Thomson scattering on a low-pressure, inductively-coupled gas ...

Thomson scattering on a low-pressure, inductively-coupled gas ...

M J van de Sande andJJAMvanderMullenfor lower electron temperatures (down to below 0.2 eV) forapplication to gas discharge lamps.In section 2, the experimental system designed for andapplied in this paper is described. Section 3 summarizes themodifications of the QL lamp required to focus the high powerlaser beam into the plasma and detect ong>Thomsonong> ong>scatteringong>.Results of the experiments are presented in section 4. Insection 5, the measurements are discussed qualitatively onthe basis of the electron particle and energy balances, andcompared to results that were previously obtained in ourlaboratory by DLA measurements [2, 3]. Conclusions aredrawn in section 6.2. Experimental arrangement for ong>Thomsonong>ong>scatteringong>2.1. ong>Thomsonong> ong>scatteringong>ong>Thomsonong> ong>scatteringong> is ong>scatteringong> of radiation by free electronsin the plasma, and hence provides a very direct methodto measure properties of the free electron gas [10–12].For relatively low electron density plasmas, such as theQL discharge, ong>scatteringong> is incoherent. In that case,the ong>Thomsonong> scattered intensity is directly proportional to theelectron density n e , and the shape of the ong>scatteringong> spectrum isdetermined by the Doppler shift caused by the electron motion.The absolute electron density can be determined fromthe ong>Thomsonong> ong>scatteringong> intensity I T by comparison with, forinstance, the intensity I Rm of rotational Raman ong>scatteringong> byN 2 with a known density n N2 [5, 13, 14]:()I T 1 ∑ n J dσ J →J ′ I Tn e = n N2≡ n N2 Ɣ Rm .I Rm dσ T /d nJ,J ′ N2 d I Rm(1)Here, dσ T /d is the differential cross section for ong>Thomsonong>ong>scatteringong>, dσ J →J ′/d is that for Raman ong>scatteringong>accompanied by a transition from rotational state J to J ′ ,and n J /n N2 is the fraction of nitrogen molecules in state J .The factor Ɣ Rm represents the ratio of the total Ramanong>scatteringong> cross section and the ong>Thomsonong> ong>scatteringong> crosssection [14, 15], taking into account relative occupationsof the different rotational states J . As discussed below,the experimental system used in this paper employs aperpendicular ong>scatteringong> geometry and a laser wavelengthof λ i = 532 nm. For these conditions, and at a nitrogentemperature of 300 K, Ɣ Rm ≈ 8.15 × 10 −5 [14, 15].If the electron energy distribution function (EEDF) of theplasma is Maxwellian, the ong>scatteringong> spectrum is a Gaussianwith a half 1/e width, λ 1/e , that is related to the electrontemperature T e according to[]m e c 2T e =λ 28k B λ 2 i sin2 1/e(θ/2), (2)where θ is the angle of ong>scatteringong>, m e the electron rest mass,c the speed of light, and k B the Boltzmann constant. For theconditions used in this paper, θ = 90˚ and λ i = 532 nm, thefactor between brackets equals 5238 K nm −2 .2.2. Basic systemThe experimental system that was used in this study is shownschematically in figure 1. A frequency-doubled Nd : YAGlaser produces 400 mJ, 7 ns laser pulses at a wavelength ofλ i = 532 nm. A plano-convex lens (f = 1 m) focuses the laserbeam to a diameter of approximately 200 µm in the plasma,where electrons scatter the laser radiation. The detectionvolume is imaged onto the entrance slit of a TGS, which rejectsstray light and disperses the scattered light. An intensifiedCCD camera records the ong>scatteringong> spectrum.The entrance slit of the system is horizontal, i.e. parallelto the laser beam. Together with a 90˚ image rotator inside thespectrograph system and the two-dimensional iCCD camera,this provides a spatial resolution of about 0.1 mm over a rangeof 11 mm in a single measurement. However, when lessspatial information is required, or when the electron densityis low, multiple pixel arrays can be binned, thus extending theeffective length of the detection volume (integration length).Since the QL discharge is relatively large (110 mm diameter),the integration length was chosen to be 5.5 mm in this study, sothat only two spatial positions were measured simultaneously.With a demagnification, the whole discharge might have beenimaged onto the entrance slit, but using a 1 : 1 image benefitsthe solid angle of detection and image quality, and is thereforepreferable in most cases.Figure 1. The experimental system for ong>Thomsonong> ong>scatteringong> that was used in this study. Light from a frequency doubled Nd : YAG laser isscattered by electrons in the plasma. Scattered light is collected and dispersed by a TGS. The first two gratings and the mask between themserve as a stray light filter. An intensified CCD camera records ong>scatteringong> spectra with spatial resolution.1382

ong>Thomsonong> ong>scatteringong> on an inductively-coupled gas discharge lampThe setup employs a perpendicular ong>scatteringong> geometry,which implies that the ong>scatteringong> angle is θ = 90˚, the laserbeam is polarized perpendicular to the plane of ong>scatteringong> (i.e.vertical in this case), and only scattered radiation with thesame (vertical) polarization direction is detected. The latterhas the advantage that stray light and plasma emission, whichare (partly) unpolarized, are reduced.2.3. The triple grating spectrographStray light is a persisting problem for ong>Thomsonong> ong>scatteringong>on gas discharges close to glass walls. It originates fromong>scatteringong> of part of the laser light on the static environment ofthe plasma, and is usually much more intense than ong>Thomsonong>ong>scatteringong>. In contrast to ong>Thomsonong> ong>scatteringong>, stray light isvirtually monochromatic. Therefore, it mainly contributes inthe centre of the ong>scatteringong> spectrum. However, the finite widthof the instrumental profile of a spectrograph causes a fraction ofthe stray light to be redistributed to other parts of the spectrum(typically around 10 −3 –10 −2 nm −1 at 0.5 nm from the laserwavelength). Thus, a high stray light intensity severely affectsthe accuracy of the measurement. The problem of stray lightcan be reduced by a narrowband notch filter in front of the(final) spectrograph.Two gratings in subtractive configuration can be used as anarrowband notch filter [6–9]. The first grating dispersesincident light (see figure 2). Subsequently, a mask blocksthe central part of the spectrum that is formed, and the secondgrating recombines (‘cross disperses’) the light again at the exitslit. Such a double grating filter (DGF) essentially consistsof two simple spectrographs. Combining it with a thirdspectrograph, which disperses the ong>Thomsonong> scattered radiationfor detection, results in a TGS. The intermediate slit in figure 1is the exit slit of the DGF and the entrance slit of the thirdspectrograph. Below, the design of the TGS used in this study(cf figures 1 and 2 and table 1) is discussed on the basis of therequirements for the measurements on the QL lamp. In thisdiscussion we follow the path of incident photons.The entrance slit of the system must be wider than thelaser beam (200 µm), and is taken as 250 µm. The lengthof the entrance slit (11 mm) equals that of the iCCD detector.A 90˚ image rotator, consisting of three plane mirrors, is placeddirectly behind the entrance slit (see figure 1) to facilitatespatially resolved measurements, as discussed above.The first achromatic doublet lens in the system producesa collimated beam for the first grating. Since lenses canbe used on-axis, they produce much less astigmatism thanmirrors. Therefore, unlike for mirror-based spectrographs, ahigh spectral resolution can be combined with a high spatialresolution. In addition, achromatic lenses exhibit muchless spherical aberration than single-element lenses, which isessential for multi-lens systems. Chromatic aberrations are notsignificant due to the limited wavelength range (a few nm) ofthe ong>Thomsonong> spectra. The clear aperture of all lenses in theTGS is φ = 95 mm, and the focal length is f = 600 mm; thisis a trade-off between a large dispersion and a large solid angleof detection.The holographic grating has a groove density ofn = 1800 mm −1 . This is sufficient to reach a dispersion of1–2 mm nm −1 , which is required for a high spectral resolutionand to image the entire spectral range of interest (∼10 nm) ontothe iCCD camera (16.5 mm wide). The angles of incidence αFigure 2. A DGF for stray light rejection. The first grating disperses incident light, a mask blocks the central part of the spectrum, and thesecond grating cross disperses the light again. The most important design parameters are the grating constant n, angles of incidence α andreflection β on the first grating, the focal length f of the lenses, and the length of the collimated beam, a = a 1 + a 2 . The second grating ismirrored with respect to the first, so that the angles α and β are reversed, while all other parameters are similar.Table 1. Chosen instrumental parameters and the resulting performance characteristics.Instrumental parametersPerformance characteristicsGrating constant n = 1800 mm −1 Dispersion d = 1.52 mm nm −1Angle of incidence a α = 15˚ Solid angle = 0.0197 sr (f/6.3)Angle of reflection a β = 45˚ Bandpass λ bp = 0.23 nmFocal length f = 600 mm Spatial res. x = 0.1mmLens diameter φ = 95 mm Efficiency η = 10%Collimated beam a = 600 mm Half 98% width λ 98 = 0.45 nmSlit width s = 250 µm Lowest temp. T e,min = 0.16 eVMask width m = 1.0 mm Eff. redistribution R eff = 7 × 10 −9 nm −1Det. lim. n e,lim = 10 16 m −3a In the second spectrograph these angles are reversed.1383

M J van de Sande andJJAMvanderMullenand reflection β on the grating (see figure 2) are related to thegroove density n and wavelength λ i via the grating equationsin α + sin β = knλ i , (3)where k is the order of dispersion, which is taken as unity inthe present design. We chose |β − α| =30˚. In that case, andwith λ i = 532 nm, the angles of incidence and reflection canbe α = 15˚ and β = 45˚, or the reverse. This choice influencesthe width of the instrumental profile and the dispersion of thesystem [16]. A small angle α leads to a broader instrumentalprofile, but also to a larger dispersion, which reduces theinfluence of image aberrations on the instrumental profile.In addition, for small α, the reflected beam is narrower thanthe incident beam, so that no signal is lost and vignetting inspectral direction (see below) is minimized. Therefore, wetook α = 15˚ and β = 45˚. For these parameters, the lineardispersion is d = knf/ cos β = 1.52 mm nm −1 .Vignetting is the decreased transmission of an opticalsystem for off-axis objects (see for instance [17]). In aspectrograph, vignetting may occur for objects at differentspatial positions and for different wavelengths. The totallength a of the collimated beam (see figure 2) influences theamount of vignetting produced by the system. Vignetting inspatial direction by the TGS system is at a minimum whena = 2f [14]. While a < 2f , increasing a leads to largerlosses at the second lens, but this is compensated further inthe system. When a = 2f , the (relative) transmission of thesystem at the edge of the field of view (5.5 mm off-axis) wouldbe about 85%. However, in our spectrograph we chose a = fsince a much larger value would result in an inconvenientlylarge system. For this value, the transmission at the edge of thefield of view is expected to be approximately 71% of that in thecentre. In practice, it is found to be around 50%, which is theresult of other elements, such as the image rotator and the lensesin front of the TGS system, in the optical path. This vignettingeffect is taken into account by the calibration measurement,in which the same problem is encountered. Vignetting inspectral direction is negligible, because firstly only three ofthe eight lenses contribute to it, and secondly the dispersedbeam is narrower than the beam incident on the first grating,as described above.The mask width m determines the width and depth of DGFfilter (transmission) profile; a broader mask results in a deeper,but wider profile. The width must be at least the width of theimage of the entrance slit. This is larger than the width of theentrance slit (250 µm) by a factor 1.4 because of the horizontalmagnification produced by the grating. Unlike a mirror, agrating produces a change dβ ≠ dα of the angle of reflectionβ for a change in the angle of incidence α. This follows directlyfrom the grating equation (3), and results in a magnificationfactor |dβ/dα| =|cos α/ cos β| of the image in horizontal(spectral) direction. In this paper, we take m = 1.0 mm.The second grating in the DGF is mirrored with respectto the first. In this way, the dispersions of both gratingscancel, and the image curvature produced by the first grating iscompensated by the second. The intermediate slit has the samewidth (250 µm) as the entrance slit. The third spectrograph inthe TGS is identical to the first. Table 1 summarizes the chosendesign parameters and the resulting TGS performance.The spectral resolution of the system (the bandpassλ bp ≈ 0.23 nm) equals the spectral range corresponding tothe width of image of the entrance slit. The efficiency η of thesystem (10%) was calculated from the efficiency of each of theoptical elements in the system.The half 98% width λ 98 is the distance from thelaser wavelength λ i at which the transmission of the filter isapproximately 98%; the ong>Thomsonong> spectrum is not distortedsignificantly further than λ 98 away from λ i . This determinesthe lowest electron temperature T e,min that can be measuredwith the system. A reasonable accuracy (better than ∼30%) ispossible when an electron energy of 1 2 k BT e can be measured.For λ 98 = 0.45 nm, this results in T e,min = 0.16 eV.The effective redistribution R eff in table 1 is the fractionof the incident stray light that is detected per spectral range at adistance of λ 98 = 0.45 nm from λ i . As described below, theredistribution of a single spectrograph is 3 × 10 −3 nm −1 at thisposition. This is effectively decreased to R eff ≈ 7×10 −9 nm −1by the DGF, which has a (normalized) transmission of 3×10 −6at the central wavelength, and the polarizer in front of the iCCDdetector, which reduces the (partly polarized) stray light byapproximately 25–50%.The electron density detection limit, n e,lim ≈ 10 16 m −3under standard experimental conditions in this paper, isdiscussed below.The DGF filter profile F (λ) can be calculatedfrom the instrumental profiles f 1,2 (λ ′ − λ) of the twosingle spectrographs that constitute the filter. For simplicity,we take the single spectrograph transmission unity. First, weassume that no mask is placed between the two spectrographs,and we follow the path of a photon at the laser wavelength λ i .The probability p 1,λi that this photon passes the firstspectrograph’s focal plane at a position assigned to a rangedλ ′ around wavelength λ ′ is given by the instrumental profilef 1 (λ ′ − λ i ) of this spectrograph:p 1,λi dλ ′ = f 1 (λ ′ − λ i )dλ ′ . (4)The upper graph in figure 3 schematically illustrates thisredistribution of photons by the first spectrograph. If theFigure 3. Calculation of the probability that a photon ofwavelength λ passes the DGF via a position that is assigned to λ ′(see text for an explanation).1384

ong>Thomsonong> ong>scatteringong> on an inductively-coupled gas discharge lampphoton λ i is redistributed to a position associated with adifferent wavelength λ ′ (λ ′ ≠ λ i ), this photon is most likely tobe imaged next to the exit slit by the second spectrograph; this isexpressed by the lower graph in figure 3. Nevertheless, there isa probability p 2 that it is redistributed again and passes the exitslit of the filter. This probability is given by the instrumentalprofile f 2 (λ ′′ − λ ′ ) of the second spectrograph integrated overthe width of the exit slit:∫p 2 = f 2 (λ ′′ − λ ′ ) dλ ′′ . (5)exitThus, the probability that a photon λ passes through the DGFvia the route λ ′ is given by the product p 1,λ p 2 . The integralof this probability over every possible route λ ′ yields thetransmission T 0 of the DGF without a mask:∫T 0 ≡ p 1,λi p 2 dλ ′∫ [ ∫]= f 1 (λ ′ − λ i ) f 2 (λ ′′ − λ ′ ) dλ ′′ dλ ′ . (6)exitThis transmission factor is due to the redistributions by bothspectrographs. For sharp instrumental profiles, such as Diracor block functions, it approaches unity.A mask between the two spectrographs can block certainroutes λ ′ around λ i , so that only photons that follow a path thatdeviates from the ‘proper’ one (λ ′′ = λ ′ = λ i ) can reach theexit slit. Thus, the transmission F(λ i ) of the DGF at the laserwavelength equals T 0 minus the probability of hitting the mask:∫ [ ∫]F(λ i ) = T 0 − f 1 (λ ′ − λ i ) f 2 (λ ′′ − λ ′ ) dλ ′′ dλ ′ .mask(7)With a similar approach for other wavelengths than λ i ,the complete filter profile F (λ) can be calculated. Dividing thisby T 0 yields the filter profile normalized to unity outside thenotch region.The instrumental profiles f 1 and f 2 can be estimatedfrom the design parameters of the system. The instrumentalprofile of the first spectrograph is the convolution of thecontributions of the entrance slit, image aberrations and thegrating. The contribution of the entrance slit is a block functionof 0.23 nm wide, this being the spectral range associated withthe entrance slit width via the dispersion of the spectrographand the horizontal magnification produced by the grating. Thecontribution of the image aberrations is more or less Gaussianwith a spectral width of 0.05 nm, which follows from theestimated resolution of the lenses (∼75 µm). The contributionexitof the grating is a (sin x/x) 2 function, which is approximatelyLorentzian. Its half width, 4 pm, follows from the resolvingpower of the grating, λ/λ = N, where N is the numberof illuminated grooves on the grating [16]. The instrumentalprofile of the second spectrograph is similar to that of the firstspectrograph except for the contribution of the entrance slit,which is absent in the former.The left-hand side of figure 4 shows the calculatedand measured instrumental profile of the first spectrograph.According to the calculated profile, the redistribution producedby a single spectrograph at 0.5 nm from the laser wavelengthis R ≈ 3 × 10 −3 nm −1 . The measured instrumental profile is,apart from the spectrograph, influenced by cross-over effects inthe iCCD camera as well. This is the cause of the wings of themeasured instrumental profile being much more intense thanthe true instrumental profile of the spectrograph. The righthandside of figure 4 shows the measured and calculated filterprofile. The mask width is 1 mm, and the entrance and exitslits are 250 µm wide. The measured filter profile matchesclosely to the calculated profile, which indicates that theapproximations above are reasonable. The minor differencesbetween the measured and calculated filter profile may becaused by imperfections of the optics, alignment, or the model.The DGF filter profile depends on the width of the maskand slits that are used. A narrower mask results in a narrowerfilter profile, so that lower electron temperatures can be studied.This, however, increases the stray light transmission, so that theeffective stray light redistribution of the TGS is deteriorated.The left-hand side of figure 5 illustrates this for a number ofmask widths. The effect of the slit width on the filter profile isshown in the right-hand side of figure 5. Wider slits bothincrease the width of (the wings of) the filter profile andthe stray light transmission. Each combination of mask andslit widths can be advantageous for particular experimentalcircumstances, such as the stray light level, the temperature ofthe plasma under study, and the stability of the position of thelaser beam.Table 2 shows the half widths at 98% λ 98 of the filterprofile, the effective TGS redistribution at a distance λ 98from the laser wavelength, and the lowest measurable electrontemperature T e,min for the mask and slit widths of figure 5.The experimental system described above showssimilarities with that of Greenwald et al [8] and those usedin recent studies by Kono et al [9] and Noguchi et al [18].A difference between our TGS system and that describedby Greenwald et al is that the latter is of the near-Littrow typeFigure 4. The measured and simulated instrumental profile of the first spectrograph of the DGF (left) and the measured and simulated DGFfilter profile (right) with 250 µm slits and a 1 mm mask that is positioned to block light of wavelength λ i .1385

M J van de Sande andJJAMvanderMullenFigure 5. The normalized DGF profiles with various mask widths (left) and slit widths (right).Table 2. TGS performance characteristics for various mask and slitwidths.Mask width λ 98 T e,min R eff (λ 98 )(mm) (nm) (eV) (nm −1 )Slit width 250 µm0.5 0.28 0.07 6 × 10 −81.0 0.44 0.17 7 × 10 −92.0 0.77 0.54 7 × 10 −10Slit width 500 µm1.0 0.55 0.27 1 × 10 −8(α ≈ β), so that only three lenses are needed. However, near-Littrow type spectrographs are known to produce a relativelylarge amount of stray light because of the proximity of thelight beams incident on and reflected by the grating, and bothbeams sharing the same lens. In addition, a near-Littrowdesign involves off-axis use of the lenses, which introducessome astigmatism, thus deteriorating either spatial or spectralresolution. Another difference with the system of Greenwaldet al is the absence of additional field lenses to controlvignetting in our case. Field lenses only have a positiveeffect for short lengths a of the collimated beam, which ispossible only for near-Littrow spectrographs. In our design,the use of field lenses would improve the transmission at theedge of the field of view by only about 15%, while they woulddeteriorate the resolution and produce additional stray light.A third distinction is the symmetric arrangement of the first twogratings in our case, so that the image curvatures introducedby both gratings cancel. Finally, the system of Greenwald et alis designed to image just one half of the ong>Thomsonong> spectrum.However, the main difference between our setup and thosedescribed in previous work is that our setup is designed formeasurements on plasmas with a lower electron temperature(T e < 1 eV). This is expressed in the choice for a larger focallength f of the lenses and grating constant n, and differentangles α and β. This results in a larger dispersion of the systemand a narrower instrumental profile. Therefore, the width of thenotch filter profile is much narrower; 98% relative transmissionof the system is achieved at only 0.45 nm from the centralwavelength. This makes the setup presented here especiallysuitable for low electron temperature plasmas, such as the onesin gas discharge lamps.2.4. Detection limitThe detection limit n e,lim is the electron density for which n eand T e can be determined from the ong>scatteringong> spectrum with a‘reasonable’ accuracy, say 30%. It is determined by propertiesof the experimental system, such as the transmission of theTGS, and by experimental conditions, such as the integrationtime (30 min in this paper), the length of the detection volume(5.5 mm), and the width of the ong>scatteringong> spectrum (determinedby T e ∼ 1 eV). The detection limit of the present system underthese conditions isn e,lim ≈ 10 16 m −3 . (8)This is supported by both the measurements and a detailedcalculation of the various noise sources, such as dark currentof the iCCD camera, readout noise, residual stray light, andstatistical noise on the ong>Thomsonong> ong>scatteringong> experiment itself.Unfortunately, the detection limit achieved during themeasurements described in this paper is about a factor of 40higher. This is the result of two of the three gratings deliveredby the manufacturer having an efficiency that is a factor ofabout 6 below the specified 70%. This is also the reason forthe long integration time used in the measurements (typically30 min for ong>Thomsonong> ong>scatteringong>). In addition, the width of theslits in the TGS were taken to be 500 µm to allow for a smalldrift of the laser beam during lengthy measurement sessions,although this reduced the stray light rejection (cf figure 5 andtable 2). Meanwhile, the two inefficient gratings have beenreplaced.Measurements are performed by simply integrating theiCCD signal. A two-dimensional photon counting technique,as described by Kono et al [9], was not applied. A calculationof the relative importance of the noise sources in the experimentshows that in our case, the most important noise source is byfar the statistical noise on the ong>Thomsonong> ong>scatteringong> experiment,which cannot be eliminated by photon counting. Experimentswith and without photon counting confirm this presumption.3. Experimental version of the QL lampThe Philips QL lamp is a low-pressure, inductively powered(electrode-less) gas discharge lamp. The RF frequency of thelamp is 2.65 MHz, and the power delivered by the RF coil is85 W [2, 3, 19]. Due to the absence of electrodes, this lampcombines a high efficacy with a long lifetime. The lampsstudied in this paper are filled with 66 and 133 Pa argon buffergas. Mercury is supplied by an amalgam (Bi/In/Hg in a massratio of 68/29/3).A number of modifications were made to the commerciallyavailable lamps in order to perform ong>Thomsonong> ong>scatteringong>1386

ong>Thomsonong> ong>scatteringong> on an inductively-coupled gas discharge lampFigure 6. The experimental version of the Philips QL lamp that was used for the measurements. The extension tubes and Brewster anglelaser windows are heated to 50˚ by water hoses to prevent mercury condensation; copper tubes heat the air in front of the Brewster windowsas well. The amalgam is thermostrated to control the mercury pressure in the lamp. The position of the detection volume is expressed in thecoordinates r (radial distance) and h (height) with respect to the centre of the RF coil. The coil can be moved in vertical direction.experiments. First of all, the fluorescent coating is absentin the experimental QL bulb in order to have optical accessto the discharge. Secondly, the amalgam is thermostratedso that the mercury pressure in the lamp can be controlled.Finally, in order to allow the high intensity laser beam to enterthe discharge, extension tubes with quartz laser windows weremounted onto the lamp (see figure 6).The quartz laser windows are required since the glass ofthe QL bulb is too rough and weak for a high intensity laserbeam. In addition, the windows must be placed far from thefocal volume to withstand the high laser intensity close to thefocal point inside the lamp. This also reduces the effect of straylight produced by these windows. Therefore, 60 cm extensiontubes with quartz windows were mounted on either side ofthe lamp. The windows were mounted at Brewster angle tominimize reflections of the laser beam.Possible complications introduced by the large extensiontubes are mercury condensation in the relatively cold tubesand a drop of the operational pressure of the lamp. Mercurycondensation was prevented by heating the extension tubes to50˚ by a flat water hose wrapped around the tubes. Copperpipes were placed over the ends of the extension tubes to heatthe air in front of the laser windows as well.The drop of the operational pressure arises from thelarge temperature difference between the gas in the lamp andthe extension tubes. Since the volume of the tubes is notnegligible compared to that of the lamp (175 versus 740 ml),a significant fraction of the gas will escape to the extensiontubes when the lamp is switched on, thus decreasing theoperational pressure of the lamp. In order to compensatefor this effect, the experimental lamps were filled at slightlyhigher pressures (80 instead of 66 Pa, and 160 instead of133 Pa). The filling pressure correction factor is calculatedfrom the volume ratio of the lamp and the extension tubes,the temperature of the extension tubes, and the operationalpressure in an unmodified lamp (∼270 Pa for the 133 Pa lamp).The latter follows from the gas temperature distribution in thelamp. This distribution is not known for the entire lamp, but canbe estimated roughly with the help of the radial gas temperatureprofile at the central height in the plasma, which was measuredby Jonkers et al [2].The lamp was moved along the laser beam in order tomeasure at different radial positions r in the plasma. Theminimum radial position r min and height h of the detectionvolume with respect to the centre of the RF coil are determinedby the positions of the extension tubes on the QL bulb. In the66 Pa lamp, r min ≈ 23 mm and h ≈ 18 mm; in the 133 Palamp, r min ≈ 28 mm and h ≈ 34 mm. In order to measurecloser to the centre of the discharge, the RF coil was raised byapproximately 21 mm in a second series of measurements, sothat h decreases. The shape of the plasma with respect to theRF coil is assumed not to change significantly if the positionof the coil inside the QL bulb is varied.As discussed in section 2.1, the experimental systemis calibrated with rotational Raman ong>scatteringong> on N 2 . Forthis purpose, the lamp is removed and the detection volume isflushed by a gentle flow of nitrogen at atmospheric pressureand room temperature. However, placing the lamp in thedetection area causes the laser beam to be displaced (∼1 mm)by refraction in the Brewster angle laser windows. Therefore,the system must be adjusted slightly so that the image of thelaser beam coincides with (the centre of) the TGS entrance slit.If the image of the laser beam is on the edge of the entranceslit, the spectrum is shifted with respect to the stray light mask,which introduces a slight asymmetry of the recorded spectrum.The lenses in front of the TGS were moved slightly in verticaldirection until the spectrum is symmetric and the ong>scatteringong>intensity is at a maximum.For a correct measurement of the electron density, thetransmission of ong>Thomsonong> scattered light by the QL bulbmust be taken into account. The reflection coefficient ofglass is approximately 8% at normal incidence. In addition,the QL bulb is coated to prevent mercury absorption bythe glass, which lowers the transmission by about 15%.Therefore, the measured electron densities are underestimatedby approximately 20%. The measurements presented insection 4 are corrected for this effect.4. ResultsFigure 7 shows a rotational Raman spectrum used forcalibration of the experimental system. The peaks in1387

M J van de Sande andJJAMvanderMullenthe spectrum correspond to the even rotational transitions.The weaker odd transitions, located between them, couldnot be resolved individually (cf [22]). The dispersionof the system, which can be derived from this spectrum,is d = 1.52 mm nm −1 , corresponding to the dispersioncalculated in section 2.Figure 8 shows two typical ong>Thomsonong> ong>scatteringong> spectrathat were measured in the 133 Pa lamp with a mercury pressureof p Hg = 0.95 Pa. These spectra are taken at the same radialposition r, but at different heights h and on different sides ofthe glass core of the QL bulb. The spectrum on the left-handside was obtained at the side from which the laser beam enteredthe lamp. At this position, reflection of laser light on the glasscore strongly increases the stray light intensity, as expressedby the residual stray light peak in the centre of the spectrum.From this figure, it is clear that the electron density is higher atpositions closer to the RF coil. The electron temperatures arecomparable, seeing the uncertainty of approximately 10–15%in T e , as discussed below.The relative uncertainty in the measured electrontemperatures ranges from about 7% at high electron densities(10 19 m −3 ) to 30% at the electron density detection limit.This uncertainty is mainly determined by the accuracy of theGaussian fit to the measured spectrum, which deterioratesrapidly for decreasing electron densities.The relative uncertainty in the measured electron densities,ranging from about 15% to 30%, is primarily determined bythe sensitivity calibration of the system. Firstly, the Ramanong>scatteringong> cross section used for calibration has an accuracy ofapproximately 8% [15]. Secondly, the transmission of the glassFigure 7. Rotational Raman ong>scatteringong> spectrum of atmospheric N 2at room temperature. This spectrum was used for calibration of thesensitivity and dispersion of the experimental system.of the QL bulb is not known precisely. Thirdly, the alignmentof the image of the laser beam onto the entrance slit mayintroduce an extra uncertainty. Note that part of the error in n eis systematic. Therefore, the measured values with respect toeach other generally correspond better than suggested by theestimated error.Figure 9 shows radial profiles of the electron density inthe 66 and 133 Pa lamps. Note that this argon filling pressurep Ar refers to the pressure when the lamp is off (cold); theoperational pressure is about a factor of 2 higher. The amalgamtemperature was 100˚C during these measurements, so that themercury pressure is p Hg = 0.95 Pa. Measurements are doneat the standard height above the centre of the RF coil (18 and34 mm for the 66 and 133 Pa lamps, respectively) and with theraised RF coil, i.e. 21 mm lower with respect to the coil. Theplasma walls are located at r = 9 and 55 mm.From this figure, it is clear that the electron densitydecreases further from the RF coil (larger radial positions ror heights h). The highest measured electron density is inall cases located at the closest position to the coil that couldbe measured with the present experimental lamps. Therefore,no accurate statement can be made about the position of themaximum electron density in the lamp. The electron density inthe 133 Pa lamp is higher by a factor of about 1.5–2 comparedto that in the 66 Pa lamp, as can be seen by comparing theprofiles at h = 18 mm in the 66 Pa lamp and h = 13 mm inthe 133 Pa lamp.In figure 10, radial profiles of the electron temperatureare shown for the same experimental conditions. The electrontemperature does not show a significant dependence on theheight above the RF coil. The measurements suggest a smallincrease of T e towards the edge of the discharge and a lower T ein the 133 Pa lamp than in the 66 Pa lamp.Figure 11 shows the electron density n e as a function ofthe mercury pressure p Hg in the lamp. The electron densityshows only a weak dependence on p Hg , although it seems togo through a minimum at p Hg ≈ 0.5 Pa. The electron densityin the 133 Pa lamp is again approximately 1.5–2 times higherthan that in the 66 Pa lamp, and is larger at heights comparableto that of the RF coil (small |h|).Finally, figure 12 gives the electron temperature T efor different mercury pressures. Clearly, T e decreases forincreasing mercury pressure, especially between 0.5 and 1 Pa.Again, the electron temperature in the 133 Pa lamp is lowerthan that in the 66 Pa lamp, and slightly higher closer to theRF coil (smaller |h|).Figure 8. Typical ong>Thomsonong> ong>scatteringong> spectra obtained with the 133 Pa lamp (p Hg = 0.95 Pa) at r = 29 mm and height h = 34 mm (left)and h = 13 mm (right). The spectrum on the left-hand side shows a relatively strong stray light residue in the centre.1388

ong>Thomsonong> ong>scatteringong> on an inductively-coupled gas discharge lampFigure 9. Radial electron density profiles of the 66 and 133 Pa lamps (p Hg = 0.95 Pa).Figure 10. Radial electron temperature profiles of the 66 and 133 Pa lamps (p Hg = 0.95 Pa).Figure 11. Electron densities in the 66 and 133 Pa lamps for varying mercury pressures.Figure 12. Electron temperatures in the 66 and 133 Pa lamps for varying mercury pressures.5. DiscussionIn previous work of Jonkers et al [3], the electron density andtemperature of the QL lamp were estimated on the basis ofthe measured heavy particle temperature and argon metastabledensity in the plasma. This section compares the results ofsection 4 to the findings of Jonkers et al. In addition, a numberof rough trends in n e and T e are deduced from the electronparticle and energy balances and the plasma’s operationalconditions and compared to experimental results in order toassess their reliability.1389

M J van de Sande andJJAMvanderMullen5.1. Electron particle and energy balancesThe electron density and temperature in (quasi) steady-stateplasmas of small dimensions can be related to the operationalconditions of the plasma, such as size (expressed in an electrondensity gradient length ne ), power density ε, and pressure p.This relation is established by the electron particle and energybalances [3, 20–22]. The former mainly determines T e , whilethe latter is related more directly to n e .A simplified version of the steady-state electron particlebalance,D an e n Hg1 SHg ion ≈ n e , (9) 2 n eequates electron production by ionization (left-hand side) toelectron loss by ambipolar diffusion (right-hand side). Recombinationis negligible due to the strongly ionizing character ofthe discharge, as follows from measured values of n e and T e .The ionization rate is mainly determined by mercurybecause of its relatively low ionization energy (10.43 eV versus15.76 eV for argon). Therefore, the ionization rate is theproduct of the ground state mercury density n Hg1and aneffective ionization rate coefficient S Hgionof mercury, whichis a strong function of the electron temperature and can bedetermined from a CRM [19]. The diffusion rate depends onthe electron density gradient length ne and the coefficient forambipolar diffusion D a . This diffusion coefficient is inverselyproportional to the argon density n Ar , argon being the mostimportant elastic collision partner of ions in the plasma.The simplified steady-state electron energy balance,ε RF ≈ ε rad + n e [n Hg1 SHg ion (I Hg + 3 2 k BT e )+n Ar 3Q heat 2 k B(T e − T h )], (10)states that the energy delivered to the electrons by the RF coilis converted into radiation, leads to ionization of mercury, andheats the argon gas.The ionization term is the product of the ionizationrate n e n Hg1 SHg ion(cf equation (9)) and the energy it costs toionize a mercury atom (I Hg ) and to heat the electron to T e .Heating of the argon buffer gas, which is mainly due to elasticcollisions of electrons with argon atoms, is enhanced by higherelectron and argon densities and a larger difference betweenthe temperatures of electrons (T e ) and heavy particles (T h ). Theparameter Q heat is proportional to the effective rate coefficientfor momentum transfer from electrons to heavy particles. Theradiative term depends on the density of excited mercury in theplasma and the escape factor esc of resonant radiation. Whenε rad is small compared to other terms in equation (10), it followsthat n e directly scales with ε RF . In the field of surface wavedischarges, the proportionality constant is referred to as θ, andthe relation between n e and ε RF is known as the θ theorem [23].5.2. Observed trendsA number of trends of n e and T e related to the distance to the RFcoil and argon and mercury pressures can be deduced from theparticle and energy balances given above. Here these trendsare compared to the experimental results.At increasing distances from the RF coil, the electric fieldstrength decreases due to the smaller magnetic flux and the skineffect, thus leading to a lower power density ε RF . In addition,the radiative losses ε rad can be expected to increase towards theedge of the lamp because of the increasing escape factor esc .Thus, equation (10) predicts n e to decrease further from the RFcoil (either radially or axially), as observed (cf figure 9). Thistrend is comparable to the decreasing n e along the direction ofwave propagation in surface wave discharges [23]. Towards thedischarge wall, diffusive losses of charged particles increase,which is reflected by a shorter gradient length ne . Thenequation (9) requires that the ionization rate be higher, so thatT e must be higher. This effect is weakly visible in figure 10,but is expected to be more pronounced at the central dischargewall, where no measurements could be done. However, largetemperature gradients are not likely to be found due to the highelectron heat conductivity.A higher argon pressure p Ar results in a lower diffusioncoefficient D a in equation (9). Thus, this equation predictsa smaller ionization rate, or equivalently a lower T e , whichis seen in figures 10 and 12. The smaller ionization termn Hg1 SHg ionin equation (10) is expected to lead to higher electrondensities. In addition, the plasma is located closer to the RFcoil for higher argon pressures [2]. This enhances the couplingbetween the coil and the plasma, so that ε RF increases and n eincreases correspondingly. Comparing the measurements ofn e at h = 18 mm in the 66 Pa lamp and h = 13 mm in the133 Pa lamp, the expected increase of n e with p Ar is indeedfound in figures 9 and 11.A higher mercury pressure p Hg allows for a smallerionization rate coefficient S Hgionin the particle balance (9), andthus a lower electron temperature. This effect is clear fromfigure 12. The light production of the lamp is also affected byp Hg . Via the electron energy balance (10), this influences theelectron density. Figure 11 shows only a weak dependence ofn e on the mercury pressure since ε rad is small compared to ε RF .5.3. Comparison to previous resultsBased on diode laser absorption measurements [2], Jonkerset al estimated n e and T e from the heavy particle energy balanceand an argon CRM [3]. For the 66 Pa lamp, they estimatedn e ≈ 1 × 10 19 m −3 and T e ≈ 1.5 eV, while for the 133 Pa lampn e ≈ 2 × 10 19 m −3 and T e ≈ 1.2 eV were estimated. Thesevalues apply in the most active region of the plasma, i.e. wheren e is at a maximum. Unfortunately, this maximum is locatedcloser to the load coil than could be measured with the presentexperimental lamps.The highest electron densities measured in this studyagree fairly well with the results of Jonkers. Note that thehighest electron density in the 133 Pa lamp was measured atapproximately 13 mm above the RF coil (see the right-handside of figure 9). Therefore, the maximum value of n e isexpected to be slightly higher than measured.The measured electron temperatures are systematicallylower than those calculated by Jonkers. This may be attributedto the different conditions used in the present paper. Firstly,Jonkers only gives values of n e and T e at smaller radialpositions, where no measurements could be done. It is tobe expected that, due to the steep electron density gradient ne near the core of the lamp and associated high electronlosses, the electron temperature is higher at that position(cf equation (9)).1390

ong>Thomsonong> ong>scatteringong> on an inductively-coupled gas discharge lampSecondly, the amalgam in the lamp was not heated andthermostrated during the experiments of Jonkers. Therefore,the amalgam is likely to have been much colder and hencethe mercury pressure p Hg much lower. As shown insection 5.2, a low mercury pressure leads to a higher electrontemperature.6. ConclusionsIn this paper, the electron density and temperature in the PhilipsQL lamp were measured with laser ong>Thomsonong> ong>scatteringong>. Forthis purpose, a low stray light TGS was built.The technique of ong>Thomsonong> ong>scatteringong> provides directaccess to the electron gas parameters, but is not easilyapplicable on low electron density plasmas contained in glass.The main problem for such a measurement is stray light.By using a TGS instead of a single spectrograph, the effectiveredistribution R eff (the fraction of stray light detected perspectral range) at 0.5 nm from the laser wavelength waslowered from about 3 × 10 −3 nm −1 to around 7 × 10 −9 nm −1 .The ong>Thomsonong> spectrum was not distorted significantly furtherthan 0.5 nm from the laser wavelength, so that electrontemperatures of ∼0.2 eV can readily be measured. Theelectron density detection limit is below 10 16 m −3 .For the measurements described in this paper, a numberof modifications were made to the commercially availablelamps. First of all, the experimental version of the QL lamplacks a fluorescent coating in order to have optical access tothe discharge. Secondly, quartz laser windows at Brewsterangle and far from the detection volume were mounted ontothe lamp to allow a high power laser beam to enter thedischarge. Thirdly, mercury condensation on cold spots,especially the Brewster windows, was prevented by additionalheating. Finally, a small correction was made to the argonfilling pressure of the lamp to compensate for the increasedlamp volume. Together with the high stray light rejection of thedetection system, these modifications are sufficient for reliableong>Thomsonong> ong>scatteringong> measurements on the QL lamp.The electron density and temperature measured in the QLlamp are approximately n e ≈ 10 19 m −3 and T e ≈ 1.0 eV, anddepend slightly on the operational conditions, such as the argonpressure p Ar and mercury pressure p Hg .A number of trends of n e and T e for varying p Ar and p Hgand distance to the RF coil were deduced from the electronparticle and energy balances. The measurements reproducethese trends quite well, suggesting that they can be relied on.In addition, the measured electron densities are in agreementwith those reported in the work of Jonkers et al [3]. However,the measured electron temperatures are systematically lowerby approximately 0.3–0.4 eV. This is most likely caused by thedifference in the experimental conditions, such as the radialposition and mercury pressure.AcknowledgmentsThe authors would like to express their gratitude toMJFvandeSande, J F C Jansen andHMMdeJong for theirassistance with the present experimental system, J Jonkers forfruitful discussions, and JWAMGielen, FAWKuijpers andH Vogels for providing the experimental lamps. This workis supported by the Dutch Technology Foundation STW andPhilips Lighting Eindhoven.References[1] Waymouth J F 1971 Electric Discharge Lamps (Cambridge,MA: MIT Press)[2] Jonkers J, Bakker M and Van der Mullen JAM1997J. Phys. D: Appl. Phys. 30 1928[3] Jonkers J and Van der Mullen JAM1999 J. Phys. D: Appl.Phys. 32 898[4] Johnston C W and Van der Mullen JAM2002[5] Bakker L P, Freriks J M, De Hoog F J and Kroesen GMW2000 Rev. Sci. Instrum. 71 2007[6] Siemon R E 1974 Appl. Opt. 13 697[7] Fellman J and Lindblom P 1977 Appl. Opt. 16 1085[8] Greenwald M and Smith WIB1977 Appl. Opt. 16 587[9] Kono A and Nakatani K 2000 Rev. Sci. Instrum. 71 2716[10] Sheffield J 1975 Plasma Scattering of ElectromagneticRadiation (New York: Academic)[11] Muraoka K, Uchino K and Bowden M D 1998 Plasma Phys.Control. Fusion 40 1221[12] Kempkens H and Uhlenbusch J 2000 Plasma Sources Sci.Technol. 9 492[13] De Regt J M, Engeln RAH,DeGroote FPJ,Van der Mullen JAMandSchram D C 1995 Rev. Sci. Inst.66 3228[14] Van de Sande M J 2002 Laser ong>scatteringong> on low temperatureplasmas—high resolution and stray light rejectionPhD Thesis, Eindhoven University of Technology[15] Penney C M, St Peters R L and Lapp M 1974 J. Opt. Soc.64 712[16] James J F and Sternberg R S 1969 The Design of OpticalSpectrometers (London: Chapman and Hall)[17] Hecht E and Zajac A 1987 Optics (London: Addison Wesley)[18] Noguchi Y, Matsuoka A, Bowden M D, Uchino K andMuraoka K 2001 Japan. J. Appl. Phys. 40 326[19] Van Dijk J, Hartgers B, Jonkers J and Van der Mullen JAM2000 J. Phys. D: Appl. Phys. 33 2798[20] Lieberman M A and Lichtenberg A J 1994 Principles ofPlasma Discharges and Materials Processing (New York:Wiley)[21] Van der Mullen JJAMandJonkers J 1999 Spectrochim. Acta54B 1017[22] Van de Sande M J, Van Eck P, Sola A andVan der Mullen JJAM2001 Spectrochim. Acta B[23] Ferreira C M and Moisan M 1988 Phys. Scr. 38 3821391

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