Measurements of relative transition probabilities of ns-4p, nd-4p, and nf-3d transitions in neutral potassium

I, Quonl. SI)~WUSC. Rodtar. Transfer Vol. 25. pp. 221-?32 Pergamon Press Lfd 1981. Punted in Great Britain

‘MEASUREMENTS OF RELATIVE TRANSITION PROBABILITIES OF ns-4p, nd-4p, AND nf-3d TRANSITIONS IN NEUTRAL POTASSIUM? D. P. Sandia National Laboratories,

AESCHLIMAN

Division 4738, Albuoueraue. ,~ -~ 1 ~/NM 87185, l_J.S.A.

(Receid 4 August 1980) Abstract-Relative transition probability (A-value) measurements are reported for the n&p (n = 6-15), nd-lp (n = 5-13). and nf-3d (n = 7-14) series transitions in neutral potassium (KI). The results are based on intensity measurements of optically-thin KI spectral lines from a steady-state potassium emission source. The source employed was a radially-symmetric potassium-seeded argon plasmajet containing 5 5 mole per cent K-atoms. Local emission coefficients were obtained by means of the Abel transform. For the prevailing free-stream conditions (P - 11torr, 7’ - 3200 K, n, - lOI cm-‘), the potassium excited state populations are described by a Boltzmann distribution down to and including the ground state. The reported A-values are normalized to that of the 580.2nm line (7~-4p,,~ transition). The relative accuracy is estimated to be 5-20% for the ns-4p and nd-4p series and 15-25% for the nf-3d transitions. With the exception of the data for the 6s-4~ and all nf-3d transitions, the measurements agree to within estimated experimental uncertainties with the values given in the NBS tabulation [Wiese et al. (1%9)], although systematic differences are observed. For the exceptions noted, the measurements lie 25-50% below the relative NBS values. Comparison is also made to recent calculations of Lindgard and Nielson, and Ormonde.

1. INTRODUCTION

Open-cycle, coal-fired MHD generators will utilize potassium compounds to provide enhancement of the electrical conductivity.’ For anticipated MHD channel conditions, the conductivity depends primarily on the electron density, n,, and is thus a function of the electron temperature, T,, the potassium concentration, nK, and the static pressure, p. If optical access to the channel can be obtained, real-time diagnostics of the flow based on potassium spectra might prove useful for operational monitoring and control, since both T, and nK can, in principle, be obtained from such spectra.’ Values for the transition probabilities (A-values) are tabulated by Wiese et aL3 for many of the allowed transitions. They present data for the ns4p (sharp) and the nd-4p (diffuse) series which represent, where corresponding data are available, an average of the early emission measurements of van der Held and Heierman4 and the theoretical calculations of Villars.’ Estimated absolute uncertainties are t 25% and 2 50%, for the two series, respectively (estimated relative uncertainties are not given). Estimates for other allowed transitions are also given in Ref. 3 but, except for the np-4~ principal (resonance) series, are assigned larger estimated uncertainties, typically in excess of 50%. More recently, Lindgard and Nielsen6 and Ormonde’ have performed transition-probability calculations for the allowed transitions, extending them in some cases to higher upper state quantum numbers. In addition, A-values have been measured for several isolated lines by Darrigo et u/.,~ but thus far there has been no systematic experimental effort reported to redetermine or extend the ns-4p and nd-4~ series data or to study the nf-3d transitions. At the anticipated potassium concentration in an MHD channel, the np-4~ series lines will not be suitable for emission measurements because of very strong self-absorption from the ground state. They might be useful for line-reversal measurements, as described by Daily et ~1.;~however, line reversal measurements may be seriously affected by the flow boundaries.” The upper level of the candidate lines must satisfy Griem’s criterion” for partial local thermodynamic equilibrium (PLTE) at the expected electron density in the MHD channel, 10’3-10’4crnm3.”With the exception of the highest wavelength members of the ns-4p series, the nddp, nvlp, and nf-3d transitions all satisfy these criteria and are therefore potentially useful for MHD channel diagnostics, assuming that reliable transition probabilities are available, Thus, the purpose of the work reported here was to determine transition probabilities for the tThis work was supported by the United States Department 221 QSRT Vol. 25. No. )_-c

of Energy.

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F;VWI IH3S3V ‘d

‘a

ZZZ

Relative transition probabilities of ns+,

Center

nd4p,

223

and nf-3d transitions

Section

Low-Pressure Test

T

/ i Tungsten

dapper

i

1.6rnnl

Chamber

16mm x 1.6mm Groove

Circumferential

Anode

Insulator Center

Cathode

Section

Wall

(Brass)

304 SS Insert 304 SS Barrel Soft

Seed

Copper

Seal

Injection

Port

D&ail

(1

of 3)

Fig. 2. Schematic of the plasmajet head and injection ports; c.w., cooling

water.

romator (0.75 m, 1200 line/mm grating blazed at 750 nm, 0.1 nm spectral band pass) by lenses L, and Lz; the image was translated at a fixed rate (3 se&can) along the vertical slit by the scanning mirror MI which was driven about a horizontal axis by a reversible synchronous motor. A highpass filter was used to suppress second-order radiation at first-order wavelengths greater than -7OOnm, and neutral density filters were used to reduce the signal from the stronger lines to avoid detector saturation. The detector was a cooled and shielded EM1 9658R PMT (extended S-20 response) at the 100pm wide exit slit. A 1 megohm load resistor provided the signal voltage; the signal was filtered to remove noise above 30Hz and amplified as necessary prior to transmission to an on-line data acquisition and control system (DACS). The DACS consisted of a 5000 word/set input multiplexer, an A/D converter and a 16 bit, 32 K digital minicomputer with magnetic tape drives. Control Air

Supply

I I I

(5 MPal

Liter Seed Reservoir

I

T

1

Fig. 3. Schematic of the plasmajet-potassium seed system.

224

D. P. AESCHLIMAN

To compensate for low-frequency fluctuations in the potassium emission strength, an EMI 9785B PMT (S-20 response) was used in conjunction with a 693.9 nm NBP filter (40% peak transmission, 0.8 nm FWHM) and a high-pass filter (85% transmission at 694 nm. c: 0.1% transmission below 650 nm) to monitor the K1693.9 line intensity along a line-of-sight through the jet midplane at the axial location viewed by the scanning mirror. These data were used to correct the emission data for both short term variations within a jet scan, and for long term fluctuations or drift occurring over the course of a run (up to 80 min). A slow spectral scan at normal slit settings of the seeded jet through its mid-plane was used to determine the spectrometer wavelength setting for each line and to select a corresponding continuum wavelength free of interference. The trapezoidal slit function totally captured each line observed but was sufficiently narrow to separate the overlapping n.s-4~ and nd-4p Teries lines up to n = IS and n = 13. respectively. Extension of the data to higher values of n by decreasing the slit widths to improve resolution could not be realized, since the drop in spectrometer throughput. coupled with the decrease in line intensity with increasing upper state quantum number, led to inadequate signal to noise ratios. Similar constraints limited the lines of the nf-3d series that could be examined to n 5 14. The integrated intensity profiles for each spectral line, its adjacent continuum and the monitor data were obtained in digital form, as described in detail in Ref. 13. For the stronger lines, the continuum contribution was negligible in comparison to the line emission. For the weakest lines, however, the continuum contributed as much as SO%to the total signal. The shields indicated in Fig. I were necessary to control the deposition of a dry powder film of potassium carbonate on the test chamber windows. Without the shields, the transmission loss was in excess of S%/min under normal operating conditions. Addition of the shields reduced the transmission loss rate to a constant value of less than O.l%/min, which was then accounted for with transmission measurements prior to and immediately following each data run. Because there was a slight dependence of transmission loss on wavelength, this measurement was performed at each spectral line wavelength observed. It was found necessary to perform the post-run calibration within several hours of the completion of a run, while the chamber was still warm and above the dew point for the moisture-laden gases within the chamber; after cooling to room temperature, the K*CO? film would combine with water to alter dramatically the transmission and scattering characteristics. In addition to the potassium emission measurements, the hydrogen HP line half-width was measured using 20 pm entrance and exit slits in an effort to determine the electron density and to evaluate the partial local thermodynamic equilibrium (PLTE) criterion.” This attempt was complicated by the fact that, at the temperature of the flow ( - 3200 K), the H, intensity (1,) is extremely sensitive to variations in the electron temperature Te, dl,JZp - 50 dT,/T,, with the result that, while sufficient stability prevailed to permit HP line profiles to be obtained at one scanning mirror position over a period of IO-20sec. minor temporal variations in T, caused intensity fluctuations too large to allow the repeated scans required for both line profile and Abel transform analysis.14 Moreover, it was necessary to conduct the H, measurements at temperatures near 3400 K in order to generate an adequate signal to background level. At -3200 K, the HL3intensity was weak and at the lower temperature extreme ( -2800 K), H, was not detectable. As a result only spatially-averaged values of n, at one extreme of the experimental range could be obtained. 3. RESUI.TS

(A) KI line data Following completion of each run, the DACS was used to correct the integrated line intensity data, Z(x), for continuum contribution, PMT dark current, and short term monitor variations, and to transcribe the line data into a format suitable for further analysis as described previously. I3 Porter’s numerical method” was employed for the Abel inversion of Z(X) into radial emission coefficient profiles, E(T). Typical I(x) and e(r) profiles for the strong KI 693.9, 6s-4~ line and, for comparison, the much weaker KI 774.2 nm l4f-3d line amplified by a factor of 200, are shown in Fig. 4. The envelopes attached to the e(r) profiles, each of which represents the average of four consecutive scans, indicate the scan-to-scan variability. The E(r) data were corrected for spectral response of the optical system using a calibrated

Relative transition probabilities of ns+,

T(r)

(A-VALUES

I

O-

0

RADIUS

FROM

THIS

WORK)

I

0.5 JET

nd-4p. and nf-3d transitions

1.0 ,R. OR

LATERAL

DISPLACEMENT,X

1.5 (cm)

Fig. 4. Distributions of relative integrated intensity, I(x), and emission coefficient, c(r), for the 6s4p,,, line, e(r) x 200 for the 14f-3d line, and temperature. Envelopes indicate the range of e(r) over four consecutive scans at nominally constant plasmajet conditions.

tungsten ribbon lamp positioned on the plasmajet axis and the tungsten emissivity data of Latyev et ~1.‘~The E(T) were also corrected for the small (< 6%), time-dependent loss in window transmission noted above and for long term monitor signal variation over the course of arun. As a check on this procedure, the first line was reexamined near the middle and again at the conclusion of each run. The corrected emission coefficients generally repeated to within 10% or less and variations were random. (B) Relative transition probability determination The approach used here to determine the relative transition probabilities was to vary the individual relative A-values, Akh,,, as necessary to yield least-squares fit Boltzmann plots, ln[z]vs[+] over a range in temperature sufficiently large to distinguish the change in temperature (slope) from the statistical uncertainties in the temperature. The upper state energy levels Ek and degeneracies gk were taken from Moore.” Untabulated energy levels at high principal quantum numbers n were calculated from Rydberg-Ritz formulae developed from Moore’s data at lower n. The wavelengths, hki,are the air values3 and k is Boltzmann’s constant. Starting with the transition probability data of Ref. 3 for the ns-4p and nd-4p transitions, least-squares Boltzmann plots (straight line fits) were obtained for each data run. The A-values were adjusted and each set of data refitted, thus yielding a new slope (temperature) for each set.

D. P. AESCHI IMAN

226

This process was iterated until the quantity

was minimized for each spectral line. The subscripts “meas” and “1.~.fit” indicate, respectively, the experimental and least squares fit values of (EkiAk;/A~i,,,g~)for each Boltzmann plot. The temperature range which evolved in the process of minimizing the residues was 2800 k 100 K to 3500lr 100K. Figure 5 shows a representative Boltzmann plot incorporating the final A,,, values as obtained above, and for comparison the A,,, values from Ref. 3. The best-fit temperatures are indicated for each, 3403 2 62 K and 3901 t 186K, respectively. The expression used to assess the overall statistical accuracy of the method was

with the requirement that 0% 1; T, is the average temperature, @_I;is the average statistical uncertainty in T, at the 68% confidence limit, and T,,,” and TpmaX are the lowest and highest temperatures observed, respectively. For the temperature range indicated above, 19.0> B> 10.4, implying a statistical uncertainty in A,,, of j-IO% for the transitions most distant in energy from the 7.~4~ transition used for normalization. The relative A-values obtained here and the data of Wiese et d3 normalized to the value for the KI 580.2 nm, 7s-4p3,, line from Ref. 3, are presented in Table I. The estimated total uncertainties (random and systematic) in the present data are indicated. The relative A-values for the ns-4p, nd-lp, and nf-3d transitions have been converted to n*‘fik for presentation in conventional graphical form.’ Here, fiL is the absolute oscillator

I

I

I

\

(O)Te=3401+62K

I-

(+)Te=3901?138K

l-

-

-

27

28

29

30 E,

Fig. 5. Typical Boltzmann literature values of Wiese

31

32

33

(103cm-3)

plots, In[&A,,,g] vs (E/k), based on relative A-values from this work (0) and on et al.’ (t). The standard deviation, g, of the fitted curve for the present data it 0.053; CTfor the curve using data of Ref. 3 is O.l?O.

Relative transition probabilities of n&p. nd4p, and nf-3d transitions

227

Table 1. Relative transition probabilities of ns-4p. nd4p, and nf-3d spectral lines of neutral potassium.

Transition

:tatistical Weight

693.9, 691.1 580.2, 578.2 534.0, 532.3 509.9, 508.4 495.6 486.4 480.0 475.5 474.2 472.0 469.4

6s-4~(3/2).

2,2

7s-4~(3/2),

2,2

583.2, 581.2 536.0, 534.3 511.2, 509.7 496.5, 495.1 487.0, 485.6 480.4, 479.1 415.1 472.2 469.6

+5d-4p(3/2),

890.3 850.4 825.1 808.0 795.8 786.6 719.6 174.2

§7f-3d 8f-3d 9f-3d lOf-3d llf-3d 12f-3d 13f-3d 14f-3d

Line Cm)

(l/Z) (l/2)

8s-4~(3/2),

2,2

(l/2) 9s-4p(3/2),

2,2

(l/2) lOs-4p(3/2) lls-4p(3/2) 12s-4p(3/2) 13s-4p(3/2), (l/2) 14s-4p(3/2) 15s-4p(3/2)

2 2 1

;,2 2 2 10,4

(l/2) 10,4

6d-4p(3/2),

(l/2) 7d-4p(3/2), (l/Z) 8+4p(3/2) r

10,4 10,4

(l/2) 9d-4p(3/2), (l/2) lOd-4p(3/2),

10,4

2.20, 1.11 1.000, 0.500 0.512 0.256 0.285, 0.142 0.173 0.118 0.0841 0.0650, 0.0325 --

0.105(0.015), 0.124(0.017) 0.136(0.011), 0.149(0.028) 0.103(0.010), 0.123(0.012) 0.0722(0.0045), 0.0873(0.00651

0.087, 0.114 0.124. 0.163.

0.0524

iO.O036j,

10,4

0.0379(0.0027),

10 10 10

0.0455(0.0037) 0.0270(0.00353 0.0172(0.0026) 0.014(0.002)

(l/2)

t Estimated

1.679(0.120), 0.813(0.0058) 1.000. 0.486CO.026) 0.534(0.037), 0.250(0.026) 0.285CO.020) 0.150(0.008) 0.175(0.012) 0.123(0.016) 0.0759(0.0090) 0.0444(0.0090), 0.0267(0.004) 0.0292CO.006) 0.0263(0.004)

0.0675(0.0067)

lld-4p(3/2) 12d-4p(3/2) 13d-4p(3/2)

14 14 14 14 14 14 14 14

uncfrtainties

T The relative transitions,

Relative A-value, NBS

Relative A-value,? This Work

are given

0.594

?- 0.089

0.380 0.195 0.128 0.084 0.0655 0.0527 0.0343

t t + ?

30274

31756 32684 33214 33598 33870 34069 34222 34340 30185 31696 32599

0.118 0.0707, 0.0894

33178

0.0569,

33572

_0.854 0.569 0.386

-_---

33852 34057 34212 34332 32765 33291 33652 33910 34101 34247 34359 34449

in parentheses.

A-values for the combined nd(5/2) + nd(3/2) with statistical weight of 10, are shown.

§ The relative A-values are shown with a total statistical weight

(cm-11 27451

0.095,

0.0732 0.0431, 0.0528 0.0324 --

0.058 0.025 0.019 0.012 + 0.013 + 0.011 * 0.0069

Energy

for the combined of 14.

nf-3d

-t 4p(3/2)

transitions,

strength, given by fik = 3.665 X lo-” Aii 9 A,&,, I

where Akiis in nanometers and g’ is the degeneracy of the lower state, n* is the effective quantum number, n* = n -An, where An is the quantum defect.” These results for the ns-4p, nd-4p, and nf-3d transitions are compared to available data= in Figs. 6-8, respectively. The data of Refs. 6, 7, and 8 are not normalized. (c) Efectron density

The electron density n, was determined from the integrated H, line profiles using the Balmer line half-width calculations of Hill” for Vidal-Cooper-Smith theoretical profiles” convolved with the measured spectrometer slit function (Gaussian of 0.03 nm FWHM) and a Doppler width corresponding to 3000 K. The observed half-widths varied from 0.06 to 0.10 nm and yielded np in the range l-2 X lOI cmm3,with an additional uncertainty of perhaps another factor of two due to spatial averaging, distortions of the integrated H, profile due to variations in flow conditions, etc. Hence, n, > 5 x lOI cmm3. 4. DISCUSSION

(a) Equilibrium Griem’s minimum n, criterion for partial LTE to hold to within 10% for a particular energy

228

D. P. AESCHLJMAN l-

l.( I-

0.2

i EFFECTIVE

‘I

QUANTUM

I,

II

NUMBER,

n*

Fig. 6. Reduced oscillator strength n*‘f,a vs effective quantum number n* for ns-4p transitions in KI: 0. this work; A, Wiese et al.; V, Lindgard and Nielsen; 0, Ormonde; +, Darrigo et al. The present data are scaled to n*‘f;e for the 7s+,z transition from Ref. 3. The data from other sources are presented in absolute terms as published.

6 EFFECTIVE Fig. 7. As in Fig. 6 for the nd-4p

transitions.

QUANTUM

Flagged

7d4p

NUMBER,

circles represent calculation.

n* the present data scaled to Ormonde’\

Relative transition probabilities of nsdp, nd-4p,and nf-3d transitions

6

8

10

12

14

229

lb

EFFECTIVE QUANTUM NUMBER,n* Fig. 8. As in Fig. 6 for the nf-3d transitions. Flagged circles represent the present data scaled to Ormonde’s 8f-3d calculation.

level is n,?7xlO’*~

2’

kT

(

e

I’* >

cme3

where z is unity for neutral potassium, n is the effective quantum number n* for the level, and EH is the ionization potential for hydrogen. This expression was evaluated at 3200 K to give the minimum ne curves for the s, p, d, and f shells; the results are shown in Fig. 9, where it is seen that only the 4s ground state, the 4p first resonance level, and perhaps the 5s and 5p second resonance levels, will fail to be in PLTE with the electrons at the measured electron density. The minimum n, required to yield LTE (i.e. Saha equilibrium; PLTE down to and including the ground state) is generally much more restrictive.” For potassium atoms at - 3000 K, this value is of the order of 10’6cm-3. The requirement can be greatly relaxed, however, if the resonance radiation is strongly self-absorbed. The situation with KI is favorable in this regard since the 4p and 5p levels are resonantly coupled to the 4s ground state. The analysis of Mitchner and Kruger*’ was used to estimate the degree to which the 4p level and n, may be out of equilibrium with the ground state; this analysis shows that the potassium will be in LTE at the conditions of the experiment, even for the radiation escape parameter p as large as O.O1.t Measurements of the individual line intensities within the 4p-4~ and 5p-4~ doublets showed complete self-absorption, as evidenced by identical signals for the two lines (after correction for the small wavelength dependence). Assuming blackbody radiation, the Planck function and an absolute intensity calibration yielded a temperature of - 2500 K, indicating that the flow becomes opaque to resonance radiation at some point in the cooler external flow boundary. The equilibrium composition of uniformly-mixed, seeded flow for a range of seed and argon flow rates and jet static pressures was calculated as a function of temperature, initially as an aid in choosing an appropriate set of experimental conditions. The major species concentrations calculated at the nominal flow conditions (0.60 ml/set seed, 3.6 gmlsec argon, 11 torr static tEstimates based on the approximate KI atom density, path length, and line shape indicate /3 is a few times lo-).

D. P. AESCHLIMAN

230

0 PRINCIPAL OUANTUM

Fig. 9. The minimum

electron

density

required

NUMBER,

for excited

n

state populations

within

10% of LTE.

pressure) are shown in Fig. 10. Also shown are the 6s and 13s level populations, which are seen to peak in the vicinity of 3500 K. The measured electron density, l-2 x 10’4cmm’. lies approximately in the range expected for LTE, but the large uncertainty precludes the use of the n,. data to draw any firm conclusion about the existence of LTE. (b) Self -absorption The doublets of the ns4p lines in potassium offer a useful check for self-absorption. In the

TEMPERATUREIIO'KI

Fig. IO. Equilibrium composition of the seeded Row for a uniform mixture of 0.60ml/sec Feed with 3.6gm/sec argon at 11 torr as a function of temperature. Also shown are the equilibrium 6\ and 13s level populations.

Relative transition probabilities of nsdp,

nd-4p.

and nf-3d

transitions

231

absence of self-absorption, the members of each doublet will have, after accounting for any wavelength-dependent effects, a line intensity ratio equal to the ratio of the upper state degeneracies, 2.0. Self-absorption would reduce this ratio, with a lower bound of 1.0. The relative A-value data of Table 1 for the n&p lines show a ratio of 2.0 within the experimental uncertainties, indicating that the ns-4p transitions are optically thin at the conditions of the experiment. Since the ns4p emission would be the most susceptible to self-absorption, the nd4p and nf-3d emission is concluded to be optically thin also. (c) Comparison

to available data

The relative A-value data obtained here for the 7&p to 12s-4~ and 5d-4p to 9d4p lines agrees to within the estimated experimental uncertainties (5-20%, depending on the specific transition) with the normalized data of Wiese et al.’ The nf-3d data lie 3&50% below the published values3 for which there is no prior experimental confirmation. The present 6&p and 13s-4p are - 25% lower. The discrepancies for the n&p data at high n are perhaps not surprising since these lines are subject to larger uncertainties, (lower signal strengths, higher relative continuum contributions, and larger inversion errors). The difference for the 6s-4~ lines, however, is difficult to explain. Excepting the presence of an undetected, large systematic error in the present work, the conclusion is that the published value is significantly in error. This would be especially important for emission-based T, measurements since these strong, well-isolated lines would very likely be used in the T, determination. The large spread in energy from the 6s to 7s levels and above has a large lever arm in the Boltzmann plot, as seen in Fig. 5, so that the error in A,,, (6s-4~) would cause a serious overprediction of T,, AT, = 500 K for the example shown in Fig. 5. In comparison to the NBS tabulation,3 Lindgard and Nielsen,6 and Ormonde’ both predict significantly lower values for the 6s-4~ transition probability on both relative and absolute scales (see Fig. 6), seemingly in better agreement with the present results. However, if the data of Refs. 6 and 7 are also normalized to the 7s-4p3,, value of Wiese et aL3 the apparent agreement disappears and, in fact, worsens the agreement with the present results for n 2 12. For the nd4p and nf-3d series, the conclusions are somewhat different. Here’ the agreement of the present data with the calculations of 0rmonde,7 again on a relative basis, is significantly better than with Refs. 3 or 6. Normalization within each series to 7d4p and 8f-3d values of Ref. 7, respectively, yields good overall conformity as indicated by the flagged circles of Figs. 7 and 8, respectively, although Ormonde’s calculation for the 1id-4p transition appears to be in error. (d) Systematic errors The potentially most serious source of systematic experimental error lies in the relative spectral response calibration. This calibration was performed three times over the course of the experiment, using two lamp currents (12.00 and 14.OOAd.c.)provided by a current-regulated ( 2 0.01 A) power supply. A 475 nm high pass filter was used to suppress second-order radiation. The calibrations were performed with this filter in place and reproduced to within ? 5%. Each of the neutral density filters was calibrated for transmission at each wavelength employed. The maximum uncertainty in transmission for the ND filters used for the strong lines of the ns4p series was ? 1%. Allowing for errors in the lamp calibration, the maximum systematic error in the relative response function is estimated to be 2 5% at up to 700 nm, increasing to t 10% at 850 nm. Over the range 450-600 nm, where the relative response function was fairly flat, the estimated systematic uncertainty in the relative response is + 2%. Another potential source of systematic error is in the Abel inversion technique employed.” The inversion program has been tested with various analytical input functions for which the inverted solution is known exactly. The program exhibits no systematic errors when tested in this manner. The technique is, however, sensitive to noise in the input data which can lead to unstable behavior, especially near the profile center (r s 0.1 cm) and near the jet boundary (r > 1.5cm) where the SNR was poor. This effect is seen, for example, in the larger scan-toscan intensity variations noted in Fig. 4 for the 14f-3d emission coefficient. Detector saturation effects might explain the reduced A-value for the 6s-4~ transitions. This

232

D. P. AESCH~ IMAN

effect would, if present, have manifested itself in a reduced line intensity ratio, ~6r4p7,2/~6s+,~ ( 2, which was not observed to occur. Acknowledgemenfs-The aid of C. A. Sullivan, Jr.. and D. A. Powers in the operation for help in the equilibrium composition calculations is gratefully acknowledged.

of the plasmajet

facility.

and K. Putz

REFERENCES I. J. B. Heywood and G. J. Womack, Open-Cycle MHD Power Gmerurion. Pergamon Press, Oxford (1969) 2. 0. D. McGregor and M. Mitchner. Phys. &ids 17. 2155 (1974). ? W. 1.. Wiese. M. W. Smith, and B. M. Miles. Atomic Truntition Proh~lhilifie.\. l’ol~me II-Sodium throwh Calcium. U.S. Government Printing Office, Washington DC (1969). 4. E. F. M. van der Held and J. H. Heierman. Physical 3. 31 (1936). 5, D. S. Villars. 1. Opf. Sac. Am. 42, 552 (1952). 6. A. Lindgard and S. E. Nielsen, Af. Datu Nucl. Datu Tables 19. 533 (1977). 7. S. Ormonde, Quantum Systems, Inc. TR-77-20 (1978). Albuquerque, New Mexico. 8. R. Darrigo, J.-N. Le Touiouzan, and B. Chappey, C. R. Acud. Sci. Paris B 276. I I9 (1973) 9. J. W. Dailv. C. H. Krueer. S. A. Self. and R. H. Eustis. AIAA J. 14,997 (1976). IO. J. W. Daily and C. H. Kruger, JQSRT 17, 327 (1977). II. H. Griem, Phma Specfroscopy. McGraw-Hill, New York (1964). I?. S. A. Self and C. H. Kruger, J. Energy 1,25 (1977). 13. D. P. Aeschliman and D. L. Evans, JQSRT 16. I91 (1976). 14. D. L. Evans. D. P. Aeschliman. and R. A. Hill, Phys. Rec. A 10.2430 (1974). 15. R. W. Porter. SlAMRev. 6, 228 (1%4). 16. L. N. Latyev, V. Ya. Chekhovskoi, and E. N. Shestakov, High Temp.-&h Press. 2. 175 (1970). 17. C. E. Moore, Atomic Energy Levels. Circ. No. 467. Vol. I. U.S. Government Printing Office, Washington, D.C. (1949). 18. R. A. Hill, Sandia Laboratories, Private communication. 19. C. R. Vidal, J. Cooper, and E. W. Smith, A,lrophys. J. Suppl. No. 214 25, 37 (1973). 20. M. Mitchner and C. H. Kruger, Putiiallp Ionized Gases. Wiley. New York (1973).