Single-shot Thomson scattering on argon plasmas created by the Microwave Plasma Torch; evidence for...

62 (2007) 1135–1146www.elsevier.com/locate/sab

Spectrochimica Acta Part B

Single-shot Thomson scattering on argon plasmas created by theMicrowave Plasma Torch; evidence for a new plasma class

J.J.A.M. van der Mullen a,b,⁎, M.J. van de Sande a,1, N. de Vries a,B. Broks a, E. Iordanova a,c, A. Gamero b, J. Torres b, A. Sola b

a Eindhoven University of Technology, Faculty of Applied Physics, P.O. Box 513 5600MB Eindhoven, The Netherlandsb Departamento de Física, Universidad de Córdoba, Campus de Rabanales; ed. C-2, 14071 Córdoba, Spain

c Faculty of Physics, Sofia University, 5 James Boucher Blvd, BG-1164 Sofia, Bulgaria

Received 28 February 2007; accepted 12 July 2007Available online 27 July 2007

Abstract

To determine the fine-structure size of plasmas created by a Microwave Plasma Torch (MPT), single-shot Thomson scattering (TS)measurements were performed. The aim was to find a solution for the long-standing discrepancy between experiments and Global Plasma Models(GPMs). Since these GPMs are based on the assumption that (ambipolar) diffusion is the main loss process for charged particles, the diffusionlength and thus the fine-structure size should be known with high precision before an appropriate theory-experiment comparison can be carriedout. In order to avoid the effect of blurring, which is created during the accumulation of multi-shot TS signals and which obscures the fine-structures, single-shot measurements are indispensable to determine the diffusion length.

The results of the present study reveal that the impression created by multi-shot TS that MPT plasmas resemble stable cones is not (always)correct; instead it is found that the plasmas we investigated are tiny filaments that rotate on the mantle of a virtual cone. However, the fine-structure, especially the thickness, of these filaments is not substantially smaller than that of the virtual cone. By applying the theory-experimentcomparison to the filament we found that the disagreement is even worse than what we found for the cone. It is therefore inevitable to concludethat the main proposition of the GPM is incorrect. Apparently the plasma is not diffusive in nature; that is, the main loss process of chargedparticles is not provided by diffusion but by local chemistry. Swirling in a cool nitrogen-containing environment favors the production ofmolecular ions such as Ar2

+ and N2+ inside the plasma filament. The destruction of these molecular ions leads to recombination frequencies that are

more than a factor 100 larger than what ambipolar diffusion can provide. Thus we are dealing with another plasma class and it is useful to divideplasmas into diffusive and reactive plasmas. The well-known ICP belongs to the first class; the MPT to the second.© 2007 Published by Elsevier B.V.

Keywords: Single-shot Thomson scattering; Microwave Plasma Torch; Global Plasma Models; Filamentary structure

1. Introduction

Microwave Induced Plasmas (MIPs) continue to be interestingsources for atomic spectrometry [1]. The main reasons are thatthey are easy to operate with atomic and molecular gases [2] andthat the electrical power and gas consumption are low. These lowcosts of ownership make them interesting alternatives for the

⁎ Corresponding author. Eindhoven University of Technology, Faculty ofApplied Physics, P.O. Box 513 5600MB Eindhoven, The Netherlands.

E-mail address: [email protected] (J.J.A.M. van der Mullen).1 Present address: Philips Applied Technologies, P.O. Box 218, 5600 MD

Eindhoven, The Netherlands.

0584-8547/$ - see front matter © 2007 Published by Elsevier B.V.doi:10.1016/j.sab.2007.07.006

Inductively Coupled Plasmas (ICP). However, they still havesome shortcomings that can be attributed to the fact that, incontrast to the ICP, the MIPs are generally small in size andtherefore not capable to create large volumes with high gastemperatures. This implies among others that the evaporation ofwater droplets or solid-phase particles is not effective. Neverthe-less, there are many other fields in chemical analysis where thehigh amount of heat generation is not or less important. There theMIPs can play an active role such as an ion-source for massspectrometry, as a component of a plasma tandem or as an exci-tation-source for element specific detection in chromatography.

There is a wide variety of MIPs for which basically a threefoldclassification can be made: the cavities (resonators), as those

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1136 J.J.A.M. van der Mullen et al. / Spectrochimica Acta Part B 62 (2007) 1135–1146

introduced in [3] and [4], the surface wave plasmas [5] and thetorches [6,7].More recently a new typewas introduced namely theMIP based onmicrostrip technology [8]. It belongs to the categoryof “microplasmas”, plasmas for which the investigation is drivenby the urge of miniaturization with as final goal to construct labs-on-the-chip.

In this paper we will confine ourselves to the torches, morespecifically to theMicrowave PlasmaTorch (MPT). Introduced by[7] and improved by [9], theMPTcan be seen as a smaller sister ofthe axial injection torch (TIA) [6] in the sense that both the TIAandMPTare based on the launching of a TEM00 microwave in anargon flow expanding into the open air. However, the MPT has alower energy (typically 100 W versus 600 W) and gas con-sumption (1000 sccm versus 3000 sccm) than the TIA, whereas ithas two instead of one gas flow inlets. This implies that theMPT isbetter equipped for spectrochemical analyses.

Due to the torch structure, i.e. the creation of the plasma in anargon gas flow expanding into the open air, it is possible andinstructive to compare the MPTwith the ICP and to continue thestudy initiated in [10] where results of Thomson scattering on theICP and TIAwere compared with each other and with theoreticalresults. It was found in [10] that for the ICP the theory andexperiment fairly agree with each other whereas for the TIA theagreement is totally absent. Later on TS experiments wereperformed on theMPT [11] in a joint cooperationwith the researchgroups of Broekaert andVoges (DortmundUniversity). One of themain conclusions of that studywas that for theMPT the same typeof theory-experiment conflict is present as for the TIA [10]. As apossible explanation we suggested that our TS setup was notsuitable for tiny plasmas.

In [12] the TS setup was renewed by a novel detection-branchin which a two-dimensional iCCD was used to collect the imagecreated by a Triple Grating Spectrograph. In this way the detectionwas improved with a factor of 500 and it is possible to obtain inone minute a complete spectrum of the Thomson scatteredphotons for all the positions along the plasma-laser intersection.Such a setup largely facilitates the mapping of the electron gasproperties so that better and more precise insights can be obtainedin plasma properties.

The experimental results were compared with those ofmodeling and we found [12] indeed that the new setup is largelysuperior to the old one. However, the differences between theresults obtained with the new and old setup were found to bemuchsmaller that those between the theory on one hand and theexperimental results (old and new) on the other hand. In short: themeasured Te was found to be much larger (1.4 instead of 0.8 eV)whereas the experimental ne-value turned out to be much smallerthan the theoretical result (2 ·1021 m−3 versus 3·1022 m−3).

The model that we used is a global plasmas model (GPM)based on the two balance equations for the electron gas: one for theelectron density and the other for the electron energy. The basicassumption used for both equations is that the plasma is diffusiondominated. The ambipolar diffusion losses of electron–ion (e–i)pairs must be supported by the production of these e–i pairs in theactive plasma core. This basically sets a demand for the electrontemperature: sharper plasma edges produce large effluxes and thusdemand for higher Te-values.

The fact that the experiment points towards higher Te-valuesthan what could be computed via the measured plasma size,suggests that the actual plasma is smaller than what could beobserved. This observation was based on pictures that werecomposed by adding the TS signals of typically 600 laser shots.Thus, if the plasma is not stable and fluctuating in position, themulti-shot (MS) addition gives a picture that is smoother thanreality. The only way to get insight in the factual sharpness is bydoing single-shot (SS) measurements.

In the present study we report on SS measurements. The ideabehind this method is that, if the plasma has sharp edges, thenthesemust be visible during the 8 ns of the laser pulse used for TS.In that short time duration the plasma stands still. Of course, suchan observation is only useful if the photon statistics is not too poor,but a feasibility study showed that the new setup must be capableto handle this.

The main experimental result of the present study is that thefluctuations in the shot-to-shot results are very large and muchlarger than what photon statistics predicts. This indeed pointstowards unstable plasmas. More insight was obtained by fastphotography. By reducing the exposure time it was observed thatthe plasma is a tiny filament that rotates on the mantle of a virtualcone. This explains the large shot-to-shot variations since it isconceivable that the laser does not always hit the filament, but italso clarifies why the lazy responding eye (or a camera with long-exposure time) gives the impression that, in contrast to reality, theplasma has a nice and quite smooth cone-structure.

The theory-experiment comparison was again performed butnow by applying the Global Plasma Model to the tiny plasmafilament. However, the discrepancy remained and became evenstronger. This brings us to the proposition that the basicassumption of the GPM, namely that the e–i pairs are removedfrom the plasma by ambipolar diffusion, is not correct. Apparentlythe MPT is not a diffusive but a reactive plasma. It is a member ofanother plasma class for which the loss processes of chargedparticles by local chemistry is much more important thandiffusion.

As candidates for the local recombination enhancing chemis-try, we present the formation and destruction of molecular ions.The cooling of the argon gas and/or entrainment of the air willfacilitate the recombination via creation and destruction ofmolecular ions; Ar2

+ and/or N2+. However, a precise model cannot

be given, yet.This paper is organized as follows. Section 2 introduce the

plasma source; global observations from the photograph pointtoward global plasma properties such as the size, the heatgeneration and the power density. These are used in Section 3 toderive properties of the electron gas, the temperature Te anddensity ne using a GPM. Section 4 presents the setup and theexperimental results while Section 5 is devoted to SS measure-ments. The results are discussed in Section 6while conclusions andrecommendations for further studies are presented in Section 7.

2. The plasma source

TheMPTused in the present work is the same one as that usedin [12]. It is built at the Technical University of Eindhoven and

1137J.J.A.M. van der Mullen et al. / Spectrochimica Acta Part B 62 (2007) 1135–1146

based on the design of the modified torch of Bilgic et al. [9]. Asshown in Fig. 1a, the inner conductor consists of two co-axialtubes so that the torch can be fed with two different gas flows.These inner tubes are made of copper whereas the outer tube ismade of brass. In the application of spectrochemical analysis theouter gas consists of argon, while the inner (Ar) gas flow is usedfor the introduction of the analyte. For the plasmaswe investigatedboth gas flows consist of pure argon. Computations show that theEM field strength attains the highest value at the nozzle [9].

The photograph in Fig. 1b of the MPT plasma, created by atotal EM power of 100 W in a (total) gas-flow of 1100 sccm,suggests that the plasma can be divided into two parts; aconvergent plasma cone, with an apparent stable hollow structuredirectly above the nozzle and a divergent plasma cone, moredownstream. For themoment we assume that the converging conerepresents the active plasma part, where the plasma is created,whereas the divergent plasma is a (spatial) afterglow.

The following observations can be made:

Ob1) The mantle of the plasma cone is thin and has an estimatedthickness of d=0.3 mm.

Ob2) Together with the radiusR=1mm of the base circle and thecone height h=5 mmwe find that this active plasma regionhas a volume Vac=πRdh≈4.710−9 m3. The deposition of100 W in this volume leads to a mean power density ofε=2.1·1010 W m−3.

Ob3) The tip of the inner tube remains rather cold, whichsuggests that the local gas temperature is low.

The first two observations can be deduced from Fig. 1 and thepower settings. The last one is in line with the gas temperaturemeasurements done on a TIA plasma [10] where the Th close tothe nozzle was found to be in the range of 600 K.

Fig. 1. A sketch of the MPT (left) and a picture of the plasma produced by theMPT (right).

3. Global plasmas models

Global plasmas models (GPMs) are of great use for thecharacterization of plasmas. They are constructed to fulfill thedream of the plasma operator to have quasi-analyticalexpressions that predict internal plasma properties, such as neand Te as functions of the external plasma control parameters(the knobs) such as pressure, filling composition and plasmasize. Several success-stories can be found in literature. In [13]and [14] GPMs were employed for low-pressure plasmas usedfor IC technology. Reference [15] gives an application to anICP whereas [16] and [17] use GPMs to describe the plasmacreated in the Philips QL lamp. In [18] a GPM was used tosupport the interpretation of time-resolved TS measurement ona capacitively coupled helium RF discharge while the topic of[19] was the characterization of an atmospheric hydrogenplasma created by a TIA. Recently we presented in [20,21] aGPM that apart from ne and Te also delivers values of theheavy particle temperature Th while [22] describes a GPM thatis capable to model the temporal behavior on the ns-scale ofplasmas used for the generation of EUV. In the studies [19–22]the global plasma properties were related to the atomic statedistribution function using the method of disturbed bilateralrelations [10].

In [10,12] we used a GPM to compare the ICP with MIPsand to study the influence of ‘chemistry’ by replacing argon byhelium. There, where possible, this comparison was supportedby experimental results. In contrast to the success-stories givenabove [13–22] we found in [10,12] that for microwave torchesthe results of the GPM are in strong conflict with experimentalresults. The present study can be seen as a continuation of thesestudies.

3.1. The electron density balance, the electron temperature

The GPM used in this paper is basically the same as thatdescribed in [10,12]. It is formed by the balance equations for theelectron density and the electron energy, which are applied to theactive plasma zone. The most essential assumption is that theelectron–ion (e–i) pairs created by effective ionization areremoved by means of ambipolar diffusion. This implies that theelectron density balance reads

nen1KionðTeÞ ¼ jd ðneweÞionization

or KðionÞðTeÞ ¼ Da=ðn1K2nÞ

diffusive efflux

ð1Þ

where Kion (Te) is the rate for effective ionization and Da theambipolar diffusion coefficient. The second equation isobtained by the assumption that the efflux ∇· (newe) isdiffusive, meaning that newe=Da∇· ne. This gives∇· (newe) =Da ∇·∇ne. Defining Λn

−2≡ne−1∇·∇ne, where Λn is known as

the gradient length of the electron density, we get the secondexpression. The effective rate coefficient for ionization[10,12,20]

Kion ¼ 7:2910�15T̂0:5

e expð�12:06=T̂ eÞ ð2Þ


strongly depends on the electron temperature which, as givenby T̂e, is expressed in eV. Eq. (1) basically gives an expressionfor T̂e [10,12] of the form

T̂ e ¼ 12:06½2 ln K̂n þ CT ��1 with CT ðArÞ ¼ 20 ð3Þ

where Λ̂n is expressed in mm. The values of CT is obtained byusing Eq. (2) for Kion and by taken for the ambipolar diffusioncoefficient the valueDa=2 ·10

−4 m2 s−1. For the latter we usedthe formula given in [15] that is based on the work of Devoto etal. For the heavy particle temperature we take Th=600 K. ThisCT-value differs somewhat from the one used in [10,12]. Thereason is that the value in [10] is a sort of mean value chosen suchthat a comparison between the ICP and TIA could be made; hereCT is dedicated to MPT conditions.

The aim of the structure of Eq. (3) is to highlight the role ofΛn.This equation shows that a small Λn-value leads to a highTe-value. The underlying reason is that larger effluxes generatedby steeper gradients demand for larger particle productions andthus for higher Te-values. We stress the fact that the electrondensity balance does not give ne but the electron temperature in away that does not depend on the magnitude but on the shape ofthe ne-profile (as characterized by Λn).

3.2. The electron energy balance, the electron number density

The electron energy balance in simplified from

e ¼ nenhKheatðkBTe � kBThÞelasticYheat

þ nen1KionðI þ 3=2kBTeÞinelasticYcreation

ð4Þ

shows that the power density ε=P /Vac, is divided over twochannels; the heat channel, along which heavy particles gainkinetic energy due to elastic collisions and the plasma creationchannel, throughwhich the energy flow associatedwith excitationand ionization takes place (I is the ionization potential). Using theassumption that kTh≪kTe≪I and replacing n1Kion by DaΛn

−2

(cf. Eq. (1)) we get

ecnen1KheatkTe þ neDaK�2n I : ð5Þ

Note that this is only justified if (most of) the inelastic energylosses lead to the diffusive efflux of e–i pairs. In contrast to agood radiator, such as e.g. Hg, such an assumption is justified forAr.

For the rate of heat transfer we use Kheat=3 (me/M)Kmom withKmom=σeh (8 kTe/πme)

1/2 the rate for momentum transfer betweenelectrons and heavy particles for which we assume that it can beapproximated with the product of an (average) electron–atomcross-section and the thermal velocity of the electrons. Takingσeh=1.4·10

−20 m2 for 1 eV [23] we get the numerical value ofKheat=3.8 ·10

−19 m3 s−1.An important parameter is the creation efficiency. It is the

fraction of ε that leads to creation (i.e. ionization); it reads

n ¼ nen1KionI=e ¼ ½1þ KheatkTe=ðKionIÞ��1 numerically

n ¼ ½1þ 1:4103K̂2

n��1 ð6Þ

where the second numerically: formula is obtained by replacingn1Kion by DaΛn

− 2, using Kheat =3.8 · 10−19 m3 s−1, Da=

2·10−4 m2 s−1 and the temperature values Te=1 eV andTh=600 K. Thus, if Λn is known we can determine the creationefficiency ξ. The electron density can subsequently be found,using

ne ¼ neK2n=½DaI �: ð7Þ

Summarizing: the assumption that e–i pairs are removed bydiffusive transport and that the creation of e–i pairs is the onlyimportant inelastic process, leads to the determination of Te and nevia the electron particle Eqs. (1) and (3) and electron energyEqs. (4), (6) and (7) respectively. It is seen that

1) a plasma (region) with a small size has a high Te-value;2) a plasma (region) driven by a large ε has a large ne-value.

Note that although this Global Plasma Model is zero-dimensional, and thus only gives mean values for ne and Te, weexpect that Eqs (3), (6) and (7) can be used in some situations toget insight in plasma structures. That is why we added “(region)”in the two statements.

Applying statement 2 to different plasma regions of the sameplasma is e.g. possible for surface wave sustained plasmas, whereplasma is created and fed by a traveling surface EM wave. In thepropagation direction the ne decreases since the wave loses powerso that ε decreases along the wave.

If we use the observations Ob1–Ob2 given in Section 2 thatresult in Λn=0.15 mm and ε=2.1·1010 m3 we get, employingEqs. (3), (6) and (7), the following values:

Te ¼ 0:8eV; ne ¼ 3 1022m�3 and n ¼ 7%: ð8ÞEspecially the low ξ-value has interesting consequences. If 93%

of the power ofP=100Wis used for gas-heatingwe find, using thedensity (ρ=1.78 kg m−3), the specific heat (cp=0.52·10

3 J/kg K)and the gas flow rate of 1100 sccm, that the heavy particletemperature will rise to about Th=5800 K. Of course, the mixingwith the surrounding air will lead to a lower heavy particletemperature but especially in the active plasma part we expect thatdue to the high viscosity the influence of this mixing will belimited. So that, if the GPM would be applicable, we could expectheavy particle temperatures in the range of 5000 K, and this iscertainly much too high (cf. Ob3 given in Section 2).

The comparison between theory and experiment will becontinued in Section 4.2.

4. Experimental results

4.1. The Thomson scattering setup

For more details concerning the laser setup we refer to [17] andreferences therein. Here a short description is given to make thispaper more self-contained.

For TS a frequency doubled Nd:YAG laser (10 Hz of 450 mJ@ 532 nm) was used while the detection was done with a home-

Fig. 2. Right hand-side; the accumulation of scattered photon-counts of 600 laser shots as collected by the 2D-iCCD. The horizontal dimension corresponds with thewavelength (dispersion); the black band is the result of blocking the central wavelength λi. The vertical dimension is the spatial dimension along the laser beam. Thestructures at the top and the bottom show the Raman scattering just outside the plasma, the two branches in the middle are TS photons corresponding to the upper andlower part of the laser-plasma intersection (cf. the left photograph).


made Triple Grating Spectrograph (TGS). The first two gratingsof the TGS form a notch filter, so that the high intensity at thecentral wavelength caused by Rayleigh scattering and false straylight can be filtered out. As a consequence observations close tothe nozzle can be done. After this filtering the signal is directed tothe third grating where the final dispersion takes place. Thisspectrum is offered to a two dimensional 2D-iCCD array so thatone gets the spectrum of the TS photons for several positionsalong the laser beam.

Fig. 2 shows a typical example of a 2D-iCCD frame. Thismulti-shot (MS) image is obtained by accumulating the detectedphotons of 600 subsequent laser shots. The vertical direction is thespatial dimension, i.e. the length along the laser beam, thehorizontal direction gives the wavelength dimension, exhibitingthe dispersion. The black central vertical band is the result ofblocking the central wavelengthλi; the action of the notch filter. Atboth sides of the central black line we first observe, coming fromabove, a strong Raman spectrum, caused by the scattering of thelaser light on N2 and O2 molecules in air. Further downwards, the

Fig. 3. Contour plots of the electron densities (left) and e

Raman spectrum disappears andmakes place for the TS spectrum;so apparently the molecules are absent in the regions whereelectrons can be detected, which is in-line with results obtained onan ICP [24]. In this plasma regionwe observe two branches. Thesetwo so-called TS branches show the photon counts created by TSat the two intersection zones of the laser with the plasma cone.

4.2. Mapping ne and Te; comparison with model results

In [12] we described how these 2D-iCCD frames, that containinformation of both ne and Te along the plasma laser-beamintersection, are composed to contour plots of ne and Te for theplasma as awhole.A typical result is given in Fig. 3 for a total flowof 1100 sccm and a power of 100 W.

The results were, in [12], compared with those of the olderexperimental TS setup [11] and with results of the GPM. Incontrast with the older setup the agreement between the shape ofthe contour plots (especially that for ne) with the photographs werefound to be excellent. However, a striking discrepancy was found

lectron temperature (right) as found by TS (cf. [12]).

Fig. 4. Four CCD frames corresponding to four single-shot Thomson scattering measurements (cf. Fig. 2). In frames 1 and 3 (left upper and lower) the plasma is absentwhereas frame 2 only shows the upper branch and frame 4 the lower branch.


between the experiments on the one hand (old and new) and theGPM on the other hand. They are summarized below:

1a) The Te as found by TS (cf. Fig. 3 (right)) is about 75%higher than what the GPM predicts, 1.4 instead of 0.8 eV.

1b) The highest Te-values are found at the edges; in the cone-tipregion where ne is high, Te is low.

2a) The experimental ne-value is, for all plasma locations,substantially lower than the value predicted by the GPM.

2b) The ne-distribution suggests that the power density at thenozzle, where ne=10

20 m−3, is lowest and attains amaximum at the cone-tip (where ne=2·10

21 m−3). This isin contrast with the fact that the field intensity (and thus thesource of ε) is higher at the nozzle [9].

3) The gas temperature found experimentally is much lowerthan the 5800 K based on the low ξ-value as found inSection 3.2.

Fig. 5. Photographs of the MPT taken with different exposure times of 10 ms,1 ms, and 100 μs from left to right. The short exposure times clearly show thefilamentary structure.

The items 1 and 2 given above are divided in statements: a) forthe plasma as a whole and b) for the plasma structure. This isrelated to the note given below Eq. (7). For completeness weadded item 3 although it is not directly related to the results of TSbut deduced from the similarity between theMPTand the TIA (cf.Fig. 8) and supported by the observation that the heating of thenozzle by the plasma is limited (cf. Section 2, Ob3).

5. Single-shot measurements

In [12] the following reason was proposed as a bases for thediscrepancy: In the accumulative process of adding 600 TS shotsthe original fine-structures can be lost, especially if the plasmaposition is unstable. Thus theΛn-values obtained bymulti-shot TS(MS-TS) will be overestimated which implies that Te as found bythe GPM (Eq. (3)) will be underestimated. Therefore we promisedfuture studies [12]. Here this promise is fulfilled.

Fig. 6. Left hand-side: a single-shot iCCD frame showing two Raman branchesand one (the lower) TS branch; each dot represents a photon-count. Gatheringthe counts of each horizontal line we get, after applying a calibration factor, theelectron density. This is given at the right hand-side as a function of positionalong the laser line. Note that this only applicable to the TS branch and not to theRaman branches (dotted part).


The effect of the blurring can be studied by doing single-shot(SS) measurements. If they reveal that the factualΛn is lower thanwhat MS-TS measurements suggest, two problems are solved atonce: first the Te-value will increase (cf. Eq. (3)) second ξ will behigher (Eq. (6)), so that gas-heating will be lowered.

Single-shot measurements were performed for anMPT plasmaoperated at 100 W and a flow of 1100 sccm. Fig. 4 presents fouriCCD frames that were obtained at z=3mm. Comparison with the‘accumulative’ picture (the MS-iCCD frame) given in Fig. 2shows the following. In the SS-case the TS signal is sometimescompletely absent such as e.g. in frames 1 and 3 whereas frame 2only shows the upper branch and 4 only the lower branch. It wasimpossible to find SS–iCCD frameswith both the upper and lowerTS branch. This suggests that the plasma is very unstable. To get aproper understanding of the instabilities, photographs with shortexposure times were made. The results are given in Fig. 5, whichshows that on the sub-ms time-scale the plasma does not have astable cone shape but appears to be a filament that rotates on thesurface of a cone.

To get more insight in this filamentary behavior we analyzedseveral SS–iCCD frames in more detail. Fig. 6 gives an example

Fig. 7. Histogram giving the number of shots for the corresponding maximum elecThe total number of shots equals 51 for each z-value. The vertical axis is maximizedne, max=0 which corresponds to the case in which the laser missed the plasma fila

of such an analysis. Each dot in the frame represents one photoncount. For each position along the laser line these counts arecollected and by using a calibration factor this sum is transformedinto a value of the electron density. This ne-value is given inthe graph at the right hand-side of the iCCD frame. Of course thisne-value only makes sense for the plasma region; so only thebranch in the middle represents the TS photons. The upper andlower part of the frame show the photon-counts obtained byRaman scattering.

Fig. 6 corresponds to an axial position of z=1mm, that is 1mmabove the nozzle. As can be seen, this leads to a maximumne-value of 2.5·1021 m−3 while the width of the spatial nedistribution of 0.3 mm. This implies that the answer to our leadingquestion: is the thickness of the plasma smaller than what isobserved by MS-TS and normal photography, can now beanswered with: no, theΛn-value deduced from SS-TS is not muchdifferent from the value deduced from the long-exposure-timepicture given in Fig. 1 and the ne-plots of Fig. 3.

Before to proceed we have to realize that the actual maximumof the electron density in the filament can be larger than the ne,maxdeduced from frames like those given in Fig. 6. The reason is that

tron density, ne,max (horizontal axis) at different axial position z=1, 2… 8 mm.at 12 shots. Surpassing this maximum is marked with an arrow. In most casesment.

Fig. 8. From [10]; contour plot of the heavy particle temperature as found byRayleigh scattering on a TIA operated at a power of 1 kWand fed with an argonflow of 3 slm. Each gray shade denotes a temperature interval of 700 K, fromwhite (300–1000 K) to black (3800–4500 K). The highest measuredtemperature equals 4480±130 K at 19 mm above the nozzle. Also depictedare the positions of the maxima in Te (black dotted) and the upstream maxima inTh (white dotted) which form two cones.


we cannot be sure that the overlap of the laser beam with thefilament is optimal.

A statistical analysis can give more insight in this matter. Suchan analysis was applied to a total 408 SS–iCCD framescorresponding to 8 axial positions of z=1, 2,…, and 8 mm. Foreach z-values we processed 51 frames and the constructed ne-plotslike the one given in Fig 6. The maximum ne-values of allcorresponding graphs are shown in the histogram given in Fig. 7for 8 different axial positions.

The following can be observed.

• The most frequent result is ne,max=0; i.e. the laser missed theplasma.

• Hitting the plasma most frequently occurs at z=4 or 5 mm atthe cone top location.

• The highest value of ne,max is found close to the torch; goingdownstream ne,max decreases; the same trend as found forsurfatron plasmas, cf. Section 3.2.

Combining the insights obtained by SS-TS with those offast photographs we can now understand the previously

obtained MS-TS results and the photographs of long-exposureperiods.

1) The plasma is a filament of which the foot-point rotates alongthe nozzle while the point midway has more or less a fixedposition.

2) Since the filament rotates on a virtual cone mantle, thephotographs of long-exposure times will exhibit the cone-structure as found in Fig. 1b.

3) For these photos we find the highest light intensity at the cone-tip; since there is nearly always plasma at that location.

4) The laser used for TS, acting during only 8 ns, will not alwayshit the plasma.

5) The hit probability depends on the axial position. For the cone-tip the probability is high, close to the nozzle it is low.

6) The ne-determined by MS-TS will, in general, be lowerthan the maximum value determined by single shot: ne (MS)bne,max (SS).

7) Close to nozzle we have ne (MS)bbne,max (SS) due to thesmall hit probability; at the cone-tip ne (MS)≈ne (SS).

6. Discussion

The fact that the plasma is a filamentary helix that rotates on themantle of a cone shed new light upon the interpretation of the TSsignal and the first thing we realize immediately, is that theapplication domain of the GPM should be adjusted. In this sectionwe start in 6.1 to apply the GPM to the filament. It will be shownthat most of the discrepancies between experiments and theoryremain unresolved; in fact the conflict has become more severe.Therefore, to find a solution for this discrepancy, we have no otherchoice than to abandon (the basic assumptions of) the GPM.Apparently the plasma created by the MPT is not a member of thefamily of plasmas ruled by diffusion but belongs to anothercategory, the plasmas ruled by local chemistry. These localreactions are much more important for the losses of chargedparticles than diffusion. In the subsections 6.2 and 6.3 wewill dealwith the questions “how local are global models?” and “are allplasmas filamentary?”

6.1. The GPM applied to a filamentary plasmas tube

The combination of single-shot TS and fast photography givesvaluable insight into the geometrical structure of the plasma. Thefirst lesson is that for a proper theory-experiment comparison, theGPM should be applied to a (rotating) plasma filament rather thanto a (stable) plasma cone. One of the initial disagreements betweenexperiment and theory, namely that concerning of the distributionof ne, is then solved. Along the filament this ne-distribution is in-line with that what we can expect from the power densitydistribution; i.e. more like the one known from surfatron plasmas;thus high ne-values close to the launcher and decreasing values inthe direction of the wave propagation.Wemay also expect that theTe-value as predicted by the GPM will be higher, since theeffective diffusion lengthΛn of the plasma filament is smaller thanthat of the cone–mantle with the same thickness. However, due tothe fact that Λn enters Eq. (3) as the argument of a logarithm, it is


not to be expected that Te will change much. But also ξ willremain too low, so that, if we believe theGPM,most powerwill beused for gas-heating instead of e–i creation. Moreover also thedisagreement between the theoretical and experimental ne-valueremains unsolved; in fact this discrepancy ismore severe now. Thevolume of the thin plasma helix with a length of 10 mm and adiameter of 0.3 mm is with 7.1 ·10−10 m3 about 3 times smallerthan that of the virtual cone–mantle described in Section 2.Thus the power density will increase with this same factor 3 andthe ne-value in the filament predicted by the GPM is now on theorder of 9 1022 m−2. This is a factor of 45 larger than what is foundexperimentally!!

The single-shot experiments were conducted by the idea thatthe solution of the experiment-model conflict lies at theexperiment-side. Now, with the new insights obtained by theexperiments there is no other choice than doubting the model. Werecall that the basic assumption of the GPM is that the mainparticle loss process as given in Eq. (1) is diffusive in nature. Thisalso was the justification to simplify the energy balance (the stepfrom Eq. (4) to (5)) by replacing nen1 Kcrea (I+3/2kBT) by neDaΛn

−2I.If we retain the original version Eq. (4) and work in the

opposite direction by inserting the experimental results of ne≈2·1021 m−3 and Te≈1.4 eV, we find a power density ofε≈ 9.5 · 1010 W/m3. For a filament with a volume of7.1 ·10−10 m3 this implies that the power is 67 W which is reason-able in view of the fact that 100W power is supplied to the plasma.

In search of the solution of this discrepancy it is instructive totranslate the particle production and loss processes intofrequencies. Inserting the measured value of Te=1.4 eV intoEq. (2) we find that the frequencies at which e–i pairs areproduced (νp=n1 Kcrea) equals 1.9 ·10

7 Hz. This is about 103

times (!!) larger than the frequency at which e–i pairs can beremoved by ambipolar diffusion, which for Λn=10

−4 m andDa=2 ·10

−4 m2 s−1 equals (DΛ−2)=2 ·104 Hz. Thus, diffusioncannot be the mechanism that is responsible for the removal ofcharged particles!

One might think that convection could give the solution.Estimations, using the pictures of Fig. 5, show that the rotationperiod must be in the order of 0.5 ms. For a radius of r=1 mm thisleads to a rotation velocity of about 13 m/s. This velocity of thefoot-point of the filament along the nozzle is comparable with thegas injection velocity. If a gas-element crosses a gradient length of10−4 m with 10 m/s the transient time will be 10 μs. This must beassociatedwith to a local production frequency of 105 Hz,which isindeed a factor 10 larger than the diffusion. However, it is stillmuch lower than the requested value of νp=2 107 Hz. Moreoverthis does not explain why the plasma disappears so quickly afterthe filament is passed by. Therefore we have to look to fastrecombination processes.

The inverse process of ionization, two-electron (2e) recombi-nation given by the reaction equation

eþ eþ ArþYAr⁎ þ e ð9Þ

has a rate K(2e)rec that can be found by applying the principle of

detailed balancing to the balance of ionization with 2e-

recombination so that ne2n+K

(2e)rec=nen

s(1) Kion. This gives arecombination frequency of nen+K

(2e)rec=n

s(1) Kion≈10 s−1,which obviously is far too low.

Another recombination process is that via the formation anddestruction of molecular argon ions for which Atom AssistedAssociation

Ar þ X þ ArþYArþ2 þ X ð10Þwhere X is a heavy particle, is the first step. This can be followedby dissociative recombination (DR)

Arþ2 þ eYAr⁎ð4p; 5s; N Þ þ Arð3pÞ ð1� vÞorArþ2 þ eYArð3p; 4sÞ þ Arð3pÞ v:

ð11Þ

In the first line the dissociative recombination delivers a groundstate atomAr(3p) and an highly excited atomAr ⁎ (in 4p or higher)that will most likely be re-ionized immediately. In the lower casetwo ground state atoms are created directly, or via an atom in theground state plus one in a level of the 4s groupwhich subsequentlydecays to the ground state. The branching ratio between the twolines in Eq. (11) is given by χ. The value of χ is important, sinceonly the lower line of Eq. (11) (thus the fraction χ) will contributeto effective recombination. Unfortunately χ is not well-known,only that χ is a “non-negligible factor” [25].

We follow [26] by taking χ=5%. In that study a model wasconstructed that describes the electron and heavy particle inducedtransformation from atomic into molecular ions and vice versa.One result of that model is the ratio n[Ar2

+]/ne as a function of ne,Te and Th. It can be found using [26] that for the conditions in theMPT plasma the ratio ζ=n[Ar2

+]/ne can reach a value of 20%. Fora dissociative recombination rate ofKDR=5.9·10

−14 m3 s−1 and aχ-value of 5% we then find an electron destruction frequency ofνd=ζ χ ne KDR≈1.2·106 Hz. This is much higher than thedestruction frequencies associated with diffusion and convectionbut about a factor of 20 smaller than the production frequency ofνp=2·10

7 s−1.It should be noted that especially low Th-values will favor the

molecular fraction ζ and the χ-value. Thus, the fact that thefilament sweeps around in a cold background gas will lead to highrecombination rates and there is room in the possible ranges of ζand χ to make dissociative recombination of Ar2

+ (partly)responsible for the destruction of the electron density.

Another route is offered via the production and destruction ofN2+. Since the plasma operates in open air, we must consider the

route that goes along charge transfer (CT) from argon to nitrogen:

Arþ þ N2YAr þ Nþ2 ð12Þ

followed by dissociative recombination

Nþ2 þ eYNþ Nþ ðEnergyÞ: ð13Þ

The first reaction is with KCT=4·10−16 m3 s−1 [27] the

limiting step so that, neglecting the reverse processes, we findfor the destruction frequency: νd=4·10

−16 [N2]. For a density of[N2]=10

23 m−3 this would give a recombination frequency ofνd=4·10

7 s−1. This is on the right order of magnitude!


In fact both molecular routes (via Ar2+ or N2

+) might lead torecombination frequencies that are high enough. But we needmore information to come to a conclusive answer. In the case ofthe Ar2

+-route the χ- and ζ-values must be known and in the casethat the recombination goes via N2

+ we have to know more aboutN2 entrainment. This implies that a model is needed with a well-developed gas-dynamic component. The role of air entrainmentcan be excluded if we let the plasma expand into a pure Arenvironment. This was done in the past for the TIA and asdescribed in [10] the Te-value in an Ar environment is indeedlower than in air while the electron density is higher.

Anyway, the main conclusion is that this plasma cannot bediffusive. The removal of electron–ion pairs has to be a localchemistry process and there are indeed two possible moleculardissociation routes. But since the nature of the local destructionprocess is not clearly established we remain with the dis-appointing outcome that there is no simple way to predict theelectron temperature and density. Thus, in contrast with diffusiveplasmas where internal plasma properties can be derived viaexternal control parameters, reactive plasmas are not easilypredictable.

6.2. How local are global models?

In section 3 we addressed the point that although GPMs arezero-dimensional they can, in some cases, be used to get insight inplasma structures. As an example we gave the distribution of thene in surfatron plasmas, which decreases in the wave-propagationdirection since the local ε-value decreases along the EM wave.Another example is found in the outer regions of the ICP where itwas found that Te goes up at the edges of the plasmas. The reason,as given in [15], is that for these locations the diffusive lossesare large so that high local Te-values are requested. In acomparable way we can try to get explanations for the Te-dis-tribution in Fig. 3.

The predictions of these local plasmas aspects with a globalmodel are in principal possible since Eqs. (1) and (4) are in factlocal plasma equations. So, in a certain sense, it is moreappropriate to pose the opposite question: how global are GlobalPlasma Models?

The justification of this question can be illustrated byFig. 8 thatpresents the Th distribution for a TIA as published in [10]. Thiscontour plot was obtained by means of the combination ofRayleigh and Raman scattering and the surprising feature is that amaximum in Th is attained far downstream, in a region whereelectrons are absent! So the heating cannot be realized by theelastic collisions between electron-heavy particle, the second termin Eq. (4). The explanation for this delay in gas-heating given in[10] is that the nitrogen atoms created by the reaction chain givenin Eqs. (12) and (13) will be followed by

N þ N þ XYN2 þ X þ ð9eVÞ ð14Þ

in which the spectator X can be Ar or N2. This so-called after-heating takes place due to the release of the dissociation energy(9 eV). It is striking that the maximum in the gas temperature is,with 4500 K, in the same order as the value predicted below

Eq. (7) and corresponds with a low ξ-value. Indeed the globalξ-value will be low since after (molecular) recombination (almost)all energy will be converted into heat; except the energy that isradiated away from the active plasma zone. But as Ar is a poorradiator we can expect that the related fraction is very low. In theactive plasma zone the local ξ-value must be high since e–i pairswill be produced at a high rate. We recall that Fig. 8 deals with aplasma created by a TIA and that similar measurements on theMPT should be done in future. However, we strongly believe thatthe same type of after-heating will be found there. The TIA andMPT are very similar, they have the same EM structure, acomparable geometrical structure and show the same discrepan-cies between the Global Plasma Model and TS.

6.3. Are all plasmas filamentary?

The discussion above shows that filamentary aspects can havelarge consequences for the plasma properties. It is thereforeimportant to get an answer to the question whether all plasmashave filamentary structures. Or better: what are the conditionsunder which certain type of plasma sources will create filamentaryplasmas?

A preliminary study was done in Eindhoven and Cordobausing fast photography. It was found using exposure times downto 15 ns that the ICP and the plasmas in fluorescence lamps such asthe TL tube [28] and QL lamp [16,17] are not filamentary. Theseplasmas are diffusion dominated and they are objects to which theGPM can be applied successfully. However, for both the TIA inEindhoven and the TIA in Cordoba we found that they consist inmany cases of turbulent filament(s). In Cordoba we also foundhigh Te-values using the Stark Intersection Method [29]. Valuesthat are in agreement with the results of TS reported for the MPTand TIA [10] and that, due to their magnitude, point towards highlocal production and thus destruction rates. But also differenceswhere found between the MPT and the TIA. In contrast to theMPT the TIA does not consist of one single nicely rotatingfilament. The filaments found in the TIA plasma turn out to beviolently vibrating snaky filaments.

The criterion for the presence of filaments, the precise struc-tures of filamentary plasmas and how they respond to power andflow variations remains an extremely interesting topic for futureresearch. An important aim of such an investigationwill be to lookfor conditions for which microwave plasma torches turn from thefilamentary to the diffusive mode. Apart from SS-TS andfast photography also the method of noise analysis [30] can beused.

7. Concluding remarks

Normal photographs support the visual appearance thatplasmas produced by the MPT have the shape of a cone–mantle.If the thickness of this mantle is used to calculate the electrontemperature by applying a Global PlasmaModel (GPM)we find aTe-value that is much lower than what is found via ThomsonScattering TS (0.8 instead of 1.4 eV). The value of the electrondensity predicted by the GPM is much higher than the TS value(3·1022 versus 2 1021 m−3). In order to get better insight in this


conflict, single-shot TS measurements were performed incombination with fast photography. This leads to the insight thatthe plasma is a rotating filamentary helix rather than a stable cone–mantle. However, applying the GPM to the filament does notresolve the discrepancy between model and experiments. On thecontrary the disagreement is even more conflicting in that case.That is why we are forced to abandon the basic assumption of theGPM, namely, that the plasma is diffusion dominated. Using theresults of the TS and inserting these into the formula for theionisation rate shows that the production rate of charged particlesis much higher than what can be compensated by ambipolardiffusion losses.And since atomic channels are not fast enoughweneed recombination processes via molecular routes. One possibleroute is the creation and destruction of Ar2

+; another is thecreation of N2

+ via charge transfer and the subsequentdestruction via dissociative recombination. Estimative calcula-tions show that both routes might provide explanations but extrainformation is needed to get a decisive answer. However, there is asevere lack of knowledge on elementary processes and turbulentmixing.

The applicability of the GPM provides the tool to classifyplasmas into diffusive and reactive plasmas. The ICP, the planarplate reactor used for the fabrication of integrated circuits and thefluorescence lamps such as the TL and theQL lamps, belong to thefirst category. The MPT and the TIA are members of the secondclass. If a plasma source can be characterized by a GPM it ispossible to get quasi-analytical relations between the plasmascontrol parameters, i.e. the knobs, and the plasma properties. Thismakes the dream of the plasma operator to become true. However,these simple rules are, as we have seen, not applicable to reactiveplasmas. Due to the loss of contact with the environment (i.e. duethe absence of diffusion dominancy) the plasma has more localfreedom, will behave filamentary and sweeps around in a cold gasinwhich the surrounding air is entrained. It is this very entrainmentthat enhances the local chemistry and supports molecularrecombination channels.

As stated before, a better understanding of these types ofplasmas needs more information on elementary processes andinsight in turbulent mixing phenomena. Such a study must beguided by experiments bywhichmany aspects can be studied. Forfuture studies we suggest to investigate the rotation velocity of thefilament as a function of external parameters, to look under whatcircumstances the orderly rotation as found for the MPT makesplace for the more snaky twisting behaviour of the TIA filaments,how changing the environment will influence the electrontemperature and density and if it is possible find for the MPT atransition from the reactive to the diffusive mode.

Acknowledgments

The Bilateral Collaboration Framework between the Univer-sity of Codoba (E) and the Technical University of Eindhoven(NL) is highly acknowledged.

We thank Guillaume Boidin, at that time student at theLaboratoire de Genie de Procédés Plasmas Université Pierre etMarie Curie (Paris, France), for his role in the Thomson Scatteringmeasurements.

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