Vibrational CARS measurements in a near-atmospheric pressure plasma jet in nitrogen: I. Measurement procedure and results
Jan Kuhfeld, Nikita Lepikhin, Dirk Luggenhölscher, Uwe Czarnetzki
VVibrational CARS measurements in anear-atmospheric pressure plasma jet in nitrogen:I. Measurement procedure and results
J Kuhfeld, N Lepikhin, D Luggenh¨olscher, U Czarnetzki
Ruhr University Bochum, Institute for Plasma and Atomic Physics, GermanyE-mail: [email protected]
Abstract.
The non-equilibrium ro-vibrational distribution functions ofmolecules in a plasma can heavily influence the discharge operation and theplasma-chemistry. A convenient method for measuring the distribution functionis by means of coherent anti-Stokes Raman scattering (CARS). CARS spectra aremeasured in a ns-pulsed plasma between two parallel, 1 mm spaced molybdenumelectrodes in nitrogen at 200 mbar with pulse durations of 200 ns / 250 ns and arepetition rate of 1 kHz. The CARS spectra are analyzed by a fitting routine toextract information about the vibrational excitation of the nitrogen molecules inthe plasma. It is found that during the discharge the vibrational distribution for v (cid:46) Submitted to:
J. Phys. D: Appl. Phys. a r X i v : . [ phy s i c s . p l a s m - ph ] F e b
1. Introduction
Since several years atmospheric pressure plasmas are a very active research topicwith respect to multiple practical applications, e.g. plasma assisted ignition [2, 3],plasma catalysis [4–7] and plasma medicine [8–11]. Many of these applications dependon the unique chemical properties of atmospheric pressure plasmas which have theirroots in the different non-equilibrium conditions in these kinds of discharges [12]. Avery important non-equilibrium can be found in the vibrational distribution functions(VDFs) of molecular plasmas. Strong excitation through resonant interaction withthe plasma electrons and the anharmonicity of the vibrational potential usually leadto a strong overpopulation of the higher vibrationally excited states compared toa Boltzmann distribution [12]. On the other hand the translational and rotationaltemperatures can be very low (close to room temperature) due to the low couplingof the electrons to the translational and rotational modes of the molecules and slowvibrational-translational (V-T) relaxation [12]. This means that energy to be usedin chemical reactions can be stored in the gas without increasing the translationaltemperature. There are several ways how this can be leveraged in industrialapplications. For example catalysts could potentially be used at gas temperaturesbelow their traditional operating temperature which could increase their durabilityand efficiency [7, 13]. Another process of interest over the last years is carbon dioxidedissociation by step wise vibrational excitation which might be more efficient thandirect dissociation by electron impact [14–16].All these examples clearly state an interest in tailoring the vibrational excitation ina plasma for the specific application by using different plasma sources, e.g. (surface)dielectric barrier discharges, plasma jets or micro-structured array devices. For thispurpose the influence of the plasma parameters on the VDF needs to be understoodin detail, so kinetic modelling as well as detailed measurements need to be performedin parallel for different discharge types and conditions.Measurements of the VDF can be performed for some gases or vibrational modes byTDLAS or FTIR [7, 13, 17], but this is not possible in other cases as e.g. nitrogenor the symmetric stretch mode of carbon dioxide. In these cases other methodsneed to be employed like spontaneous Raman scattering or coherent anti-StokesRaman scattering (CARS). A detailed description of previously performed CARS andspontaneous Raman scattering measurements in plasmas is given in [18] so here only ashort summary is provided. Some of the first CARS measurements in nitrogen plasmasknown to the authors were performed in low pressure DC discharges for example byShaub et al [19] who also developed a scheme for the evaluation of CARS spectra withnon-Boltzmann vibrational distributions. Their scheme is valid under the assumptionthat the bulk of the molecules follows a Boltzmann distribution and only a very smallnumber is excited to higher vibrational states, leaving the distribution of the bulk.This might be the case for low pressure DC discharges but for pulsed high currentplasmas a significant amount, i.e. in the range of some 10 %, of the molecules can beexcited during one pulse.Measurements in pulsed nitrogen plasmas where performed among others byValyansky et al [20], Deviatov et al [21], Vereshchagin et al [22], and Montello et al [23]. In general the vibrational excitation in these works can be describedon three time scales: The excitation during the discharge (mainly) by resonantelectron collisions usually happens on time scales of nanoseconds, the redistributionof vibrational-vibrational (V-V) transfer collisions in the first microseconds after thepulse and the loss of vibrational excitation by diffusion or deactivation at the walls,typically some hundreds of microseconds or a few milliseconds after the discharge.Depending on the experimental conditions, loss through V-T collisions can also bean important mechanism. In some of the mentioned works an increase of the lowerlying vibrational excited states in the first microseconds of the afterglow was observedwhich could not be explained purely by V-V transfer mechanisms leading the authorsto the conclusion that quenching from metastable electronic states [21,23] might have asignificant impact on the vibrational excitation. This was not observed in [20] and [22]where no significant deviation from the populations predicted by V-V models was seen.More recently Yang et al [24] tried to explain the measurement results by numericalmodelling but were also not able to reproduce the increase of the total number ofvibrational quanta observed in the measurements. Consequently, the mechanismbehind this process is still an open research question and will certainly be different fordifferent discharge conditions and geometries.In this work measurements of the VDF of nitrogen are performed in an nearatmospheric pressure ns-pulsed plasma jet with plan parallel molybdenum electrodessimilar to the ones used in [25]. In contrast to some earlier works mentioned above thevibrational distribution is not determined by comparing the intensity of the differentpeaks in the CARS spectrum. Instead, it is determined by fitting a calculatedspectrum like it is traditionally done for rotational temperature measurements byCARS [26], but on a larger spectral range to capture multiple vibrational transitions.
2. CARS method
There are multiple reviews about coherent anti-Stokes Raman scattering (CARS) as adiagnostic method for temperature and concentration measurements in gases and othermedia [27–31], so here we will only give a short summary of the aspects relevant for thiswork. Coherent anti-Stokes Raman scattering is a non-linear optical process of thirdorder, in which three electromagnetic waves with angular frequencies ω P u , ω S and ω P r induce a non-linear polarization in a medium at frequency ω aS = ω P u + ω P r − ω S . ω P u , ω S , ω P r and ω aS are called pump, Stokes, probe and anti-Stokes beam respectively.The energy scheme of the process is illustrated in figure 1 for two transitions. Theprocess is resonant if ω P u − ω S is close to a state transition of the used medium.In this work the transition energy (cid:126) ω k belongs to vibrational transitions of nitrogen.The intensity of the generated anti-Stokes beam is proportional to the square of theso called CARS susceptibility and the product of the three input laser intensities: I aS ( ω R ) ∝ | χ CARS ( ω R ) | I P u I P r I S ( ω R ) (1)where ω R = ω P u − ω S is the Raman shift. The CARS susceptibility in the pressurebroadening regime for parallel polarized light far from electronic resonances can bewritten as χ CARS ( ω ) = χ NR + χ R ( ω ) = χ NR + (cid:88) k a k ω k − ω − i Γ k (2)where the sum includes all possible ro-vibrational transitions k with the energydifference (cid:126) ω k = E ( v k,f , J k,f ) − E ( v k,i , J k,i ) and the linewidth (HWHM) Γ k . TheFigure 1: Energy scheme of the CARS process. ω pu , ω S , ω pr and ω aS denote theangular frequencies of the pump, Stokes, probe and anti-Stokes beams respectively. ω k is the angular frequency corresponding to a vibrational transition of the probedmolecule. The prime denotes a second transition with lower energy (e.g. because ofthe anharmonicity of the vibrational potential) enforcing a slightly different Stokes ω S (cid:48) and anti-Stokes ω aS (cid:48) frequency.Table 1: Dunham coefficients Y ij in units of cm − . The data marked with ( a ) isfrom [32], ( b ) from [33] and ( c ) from [34, 35]i j 0 1 2 30 0 1.998 ( c ) − . × − c )
01 2358.535 ( a ) − . ( a ) − . × − b ) − . × −
13 ( b ) ( a ) − . × − a ) − . × −
10 ( b ) − . × − a ) − . × − a ) E ( v, J ) = (cid:88) i,j Y ij ( v + 12 ) i ( J ( J + 1)) j (3)With the assumptions above the amplitude of the lines depend on the populationdifference between the lower and the upper state of the transition ∆ N k = N k,l − N k,u and the differential cross section for spontaneous Raman scattering: a k = (cid:18) c (cid:126) ω S (cid:19) ∆ N k d σ dΩ (cid:12)(cid:12)(cid:12)(cid:12) k . (4)The Raman cross section for the Q branch (∆ v = 1 , ∆ J = 0) can be written as [26,35]d σ dΩ (cid:12)(cid:12)(cid:12)(cid:12) Q = (cid:16) ω S c (cid:17) (cid:126) ω (cid:20) α (cid:48) M + 445 γ (cid:48) M b JJ (cid:21) ( v + 1) (5)The cross sections for the O and S branch are given by [26, 35]d σ dΩ (cid:12)(cid:12)(cid:12)(cid:12) O = (cid:16) ω S c (cid:17) (cid:126) ω γ (cid:48) M b JJ +2 ( v + 1) C O ( J ) (6)d σ dΩ (cid:12)(cid:12)(cid:12)(cid:12) S = (cid:16) ω S c (cid:17) (cid:126) ω γ (cid:48) M b JJ − ( v + 1) C S ( J ) (7)with the centrifugal force corrections [26] C O ( J ) = (cid:18) B e ω e µ (2 J − (cid:19) (8) C S ( J ) = (cid:18) − B e ω e µ (2 J + 3) (cid:19) (9)In the equations above ω is the oscillator frequency of the molecule, α (cid:48) M and γ (cid:48) M arethe squared isotropic and anisotropic derived polarizabilities over the reduced mass ofthe vibration, B e and ω e the Herzberg molecular parameters and b JJ = J ( J + 1)(2 J − J + 3) (10) b JJ +2 = 3( J + 1)( J + 2)2(2 J + 1)(2 J + 3) (11) b JJ − = 3 J ( J − J + 1)(2 J −
1) (12)are the Placzek-Teller coefficients for diatomic molecules [35].The constants α (cid:48) M and γ (cid:48) M in (5),(6) and (7) are calculated following the approachof [26] from experimental measurements of the Q branch cross section for v = 0 → σ Ω (cid:12)(cid:12)(cid:12)(cid:12) Q,v =0 ≈ (cid:126) ω S ω c α (cid:48) M (13)and the Q branch depolarization ratio ρ J = 3 b JJ ( γ (cid:48) /α (cid:48) )
45 + 4 b JJ ( γ (cid:48) /α (cid:48) ) . (14)While the line positions ω k in (2) depend only on the molecular parameters, thelinewidths Γ k depend on the gas mixture, the pressure and the temperature. Thereexist multiple scaling laws for the linewidths in nitrogen, for example the so calledpolynomial-differential exponential gap law (PDEGL) or the modified exponentialgap law (MEGL) [36]. In this work the linewidths are calculated with [36]Γ j = (cid:88) i>j γ ij . (15)Note the different index notation compared to the one used in (2) where the index k corresponds to a transition between to ro-vibrational states. In (15) i, j correspond torotational quantum numbers. The relation between the two notations is that - for aQ branch transition - j is the rotational quantum number which stays constant duringthe transition k . For O and S branch transition the rotational quantum numbers u and l for the upper and lower state respectively are different and the line width fortransition k is calculated asΓ k = 12 (Γ u + Γ l ) . (16) γ ij in the above equations is the collisional transfer rate for rotational states j → i . Ifthe rotational states are Boltzmann distributed detailed balance requires for the backand forth rates: g ( i ) exp( − E i /k B T ) γ ji = g ( j ) exp( − E j /k B T ) γ ij (17)where g are the statistical weights for the rotational states. In this work the MEGLis used which gives for the uprates [36] γ ji = pα − e − m − e − mT/T (cid:18) T T (cid:19) / (cid:18) . E i /k B T ∆1 + 1 . E i /k B T (cid:19) exp( − β | ∆ E ji | /k B T ) (18)where p is the pressure in bar and T the gas temperature (in the following discussionsassumed to be equal to the rotational temperature). The parameters for nitrogen are α = 0 . − bar − , β = 1 .
67, ∆ = 1 . m = 0 . T = 295 K.In this context it should be mentioned that the line profile in (2) is only valid in lowor medium pressures as it assumes that the lines are isolated. For pressures close toatmospheric pressure this is not necessarily true and more complex line shapes arerequired like they are given in the rotational diffusion model or the exponential gapmodel [36]. To verify if the isolated line model is appropriate under the conditions inthis work (nitrogen at 200 mbar) nitrogen CARS spectra of the Q branch transition v = 0 → Raman shift / cm − C A R SS i g n a l /a . u . Figure 2: Comparison of spectra calculated with the isolated lines model (dashed)compared to calculations with the exponential gap model (solid) in pure nitrogen( T = 350 K) at 1 bar (red) and 200 mbar (blue).rotational temperature is naturally lower.A popular approach to determine the vibrational distribution from these low-resolutionspectra is to first normalize the spectrum to either the Stokes laser spectrumor a non-resonant spectrum from another gas without vibrational resonances inthat wavelength region. Then the square root of the normalized spectrum istaken and for each transition the integral over the corresponding peak I v,v +1 iscalculated. Under the assumption that the non-resonant and the real part of theresonant susceptibility are negligible compared to the imaginary part of the resonantsusceptibility, χ NR , Re( χ R ) (cid:28) Im( χ R ), it follows that I v,v +1 ∝ ∆ N v,v +1 ( v + 1) , (19)where the factor v + 1 accounts for the dependence of the Raman cross section on thevibrational quantum number (see (5)).As this approach relies heavily on the made assumptions, which are certainly not validfor small admixtures of the probed gas species [36] and probably also not true for theweak signals of the higher vibrational states, in this work the population densities areextracted by fitting the full theoretical spectra to the measured ones.To calculate the population differences in the susceptibility expression different modelsare used depending on the corresponding conditions. One possibility would be toassume that the vibrational states are Boltzmann distributed but with a differenttemperature than the rotational states like it was done for example by Messina et al [39]: N ( v, J ) = g ( J ) Z e − E ( v,J ) − E ( v, kBTrot × e − E ( v, − E (0 , kBTvib (20)with the partition function Z = (cid:88) v,J g ( J )e − E ( v,J ) − E ( v, kBTrot × e − E ( v, − E (0 , kBTvib (21)and T vib (cid:54) = T rot . Another approach would be the Treanor distribution assumingdominant V-V transfer collisions between the molecules: N ( v, J ) = g ( J ) Z e − E ( v,J ) − E ( v, kBTrot × e − v ( E (1 , − E (0 , kBTvib × e − v ( E ( v, − E (1 , kBTrot (22)with Z = (cid:88) v,J g ( J )e − E ( v,J ) − E ( v, kBTrot × e − v ( E (1 , − E (0 , kBTvib × e − v ( E ( v, − E (1 , kBTrot . (23)The degeneracy of the rotational states is given by g ( J ) = (cid:26) J + 1) , if J even3(2 J + 1) , if J odd. (24)Both distributions assume a single vibrational temperature and are for thetemperatures and relatively low vibrational states measured in this work essentiallyindistinguishable considering the uncertainty of the CARS measurements.As in previous measurements of the ro-vibrational distribution [20–23], here, it wasfound that a single vibrational temperature is not sufficient to fully describe thevibrational distribution for v >
3. Therefore, here a distribution function consideringtwo vibrational temperatures, a cold and a hot one, is introduced similar to theone used in [40]. The subtle difference compared to [40] is that the hot part of thedistribution only includes states with v ≥
1. This is rooted in the interpretation thatthe hot distribution is made up by molecules which are excited during the currentdischarge cycle. The further motivation of this two-temperature distribution function(TTDF) is discussed in more detail in the companion paper [1] and here only theformula is given: N ( v, J ; T r , T vib,c , T vib,h , R h ) = g ( J )e − E ( v,J ) − E ( v, kBTrot × (cid:104) − R h Z c e − E ( v, − E (0 , kBTvib,c + R h Z h e − E ( v, − E (0 , kBTvib,h (cid:124) (cid:123)(cid:122) (cid:125) for v> (cid:105) (25)with the partition function for the cold molecules Z c = (cid:88) v,J g ( J )e − E ( v,J ) − E ( v, kBTrot × e − E ( v, − E (0 , kBTvib,c (26)and Z h = (cid:88) v> ,J g ( J )e − E ( v,J ) − E ( v, kBTrot × e − E ( v, − E (0 , kBTvib,h (27)for the hot molecules.The last condition investigated in this work is several microseconds after the dischargepulse. On this time scales the V-V collisions determine the temporal behavior andthe two-temperature description is not valid anymore. Indeed, all of the distributionsmentioned above fail in this regime. To make a distribution function independentanalysis possible only the Q branch, ∆ v = 1 , ∆ J = 0 is considered.If the rotational states in a vibrational level v follow a Boltzmann distribution f v ( J, T v,rot ) with rotational temperature T v,rot , the population difference for a giventransition v → v + 1; J is∆ N v,v +1; J = N v f v ( J, T v,rot ) − N v +1 f v +1 ( J, T v +1 ,rot ) (28) ≈ ( N v − N v +1 ) f ( J, T rot )= ∆ N v,v +1 f ( J, T rot )Here, in the second step it is assumed that the rotational temperature in thedifferent vibrational states is the same and that the vibrational corrections to therotational distributions are negligible. In this way the fitting parameters concerningthe vibrational states are reduced to ∆ N v,v +1 . To benchmark our CARS code and the determination of vibrational temperatures fromthe fitting parameters several spectra are generated by the popular CARSFT code [37]with a spectral resolution similar to our experiments for thermal equilibrium conditionsand evaluated by our fitting routines assuming Boltzmann distributed vibrational androtational states where T rot and T vib are independent of each other. An example fitfor an equilibrium temperature of 2000 K is shown in figure 3. In figure 4 the fittingresults are shown for several spectra generated by the CARSFT code. The agreementfor both the rotational and the vibrational temperature is very good over the wholerange ,and it is reasonable to assume that the code used in this work accuratelydescribes real CARS spectra in the given temperature range even if T rot (cid:54) = T vib .
3. Electric field measurements
To understand the plasma processes leading to the measured ro-vibrationaldistributions knowledge about the electric field in the discharge is essential. Tomeasure the electric field value in the discharge the Electric Field Induced SecondHarmonic generation (E-FISH) technique [41–50] is used. It is a third-order nonlinearprocess involving an electric field of a light wave with frequency ω (laser emission)and an external applied electric field, E . As a result, light with doubled frequency isgenerated with intensity proportional to E : I (2 ω ) = kN I laser E , (29)where k is a constant value depending on the gas mixture, its susceptibility and theoptical system, N is the gas density and I laser the laser pulse energy.To obtain the absolute value of the electric field a calibration is necessary.Signal intensities at known electric field values are usually measured to determinethe proportionality coefficient between I (2 ω ) /I laser and E . Without the plasmathe electric field is Laplacian and depends only on the discharge cell geometry andthe voltage applied to the electrodes. Taking the discharge cell configuration intoaccount, see figure 9, it is assumed that the electric field is uniform in the vicinityof the measurement points and corresponds to the capacitor like configuration with E = U/d , where U is the applied voltage and d = 1 mm is the inter-electrodegap. It was shown [50] that if a DC voltage is used to provide the Laplacian field0 s C A R S s i g n a l /a . u . CARSFTThis work − . − . . . . Raman shift / cm − R e s i du a l Figure 3: CARSFT [37] spectrum at T = 2000 K and fit by the code developed inthis work with independent vibrational and rotational temperatures T vib = 2000 Kand T rot = 1996 K.the slope of the calibration curve, I (2 ω ) /I laser vs E , may be too low leading to anoverestimation of the electric field in the discharge. It was proposed that the appliedfield is shielded by the charges generated due to tightly focused laser emission, thusthe field in not Laplacian even without the discharge. If a DC voltage is applied, thesecharges are separated between the electrodes by the constant electric field, drift to theelectrodes and, thus, do not recombine forming an electric field, which shields theapplied one. To avoid this problem it was proposed [50] to use nanosecond pulses ata low repetition rate instead of DC voltage. The same approach is used in this work.The calibration curve obtained with 150 ns pulses with sub-breakdown amplitude ispresented in figure 5. It is clearly seen that the PMT signal normalized by the laserenergy linearly depends on the square of the applied electric field in accordance with(29). The parameters of the fit are used to obtain the longitudinal electric field value1 CARSFT temperature / K F i tt e m p e r a t u r e / K CARSFTRot. temperatureVib. temperature
Figure 4: Comparison of the vibrational and rotational temperatures extracted bythe fitting routine and the equilibrium temperatures used to produce the CARSFTspectra. The diagonal line corresponds to perfect agreement between theoretical andfitted temperatures.from the measured signal intensity during the discharge. It should be noted here, thatthe gas temperature - and therefore the particle density - is different in the discharge(see section 5) than in the calibration performed at room temperature, this has to betaken into account.
4. Experimental setup
The experimental setup used in this work consists of optical setups for the CARS andE-FISH measurements and the electrical setup of the plasma jet. The optical setupsare synchronized with the discharge by a synchronization unit.
The optical setup - a modified version of the one used in [51] and [52] for CARS-based electric field measurements - is shown in figure 6. The second harmonic of aninjection seeded Nd:YAG laser (532 nm) is used both as pump laser for two dye lasersand as pump beam in the CARS process. One of the dye lasers is a narrowbanddye laser (NBDL), which is used as probe beam. The laser emission at 560 nm isproduced by a Rhodamine 6G dye solution and a spectral width of about 0 .
05 cm − ( U/d ) / ( kV / cm ) n o r m a li ze d s i g n a l /a . u . ExperimentLinear fit
Figure 5: Calibration curve used for E-FISH measurements obtained with 150 nsrectangular pulses at 10 Hz: measured second harmonic intensity normalized by thelaser energy as a function of square of applied Laplacian electric field strength(symbols) together with the linear fit (solid curve).is reached with a double grating configuration. Here, light with 560 nm was chosenfor the probe beam to be able to perform CARS measurements in carbon dioxide andnitrogen simultaneously [53] at a later stage. In the broadband dye laser (BBDL) thedouble grating configuration for the wavelength selection is bypassed by a mirror toallow broadband operation. The desired spectrum of the BBDL - which is monitoredby a broadband spectrometer - is reached by using a mixture of Pyrromethene 597and Rhodamine B/101. Initially a mixture of Pyrromethene 597 and Pyrromethene650 was used as in [54], but was found to drift to lower wavelengths too quickly. Asan attempt to increase the lifetime of the mixture Pyrromethene 650 was replaced bythe two Rhodamine dyes. To adjust the temporal overlap of the three laser beamstwo delay stages are used: One for the part of the Nd:YAG beam which is used inthe CARS process and the other one for the pump beam of the BBDL. All threelaser beams are first attenuated to pulse energies around 5 mJ and then focused tothe probe volume by an achromatic lens with 50 cm focal length. A three-dimensionalfolded BOXCARS [55] geometry is used as depicted in figure 7 with a spatial resolutionof about 1 cm along the laser path and a few 100 µ m perpendicular - defined by theoverlapping volume of the three laser beams. The anti-Stokes signal beam passesthrough a low pass filter to reduce stray light from the lasers and is guided to theCARS spectrometer. Furthermore, a photo diode is used to measure the timestamp of3 USB HV Nd:YAG BBDLNBDL
CARSSpectrometer
Figure 6: Optical setup of the CARS measurements. The broadband dye laser(BBDL) and the narrowband dye laser (NBDL) are both pumped by the injectionseeded Nd:YAG laser. The spectrum of the BBDL is recorded during themeasurements with a compact USB spectrometer (USB). Further information aboutthe setup are given in the text. xyz yz
Figure 7: Three-dimensional phase matching in folded BOXCARS geometry. Fortechnical reasons in this work only the blue anti-Stokes beam is collimated (see alsofigure 6).4
C1 C2 C3 C4 EXT k Ω Ω SyncPDSyncHV- Voltage probe Current probe
Figure 8: Electrical setup of the plasma jet.the laser on the oscilloscope, which also measures the current-voltage waveforms of theplasma jet. The trigger of the Nd:YAG laser, the spectrometers and the oscilloscope(Lecroy WaveSurfer 510) are synchronized by a synchronization unit to allow theaccumulation of single shot measurements. Finally, all measured data are collected bya custom made DAQ software on the computer.
The emission of a Nd:YAG laser (EKSPLA SL234) at 1064 nm with a pulse durationof 100 ps is focused to the middle of the discharge gap by a lens with focal lengthof 200 mm. The light at the second harmonic (532 nm) generated in presence of theexternal field is separated from the fundamental harmonic by a dichroic mirror anddetected by a photomultiplier tube (PMT; Hamamatsu H11901-210) with laser linefilter (Thorlabs FL532-1) installed at its entrance. For the schematic view and moredetailed description of the experimental setup used for the measurements of the electricfield, please see [50], where a discharge with the same geometry was investigated.
The electrical setup of the plasma jet is depicted in figure 8.A negative DC high voltage (Heinzinger LNC 6000-10neg) is applied to the input of ahigh voltage switch (Behlke HTS 81). In order to protect the switch and increase thedischarge stability the current is limited to <
30 A by a 255 Ω series resistor betweenswitch and anode of the plasma jet. Additionally, a 2 kΩ resistor ensures that residual5
Front ViewSide View
Gas Flow Gas FlowGas Flow
CARS Volume 1 mm1 mm20 mm
Figure 9: Front and side view of the discharge jet. The 1 mm gap between theelectrodes is enclosed by two glass plates. One of the glass plates has a smallborehole in the middle which serves as inlet for the gas flow. From the center of thedischarge gap the gas travels to the exits on both sides yielding two identicaldischarge channels with a cross section of 1 mm and a length of 10 mm.charges are removed after each discharge pulse. The voltage at the cathode relativeto ground is measured by a high voltage probe (Lecroy PPE6kV) and the current ismeasured between the anode and ground by a current probe (American Laser Systems,Model 711 Standard). The Behlke switch is triggered by a 1 kHz TTL signal whichis synchronized to the 20 Hz trigger signal of the Nd:YAG laser through a frequencydivider. The duration of the high voltage pulse can be controlled by the duration ofthe trigger pulses at a digital delay generator (DDG) with a minimum pulse length of150 ns.The plasma jet itself consists of two plan parallel molybdenum electrodes with anarea of 1 mm ×
20 mm and a distance of 1 mm, which are positioned between twoglass plates. To allow operation in pure nitrogen at pressures around 200 mbar theelectrode surfaces must be prepared carefully in order to avoid arcing. For this purposethe electrodes here were polished with a final grit size of P2000.To illustrate the gas flow the front and the side view of the jet are shown in figure 9.The gas enters the electrode gap through a hole in the lower glass plate and exits on6 −
50 0 50 100 150 200 250 300 3500 . . . . . . . Time / ns V o l t ag e / k V C u rr e n t / A Figure 10: Voltage (solid lines) at the powered electrode and current (dashed lines)to ground during the discharge for the different applied voltage pulses. While themaximum peak voltage at the time of the breakdown increases for the higher appliedvoltage it can be noted that the voltage drop over the discharge gap during thefollowing plateau is nearly the same for all three conditions. The current on theother hand is significantly higher for the 4 kV case.both sides after being exposed to multiple discharge pulses due to the gas residencetime. This design allows the laser beams to pass through the jet along the electrodes.It should be noted, that the measurement volume of the CARS setup is not in thecenter of the jet as there mostly unexcited gas would be measured, which was notexposed to the discharge yet. Instead, it stretches from the gas inlet in the middle toone of the exits.To ensure a controlled atmosphere the jet is enclosed in a discharge chamber whichallows controlling the pressure and the gas flow through the jet.
5. Results and discussion
Three time resolved measurements are performed in pure nitrogen discharges fordifferent voltage pulse forms. The other input parameters are fixed for all threemeasurements: The nitrogen flow is 20 sccm at a pressure of 200 mbar and the pulserepetition frequency is 1 kHz. The pulse waveforms are illustrated in figure 10 togetherwith the resulting current waveforms.7In the following the different measurements will be referred to by the voltage appliedby the DC high voltage generator (which is not the same as the measured amplitudevoltages at the electrodes) and the pulse duration.First the results during the discharge pulse will be discussed and afterwards thedynamics during the afterglow will be presented.
Time / ns E , U / d / k V / c m U/d (3 kV, 250 ns)3 kV, 200 ns3 kV, 250 ns4 kV, 200 ns
Figure 11: Longitudinal electric field temporal development at 500 µ m from thecathode measured by E-FISH technique (symbols) for different HV pulses comparedwith the electric field profile calculated as voltage over gap ratio for the 3 kV, 250 nsmeasurement (line). As the voltage amplitude during the plateau phase is quitesimilar for all three measurements (see figure 10) only one waveform is shown.The electric field during the current plateau is shown in figure 11 for different DCvoltages used to feed the high voltage switch and different HV pulse duration. Theelectric field has constant value of ≈ . ≈
81 Td during the plateau, whichis about the same for different pulse duration. Moreover, the electric field amplitudeonly very weakly depends on the DC voltage as well. Despite the different DC voltage,after the breakdown the cathode voltage is about the same, see figure 10. This can beexplained by a higher electron density generated during the breakdown at the higherDC voltage leading to a higher electric current and consequently a higher voltage dropat the series resistor. According to calculations with Bolsig+ [56] using the IST-Lisbondata set [57] the measured field corresponds to a mean electron energy of 1 . Raman shift / cm − s C A R S s i g n a l /a . u . MeasurementFit with one vib. temperatureFit with two vib. temperatures − . − . − . − . − . . . Raman shift / cm − R e s i du a l /a . u . Figure 12: Comparison of a measured spectrum with theoretical spectra forBoltzmann distributed vibrational states with T vib = 1800 K and for atwo-temperature distribution with T vib,c ≈ T vib,h ≈ t = 300 ns in the measurement set for an applied voltage of4 kV (approx. 50 ns after the pulse).electron temperature of T e = 1 . R h and T vib,h are determined from the local Jacobian ofthe corresponding best fit solutions. During the discharge pulse the fraction ofvibrationally hot molecules, R h , increases linearly. This agrees well with the essentiallyconstant current and electric field after the ignition suggesting constant excitation9 . . . . . Time / ns R h Figure 13: Time development of the fraction of vibrationally hot molecules R h in(25). As guide for the eye the starting point of the voltage pulses is marked by theblack dashed line and the end points of the 200 ns and 250 ns pulses are marked withthe green and the orange dashed lines respectively. The uncertainties of R h aredetermined from the local Jacobian of the best fit.conditions during the whole discharge pulse. It is clearly visible, that the slope of R h is the highest for the pulse with the higher current amplitude (4 kV applied DCvoltage) while the two measurements with 3 kV applied voltage share a lower slopeand differ only by a small offset due to different initial conditions. As the electricfield is the same in all three cases, the difference in slope should be mainly caused bya higher electron density in the 4 kV case. A more detailed discussion of the slope,˙ R h , is given in the companion paper [1]. The fact, that one of the measurementsis performed with a longer pulse duration, is also reflected in figure 13 by a longerrise time of R h (note the two vertical lines at about 200 ns and 250 ns marking thecorresponding ends of the pulses).In regard to the temperature of the hot population it has to be noted that the valuesat the beginning, when the amount of excited molecules is small, are not reliable orsuitable for a direct interpretation. Firstly, at these time only states up to v = 3 can bedetected as the densities of the other states are below the detection limit. Secondly,(25) is proposed to analyze the characteristics of the newly excited molecules (forfurther details the reader is referred to the companion paper [1]). Before the dischargepulse there are no ”newly” excited molecules yet and the non-zero value of thefitting parameter R h only accounts for the small deviation from a normal Boltzmanndistribution remaining from the previous voltage pulse still visible in the excited states0 Time / ns T v i b , h / K Figure 14: Time development of the temperature of the vibrationally hot molecules T vib,h in (25). The gray areas are used to emphasize that temperatures for timeslower than 50 ns (4 kV) or 100 ns (3 kV) are not reliable for physical interpretation(see text). The uncertainties of T vib,h are determined from the local Jacobian of thebest fit. v = 1 − T vib,h suffers a large uncertainty, as it strongly depends on the higherstates, which are not detected. So, to be able to use the two-temperature distributionin its original intent the newly excited molecules need to overtake the remainingdeviation from a Boltzmann distribution. The criterion used here and in [1] is that R h needs to at least surpass two times its initial value from before the discharge, so thatthe majority of the molecules belonging to the hot distribution consists of moleculesexcited during the current discharge pulse. The data points which are excluded fromfurther discussion by the mentioned criterion are marked by a gray background infigure 14. Please note, that this criterion agrees quite well with the uncertainties of T vib,h . Considering the previous remarks it stands out that T vib,h stays constant forall three measurements in the usable range. While the 200 ns-pulse measurements for3 kV with (5200 ± ± ± − . . . . . Time / ns v i b . E n e r g y G a i n / m J . × input energy3 kV, 250 ns . × input energy4 kV, 200 ns . × input energy Figure 15: Gain of vibrational energy during the discharge pulse. The average of thefirst three data points in each data set is used as baseline, i.e. the initial vibrationalenergy before the discharge. The solid lines refer to the electrical energy coupled intothe plasma obtained from the voltage and current waveforms in figure 10 multipliedby the factors given in the legend.measurement sets. As this mainly affects the higher vibrational states due to theirweaker signal, the effect is stronger on the fitting parameter influenced by those states,namely the hot vibrational temperature T vib,h . R h on the other hand corresponds tothe total amount of newly excited molecules and as the higher vibrational states onlycontribute by a small number - even at temperatures around 5000 K - the effect issmall. This explains why there is no deviation from the expected behavior visible infigure 13. As one would expect the rotational temperature stays constant on timescales of the discharge with about T rot = (330 ±
8) K (mean value and standarddeviation over all three measurement sets). Likewise, the vibrational temperaturesof the cold bulk molecules stays nearly constant during the discharge pulse as well,but differ slightly for the different measurement sets. The two measurements with3 kV applied DC voltage are quite close to each other with (1190 ±
40) K (200 nspulse) and (1180 ±
40) K (250 ns pulse). For the 4 kV case the vibrational backgroundtemperature is slightly higher with (1300 ±
50) K.As the densities of the vibrational excited states are known from the fits, thegain of vibrational energy in the plasma volume during one discharge pulse canbe calculated relative to the average energy of the first three measurement points(see figure 15). By a comparison with the energy coupled into the plasma obtainedfrom the voltage and current waveforms in figures 10 it can be seen, that the energy2 − − − v N v / N g a s vib. TTDF ( t = 90 ns) N v max +1 ≈ N v max exp (cid:18) − E v +1 − E v k B T (cid:19) N v max +1 ≈ vib. TTDF ( t = 300 ns) N v max +1 ≈ N v max exp (cid:18) − E v +1 − E v k B T (cid:19) N v max +1 ≈ Figure 16: Comparison of the population densities obtained by the two-temperaturedistribution and the Q-branch-only fit with the two different evaluation methods.The solid and dashed lines correspond to the TTDF at different points in time, t = 90 ns and t = 290 ns respectively. The symbols in the corresponding colorsdenote the results at the same times from the Q-branch-only fits evaluated with thenewly proposed method (circles) and the traditional one (squares).coupled into vibrational modes is proportional to the total energy at all times duringthe discharge pulse. The corresponding factor is found close to 0.3 in figure 15 forall measurement sets, indicating that the coupling efficiency is roughly 30 % for allinvestigated conditions. This value agrees well with the 30 % reported by Montello etal [23] and Deviatov et al [21]. In the period between two pulses (25) is not suitable to describe the VDF of thenitrogen molecules as interaction between the bulk and the excited molecules makesit difficult to distinguish effects on the fitting parameters R h and T vib,h . Furthermore,it is not given, that the hot molecules - if this definition can still be applied - followa distribution which can be approximated by a Boltzmann distribution. For thisreason the fitting scheme discussed in the end of section 2.1 is used which yields thepopulation differences between two neighboring vibrational states (here normalized tothe total particle density of nitrogen) N v − N v +1 N gas as output parameters by consideringonly the Q branch transitions. The population differences ∆ N v = N v − N v +1 - inthe following ∆ N v is always assumed to be in arbitrary units - obtained by the fit3could now be processed further by either making assumptions on the populationdifference between the ground and the first excited state [19] or by setting thepopulation of the upper state for the highest detectable transition to zero [23]:∆ N v max = N v max − N v max +1 ≈ N v max . With v max as starting point the populationdensities can then simply be obtained by N v = N v +1 + ∆ N v . Finally, they arenormalized to (cid:80) v N v effectively yielding the fraction of molecules in state v comparedto the gas density. Obviously, the assumption N v max ≈ N v +1 /N v ≈ exp (cid:16) − (cid:126) ω e k B T vib (cid:17) (neglecting theanharmonicity for simplicity). At room temperature this ratio is indeed much smallerthan one and the above approximation is valid. But as it was shown in the previoussection that the highest vibrational states can have a temperature of about 5000 Kleading to N v +1 /N v ≈ .
5. Here the approximation is clearly not valid anymore.Therefore, in this work N v max +1 is extrapolated from N v max so that one obtains forthe population difference∆ N v max ≈ N v max − N v max exp (cid:18) − E v max +1 − E v max k B ˜ T vib (cid:19) (30) ≈ N v max (cid:20) − exp (cid:18) − E v max +1 − E v max k B ˜ T vib (cid:19)(cid:21) where ˜ T vib is estimated from the ratio of the two highest measured populationdifferences: ˜ T vib ≈ − E v max − E v max − k B ln ∆ N vmax ∆ N vmax − (31)In figure 16 our approximation (30) is compared with the traditional approximation N v max ≈ t = 90 ns is probably caused by the effect of the ”bend” of the distribution functionbetween the cold and the hot parts on the estimation of ˜ T vib in (31) - leading to aslight underestimation of ˜ T vib . It should be stressed, that while an underestimation of N v max by a factor of about 2 in the approximation ∆ N v max ≈ a priori .In figure 17 the relative population densities from the states 1 up to 4 are shownfor the measurement with 4 kV applied DC voltage. While the population of the firstvibrational state increases and the one of the second stays approximately constant,the higher states decrease on timescales smaller than about 100 µ s. These dynamicscan be attributed to V-V transfer between the molecules [1]. The general decreaseof all excited states on longer timescales was found to be mainly due to deactivationat the walls [1]. As one can already guess from figure 17 the number of vibrationalquanta does not seem to increase in the afterglow due to deexcitation of electronicallyexcited molecules as it was observed by other groups in their discharges [23]. This isshown explicitly for all three measurement sets in figure 18. The number of vibrational4 − − − − − Time / µs N v / N g a s v = 1 v = 2 v = 3 v = 4 Figure 17: Relative population densities for v = 1 , , ,
6. Conclusion
In this work, a plasma is generated by applying high voltage pulses of 200 ns and 250 nsduration to plan-parallel molybdenum electrodes in nitrogen at 200 mbar. In contrastto DBD discharges, more commonly used at these pressures, the metal electrodesallow for a nearly constant conduction current after the ignition phase of the plasmauntil the end of the pulse. The electric field in these conduction current plateaus ismeasured by the E-FISH method and found to be constant during the discharge with avalue around 81 Td for all conditions investigated here. CARS spectra were measuredfor three different high voltage pulses. To extract information from those spectramore reliable than from an analysis of the separate peak intensities a fitting routineis developed, motivated by existing CARS fitting routines for combustion systemsin thermal equilibrium [26, 35, 37] and benchmarked against the popular CARSFTFortran77 code [37]. Our fitting procedure allows for arbitrary vibrational distributionfunctions to account for different conditions during the discharge phase and in theafterglow. It was found, that the vibrational excitation during the discharge phasecan be described by a two-temperature distribution function consisting of a cold bulk5 − − . . . . Time / µs V i b . q u a n t a p e r m o l ec u l e Figure 18: Vibrational quanta per molecule for all three measurements. The bluerectangle marks the time during the discharge pulse.with a near-equilibrium temperature T vib,c ≈ > T rot making up the majorityof the molecules and a hot part accounting for the molecules which are excited duringthe discharge pulse. The fraction of hot particles R h increases close to linearly withtime and the hot temperature T vib,h stays constant. This indicates constant excitationconditions during the pulses and agrees well with the constant electric field obtained bythe E-FISH measurements and the quasi constant currents after the ignition phase (seefigure 10) both implying a constant electron density. The same behavior is seen in [51]where similar discharge conditions (conducting electrodes, atmospheric pressure andmillimeter gap size) are investigated. The nearly constant plasma conditions allowan easy analysis of the vibrational dynamics and a comparison with correspondingconstants in the literature. These are performed in a companion paper [1] and thereader is referred to there for more details. It can be summarized, that CARS is acomplicated but powerful technique for measuring vibrational distribution functionsin plasmas. Especially, the possibility to measure multiple species at once with thesame experimental setup will prove extremely useful for investigating the influence ofvibrational excitation on chemical and catalytic processes. These prospects will beinvestigated in future works with the same setup as introduced here.Additionally, the application of CARS to an excited medium like a plasma itselfprovides access to further open research questions and opportunity for investigation.E.g. the long living excited states in a plasma might influence the non-resonantsusceptibility depending on the amount of excited species as it was observed for thirdharmonic generation in a pre-excited gas [58]. While the non-resonant part of the6susceptibility is ignored by many works it can be important for higher vibrationalstates where the resonant and non-resonant parts are of comparable amplitude. Acknowledgements
This project is supported by the DFG (German Science Foundation) within theframework of the CRC (Collaborative Research Centre) 1316 ”Transient atmosphericplasmas - from plasmas to liquids to solids”.Furthermore, the authors would like to thank Igor Adamovich, Kraig Frederickson andIlya Gulko for sharing the CARSFT code and providing insights about the analysis ofCARS spectra.
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