Self-organization of surface wave sustained discharges in the pressure range from 10 to 200 Torr

JOURNAL OF APPLIED PHYSICS VOLUME 86, NUMBER 2 15 JULY 1999

Self-organization of surface wave sustained discharges in the pressurerange from 10 to 200 Torr

N. Djermanova, D. Grozev, K. Kirov, K. Makasheva, A. Shivarova,a) and Ts. TsvetkovFaculty of Physics, Sofia University, BG-1164 Sofia, Bulgaria

~Received 20 October 1998; accepted for publication 14 March 1999!

Experiments showing the dynamics in the self-organization of surface wave sustained discharges arepresented. Microwave~2.4 GHz! discharges maintained in an argon gas in a continuous waveregime at a constant applied power and varying gas pressure are studied. The evolution of thedischarge from a stationary plasma column at comparatively low pressure (p<10 Torr) to a plasmatorch at atmospheric pressure passes through different stages of self-organization of thewave-field↔plasma nonlinear structure showing evidence of the general trends of behavior ofnonequilibrium dissipative systems. The measurements are carried out at the stage of the dischargeself-organization into a filamentary structure with an azimuthal rotation. Macroscopic characteristics~number, size, velocity of rotation! of the filaments and their dependence on the gas pressure and itstime variation are given. The total light emission of the plasma considered as giving informationabout the plasma density is measured and different methods of signal processing~includingcorrelation-spectrum analysis! are applied. Oscillations of the filament ends are also observed. Thedifferent types of interrelation between plasma density and field intensity, registrated in the differentpressure ranges, call for variety in the instability mechanisms. Although the scenario of thedischarge self-organization is stressed in the discussions, the observations are important with theirrelation to the discharge applications, which require avoiding conditions of development ofinstabilities. © 1999 American Institute of Physics.@S0021-8979~99!06312-4#

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I. INTRODUCTION

The intensive activity in the applications of highfrequency and microwave discharges to plasma procestechnology and plasma chemistry, light sources, and gaslasers, as well as to spectroscopy analysis, holds out mpossibilities for new directions in the development of tstudies in the gas discharge physics. The stability/instabof the discharges being one of the problems of great imptance in their applications, is also a problem of basic imptance for understanding the discharge pattern. The apprto the ionization nonlinearity and to the discharges frompoint of view of the instabilities in them is, in fact, an aproach to the gas discharge production in terms of dynamof nonequilibrium dissipative systems.1 In general, the devel-opment of the processes of self-organization of such systgoes through formation of autostructures, i.e., spatially locized structures which are proper modes of the system. Thautostructures could be stationary~immovable or, e.g., uni-formly rotating! or dynamical~regularly or chaotically pul-sating!. Overthreshold conditions of the system cauchanges in the number of the autostructures in the enseand a transition to chaos with structure birth and disappance.

In the particular case of wave-sustained discharges,field–plasma nonlinear system which each gas dischargin general, is a self-consistent structure of electromagn~EM! wave-field↔plasma.

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Dynamics of discharges in EM wave beams has brecently2–24 studied both theoretically and experimentallwith the main purpose of understanding the processeprobing the atmosphere by powerful EM wave beams. Tcurrent interest in the discharges is motivated also by pspectives for their applicability to up-to-date technologieThese discharges, called ‘‘free-localized microwave dcharges’’ are at moderate and high pressures and usualair. The studies have concentrated on the propagation oionization front~after the gas breakdown in the focus of thbeams! and the time development in formation of small-scastructures, two problems which are unified in the dischabehavior. The discharge evolution20 starts from a homogeneous quasispherical plasmoid which extends along the etric field forming filaments and complicated structures wregularities and randomness in their pattern. The processtretching out of the quasispherical plasmoid is considere17

as a high-frequency streamer. The filamentary structurebeen discussed in terms of both ionization-therminstability4,6,20,23and ionization-field instability.3,24

The other type of wave-field discharges—discharges25,26

sustained by surface wave~SW!27,28propagation—which areconsidered to have many more perspectives25,29–31for tech-nological applications, have been discussed starting frtheir discovery32 as sources of quiet and stable plasmHowever, oscillations and fluctuations at the discharge enregion33 which is important for the discharge creation, asurely observed in each experiment although not reportethe literature. Moreover, recent experiments34 in pulsed re-gime operation have shown development of modulationstability, on the stationary level of the pulses, caused

© 1999 American Institute of Physics

IP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

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739J. Appl. Phys., Vol. 86, No. 2, 15 July 1999 Djermanova et al.

perturbations of the microwave power applied for the dcharge creation. The experiments reported here showvariation of the gas pressure could be another reasoninstabilities in the discharge.

The evolution in the self-organization of microwave dcharges~at frequencyf 52.45 GHz) produced in SW fieldin argon gas is experimentally studied. The nonstationaritthe regime is related to the time~t! variation of the gas pressure, fromp51 Torr until atmospheric pressure, during thexperiment. The stages in the evolution of wave-fie↔plasma nonlinear structure are qualitatively describMore attention is paid to the stage when the discharge isfilamentary structure~filaments extended along the discharlength!. By measuring the total light emission of the plasm~considered as giving information about the plasma dens!and using different methods for signal processing~includingdevelopment of a method of correlation–spectrum analys!,macroscopic characteristics of the filamentary struct~number of filaments, size, velocity of azimuthal rotatio!are obtained. Dynamical-oscillating behavior of the filameends is also observed. The scenario in the self-organizaobserved here in SW produced discharges resembles thetern in discharges in wave-field beams. Such a similacalls for considering the filamentary structure as a genbehavior of the self-organization of microwave dischargproduced in wave fields in the gas pressure range betweeTorr and 1 atm. Simultaneous measurements of plasmasity and microwave field intensity show that different typof interrelation between them mark the different stages ofdischarge evolution. This may be an indication of the retion of different types of instabilities~e.g., ionization-thermaand ionization-field instabilities! to the different gas pressurranges. Some of the results presented here have been breported recently.35

II. EXPERIMENTAL SETUP

The experimental arrangements are shown in Fig. 1~a!.The SW sustained discharge is produced by applying a perful microwave signal at frequencyf 52.45 GHz. Asurfaguide-surfatron device36 is the wave launcher. The measurements are performed at various power values inrange P540– 150 W. The discharge is produced in a cregime of excitation of an azimuthally symmetric surfawave.27,28 Radial Er and axialEz electric field componentsand an azimuthal magnetic fieldHw component constitutethe field configuration of the mode. The transverse field dtribution of the mode is characterized by a largerEz fieldcomponent over the plasma column cross section anlargerEr field component in the free space.

The experiments are in a discharge produced intapered37 quartz tube with inner diametersd151.6 cm andd254.0 cm of its narrow~10 cm in length! and wide parts.Such a shape of the discharge vessel is close to thaplasma reactors used in the applications.

The discharge is in an argon gas. The gas pressure vduring the measurements ensuring nonstationarity of thecharge regime. Almost all of the results presented are acreasing pressurep. First, a stationary discharge is created


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flowing gas atp<1 Torr and then the pressure is increasuntil p51 atm. The gas inward flow is in a direction oppsite to that of the propagation of the wave creating the dcharge. The measurements are at differentdp/dt values. Thetotal cycle of the discharge evolution, including both contions of increasing and decreasingp, has been also observe

The total light emission of the discharge, consideredgiving information about the plasma densityn, and the EMpower related to the radial electric field componentEr in thefree space, are the signals registrated. Light emission taby 1 mm collimators is sensed by photomultipliers. The oput signals from the photomutipliers are registrated by a twchannel digital oscilloscope. Two photomutipliers with colimators, which are positioned@Fig. 1~b!# at an angle ofd530° in a plane perpendicular to the tube axis, are usethe measurements of the azimuthal rotation of the filamtary structure. In the measurements on interrelation betwplasma densityn and field intensity, a photomutiplier and aantenna are simultaneously used. The signal picked upradially oriented antenna is passed through a square-lawtector and is applied to the oscilloscope. The collimator athe antenna are positioned radially in parallel, displaceddistance of 1.5 cm along the discharge length. The depdence of the time evolution of the discharge structure ontime variation of the gas pressure is watched by connecthe oscilloscope and the vacuummeter to a PC througHP-IB and RS232 busses, respectively. The results aretracted either by direct evaluation of the registrated signalby methods of correlation and spectrum analysis.

III. QUALITATIVE DESCRIPTION OF THE EVOLUTIONIN THE SELF-ORGANIZATION OF THEDISCHARGE

The experiment shows how SW sustained dischartransform with the pressure increase from a plasma colu

FIG. 1. ~a! Scheme of the experimental setup in which, a surfatrosurfaguide device~1! and a generator~2! at 2.45 GHz are used for thedischarge creation, a digital osciloscope~3!, a vacuummeter~4!, and a PC~5! complete the monitoring system and photomultipliers~6! with collima-tors ~7! and optical cables~8! as well as an antenna~9! are the detectors,~b!cross section of the discharge tube.


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740 J. Appl. Phys., Vol. 86, No. 2, 15 July 1999 Djermanova et al.

completely filling the cross section of the tube at compatively low pressure~e.g., length of the column of about 2cm at p50.6 Torr andP5140 W) to a plasma torch at amospheric pressure. The dynamics in the self-organizatiothe discharge could be provisory divided into two mastages, each one composed by substages. The first stamore turbulent. At a comparatively low rate of gas pressincrease (dp/dt,0.3 Torr s21) the evolution of the dischargis slow and easily observable.

The pressure range up top>50 Torr is marked as a firsstage. The qualitative changes in the discharge dynamwith increasingp are as follows. The length of the columdecreases and the oscillations of the discharge end becmore pronounced. The end of the discharge is cone shawith a top of the cone at the discharge end. Close tostructures of the type of slab strata or a brighter circular h~with more bright spheres moving in it! which girdles thecolumn appear. Atp>10 Torr, the plasma column is abou10 cm in length. With thep increase, the column continuesshorten and a dipole-type azimuthal structure forms atend of the column, i.e., a cone-shaped darker region incenter with the base of the cone at the discharge end.mation of such a structure can be associate with the higamplitude of the wave field close to the tube walls and wthe gas pressure force, acting on the end of the columnformation of a filamentary structure~Fig. 2! starts at p>30 Torr.

In the case of lowdp/dt values the number of the filaments ism53, and they appear consequently over the tiof a pressure increase with 10 Torr. Each filament starts fa slightly brighter core, extended along the discharge axisthe background of the plasma. The filament channels fofrom the side of the wave launcher. When a filamentstructure with azimuthal mode numberm53 is completed,the filaments still being immovable become brighter.

FIG. 2. Discharge contraction in free localized filaments with azimutrotation.


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higherdp/dt, a bigger number of filaments (m.4) appearsas if at the same instant in the outer region of the plasThe filaments are on the background of the plasma andtotal system~filaments with plasma between them! is muchtoo turbulent. The reverse transformation of the dischafrom atmospheric to low pressures was observed at a hrate of pressure decrease. In this case, the filamentary sture contains a large number of filaments.

The dynamics of the discharge evolution in the pressrangep>50– 200 Torr is marked as a second stage. Nowdischarge is self-organized in a clearly observable filamtary structure~Fig. 2!. The filaments are bright free-localizedischarge channels and there is no plasma between thExtended along the discharge tube and located in the oregion over its cross section, the filaments have azimurotation. With thep increase they become brighter and thiner. This substage lasts up top>100 Torr when the rotationbecomes slower. The length of the filaments is about 3Their ends look like whips. Oscillating in length, they aturned to the dielectric tube. Atp>120– 140 Torr the fila-ments start reducing in number. In general, thep increasecauses shortening of the length of the filaments. Howeveeach reduction of their number, their length increases. Ap.200 Torr the discharge is localized in one immovable fiment located in the center of the tube.

At lower applied power (P540– 100 W) the dischargedynamics is the same as given above~at P5140 W). How-ever, since the plasma column and the filaments are shothe process develops more quickly and some substagespear to have been missed.

Observations under different conditions showed thatpressure and its variation are the factors determining thecharge behavior. First of all, the stages of discharge sorganization, as described above, are related to the gassure values. This is determined by sustaining dischargeflowing gas at given, constant,p values changed in the pressure range from 10 to 60 Torr. At a stationary pressure,filaments are longer~e.g., about 10 cm atp>30 Torr). Theyare also immovable. Therefore, the rotation of the filamtary structure observed at varyingp is caused by the timechanges of the gas pressure. The latter is also responsibla turbulence in the discharge behavior.

Air pollution of the argon gas helps the formation of thlocalized structures in the discharge. Asymmetry of the dcharge tube with respect to the launcher gap causes stturbulence in the discharge evolution. In this case a lanumber of snake-like discharge channels with turbulmovement are initiated from that part of the tube whichcloser to the launcher, i.e., from the place where the fiamplitude is higher.

IV. RESULTS AND DISCUSSIONS

The measurements of the characteristics of the filamtary structure are carried out at the substage of its azimurotation.

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A. Mode number and velocity of rotationof the filamentary structure

The velocity of rotation of the filamentary structureobtained by evaluating the signals recorded by the two ptomultipliers. In the case of lowdp/dt values when themodal number of the filamentary structure is low and cleaobservable, the values of the circular velocity can easilyobtained by measuring the time delay between the twonals. However, for estimating the same quantity in casehigh modal numbers, an evaluation based on methodcorrelation–spectrum analysis is developed.

1. Low mode-number structures

Oscilloscope records of signals picked up by the tphotomutipliers in the case of azimuthally rotatingm53filamentary structures are given in Fig. 3. The pressure rain which the record is made is also marked. The shape ofsignals gives an indication of the spatial distribution of tplasma density in the filaments. The velocityV of the fila-ment rotation obtained at different values of the ratedp/dtof the gas pressure increase is given in Table I. The diffevalues of the velocity for a givendp/dt show its decreasewith increasingp. The increase of the ratedp/dt at P5const causes an increase in the velocity of the filamrotation, narrowing the pressure range of regular rotation

FIG. 3. Records, within the gas pressure range denoted in~a!, by the twophotomultipliers@in ~b! and ~c!# of a m53 filamentary structure with azi-muthal rotation;P5140 W, dp/dt50.38 Torr/s.


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the structure and its shift towards lowerp values. The widthof the filaments estimated from the time duration of the phtomultiplier signal is 2–4 mm in a diameter.

2. High mode-number structures

When the mode number of the rotating filamentary strture is high and not observable, the filament velocity canbe obtained directly from the recorded signals. Such caoccur at higher values of the ratedp/dt of the gas pressurevariation~e.g., Figs. 4 and 5 where cases of pressure increand decrease are depicted, respectively!. In such cases themode number of the structure and the velocity of its rotatare obtained from a numerical processing of the registrasignals based on correlation–spectrum analymethods.38–40 The procedure developed in the numericsaccording to the following analytical scheme. The Fouriintegral presentation of the registrated~real! signals is

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where A(v),B(v) are the complex amplitudes@A(2v)5A* (v), B(2v)5B* (v)# and uA(v)u, uB(v)u, andwv ,cv are amplitudes and phases, respectively. With an assution for stationarity of the signals, the autocorrelation funtions CX,Xt

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densitiesGX,Xt(v),GY,Yt

(v) of the first and second signalare, respectively,

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TABLE I. Results for the circular velocityV of three-mode filamentarystructures at differentdp/dt values and pressure ragesp of the azimuthalrotation of the structure.

dp/dt~Torr s21!

Variation of V~rad s21! withincreasingp p ~Torr!

0.32 7.7 7 6.8 76→870.38 8.5 8 7.7 64→710.9 11.3 8.5 57→62


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FIG. 4. The signalsX(t) andY(t) registrated by the two photomultiplierare given in~a! and~b!; ~c! presents their autocorrelationCX,Xt

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(t), functions @~1!, ~2! and ~3!, ~4!,respectively#. The amplitudes of the spectrum densities related to the cosponding correlation functions are given in~d!, whereas~e! presents thephases of the cross-correlation functions. Condition of increasing gassure withdp/dt51.27 Torr/s atP5110 W.


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GX,Yt~v!5S~v!exp@ iF~v!# ~7!

GY,Xt~v!5S~v!exp@2 iF~v!#, ~8!

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and are opposite in phase

F~v!5wv2cv . ~10!

This is used as a criterion for the reliability of the resufrom the numerics where the averaging is over a finite tiinterval T.

The parameters—mode numberm and circular velocityV—of the rotating filamentary structure

n5 12$N exp~ iVt2 imw!1c.c.% ~11!

are related to the characteristics—frequencyv and phaseF—of the spectral densityGX,Yt

of the cross-correlationfunction according to

m5F/d, ~12!

and

V5v/m, ~13!

whered5p/6 is the angle between the two collimators.The numerical procedure of the signal processing

cludes:~i! a transfer to PC of the digitized signals as twdatabases of 8000,~ii ! numerical integration for computingthe auto- and cross-correlation functions in 4096 sampwith averaging over 2048 samples and,~iii ! fast Fouriertransformations~FFTS! of the obtained correlation functiongiving the corresponding spectrum densities. The resfrom the procedure are given in Figs. 4 and 5. The requments related to Eqs.~7!–~10! hold at the frequency of themaximum of the spectrum densities. The obtained characistics of the filamentary structure are:m56, V57.9 rad/sandm510, V58 rad/s, respectively, in the cases presenin Figs. 4 and 5.

In all the cases, notwithstanding the different mode nuber of the filamentary structures at different values of

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rate of the pressure variation, the circular velocity of tfilaments is in the limits ofV56 – 12 rad/s.

B. Field-plasma self-consistency of the filamentarystructure

Results of the simultaneous changes of wave elecfield power and plasma density at the stage of the dischfilamentation are presented in Figs. 6–8. Cases of diffepressure ranges and different values ofdp/dt are depicted.The time variations of the signals are related to the filamrotation. Whereas the plasma density is~almost! completelylocated inside the filaments, the field only changes—w

FIG. 5. The same as in Fig. 4 but at decreasing gas pressure (P5100 W!.


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respect to the constant value it has outside the filamentsthe regions of the filament location. This means that a givbackground~threshold! field exists all over the total crossection of the discharge tube and the field in the filamentsuperimposed on it.

Figures 6–8 also show that two types of thwave-field↔gas-discharge self-consistency appear inself-organization of the filamentary discharge structure. Tin-phase variation of the two signals in Fig. 6 is registeredthe pressure range which corresponds to the beginning ostage of azimuthal rotation, whereas the out-of-phase vation shown in Fig. 7 is in ap range which corresponds to thend of the filament rotation when the filaments move slow

FIG. 6. Signals registrated by the antenna~upper! and photomultiplier~lower! at P5140 W anddp/dt50.38 Torr/s.

FIG. 7. The same as in Fig. 6 but atdp/dt54.3 Torr/s.


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The results in Figs. 6 and 7 are at differentdp/dt values. Therelation of the two different types of correlation betwephotomutiplier and antenna signals to different pressranges is shown in Fig. 8 where the registration at the bening and at the end of the filament rotation is at the sadp/dt.

The antenna signal presents the wave-field power relto the radial electric field component outside the discharAccording to studies41 on the transverse redistribution of thSW field components and the waveguide channeling ofSW field caused by the transverse changes of the pladensity at ionization nonlinearity, the nonlinear changesthe amplitudes of theEr field outside the discharge and othe Ez field component inside the plasma are opposTherefore, the cases of Figs. 6 and 8~a! correspond to a decreasing field amplitude in the plasma, whereas in the caof Figs. 7 and 8~b! the field increases. The different typeswave-field↔plasma density correlation could be relateddifferent mechanisms of instabilities involved in the formtion of the filamentary structure of the discharge: the lowpressure range may be associated with ionization-therinstability4 and the higher one with ionization-fielinstability.3 As is known, the former is a kinetic type o

FIG. 8. The same as in Fig. 6 but atdp/dt50.95 Torr/s. Registration at thebeginning and at the end of the time interval of filament rotation is givrespectively, in~a! and ~b!.


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instability which includes the neutral gas heating as a mstep in its development, whereas the latter iselectrodynamic-type of instability. In the experiments hethe formation of filamentary structures corresponds to deopment of perturbations with an azimuthal wave numbi.e., along the wave magnetic field. Estimations of the wanumbers at the maximum value of the instability incrememade according to the theoretical results obtained in Reand 4, respectively, in the cases of ionization-field aionization-thermal instabilities, give reasonable values~be-tween 2 and 8! for the mode numberm.

The same scheme of correlation-spectrum analysisgiven in Sec. IV A 2 has been applied to the records ofantenna and photomultiplier signals. The obtained resshow that density and field variation in the filaments acompletely coherent. At the frequency of maximum specamplitudes, the coefficient of coherence calculated accordto

g5ASX,YtSY,Xt

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C. Fine structure of the filaments

Density fluctuations–axial oscillations of the end offilament, obtained as a record of a signal from a photomplier, are shown in Fig. 9. A frequency of about 40 Hzmeasured. The measurement is close to the end of the sof rotating filaments where the circular velocity is low.

V. CONCLUSIONS

Evolution in the self-organization of the surface wasustained discharge in the pressure range between 10200 Torr is experimentally investigated. In the total pressrange studied, the discharge is sustained by applying poat a given, constant value. The increase of the losses indischarge with the pressure increase modifies the dischstructure: at first the plasma column shortens by keepingcross section unchanged and later it contracts into smadiameter discharge channels. Aiming to have the dischaevolution outlined, the experiment is performed at permnently increasing gas pressure. This variation of the prestransforms the regime into nonstationary. The se

,

FIG. 9. Axial vibration of the end of a filament~signal from a photomulti-plier!; P5140 W, dp/dt51 Torr/s.


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organization of the discharge, according to its qualitativescription, is in accordance with the general behavior of nequilibrium nonlinear dissipative systems. A similarity withe time evolution of discharges produced in the wave beis also observed. The transformations in the dischargedetermined by the gas pressure. A formation of a filamenstructure with a given mode number is the general trendthe discharge self-organization with the pressure increHowever, the electric-field↔plasma-density interrelation inthis filamentary structure is different in the different pressranges. This means that various mechanisms of instabilare related to the formation of the filamentary dischastructures when the pressure is different. The nonstationaof the regime associated with the pressure variation aplays a role. Causing a rotation of the filamentary structuthe rate of the pressure variation determines the azimuvelocity of the structure and the pressure range in whicrotates. Moreover, it influences the mode number ofstructure.

The experiments presented here show that the SWtained discharges are unstable with respect to gas presvariations. It has been recently34 shown that fluctuations othe applied power could cause instabilities in the dischaas well. Applied power, wave frequency, gas pressure,size of the vessel, are the external parameters which dmine the discharge behavior. Among them, the apppower and the gas pressure are the parameters which cfluctuate in the experiments, and it appears that their perbations cause instabilities in the discharge. Studies ondevelopment of these instabilities are important with respto the applications of the discharge, which require quiet astable plasmas.

ACKNOWLEDGMENTS

The authors thank Dr. Zh. Kiss’ovski for discussionsthe experimental arrangements. This work is supportedNATO Grant No. LG-971240 and DFG Project No. 43BUL-113/7410. Support from Professor Dr. H. Schlu¨ter, Al-exander von Humboldt Foundation, and German MinistryScience and Technology, for completing the experimensetup is gratefully acknowledged.

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Documents

Self-organization of surface wave sustained discharges in the pressure range from 10 to 200 Torr