Time-resolved spectroscopy measurements ofhydrogen-alpha, -beta, and -gamma emissions

Christian G. Parigger, Matthew Dackman,* and James O. HornkohlThe University of Tennessee Space Institute, 411 B. H. Goethert Parkway, Tullahoma, Tennessee 37388, USA

*Corresponding author: cparigge@tennessee.edu

Received 2 April 2008; accepted 28 May 2008;posted 24 June 2008 (Doc. ID 94471); published 16 July 2008

Hydrogen emission spectroscopy results are reported following laser-induced optical breakdown withinfrared Nd:YAG laser radiation focused into a pulsed methane flow. Measurements of Stark-broadenedatomic hydrogen-alpha, -beta, and -gamma lines show electron number densities of 0.3 to 4 × 1017 cm−3

for time delays of 2.1 to 0:4 μs after laser-induced optical breakdown. In methane flow, recombinationmolecular spectra of the Δν ¼ þ2 progression of the C2 Swan system are discernable in the Hβ andHγ plasma emissions within the first few microseconds. The recorded atomic spectra indicate the occur-rence of hydrogen self-absorption for pulsed CH4 flow pressures of 2:7 × 105 Pa (25psig) and 6:5 × 105 Pa(80psig). © 2008 Optical Society of America

OCIS codes: 140.3440, 300.6210, 020.3690, 300.6390, 350.5400.

1. Introduction

Laser-induced breakdown spectroscopy (LIBS) ad-dresses primarily atomic emission spectroscopy forthe purpose of determining the elemental composi-tion of gases, liquids, and solids [1,2]. More recently,applications have also included determination oftrace explosive materials in a standoff configuration[3,4]. The emission spectra may include both hydro-gen and molecular emissions. Time-resolved mea-surements allow us to separate spectrally broademissions early in the plasma decay from atomicand molecular species emissions later in the plasmadecay. In this work we study the Balmer series ofhydrogen, i.e., spectroscopic characteristics of the hy-drogen-alpha, -beta, and -gamma atomic lines duringthe microplasma decay.Investigations of Stark-broadened hydrogen emis-

sions included previously generation of laser-inducedoptical breakdown in H2 gas and measurements ofelectron number densities and excitation tempera-ture [5–8] from Hα line profiles. Subsequently, ana-lyses were extended to Hβ line profiles [9,10]including comparison of experimental results of

widths and shifts with theories. In this work we ex-tend our studies of nominal nanosecond infrared-radiation-induced optical breakdown to include Hγemissions. For the work reported here, we used apulsed, high-pressure methane flow [11]. Includedis also a typical measured and fitted spectrum ofthe Δν ¼ 0 sequence of the C2d3Πg → a3Πu Swansystem. The spectroscopic features of this diatomicmolecular spectrum overlap with the hydrogen-betaand hydrogen-gamma regions.

2. Experiment

The experimental arrangement for measurement ofthe emission spectra includes typical LIBS equip-ment, namely a nominal nanosecond Q-switched la-ser, intensified detection equipment coupled to aspectrometer, and a sample. The infrared radiationat 1064nm from a Continuum YG680S-10 Nd:YAGlaser, operated at 10Hz, is focused into the expand-ing plume of a pulsed methane gas flow. The laserbeam, of typically 75 mJ energy per pulse and 8 nspulse duration, was focused to an irradiance of typi-cally 700GW=cm2 approximately 2mm above the2 mm exit aperture of a custom-built nozzle.

The hydrogen and selected C2 molecular profileswere recorded by use of an intensified EG&G linear

0003-6935/08/3100G1-06$15.00/0© 2008 Optical Society of America

1 November 2008 / Vol. 47, No. 31 / APPLIED OPTICS G1

diode array, UV-enhanced detector, Model 1460 Prin-ceton Applied Research detector/controller opticalmultichannel analyzer. A 1/2 meter Model 500 Spec-traPro Acton Research Corporation spectrometerwas used with a 2400 groves=mm grating, blazedfor 240 nm. Emissions from the microplasma were fi-ber coupled to the spectrometer. The entrance slitwas set to 125 μm, resulting in an overall spectral re-solution of 0:12 nm, 0:11 nm, and 0:07 nm for Hγ, Hβ,and Hα measurements, respectively.Gate widths of 0:1 μs were used in a systematic re-

cording of spectra during the first few microsecondsfollowing optical breakdown. In the reported experi-ment, the plasma size grows for time delays tdelay ofthe order of 1 μs as L ½cm� − 0:1 tdelay ½μs�. For selectedtime delays of up to 2:1 μs, the laser-induced shock-wave only propagates to the nozzle surface; there-fore, reflected shocks did not affect themeasurement.Typical results for the electron number density are

in the range of 0.3 to 4 × 1017 cm−3 for time delays of2.1 to 0:4 μs after laser-induced optical breakdown.For these electron number densities, the electron ex-citation temperature was determined previously inthe range 10; 000–100; 000K using Boltzmann plots[5]. The Boltzmann plot approach for hydrogen emis-sions poses difficulties due to incompletely resolvedprofiles. Moreover, free-electron background radia-tion is superposed to the spectrally-wide or over-lapping atomic Balmer lines, e.g., hydrogen-betaand hydrogen-gamma.The experiments reported here were designed to

record emission spectra for delays of 0.4 to 2:1 μs.We elected a gate width of 0:1 μs. In principle, plasmadecay occurs during a finite gate-open time. Themea-sured electron number density, inferred from the fullwidth at half-maximum (FWHM), represents anaverage during the 0:1 μs gate. For delays in the firstfew hundred nanoseconds, use of a shorter gatewidth is indicated. For example, we reported numberdensities in the range of 1019 cm−3 early in the plas-ma [10] when using hydrogen gas at pressures of∼105 Pa. But within ∼0:4 μs, the electron numberdensity is reduced by a factor of 50 to 100.In the work presented here, we infer electron num-

ber density by comparing the measured FWHM ofhydrogen-alpha and hydrogen-beta lines with pre-viously computed profiles. The comparison of our ex-periments and theories has been discussed in detail[10]. Alternative methods of inferring electron num-ber densities include use of full width at half-area fornonequilibrium plasma diagnostics [12]. However,we preferred to use analysis methods that previouslyshowed convincing agreement between experimentand theory, when considering the listed errorestimates.

3. Results

The emissions from the plasma are strong enough toallow us to monitor spectra from single breakdownevents; however, we elected to average over 100 indi-vidual laser-plasma events. Typical recorded atomic

and molecular spectra are illustrated below. Wave-length (λ) calibration was accomplished using stan-dard light sources. The background subtracted datasets were corrected for detector array sensitivityacross the 1024 diodes. Relative intensity calibrationwas accomplished with a tungsten lamp,Model LS-1-CAL Ocean Optics. The displayed emission profilesrepresent the single-shot average over 100 measure-ments. For the hydrogen-gamma profiles the relativeintensity corresponds approximately to single-shotoptical multichannel analyzer counts.

Figure 1 shows recorded hydrogen-gamma emis-sion profiles for a 500 ms pulsed flow at pressureof 2:7 × 105 Pa (25psig). For time delays of 0.4 and0:8 μs, notice the “incomplete” Stark-broadenedhydrogen-gamma profiles, shifted from the low-temperature wavelength value Hγ: 434:05 nm. Alsoapparent is an asymmetric appearance. Close tosymmetric atomic profiles are recorded for a time de-lay of tdelay ¼ 1:5 μs. Yet for this time delay, present inthe spectrum are C2 Swan system emissions from theΔν ¼ þ2 progression. Clearly, for a delay of 2:1 μs,the Swan system overlaps with the hydrogen-gammaprofile.

Values for the Stark widths are inferred by findingthe FWHM from the recorded spectra using the fol-lowing procedure: find the maximum and evaluatethe width at half of the maximum. Obviously, it is dif-ficult to find the baseline for the spectra recorded atearly delays, illustrated in Figs. 1(a) and 1(b), overand above the free-electron contributions and thecontributions from nearby lines such as Hδ and Hβ.For later delays, the spectra in Fig. 1 show the pre-sence of molecular Swan emissions. Consequently,error estimates reflect these ambiguities in Table 1.This table also shows the higher pressure data setand the electron number densities obtained by aver-aging the results for Hα and Hβ. In this work, the

Fig. 1. (Color online) Hydrogen-gamma emissions at 2:7 × 105 Pa.Time delay (a) tdelay ¼ 0:4 μs, (b) tdelay ¼ 0:8 μs, (c) tdelay ¼ 1:5 μs,(d) tdelay ¼ 2:1 μs.

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electron number densities from Balmer gammawidths are inferred from previous hydrogen-alpha/hydrogen-beta experiments and associated computa-tions for these lines; however, extensions to our pre-vious theory and experimental work [10] shouldallow us to infer electron number densities directly.Alternatively, theoretical efforts along the lines pre-sented by Gigosos et al. may be extended [12] to en-compass the number density values encounteredhere. Of specific interest may be a comparison ofFWHM versus full width at half-area for numberdensities in excess of 1017 cm−3. For consistency,FWHM is listed in Table 1, and these FWHM valuesare compared with the ones for hydrogen-alpha andhydrogen-beta.Hydrogen-beta measurements display the typical

double-peaked atomic line profile. The separationof the double peak is on the order of 1/4 of the FWHM[10]. Figure 2 shows the lower pressure hydrogen-beta results. The low-temperature wavelengthposition of Hβ is 486:14nm. Similar to the hydrogen-gamma spectra, for the recorded spectra it is difficultto infer an accurate value for the baseline. Neverthe-less, the same procedure was applied, namely findingFWHM at half of the maximum value. Figures 2(c)and 2(d) show residual molecular emission spectrafrom the Swan system. Previously tabulated widthto electron number density maps, see Table 2 ofRef. [10], allow us to infer electron number densities(Ne) for our data. The previously published data forwidth and electron number densities are interpo-lated using standard cubic spline for convenientextraction of Ne for a specific width from the mea-surement. Subsequent round-off and inclusion oferror estimates yields the tabulated data. The re-sults are presented in Table 2. Note that the roundedvalues are listed over and above the error estimates

from both width measurements from the experimen-tal data and the inferred electron number densityfrom the hydrogen-alpha and hydrogen-beta theorywork.

Figure 3 shows hydrogen-alpha emission spectrafor the lower pressure 2:7 × 105 Pa (25psig). The hy-drogen-alpha widths were determined using thesame procedure as for the hydrogen-gamma and hy-drogen-beta lines. The low-temperature Hα positionis at 656:28nm. The results for the inferred electronnumber densities are collected in Table 3. As above,rounded numbers for the inferred widths and elec-tron number densities are listed together with theerror estimates.

Table 1. Measured Hydrogen-Gamma Widthsa

tdelay[μs]

2:7 × 105 Pa:width [nm]

Ne

[1017 cm−3]6:5 × 105 Pa:width [nm]

Ne

[1017 cm−3]

0.4 11:0� 2:0 3:3� 0:8 10:4� 2:0 3:0� 0:80.5 10:7� 2:0 2:8� 0:7 9:5� 2:0 2:8� 0:70.6 8:7� 1:5 2:5� 0:6 8:6� 1:5 2:5� 0:60.7 8:1� 1:5 2:1� 0:5 7:8� 1:5 2:1� 0:50.8 7:6� 1:5 1:7� 0:4 6:7� 1:5 1:3� 0:40.9 6:7� 1:5 1:4� 0:4 6:3� 1:5 1:3� 0:41.0 6:2� 1:5 1:3� 0:4 6:2� 1:5 1:1� 0:41.1 6:0� 1:0 1:2� 0:3 5:8� 1:0 0:98� 0:31.2 5:8� 1:0 1:1� 0:3 5:5� 1:0 0:92� 0:31.3 5:6� 1:0 1:0� 0:3 5:4� 1:0 0:79� 0:31.4 5:3� 1:0 0:87� 0:3 5:1� 1:0 0:75� 0:31.5 5:2� 1:0 0:75� 0:3 5:1� 1:0 0:69� 0:31.6 5:0� 1:0 0:68� 0:2 4:7� 1:0 0:63� 0:31.7 5:0� 1:0 0:67� 0:2 5:0� 1:0 0:61� 0:31.8 5:0� 1:0 0:62� 0:2 4:6� 1:0 0:56� 0:31.9 5:0� 1:0 0:56� 0:15 4:4� 1:0 0:51� 0:32.0 4:7� 1:0 0:52� 0:15 3:6� 1:0 0:46� 0:42.1 4:6� 1:0 0:48� 0:15 3:6� 1:0 0:43� 0:4

aNumber densities are inferred by averaging Ne from Hα and Hβwidths.

Fig. 2. (Color online) Hydrogen-beta emission at 2:7 × 105 Pa.Time delay (a) tdelay ¼ 0:4 μs, (b) tdelay ¼ 0:8 μs, (c) tdelay ¼ 1:5 μs,(d) tdelay ¼ 2:1 μs.

Table 2. Measured Hydrogen-Beta Widthsa

tdelay[μs]

2:7 × 105 Pa:width [nm]

Ne

[1017 cm−3]6:5 × 105 Pa:width [nm]

Ne

[1017 cm−3]

0.4 10:0� 0:9 3:1� 0:8 10:0� 0:5 3:0� 0:80.5 9:0� 0:8 2:7� 0:7 8:7� 0:5 2:6� 0:70.6 8:1� 0:7 2:5� 0:6 7:8� 0:5 2:4� 0:60.7 7:4� 0:5 2:3� 0:5 7:3� 0:4 2:2� 0:50.8 6:8� 0:4 1:6� 0:4 6:5� 0:4 1:2� 0:40.9 6:3� 0:4 1:4� 0:4 5:9� 0:4 1:1� 0:41.0 5:9� 0:4 1:3� 0:4 5:4� 0:4 1:0� 0:41.1 5:3� 0:4 1:2� 0:3 5:1� 0:3 0:96� 0:31.2 5:0� 0:3 1:1� 0:3 4:8� 0:3 0:93� 0:31.3 4:7� 0:3 1:3� 0:3 4:5� 0:3 0:82� 0:31.4 4:4� 0:3 1:0� 0:3 4:1� 0:3 0:79� 0:31.5 4:1� 0:3 0:8� 0:3 3:9� 0:3 0:78� 0:31.6 3:9� 0:3 0:78� 0:2 3:7� 0:2 0:71� 0:31.7 3:8� 0:3 0:79� 0:2 3:5� 0:2 0:75� 0:31.8 3:6� 0:2 0:77� 0:2 3:3� 0:2 0:65� 0:31.9 3:3� 0:2 0:66� 0:2 3:1� 0:2 0:61� 0:32.0 3:1� 0:2 0:61� 0:2 2:9� 0:2 0:55� 0:42.1 2:9� 0:2 0:57� 0:2 2:8� 0:2 0:54� 0:4

aNumber densities are inferred using Table 2 of Ref. [10].

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Subsidiary measurements included an investiga-tion of the Δν ¼ 0 sequence of the C2 Swan system.Figure 4 illustrates the results. Both the measuredand fitted spectra indicate excellent agreement.The inferred temperature for the C2 Swan systemamounts to T ¼ 6450K recorded and fitted with aspectral resolution of 0:11 nm. The spectroscopic fit-ting was accomplished using diatomic line strengthfiles [13,14].Figures 5–7 show the recorded atomic emission

spectra for the pulsed methane flow at higher pres-sure of 6:5 × 105 Pa (80psig). To be noted is that theemissions recorded early in the plasma decay fortdelay ¼ 0:4 μs show similar emission strengths for

each of the three hydrogen Balmer series lines. Yetfor larger time delays, typically a reduction ofsignal strength occurs. This is an indication of self-absorption of the hydrogen lines. Note that higherpressure influences plasma geometry and dynamics,consequently, the emission spectrum will be modi-fied. Details of the emission spectrum are currentlystudied by spatially and temporally resolving theplasma emissions using methods similar to the onesapplied in previous hydrogen-alpha work [6]. For thehigher of the two pressures, a reduction of the orderof 20% is indicated in the tables. Effects of self-absorption in hydrogen emissions may be further

Fig. 3. (Color online) Hydrogen-alpha emission at 2:7 × 105 Pa.Time delay (a) tdelay ¼ 0:4 μs, (b) tdelay ¼ 0:8 μs, (c) tdelay ¼ 1:5 μs,(d) tdelay ¼ 2:1 μs.

Table 3. Measured Hydrogen-Alpha Widthsa

tdelay[μs]

2:7 × 105 Pa:width [nm]

Ne

[1017 cm−3]6:5 × 105 Pa:width [nm]

Ne

[1017 cm−3]

0.4 2:8� 0:3 3:6� 0:4 2:7� 0:3 3:0� 0:80.5 2:4� 0:3 3:0� 0:4 2:3� 0:3 3:0� 0:70.6 2:1� 0:3 2:5� 0:4 2:1� 0:3 2:5� 0:60.7 1:9� 0:2 2:0� 0:4 1:9� 0:2 2:0� 0:50.8 1:7� 0:2 1:7� 0:3 1:7� 0:2 1:6� 0:40.9 1:6� 0:2 1:4� 0:3 1:5� 0:2 1:4� 0:41.0 1:4� 0:2 1:2� 0:3 1:4� 0:2 1:2� 0:41.1 1:3� 0:2 1:1� 0:2 1:3� 0:2 1:0� 0:31.2 1:2� 0:1 0:95� 0:2 1:2� 0:2 0:91� 0:31.3 1:1� 0:1 0:77� 0:2 1:1� 0:1 0:76� 0:31.4 1:0� 0:1 0:74� 0:2 1:0� 0:1 0:71� 0:31.5 1:0� 0:1 0:69� 0:2 0:92� 0:1 0:62� 0:31.6 0:89� 0:1 0:59� 0:2 0:87� 0:1 0:56� 0:31.7 0:86� 0:1 0:56� 0:1 0:78� 0:1 0:48� 0:31.8 0:79� 0:1 0:48� 0:1 0:77� 0:1 0:47� 0:31.9 0:77� 0:1 0:47� 0:1 0:69� 0:1 0:40� 0:32.0 0:73� 0:1 0:43� 0:1 0:67� 0:1 0:38� 0:42.1 0:70� 0:1 0:40� 0:1 0:61� 0:1 0:33� 0:4

aNumber densities are inferred using Table 3 of Ref. [10].

Fig. 4. (Color online) Swan system C2d3Πg → a3Πu at2:7 × 105 Pa. Measured (dots) and fitted (line) spectra fortdelay ¼ 2:1 μs, temperature T ¼ 6450K and spectral resolutionΔλ ¼ 0:11nm.

Fig. 5. (Color online) Hydrogen-gamma emission at 6:5 × 105 Pa.Time delay (a) tdelay ¼ 0:4 μs, (b) tdelay ¼ 0:8 μs, (c) tdelay ¼ 1:5 μs,(d) tdelay ¼ 2:1 μs.

G4 APPLIED OPTICS / Vol. 47, No. 31 / 1 November 2008

investigated using, for example, methods similar tothe ones used for aluminium emissions [15].Obviously, our measurements indicate a relative

self-absorption that can be seen by comparing lowerwith higher pressure data. For increased time delays,there are also noticeable differences in peak emis-sions of C2 compared with Hγ and Hβ emission [e.g.,see Figs. 1(c) and 5(c)]. The values for width andnumber densities for the higher pressure data are in-cluded in Tables 1–3, respectively. Typically lowervalues for the electron number density are inferred,in turn, indicating self-absorption.

4. Conclusions

The recorded emission spectra of the hydrogen Bal-mer series allow us to infer electron number density,using previously tabulated values. The displayed hy-drogen emission profiles are also convolved with theDoppler width that amounts to 0:05 nm at 10; 000Kand 0:015 nm at 100; 000K. Yet the effect of the Dop-pler broadening is diminished due to choice of a spec-tral resolution of the order of 0:1 nm. The effects ofStark shifts are also diminished due to choice of timedelays in excess of 0:4 μs from optical breakdown.Clearly, self-absorption and ambiguities in establish-ing the spectroscopic baseline for the measuredatomic emissions cause difficulties in determining ac-curate values. For higher pressures, larger electronnumber densities are expected to occur. However,our results for electron number densities are almostidentical for lower andhigher pressure,within experi-mental errors. Clearly, the signal strength for theatomic lines is diminished for higher pressure, actu-ally yielding a slightly lower electron number densityfrom the extracted values for FWHM. The estimatederror bars show, however, that electron number den-sity can be determined with approximately 25% accu-racy, or well within a factor of 2. Measurements ofearly plasma decay, for time delays smaller than0:4 μs, most likely will reveal number densities wellabove 1017 cm−3. But for these studies a shorter gatewidthwould be recommended.Hydrogen-gamma andhydrogen-beta appear too broad for number densitymeasurements above 1018 cm−3. For time delays ofthe order of 1 μs from optical breakdown, molecularemissions usually overlap with atomic emissions.For laser-induced optical breakdown in methane,these molecular spectra appear to be primarily fromthe C2 Swan system. Future experimental work is in-dicated to investigate in detail the level of self-absorp-tion in laser-induced spectroscopy at pressures of theorder of a few atmospheres. Spatially and temporallyresolved studies will become necessary to address thevarious degrees of self-absorption, the higher pres-sure spatial gradients of plasma emissions and/orelectron number density profiles.

The authors express their thanks for discussionsand interest of Ying-Ling Chen and J. W. L. Lewisin this work. This work is in part supported byUTSI’s Center for Laser Applications.

References1. A. W. Miziolek, V. Palleschi, and I. Schechter, eds., Laser

Induced Breakdown Spectroscopy (Cambridge UniversityPress, 2006).

2. D. E. Cremers, Leon J. Radziemski, Handbook of Laser-Induced Breakdown Spectroscopy (Wiley, 2006).

3. A.W.Miziolek, F. C.DeLucia,C. A.Munson, and J. L. Gottfried,“Recent progress in LIBS-based technologies for securityapplications,” in Biomedical Optics/Digital Holography andThree-Dimensional Imaging/Laser Applications to Chemical,Security and Environmental Analysis on CD-ROM (OpticalSociety of America, 2008), paper LThC1.

4. J. B. Spicer and C. McEnnis, “Molecular and atomic emissionin femtosecond and nanosecond LIBS of explosives on

Fig. 6. (Color online) Hydrogen-beta emission for at 6:5 × 105 Pa.Time delay (a) tdelay ¼ 0:4 μs, (b) tdelay ¼ 0:8 μs, (c) tdelay ¼ 1:5 μs,(d) tdelay ¼ 2:1 μs.

Fig. 7. (Color online) Hydrogen-alpha emission at 6:5 × 105 Pa.Time delay (a) tdelay ¼ 0:4 μs, (b) tdelay ¼ 0:8 μs, (c) tdelay ¼ 1:5 μs,(d) tdelay ¼ 2:1 μs.

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surfaces,” in Biomedical Optics/Digital Holography andThree-Dimensional Imaging/Laser Applications to Chemical,Security and Environmental Analysis on CD-ROM (OpticalSociety of America, 2008), paper LThC2.

5. C. Parigger, J. W. L. Lewis, and D. H. Plemmons, “Electronnumber density and temperature measurement in alaser-induced hydrogen plasma,” J. Quant. Spectrosc. Radiat.Transfer 53, 249–255 (1995).

6. C. Parigger, D. H. Plemmons, and J. W. L. Lewis, “Spatiallyand temporally resolved electron number density measure-ment in a decaying laser-induced hydrogen plasma usinghydrogen-alpha line profiles,” Appl. Opt. 34, 3325–3330(1995).

7. V. Sturm and R. Noll, “Laser-induced breakdown spectroscopyof gas mixtures of air, CO2, N2, and C3H8 for simultaneousC,H,O, andNmeasurement,”Appl.Opt.42, 6221–6225 (2003).

8. A. M. El Sherbini, H. Hegazy, and Th. M. El Sherbini, “Mea-surement of electron density utilizing Hα-line from laser pro-duced plasma in air,” Spectrochim. Acta, Part B 61, 532–539(2006).

9. R. Sattmann, I. Mönch, H. Krause, R. Noll, S. Couris, A.Hatziapostolou, A. Mavromanolakis, C. Fotakis, E. Larrrauri,and R. Miguel, “Laser-induced breakdown spectroscopy forpolymer identification,” Appl. Spectrosc. 52, 456–461 (1998).

10. C. G. Parigger, D. H. Plemmons, and E. Oks, “Balmer series Hβmeasurements in a laser-induced hydrogen plasma,” Appl.Opt. 42, 5992–6000 (2003), and references therein.

11. Y.-L. Chen and J. W. L. Lewis, The University of TennesseeSpace Institute, 411 B. H. Goethert Parkway, Tullahoma,Tenn. 37355, USA (personal communication, 2008).

12. M. A. Gigosos, M. À. Gonzàlez, and V. Cardeñoso, “Computersimulated Balmer-alpha, -beta and -gamma Stark line profilesfor nonequilibrium plasma diagnostics,” Spectrochim. Acta,Part B 58, 1489–1504 (2003).

13. C. G. Parigger, D. H. Plemmons, J. O. Hornkohl, andJ. W. L. Lewis, “Spectroscopic temperature measurementsin a decaying laser-induced plasma using the C2 Swansystem,” J. Quant. Spectrosc. Radiat. Transfer 52, 707–711(1994).

14. J. O. Hornkohl and C. G. Parigger, Boltzmann EquilibriumSpectrumProgram (BESP) (University of Tennessee Space In-stitute, 2002), http://view.utsi.edu/besp.

15. A. M. El Sherbini, Th. M. El Sherbini, H. Hegazy,G. Cristoforetti, S. Legnaioli, V. Palleschi, L. Pardini,A. Salvetti, and E. Tognoni, “Evaluation of self-absorptioncoefficients of aluminum emission lines in laser-inducedbreakdown spectroscopy measurements,” Spectrochim. Acta,Part B 60, 1573–1579 (2005).

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