Temperature measurements from CN spectra in a laser-induced plasma

J. Quant. Spectrosc. Radiat. TransferVol. 46, No. 5, pp. 405-411, 1991 Printed in Great Britain. All rights reserved

TEMPERATURE

MEASUREMENTS

IN A LASER-INDUCED

0022-4073/91 $3.00+ 0.00 Copyright © 1991 Pergamon Press pie

FROM

CN SPECTRA

PLASMA

JAMES O. HORNKOHL, CHRISTIAN PARIGGER, a n d J. W . L. LEwis Center for Laser Applications, University of Tennessee Space Institute, TuUahoma, TN 37388, U.S.A.

(Received 12 April 1991)

A~tract--The spontaneous-emissionspectra of the CN violet systemwere observed following excimer-laser-induced breakdown of an atmospheric-pressure CO2/N2 mixture. Using a triple monochromator and a gated linear-diode array, the spectra were acquired with spectral resolutions of 2 and 7cm -t within l#sec following the laser pulse. Comparison of the observed rotation-vibrational structure of the Av = 0 sequence and the synthetic spectra, which were calculated using direct diagonalization of the rotational and fine-structure Hamiltonians, yielded internal, molecular temperatures of approx. 8000 K. No evidence of internal nonequilibrium of the rotational and vibrational modes was observed.

INTRODUCTION

The laser-induced breakdown of gases and the subsequent inverse Bremsstrahlung-laser heating are known to produce high-temperature plasmas. Such plasmas typically exhibit rich emission spectra, first of atomic and ionic products of the parent gas at early times following the plasma formation and then, at later times, recombination molecular spectra) It is of interest to investigate the use of these spontaneous-emission molecular spectra to characterize the temperature field of the plasma decay. For an atmospheric-pressure mixture of CO2 and N2, the diatomic, recombination molecularspectra are well-developed approx. 400 nsec after the creation of the laser-plasma. Of these spectra, the Av = 0 sequence of the CN violet system is most prominent. The present work is concerned with an evaluation of the accuracy of the use of the laser-induced, spontaneous emission of this system for the determination of the plasma temperature subsequent to molecular recombination. PRODUCTION AND MEASUREMENT OF THE CN SPECTRA Laser-induced optical breakdown was generated inside a laboratory cell containing a gaseous mixture of CO2 and N2 by focusing of the 308-nm radiation from a Lambda-Physik MSC-150 and PSL4000 excimer laser system. The selected mode of operation of the laser system produced a 20-mJ pulse-energy with a nominal FWHM pulsewidth of 1 nsec. Streak camera measurements revealed that the 1-nsec laser pulse was comprised of an underlying burst of 35-psec pulses with a varying time modulation. The specific temporal shape is favorable for optical breakdown and, in turn, for production of fluorescence emission. Typically, a few hundred nanoseconds after plasma production, the molecular spectra of CN, and particularly the B2Z + -,X:Z + violet system, become prominent. The schematic experimental arrangement is exhibited in Fig. 1. A beamsplitter directs a small portion of the laser beam to a fast diode-detector which generates the trigger pulse for the measurement apparatus. A set of mirrors provides an optical delay sufficiently long for the electronic instruments to be armed before the optical pulse arrives at the sample cell. At room temperature and atmospheric pressure, a 50/50 mixture by volume of CO2 and N2 was flowing through the cell. The emission spectrum from the optical-breakdown plasma was dispersed by a triple monochromator and detected using an intensified, linear 1024-diode detector-array and an optical multichannel analyzer (OMA), which was externally synchronized to a frequency of 58 Hz. Optical multichannel analyzer software and hardware were utilized to adjust the intensifier-on time of the detector. The necessary high-voltage pulse was provided by the pulser. Typically, the laser 405

JAMES 0. HORNKOHL

406

et al

20 mJ

Laser -

Delay Generator

Pulser l/50

5

a

Lens

I\ ”

I

1 ns FWHM

Plasma Cell

I

Diode Oscilloscope

58 Hz

I

OMA

I

1

Frequency Generator

Intensified

)

Diode Array

1

Fig. I. A schematic is shown of the optical arrangement. The optical multichannel analyzer (OMA) is externally synchronized to 58 Hz, but otherwise controls the experiment by providing the excimer-laser trigger at about 1Hz and the electronic signal for the intensifier-on pulse. Single-shot spectra are stored in the OMA memory and later transferred to a PC. The oscilloscope monitors the timing for the time-resolved measurements. A 50% CO, and 50% N2 mixture is Aown at moderate speed through the laser plasma cell.

pulse-rate was 1 Hz since one had to allow for sufficient time to ensure that a fresh gas-sample was in the focal region for each laser pulse. To eliminate all memory of a previous signal and to keep dark counts to a minimum, the detector was continually read at the external frequency while only keeping the scan that immediately followed the 308-nm burst. Spectra of the AV = 0 sequence of the CN violet band system were obtained with spectral resolutions of 7.0 and 2.0 cm-’ using a JY HR-640 spectrometer and gratings of 1200 and 3600 grooves/mm, respectively. For the lower resolution measurements, the intensifier of the detector was gated on for 400 nsec at a delay of 500 nsec with respect to the arrival-time of the excitation pulse at the sample cell, while for the higher resolution experiments the gate-on time was 600 nsec at a delay of 400 nsec. The recorded CN spectrum for the lower-resolution measurements is shown in Fig. 2(a). Although spectra were measured from single laser pulses, the average over 50 measurements is displayed vs wavelength. The wavelength calibration was carried out using standard Iight sources, the sensitivity calibration was accomplished with a tungsten lamp, and the recorded spectra were detector-noise background corrected. The calculated spectrum is exhibited in Fig. 2(b). For the higher-resolution measurement, the results obtained for a 40-scan average are shown in Fig. 3(a). Shown in Fig. 3(b), for an appropriate temperature, is the theoretical spectrum whose computation will now be described. PREDICTION

OF THE

CN SPECTRA

TheoreticaI model The polarization- and angle-averaged, spontaneous-emission intensity i? of the CN transition, which is produced by the laser-induced breakdown, is related to the transition strength S(n’u’J’, n”v”J”) and the number N(n’o’J’) of excited-state molecules by E

64 n4cC4 =~ S(n’u’J’, n”tl’y”)N(n’u’J’), 3(47%)

(1)

where the set of quantum numbers n’, u’, and J’ is associated with the electronic, vibrational and rotational levels, respectively, of the upper BZZ + state. A similar meaning applies to the quantum numbers n”, u”, and J” of the lower X2, C+ state. The transition wavenumber ij is given by the

Temperature measurementsfrom CN spectra 300.

_

(a)

Slotc~t,r u m o f CN V1alet ~ s U m l

407

Exalted by Optlcal l~'eak~wn

250. c

500 rm del¢~ ~ f t l r I ~ e r

200.

0,0

1.1

pulme

2.2 J

400 r~l ~F~Q

|

150.

100, 50. 0 365.

360.

370.

(b)

300,

375. Wclvelength

380.

385.

390,

385.

390.

(nm)

Fitted ~o~atrum of CN VI~IQt S y s t ~

250. T-,S2OO K f r o m Neckw--kk~d (l{~nialll olmpltx

200.

FWHk4 -, 7.0 ~m--1

150.

o

100. 50.

-

0 360.

; ,

, : , 365.

'

' ; " ;-i 370.

375. W avltlsng~.h

380. (rim)

Fig. 2. (a) The experimental average is shown for 50 single-shot spectra recorded at a delay of 500 nsec using a 400 nsec gate, The hot CN spectra were optimized for maximum signal (OMA counts) by adjusting the coupling lenses; second-order effects are absent as checked with filters. (b) The calculated fitted spectrum yields a temperature in excess of 8000 K. The background originates from residual-free electron radiation.

term-value difference F(n'v'J')-F(n"v"J"). As is customary, =-~ the transition strength S(n'v'J', n"v"J") is written as the product of the electronic transition strength S,~(n'v', n"v"), the Franck--Condon factor q(v', v") and the HSnl-London factor S(J', J")

S(n" v'J', n"v"J") = Se~(n'v', n"v")q(v', v")S(J', J").

(2)

For the vibrational transitions of the CN violet system that are observed in this work, the Born-Oppenheimer approximation was assumed. Also, on the basis of the work by Brocklehurst et al, 5 the variation of the electronic transition moment with the vibrational quantum-numbers can be neglected. The Franck-Condon factors q(v', v") for the spectral system were obtained using the R K R method, as discussed by Tellinghuisen/and a numerical solution of the radial Schr6dinger equation, as presented by Cashion? To determine the final factor of Eq. (2), the Hrnl-London factor, semi-empirical term value equations and tabulated Hrnl-London factors could be used. However, to improve the accuracy of the predicted spectra, a numerical diagonalization of the rotational and fine-structure Hamiltonian was performed. For this computation, the Hund's case-a basis matrix-elements, as given by Zare, s were used, and the required molecular constants for the B22~+ and Xz2~~ states were taken from Engleman, 9 Kotlar et al, I° and Ito et al." Table 1 gives the constants for the Av = 0 sequence. The algorithm of the computation was to specify the pair of quantum numbers J ' and J", calculate and diagonalize the Hamiltonian, compute the Hrnl-London factors for transitions between all upper and lower states, and finally calculate the wavenumbers for the allowed transitions. Forbidden transitions yield vanishing Hrnl-London factors. This procedure is convenient for the accurate computation of the synthetic spectra for n-photon, diatomic-molecule processes and has been previously demonstrated for two-photon X2II-AZF. + transitions.~2

JAMES O. HORNKOHL et al

408 250.

(Q)

150.

.->

100.

0.0

4 0 0 rm delo~¢ clft~ IQser pubis

.-~ 200. C C

Sl~ctrum of CN Vlollt System ExeJted by Optl¢ol Brec~down

600

ne

gate

/

1.1

..3600 g / r a m grat|ng 2,2

@ n,

50.

383.

250.

384.

(b)

F-

385. Wavelength

386. (nm)

387.

388.

Fitted Speotrum of CN 'Vlo~,t Band S y l t a m

Tm7g4.0 K from Neldal---Mead downhill slrr~plex

200. C

F3NHM -- 2.0 cm--1

C

150.

¢ :~ o

100.

"

50.

0 383.

384.

385. Wavelength

386. (nrn)

387.

388.

Fig. 3. (a) The experimental average is shown for 40 single-shot spectra recorded with higher resolution than in Fig. 2. (b) Synthetic fitted spectrum. The comparison between experiment and theory is convincing. Subtle differences exist in the vicinity of the v ' = v " = 4 vibrational head. With one exception near 387.52-nm, all lines shown are superpositions of transitions with differing upper rotational quantum numbers J'.

In Eq. (1), the number N(n'v'J') represents the observed space- and time-averaged molecular number of the excited-state CN B2I + species produced by the laser-induced breakdown. During the initial stage of the CN recombination process, neither vibrational nor rotational mode thermal equilibrium can be assumed. However, because the laser-induced breakdown results in high density and temperature and because over 103 intermolecular collisions are estimated to occur during the gate-delay and gate-width times, an equilibrium distribution of temperature T was assumed for the vibrational and rotational modes of the CN B2I + molecules.

Relative intensities and fitting of synthetic spectra In the experiments, only the relative intensity I of the Av = 0 sequence of the CN violet system was of interest. Therefore, using Eq. (2), the measured and computed synthetic spectra are represented by the relation /~ = C ~ g'q5 exp[-- hcF(n'v'J')/k, T]f(f, ~,),

(3)

v'J" v'J"

where It represents the relative signal at the array detector ith pixel which, because of its finite width, possesses a discrete wavenumber ~7~,and C is a constant. The summation over v'J' and v"J" represents, in practice, a summation over all transitions that lie within the spectral slit-function f 0 7, gi), and q~ represents the product q(v'v")S(J', J"). Omitted from the absolute intensity relation are all factors that do not vary for the observed spectral sequence, and these omissions include the electronic transition moment and the quantum-number-independent molecular partition function, which varies, in these studies, approximately linearly with T. Using the downhill simplex method, t3,~4 the squared-residuals between the measured and computed relative spectral intensities are minimized by varying the temperature T. Using the

Temperature measurementsfrom CN spectra

409

Table 1. Spectroscopicconstants used to compute syntheticspectra. B2E + States

vl=0 T, + G,,

B~, D,, x 10e H~ x 101~ ~,, X 10~ 7D, x 10r

v'=l

v'=2

268?.,8.90 28952.50 81035.94 1.95871 1.93804 1.91651 6.5387 6.6984 6.8236 -8.90 -4.95 -9.29 1.695 1.718 1.59 -4.9 -5.0 -4.3

vt=4

v'=-5

35073.02

37021.?,0

v'=3 83076.92

1.89417 1.87042 7.0268 -11.8 2.22 -8.76

7.1900 -19.3 1.96 -8.8

1.845336 9.0032

1.~d

X2E+ States v":0

v"=l

v'=2

v"=3

1031.60

3073.49 1.87366

5090.61 1.8,56].8

70"79.41 1.88864

T, + G, B,,

1.89108

D~ x I0e

-6.4072 -6.4162 -6.4263

H,, x I0~2 % x 102 "/Dw X 10'

0.7417 -0.70

q(,',i")

'-6.36

-6.08

-5185

0.7272

0.7190

v"=4 '

9042.84 1.82105

-6.4387 ' -6.4445 "'5.47

-3.80

0.7212

0.354

10979.85

1.80333 -6.69,5

-0.97 -0.96 -3.0 Fra.uek-CoadouFactors I 0.9193 I 0.7776 I 0.6650 I 0.5808 I 0.5197 H6nl-LondonFactors -0.96

e-B,~aches

S(J', J") = (2~" - 1)(2~" + 1) / 4J"

O-B,~aches

S(J', J") = (2J" + 1) / 4J"(J" + 1)

R-Branches

S(J', J') = (2J"

+

1)(2J" + 3) / 4(J"

+

1)

derived temperature, the synthetic spectra were computed, and examples are shown in Figs. 2(b) and 3(b) for the lower and higher resolution data, respectively. Temperatures were determined both from the spectra obtained from individual laser pulses and from the spectral signals obtained by averaging the spectra from all laser pulses. For the 7.0 cm-'-resolution case, the results obtained were T = 8300 + 490 K from the individual-pulse data and T = 8260 K from the averaged spectra. The corresponding results for the 2.0 c m - ' resolution data were T = 7940 + 210 K and T = 7940 K, respectively. It should be noted that these spectral signals were not normalized with respect to the incident laser-beam power, and a portion of the uncertainty in these results can be attributed to this source. M O D I F I E D B O L T Z M A N N PLOTS A common method '5 of presentation of resolved, non-overlapped spectral data is the use of the Boltzmann plot, from which the temperature is determined and non-equilibrium effects can be inferred. The CN data presented here are both incompletely resolved and overlapped, which prevents use of the normal Boltzmann-plot techniques. Specifically, the total measured signal at each pixel of the OMA detector is composed of individual signals which originate from levels of different term values but share a common transition wavenumber and bandpass that correspond to the detector pixel. For the overlapped Av = 0 sequence spectra, Eq. (3) can be modified in appearance to enable a Boltzmann-plot presentation of the results. Of the entire set of quantum numbers, only a smaller subset contributes to the relative intensity Ii of the ith pixel. Equation (3) is now rewritten as Ii = C ~ g ~ o e x p [ - hcF(n'ov'oJ'o)/ka T],

(4)

where the subscript 0 designates a particular parent level of the subset (v'J', v"J") that contributes to I;. The temperature-dependent function ¢ is given by ¢ = ~ f07, ~7,). [t~/t~0]' • [~b/~bo] • exp{ - hcIF(n'v'J') - F(n'ov~J~)]ka T}. V'f' v"J"

(5)

410

JAMES O. HORNKOHLet al

Equation (4) can now be written in the standard form for presentation as a Boltzmann plot, viz. ln[Ii / {# " ~74" ~b0}] = - hcF(n 'ov 'oJ~)/kB T.

(6)

Although the unknown temperature appears within ~, as shown in Eq. (5), the sensitivity of the results on this factor depends upon the term-value difference F ( n ' v ' J ' ) - F(n'ov'oJ'o) and the ratio of the strength-factor products q~/t#0. For this work, the particular parent level for each pixel was selected to be that level which made the largest contribution to the pixel signal. To present the spectral data in the form of Eq. (6), as typified by Figs. 2(a) and 3(a), only those spectral regions and pixel elements were used that corresponded to the peak regions of the spectra. An iterative, least-squares analysis was performed using the experimental data and Eq. (6) to obtain the temperature of the parent levels. The results are exhibited in Fig. 4. For both the Boltzmannplot and simplex analyses, the spectral signals were corrected for the background radiation, and the signal-to-background ratios were on the order of 50:1 for the high-intensity spectral regions and l:l for the low-intensity regions. The modified Boltzmann-plot technique was also iteratively applied to the 7.0 cm-Lresolution data and a temperature T = 8510 K was found. This result is within l SD of the mean temperature 8300 K, as determined from the simplex fit to individual spectra. No evidence of nonequilibrium of the internal rotational and vibrational population densities could be inferred from these results. The same iterative approach was used for the high-resolution data but it produced unreliable results; the computed temperature obtained from the analysis did not converge. Numerical simulations were performed to attempt to determine the reason for the lack of convergence for these data whose appearance would not indicate such difficulties. These simulations included both random errors and systematic errors to represent, respectively, signal variations and background corrections. It was found that the combination of the reduced spectral coverage and the increased, relative imprecision of the background correction for the 2.0 cm-J resolution data were such to prevent convergence of the temperature. This result forced a review of the Boltzmann-type analysis of the lower-resolution results which revealed the requirement that the relative imprecision of the background correction must be less than approx. + 5% to achieve reasonable agreement betweeen the simplex and Boltzmann-plot analyses. The simplex analysis did not exhibit such sensitivity to the background correction. Modified

Boltzmann

Plots

7. /x

6.

o

-- 1200 g / r a m

spectrum

-- 3600 g / r n m

spect:rurra

5.

C

o U

4.

+

7_o3. D

rv.J

2. 1. 0 25000.

"~L T=8250 T=79~o K ~ I

I

35000.

I

K

I

45000. Term Value

~ T=828o K I

I

55000. (cm--1)

I

\~,~ Ix

65000.

Fig. 4. Modified Boltzmann plots are constructed from the recorded spectra. The symbols denote the peak experimental intensities. The two straight lines for each experiment contrast the results of simplex fitting (more negative slope and hence lower temperature) with least-square fitting (less negative slope and hence higher temperature). The linearity of the plots confirms the assumption of thermal equilibrium.

Temperature measurementsfrom CN spectra

411

SUMMARY Spectral measurements of the Av = 0 sequence of the CN violet system, following laser-induced, optical-breakdown, have yielded estimates of the temperature of the decaying plasma environment. The measurements were acquired with submicrosecond temporal resolution with spectral resolutions of 7 and 2 cm -1. These results were compared with synthetic spectra which were obtained by direct diagonalization of the Hamiltonian operator. Using a simplex regression-analysis, comparison of the synthetic and experimental data yielded temperatures of approx. 8000 K with experimental ltr uncertainties of < 6%. These results were achieved without normalization of the data for laser-power fluctuations, which were on the order of + 10%. A detailed error-propagation of analysis of the simplex results has not been performed, and the agreement of the results of the two different spectral-resolutions is considered to be adequate. To provide a method for the visual assessment of the data for nonequilibrium distributions, a modified Boltzmann-plot formulation was developed. It was found that for the 2.0 cm- t resolution data, the precision of the measured background-correction was inadequate for convergent results using this method of analysis. The lower-resolution data were successfully presented in this manner, and nonequilibrium distributions were not observed. The difference in the simple and the iterative Boltzmann-plot temperature results is within the la uncertainty. However, a possible reason for the actual difference is the fact that only peak spectral signals are used for the Boltzmann analysis, whereas the simplex analysis makes use of the entire spectral signature. Further analysis is required to explain this discrepancy. REFERENCES 1. K. J. Grant and G. L. Paul, Appl. Spectrosc. 8, 1439 (1990). 2. J. B. Tatum, Astrophys. J. Suppl. Ser. 14, 21 (1967). 3. E. H. Whiting, A. Schadee, J. B. Tatum, J. T. Hougen, and R. W. Nicholls, J. Molec. Spectrosc. 80, 249 (1980). 4. H. Lefebvre-Brion and R. W. Field, Perturbations in the Spectra of Diatomic Molecules, p. 246, Academic Press, Orlando, FL (1986). 5. B. Brocklehurst, G. R. Hebert, S. H. Innanen, R. M. Seel, and R. W. Nicholls, "Identification Atlas of Molecular Spectra 9: The CN BzZ+-X2Z + Violet System," York University, Toronto (1972). 6. T. Tellinghuisen, Comput. Phys. Commun. 6, 221 (1974). 7. J. K. Cashion, J. Chem. Phys. 39, 1872 (1963). 8. R. N. Zare, A. L. Schmeltekopt, W. J. Harrop, and D. L. Albrittion, 3". Molec. Spectrosc. 46, 37 (1973). 9, R. Engleman, Jr., Jr. Molec. Spectrosc. 49, 106 (1974). 10. A. J. Kotlar, R. W. Field, J. I. Steinfield, and J. A. Coxon, J. Molec. Spectrosc. g0, 86 (1980). 11. H. Ito, Y. Ozaki, K. Suzuki, T. Kondow, and K. Kuchitsu, J. Molec. Spectrosc. 127, 283 (1988). 12. J. O. Hornkohl and W. M. Ruyten, J. Molec. Spectrosc. 123, 499 (1987). 13. J. A. Nelder and R. Mead, Comput. J. 7, 308 (1965). 14. W, H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing, Cambridge Univ. Press, New York (1986). 15. A. G. Gaydon, The Spectroscopy of Flames, p. 142, Chapman & Hall, London (1957).