, "zero wave" at 744 nm) is used between thecrystals, with the purpose to rotate by 900 the polarization at 372 nm, leavingthe polarization at 744 nm unchanged. Initially, the crystal and wave platewere all mounted on separate mount, resulting in a relatively poor conversionefficiency, because of the large spacing between crystals.

We are presently recalculating the Raleigh range and reconstructing the

10

248nm toExclmeramplifier

4 8Hz, 744nm

I 14upo I S nTupo SFs6,

_744+744=>372nm 744+372->248nm

3mm KDP, I mm KDP,

Figure 7: Setup for frequency trippling.

frequency trippling setup. The two nonlinear crystals and the half wave plate

are assembled on a single mount and the distance from the front face of thefirst crystal to the rear face of the second crystal is minimzed. The assembly

ensures the two crystals are inside the focal region of the lens, to providemost efficient frequency conversion. The expected overall efficiency for third

harmonic generation is about 1%.

6.4 KrF laser UV (248nm) pulse amplifier

The 248 nm pulses are amplified by an Excimer (KrF) laser (Questek) from0.01 mJ/pulse to about 1 miJ/pulse. The KrF laser is modified into an

- - amplifier. As shown in Fig. 8, the end mirror is replaced by an externalcavity high reflector for double pass amplification.

The output pulses are focused into a spatial filter to filter out the ASEbackground.

I•• -. "

• _ 11

Spetial filter KrF laser Discharge chamber

Wam ....... ...... ....... ......248nm,- Hz

248nm, 8Hz

1 uJ/pulse

Figure 8: KrF UV fs pulse amplifier

6.5 Synchronizer

Because of the short life time (; 200 to 300 ps) of the amplifying dye(LI)S751) and the thermal instability of the second harmonic crystal of theYAG laser, timing control of the laser-amplifier-amplifier system becomesvery critical. A delay controlling electronic circuit has been designed andtested and proved to be helpful adjusting the timing with a jitter of less thanI ns. The main "clock" is provided by the mode-locker of the argon laser at40 MHz. That signal is divided down to 8 Hz by a digital divider. Each pulsefrom that divider is split, amplified and appropriately delayed to provide

* trigger for the flahlamps of the pump laser for the amplifier

* trigger for the Q-switch of the pump laser (jitter < I ns)

* trigger for the HV of the excimer laser

* trigger for the excirner discharge (jitter < I ns)

* trigger for the High voltage pulser

12

Bea retlcon

expander

62 ;G Interfometer

1 a f-a+b

Figure 9: Experimental set-up for pulse duration and chirp measurementwithout nonlinear process

With the oscillator being modified into a self-mode locked Ti'sapphirelaser, the electronics to synchronize tle triggering setup has been modified.A photo diode detects signal from the source laser and send(s it to a fre('(Iueclydivider. A divider has been constructed which reduces the frequency from80 MHz to 8 Hz and provides proper delays to each of the triggering signals.

6.6 Pulse measurement without nonlinear process

Pulses at 248 nm can not be measured with conventional autocorrelatorsince no second harmonic is available at this wavelength. A linear singleshot measurement of fs and ps pulses without nonlinear process has beendeveloped. The setup provides us a tool for measuring the 8 Hz amplifiedpulses. The basic idea is presented in Fig. 9. Other methods using correlationrequires a second harmonic crystal. For 248 nm this kind of crystal does notexist, this a new diagnostic method with all linear process is necessary. Withthis setup, we are able to determine the duration and the sign and amountof chirp of pulses.

13

VDc 30Volt_ _ _ _ _ _ aperture

Exchnzer- -T dLaser

""=1.2cm window

pump

Figure 10: Experimental set-up for three and four-photon ionization cross-sections of 02 and N 2 measurement.

6.7 Ionization cross sections

An experimental determination of the multiphoton ionization coefficients ismade by collecting and measuring the photoelectrons in 1he set qp of Fig. 10.

'lThe mean free path of the electrons in the low pressure cell (< 5 X10-4 tort) is much larger than the distance between the electrodes (4 ram).Therefore, the time integral of the current is a direct measure of the numberof photoelectrons. At that low pressure however, the number of neutralmolecules available for ionization soon saturates. Indeed, the number densityof neutral molecules NA decreases at the same rate at which the electrondensity N, decreases-

dNA dN,7-- = -0.(ft)JIhNA, (1)

where n denotes the order of ionization.Our measurement shows that the three photon ionization for 0 at 4 x

10-4 torr is #(3) = 1.28 x 10-23 J-1s2 cm6 which is sufficient to generate anelectron density of 1.8 x 101 2e-/cm3 in air (at atmospheric pressure) with a200 fs pulse at 248 am having an energy density of 1 inJ/cin'. For N2 at

14

Yi

40 36320/14

S3.3.32.0

3 4 A56 78910 20 30 40 50 60

Laser Intensity(2u10 W/cn)

Figure 11: Measurement of three photont ionization cross-section Of 02.

6 x 10-4 torr, we obtain four photon ionization ar4 4 x I o 34 j4 4~ 3 rn58

which is sufficient to generate an electron density of 1.0 x 10,2e/CM3 in thesame condition as for 02. The results are presented in Fig. I11 and Fig. 12.

We use the measured as to calculate the multiphoton attenuation co-efficients / and -1 used in Appendix A. We have nbaLo)NA I(n) = 3(n)l,i.e. 3 ,) nhrW0(n)NA, with hw being the laser photon energy. We get

1.6 x lO- 22 cm3 /,' 2 for oxygen and I = 3(14) = 2.4 x 10- 32 cm 5/WV,3 for

nitrogen at atmospheric pressure.

6.8 High Voltage Cell

The high voltage chamber shown in Fig. 13. was fabricated by Tetra Corpto simulate the air environment. It has been tested in their company as wellas in UNM. The system can be tested with an electronics triggering signalto have the current and voltage monitored during the discharge. The gatingsignal for applying HV onto the cell is synchronized with the seeding pulsesthrough the control box. The detailed operation and characteristics are listedin a note delivered with the cell.

The test cell provides a nearly uniform elecric field of 30 KV/m to 300

•,o .. .. 1.5

.0

Is

24

20

• 4

- 3.6

1.2

2.a

2.4•:• 2.0

a 4 5 0 56010 20 30 40

Lusr Intensity(2xOU1 W/cmn)

Figure 12: Measurement of four-photon ionization cross-section of N.2.

""r

Figure 13: High voltage chamber for lightning simulation.

16

Figre 4: cmplte etuhfr dscageonlgtnngepeien-n h

SUPRIV

Thirl emnl ,lbatrneyra

K ot c mb within r ten ofmMode-lockeo d

L c ec irr osing ather isato inc daetro liceh e teealindhhow aeo F

Figure 14: A complete setup for discharge of lightning experiment in thelaboratory HV cell.

KVim on the chamber within tens of microseconds. It consists of a chamberwith profiled electrodes of 8.5 inch diameter spaced at 26 cm contained in aLucite cylindrical housing. There is a two inch diameter hole at the center ofeach electrode sealed by a two inch diameter window made of MgF2. Whenthe highest voltage is applied, the field is about 1/10 of the self breakdown

field in air. The windows are recessed in a low field region to minimize theimpact of a multiphoton photoelectric effect from the window surface.

6.9 Inducing 100 kV discharge in airWe trigger routinely a 100 kV discharge in air, N2 and 02 with 248 nmpulses from an excimer (KrF) laser. The complete setup for the lightningdischarge is shown in Fig. 14 and a photograph of the discharge is reproducedin Fig. 15.

The discharge was induced with ns pulses of only 1 GW peak power, fo-cused with a 60 cm focal distance lens between the electrodes of the dischargechamber. The discharge could readily be triggered at a pressure of 1/8 of anatmosphere, even though the peak intensity is two orders of magnitude below

17

Figure 15: Electrical discharge in the laboratory cell (1/7 atmosphere) in-duced by a ns pulse of the excimer laser (peak power 1GW/cm2). The dis-charges follow the path of the beam, except that it bends towards a normalto the profiled electrodes at the two extremities.

18

that expected from the amplified fs pulses. This result confirms the excep.tionally large multiphoton ionization cross-sections of nitrogen and oxygen,which we measured independently in a low pressure cell (see next section).

The discharge is .qiided by the light, as seen in the photogralph. ''l'is resultis significant, because the prefrr, ulial palh for th.e disduiryq is, tio( oleom I/ubi at. Indeed. in contrast to the eXper'inlellnt by twh group ill ,apail [5], wherethe discharge is triggered between two needle shaped elect rodv(s (lhence hliereis a local field enhancement present prior to the craltion of Itu las.cr inihUf dplasma), our electrodes are profiled for uniform field. The holes leavingpassage to the beam are profiled also. The field is minimum on axis, and thedischarge observed at lower pressure, without laser triggering, never followthe axis of the cell, but is along the side wall of the chamber. Becausethe discharge should ultimately make contact at normal incidence with theelectrodes, the two extremities of the discharge are bent towards the normalto the profiled hole in the electrodes.

7 Conclusion

We have demonstrated theoretically the feasibility to trigger lightning withfs pulses at 248 nm. Our mea-surements of photoionization of 02 and N.2 atthat wavelength show a very large cross-section for a three and four photonprocess. We have demonstrated that, at a reduced pressure of 1/7 atmo-sphere, even the peak power of a ns pulse is sufficient, to channel a. dischargeand trigger lightning. A complete facility has been built to test the triggeringof lightning with fs UV pulses in a reduced scale. Funds are being sought tooperate this facility and proceed with a final experimental demonstration oftriggering of lightning at atmospheric pressure, using fs UV pulses.

19

References

[1] H, J. Christian. V. Mazur. B. D. Fisher, L. H. Ruhnke. K. Crouch andR. P. Perala. The Atlas/Centaur Lightning Strike Incident. J. of Geo.physical Research, 94, 169-177. 1989.

(2] S. A. Changnon. Temporal and Spatial Relaions between Hail and Light.ning°J. of Appl. Meteorology. 31, 587-604, 1992.

[3] R. P. Fieux. C. H. Gary. B. P. Huzler, A. R. Eybert-Berard. P. L. HuberA. C. Meesters, P. Hf. Perroud. J. H1. Hamelin and J. M. Person. Refsarchon artifically triggered lightning in France. IEEE Trans. Power Appar.Syst., 97, 725-733. 1978.

[4] P. LarocheA. Eybcrt-Berard and L. Barret.Triggered lightning flash char.acterizaion. Tenth International Aerospace and Ground Conference onLightning and Static Electricity (ICOLSE), Paris. pp.231-239. Les Edi-

=tions de Physique. Les Ulis, France, 1985.

(.5] K. Nakamura and C. Yamanaka. Long laser-induced discharge in atmo-spheric air. In Proc. CLEO, Optical Society of America. 1992.

(6] Xin Miao Zhao, Chao Yung Yeh, Jean-Claude Diels, and Cai Yi Wang.Ultrashort pulse propagation for triggering of lightning. In R. C. Sze andF. J. Duarte. editors. Proceedings of the int. conf. on Losn ' 91. SPIE.SPS press. McLean, Virginia. San Diego, CA, December 1991.

[7] Xiii Mine Zhao, Chao Yung Ye. .Jeani-Claude Diels. and Cai Yi \\ang.Ultrashort pulse propagation for triggering of light ning. ('unt. on Lasersand Electro-Optics, 1992. Annaheim. Ca.

(8] S. Soula and S. Chauzy. The detection of the electric field vertical distri-butiou underneath thundercloud - principle and applications -. pages 61-1 - 61-14. NASA Conference Publication 3106. Cocoa Beach. Florida.1991.

[9] Xin Miao Zhao, Chao Yung Yeh. Jean-Claude Diels. and Cai Yi Wang,Simulation on femtosecond pulse triggering lightning. In Proc. of OSAAnnual Meeting. Optical Society of America. 1992. Albucjtt rqtie. NM.

20

W .-

[10] Xin Miao Zhao, C(hao Yung Ych, .Jean-Claude Diies, and C(ai Yi Wang.A fetutosec-ond lightning rod. In A. Migus, editor, Picosrcond PIh'enomenaVIIL page , Springer-Verlag, Berlin, 1992.

[11] H. Vanherzeele, H. J. Mackey, and J. C. Diels, Spatial and TemporalProperties of a Tunable Picosecond Dye-laser Oscillator-amplifier SystrIn.Appi. Opt. B 23. 2056-2061 (1984).

21

APPENDICES

A Pulse propagation/compression

The fs pulse centered at w = we can be described by the complex envelopeC(z, t) of the electric field E(z, t):

E(z,t) = (6(), I) , (2)

If the nonlinear properties of air are neglected, the evolution of the pulseenvelope with distance can be most easily calculated in the frequency domain:

t(z + AzW) = t(z.W)e-k(w•wj)z (3)

where 6(z,w) is the Fourier transform of the envelope defined in Eq. (2).Expanding the wave vector k in a Taylor series around we, and neglectingterms of order higher than 2, we find for the evolution of the field, in theretarded frame of reference:

1(z + AzW) = C(z.w)e-+(iIw1)" (4)

where Vf = -k 0.96 10-2Ss/m for air. Considering 3 photon ionizationto be the dominant loss mechanism:

dI - (5)

The above equation is easily integrated for a slice of air A-:1 1

J2(z + Az) (7---+2 A. (b)

Our measurements of the photoionization cross-section for N., indicatethat the four photon process contributes significantly to the ionization andthe pulse depletion. The propagation equation including 3 and 4 photonionization is:

dl 7

•+:+ d"• = - 13 -'7I+(7)

The propagation problem is solved numerically by applying successivelythe linear propagation Eq. (4) and the nonlinear absorption Eq. (6) to slices ofair Az. A fast Fourier transform is used to switch between time and frequencydomains. As initial condition we take a pulse with a linear downchirp, whichis focused by a lens.

22

B Evolution towards a streamer

We approximate the results of the preceeding section by a cylinder of radius rcontaining a Gaussian distribution of electrons Ne(z) and ions N1(z). Underinfluence of the external field, the electrons and ions will separate. Howeversince the electrons are much lighter than the ions, we can assume that the

-A electrons have been accelerated to a steady state velocity before any motionof the ions has even taken place. We establish in Appendix B the equations ofmotion for the electrons and fields, taking into account cylindrical symmetryin treating this three-dimensional problem.

The equation of motion of the electrons can thus be simplified:

mdV,=me = eE - rnevV E : 0 (8)

- ~~V, f -( )E-= -p,g(9?f711

where i, is the electron mobility. We can substitute this expression (9) forthe electron velocity in the conservation equation:

ON, a (VeN.) = 0, (10)"t 9Z

to obtain:-N - ,(p,EN.) =0. (1

at az(lE )0()Poisson's equation in one dimension:

OE-' = (N, - N,), (12)

merely states that an internal field will appear as the charges separate, inter-nal field which will cancel the effect of the applied field. In a one dimensionallapproximation, the presence of the charges only srves to neutralize the ap-

plied field, Rather than to treat rigorously a three dimensional problenm, wecan solve substitute for Eq. (12) the field calculated for a cylindrical distri-bution of net charges p(z) = Nj(z) - N,(z, t). Rather than solve Poisson'sequation. this field is more easily derived from the integration of Coulomb

23

law applied to charged disks of thickness Az and radius r:

E() = - p(z' + Z)(-1- Iz 2 + r2 dz'

+ p(z' + z)(1 - ZI + )dz'I + Ert (13)

where e is the height of the cylinder of charges, and r its radius. The time.space (z) evolution of the electric field is found by simultaneous integrationof Eqs. (11) and (13), with as initial and boundary conditions:

N.(z = 0) = 0E(t = 0) = E.,t

N,(t = 0) = f(z) = Ni(z) (14)

The parameters are as follow.Pe = e/mv is the electron mobility. For L0 = 100 m,/V No 5.0 x

1018 m-3, and p. = 0.20 m2/Vs, the units to = 5.5 x 10-" s and Eo =9.1 X 1012 V/re. The average collision period 1/P with respect to the above... is 1.1 x 10-12 s. The enhancement typically occurs within several orders ofmagnitude of t o, the change of V, is negligable, so that we can approximateE = -V.. In the following numerical computation, we use the externalelectric field E.,g = 500 kV/m, and the beam size r = 1.0 x 10-2 m. ie.,Ee,t = 5.5 x 10 -B and r = 1.0 X 10-4 in the normalized unitless unit weuse. For the laboratory experiment in the University of New Mexico, we useLo = 0.5 m, r = 2.0 x 10-4 m, Eexg = 175 kV/m and No and i, are sameas before. Then E0 = 4.5 x 101° V/m and to is same as before. In our unit,E.-E = 3.9 x 10-s and r = 4.0 x 10-,

A computer program written with a flux corrected transport (FCT) algo-rithm is used to simulate the time evolution of electron density and electricfield. The initial condition for electron density comes from the laser iiced 't,ionization, discussed in Appendix A. The setup time for the initial conditionis Lo/c = .33 ps for Lo = 100 m, where c is the light speed. We denote theinitial condition symbolically as

N,(z,t = 0) = Nj(z) = (z). (15)

The boundary conditions for the equations are

N.(z 0, O 2t) = N.(- 1,t) 0, (16)

• - 24

W .•

andE(z t)= E(z 1,t)= Et,(17)

where z = 0 and z = 1 are far from the region where electron and iondensities are not equal to zero.

l.

g•25