A spectroscopic study of equilibrium in nitrogen arcs

J. Quant. Spectrosc. Radiut. Transfer. Vol. 14, pp. 19-26. PergamonPress 1974.Printedin Great Britain.

A SPECTROSCOPIC STUDY OF EQUILIBRIUM IN NITROGEN ARCS* J. B.

SHUMAKER

National Bureau of Standards, Washington, (Received

D.C. 20234, U.S.A.

21 May 1973)

Abstract-Nitrogen arc measurements of the intensity of the 4915 A - 4935 A NI doublet and of the 3995 A NII line show that local thermodynamic equilibrium cannot be assumed in nitrogen arcs at electron densities below I x IO” cmm3. Below this point, the results suggest that gas and electron temperatures differ significantly and that ground states are overpopulated with respect to upper electronically excited states.

INTRODUCTION

WE RECENTLY reported the results of a study of local thermodynamic equilibrium in argon arcs.“’ We have now carried out a similar study in nitrogen arcs. Since the experimental approach is practically identical to that used in the argon study we give here only a very brief description of the experiments. EXPERIMENTAL

The arc source was a conventional d.c. cascadeC2’ arc with 3.2 mm channel diameter. The electrodes were shielded with argon and the observation section operated in nitrogen. Periodic examination of the side-on spectrum of the observation section showd no evidence of argon or other impurities during these experiments. The arc was operated at currents from 40 to 170 A and at four pressures from 0.2 to 5.0 atm. The nitrogen spectral features used for this study are the NI 3s(‘P)+(‘S”) multiplet at 4915 and 4935 A and the NII 3s(‘P”)-3p(‘D) line at 3995 A. At each of40-50 lateral positions across the arc diameter, absolute side-on photo-electric intensity measurements were made at 42 wavelengths between 4890 and 4960 A and at 27 wavelengths between 3990 and 4000 A. The intensity measurements were Abel-inverted and the resulting spectra at 0.01 cm radial increments were least-squares fitted to appropriate line profile functions. In the case of the NII line the profile was of the form: Z(i) = B + (i - i.,)S + ILL@ - 1.0) w, a),

(1)

where L(x, w, a) = &

[g(;:l

+g(&?)I.

g(u, u) = (u + r)[arctan(u

+ v) - arctan (u)] + f In[(l + z?)/(l

+ (U + a)‘)].

* The research reported in this paper was supported in part by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, under contract No. F-33615-72-M-5031. 19

20

J.B.

SHUMAKER

Here L(i - A,, w, a) is a normalized triangular-slit-broadened dispersion profile with central wavelength &, , dispersion semi-halfwidth W, and slit semi-half width 0. By means of this fitting, the level, B, and slope, S, of the background continuum (assumed linear in A) and the total intensity, Z, , width, w, and line center, %, , of the dispersion profile line were determined. For the NI multiplet consisting of two lines 20.13 A apart, equation (1) was modified by replacing L by L(/I - 2,) w, a) + 2.2L(A - A, - 20.13, w, a); again the same five parameters were determined by least-squares fitting. In this case, it is assumed that the Stark widths and shifts of the two components are identical and that the 4935 A component is 2.2 times as intense as the weaker line. This ratio was obtained by trial-and-error adjustment during the fitting of a small sample of the data. No attempt was made to determine it with precision. The effective apparatus widths, C, at the wavelengths of the experiments were computed from the known dispersion of the monochromator and from apparatus width measurements at nearby wavelengths using a low-pressure mercury discharge. RESULTS

The total line intensities [the values of the parameter Z, of equation (l)] for the NI and NII spectral features are shown plotted against one another in Fig. 1. Points are shown for all experiments at 0.01 cm increments in radius from the arc axis out as far as statistically

10’6

IO”

1019

102”

Fig. 1. Nitrogen arc intensity measurements in photons/(cm3 set). The curves are the family of equilibrium, constant-pressure contours of Fig. 2, least-squares fitted to the 1.03 and 5.00 atm data.

significant line profiles could be fitted. Errors resulting from self-absorption are computed to be less than 1 per cent in all cases, based upon the measured intensities and the temperature profiles deduced from them as indicated below. In Fig. 2 are plotted the computed populations of the two upper levels associated with these lines under conditions of thermodynamic

A spectroscopic

IO0

study of equilibrium in nitrogen arcs

10’0

109 3995

& NLI

UPPER

LEVEL

21

IO” POPULATION

Fig. 2. Computed equilibrium upper level populations in cm- 3 for pressures of the experiments shown in Fig. I. Also shown are constant temperature and constant electron density contours.

equilibrium. At constant pressure, the population of the neutral line upper level is related to that of the ion line by a relationship of the form aNI = j&i), which is given by these equilibrium computations. By least-squares fitting of the line intensity data to the relationship M&i

= f(W&,),

the transition probability parameters, A, can be determined provided the measurements were made under conditions of local thermodynamic equilibrium (LTE). Since LTE, if it exists at all in an arc, is expected to be favored by high electron densities, it is appropriate to attempt this fitting first with the data believed to represent the highest electron density conditions. Accordingly, the 500 and 1.03 atm data were simultaneously least-squares fitted to the corresponding pair of curves of Fig. 2. The transition probabilities obtained are 2.30 x 106(f0*025 x 10”) set- ’ for the NI multiplet near 4928 A and 1.27 x lO*( f0.053 x 10’) set-’ for the NII line at 3995 A. Using these transition probabilities, the family of constant-pressure curves of Fig. 2 was then transferred to Fig. 1. It is evident from inspection of the curves in Fig. 1 that most of the 0.50 and 0.20 atm data exhibit departures from LTE. Aside from a few points at the low electron density end of the 1.03 atm data, the rest of the data is in accord with the assumption of LTE. The 1.03 atm points in Fig. 1 comprise data from experiments at 10 different arc currents chosen to provide substantial overlap between conditions near the axis at one current and those in the outer regions of the next higher current. In addition to following the general shape of the LTE curve, the data from the individual 1.03 atm experiments in the regions of overlap exhibit no systematic radius-dependent discrepancy from one another and, hence, no gradient dependence. Since collisions with electrons constitute the dominant mechanism for

22

J. B.

SHUMAKER

bringing about equilibrium in a plasma, (3) the electron density is the plasma parameter most directly correlated with the degree of approach to LTE. A comparison of Figs. 1 and 2 shows that the departures from LTE occur at electron densities below 1 x IO” cme3 and that, above that point, the data appear to be consistent with the assumption of LTE. Some support for this assumption at the higher electron densities is provided by the agreement between the values obtained for the transition probabilities and those obtained by other independent techniques. For the 3995 A NII line, both theoretical calculations and lifetime measurements(4-7) give values in the range from 1.4 to 1.64 x lo* set-‘. For the 4928 A NI multiplet, the only reported values which are not arc measurements depending in some way on the assumption of LTE are theoretical values: a Coulomb approximation valuec3’ of 2.0 x lo6 and a Hartree-Fock-Slater’8’ value of 1.4 x IO6 set- ‘. For other NI multiplets, however, the lifetime measurements of DESESQUELLES~” are in excellent agreement with Richter’s nitrogen arc transition probability measurements,“’ which were obtained relative to the 4928 A NI multiplet using a transition probability for the latter of 2.2 x IO6 see-‘. Since relative arc measurements of these transition probabilities can be expected to be fairly insensitive to whether or not there are present small departures from LTE, this agreement provides in turn a tenuous agreement with the present experiments. In an effort to obtain some additional information on the state of the nitrogen plasma in the lower electron density non-equilibrium experiments. the data were analyzed in terms of a simple two-temperature model with ground state overpopulation. For this purpose, it was assumed that data with electron density above 1 x 10” cm-j (i.e. the 1.03 and 5.00 atm experiments) were in LTE and the line-width information from the 4935-4915 8, line profile fitting results was used to estimate electron densities. The electron density dependence of the line width was first established experimentally using the LTE data. The electron density associated with each point of the 1.03 and 5.00 atm data in Fig. 1 was calculated from the closest point of the LTE curve to the experimental data point. A plot of the ratios of the experimentally measured line semi-half-widths to the corresponding electron densities determined in this manner is shown in Fig. 3. The results show good agreement with the calculations of BENETT and GRIEM,(lo) although the scatter is too great to confirm the predicted temperature dependence. For the subsequent electron-density determinations, the simple average, 0.117 x lo-l6 A cm3, of the values in Fig. 3 was used for the ratio of the line width to electron density. Under the common assumption of partial LTE, in which the free electrons are in LTE with higher excited states, the generalized Saha equation, 2

can be used to obtain the electron temperature, T,. from the measurement of electron density, n, , and excited neutral population, n o*. In this equation, Z, and n, are the internal partition function and total number density of singly charged atomic ions. The statistical weight go* and energy Eo* refer to the upper level of the NI line and x is the ionization potential of the neutral atom corrected as usual for plasma interactions. It is assumed in this equation that excited ionic levels are either in LTE or contribute negligibly to Z, and n,. It is also assumed here and in later equations that molecules, molecular ions and multiplyionized atoms can be neglected. The errors introduced by these simplifying assumptions are insignificant for the near-LTE conditions of these experiments in comparison, for example,

A spectroscopic a

study of equilibrium in nitrogen arcs

I

23

I

.

. D

1.03Ptm

5.00Atm

1

'5000

20000

I5000

TEt4PERAT”RE.K

Fig. 3. Ratio of 4928 NI multiplet semi-halfwidth to electron density measurements. is the theoretical calculation of Ref. (10).

The curve

an uncertainty of 8.5 per cent (which is the standard deviation from the mean of the w/n, values in Fig. 3) in the electron density determination. From the electron temperatures determined from equation (2), it is possible to calculate a measure of the degree of overpopulation among the lower ionic states (or of underpopulation among the higher states) by computing the ratio of the total number of atomic ions (%n,) to the LTE population computed from the measured ion line intensity and a Boltzmann factor p1 = (n,gl*/n,*Z,)[exp( - E,*/kT,)]. The quantity /?I was calculated for all the 0.50 and 0.20 atm data. This calculation is very sensitive to errors in n,; an error of 8.5 per cent corresponds to an error of a factor of 3 in pl. Within this uncertainty of half an order of magnitude, p1 is essentially 1 in all of the 0.50 atm data and, in the 0.20 atm experiments, decreases from 40 on the axis to 1 in the outer regions. Thus there is evidently no significant underpopulation of excited ionic states in the 0.50 atm experiments. In the 0.20 atm experiments, a 40-fold underpopulation occurs on the axis; in the outer regions, absorption of radiation and diffusion presumably supply enough excited ions to create an illusion of near-LTE ‘among the ionic levels at the lower electron temperatures. In a somewhat similar but less satisfactory way, an upper limit can be set on the gas temperature Tg and a lower limit on the neutral lower-level overpopulation factor &, = (n, g,,*/n,*Z,)[exp( - E,*/kT,)]. In this expression, Z, and n, are the internal partition with

24

J. B. SHUMAKER

function and total number density upon Dalton’s law in the form

of neutral

atoms. The calculation

P = (no + n,)kT,

+ n,kT,

of T, and &, is based

+ AP,

where molecules, multiply-ionized atoms. etc. have been neglected and AP is the small pressure correction due to plasma interaction. In LTE with the same n, and T,, the pressure would be P’ = (n,’ + 2n,)kT, + AP, which is easily computed

for any measured nO’ =

Thus, for each experimental

point.

(P - P’)IkT,

n, and no* using equation

(2) and the relation

(ZolgO*)n,*[exp(E,*lkT,)l. the left-hand

side of

= n,‘M,(T,/T,)

-

1I - dl - (TJT,)l

(3)

can be evaluated. From this equation alone, both PO and TJT, cannot be determined but some bounds to their values can be obtained. For arc conditions not far removed from LTE, it is expected that /I0 2 1 and T,/T, I I. Hence, ‘(’

- P’)‘no’kTel

’

’

whichever

is greater

(4)

and T,/T, I ( [(’ - P”‘(no’ + ne)kTel ’ ’ 1

whichever

is smaller.

(5)

In the application of these considerations to the 0.50 and 0.20 atm results, the uncertainty resulting from an 8.5 per cent uncertainty in n, is typically 30 per cent for the quantities calculated in equations (4) and (5). Within this degree of uncertainty, P-P‘ is small on the arc axis at both pressures and, at the higher arc currents, is negative. This leads, for example to T,/T, I 0.5 for the rightmost 0.20 atm data-point in Fig. 1. Away from the arc center, P-P’ is positive and leads, at a radial distance of 0.5 mm, to PO 2 2 for the 0.50 atm experiments and to PO 2 10 for the 0.20 atm experiments. Although these results are little better than qualitative, some general conclusions can be drawn from them. Since the electron density generally decreases with increasing radius, resulting in a lower collision frequency, T,/T, should also decrease with increasing radius. The above analysis suggests that T,/T, is significantly less than 1 even on the axis under low electron-density conditions; hence, it is probably less than 1 everywhere and, in order to satisfy equation (3), /IO must be correspondingly greater than the lower limits estimated above for the outer regions of the arc. Thus, the data show that, at electron densities smaller than about 1 x 10” cmm3, nitrogen arc plasmas exhibit a significant decoupling of the gas and electron temperatures and that, at about the same critical electron density, there begins to appear significant overpopulation of low-lying atomic and ionic states relative to states involving higher excited and free electrons. CONCLUSIONS

These results confirm other recent findings of non-equilibrium behavior in nitrogen arcso1,r2) and suggest that, at electron densities above about 1 x 10” cm-3, LTE probaby prevails. Table 1 illustrates the effect on the deduced state of a plasma produced by assuming

A spectroscopic

study of equilibrium in nitrogen arcs

25

Table 1. Possible deduced states of a non-LTE nitrogen plasma if LTE is assumed Measured quantities

P

n, x lo-‘6

n,* x lo-‘0

n,* x 10-g

(atm)

(cm- 3,

(cm- 3,

(cm- 3,

2.6 4.4 3.8 5.0 ,o -

7.8 1r 7.8 % 17

0.012 1.2 2 51-1.2

P, NI

0.20

P, NII

0%

NI, NII NI, n, NH, n,

i% 0.26 0.23

$1 12000 15000 15200 19200 14900

LTE in a non-LTE situation. The data used in this table are the on-axis data of the highest current 0.20 atm experiment, which is the rightmost O-20 atm point in Fig. 1. The values of the measured quantities in the experiment are underlined in the table. The other entries show the values which would be computed if only two of the four measurements had been undertaken and LTE had been assumed to calculate the remainder. For example, the first line shows that, if only the total pressure and neutral line intensity were measured, the deduced electron density and excited ionic-state population would be lower than the observed values by factors of 2 and 100, respectively. The deduced temperature would lie between the electron and gas temperatures : the non-LTE analysis gives T, = 19200 K and indicates that the gas temperature is not greater than 9600 K. In fact, if the neutral state populations depart from LTE to the same extent as do the ionic-state populations, then the gas temperature is only 4400 K. Arc non-equilibrium may be the explanation for the apparent need to assume a controversially high photodetachment cross section for N - in order to interpret nitrogen arc continuum measurements. (13) The arc measurements in which N - emission appears important (14s15, have all been made at low electron densities, where the present data demonstrate significant deviation from LTE. Except for a few near-axial points, all of the present measurements in which non-LTE was observed exhibited a pressure higher than that calculated from the measured n, and n,* assuming LTE. Under these conditions, the assumption of LTE and the usual measurement of P and n,,* to establish the state of the plasma lead to underestimation of the electron density (as in the first row of Table 1). Any measured continuum intensity then would appear anomalously high and, in consequence could be assumed to contain a substantial N - contribution. It is interesting that high-pressure shock experiments,(’ ‘I1s) in which n, > 1 x lo”, show no evidence of the N- continuum REFERENCES 1. J. B. SHUMAKERand C. H. POPENOE,J. Res. natn. Eur. Stands 76A, 71 (1972). 2. H. MAECKER,Z. Narurforsch. lla, 457 (1956). 3. H. R. GRIEM, Plasma Spectroscopy. McGraw-Hill, New York, (1964). 4. W. L. WIESE, M. W. SMITHand B. M. MILES,NSRDS-National Bureau of Standards 22, Vol. II (U.S. Government Printing Office, Washington, D.C., 1969). 5. A. DENIS, J. DESESQUELLES,M. DUFAY and M. C. POULIZAC, Compt. Rend. 266B, 64 (1968). 6. E. H. PINNINGTON,Nucl. Znsh. b4erh. 90, 93 (1970). 7. J. DESESQUELLES,Ann. Phys. 6, 71 (1971). 8. P. S. KELLY, JQSRT4, 117 (1964). 9. J. RICHTER, Z. Astrophysik, 51, 177 (1961). 10. S. M. BENETT and H. R. GRIEM, Technical Report No. 71-097, University of Maryland (unpublished). 11. W. H. VENABLE,JR. and J. B. SHUMAKER,JR., JQSRT 9, 1215 (1969).

26 12. 13. 14. 15. 16. 17. 18.

J. B. SHUMAKER F. P. INCROPERA and E. S. MURRER,JQSRT 12,1369 (1972). A. A. KONKOV,V. M. NIKOLAEVand Yu. A. PLASTININ, Opt. Spectrosc. 25, 380 (1968). G. BOLDT,2. P&k 154, 330 (1959). J. C. MORRIS.R. U. KREY and G. R. BACH.JOSRT6. 727 (1966). E. I. ASINOVS~II,A. V. KIRILLINand G. A.‘KGBzEv, f&h femp.‘6, 710 (1968). A. A. KONKOV,A. P. RYAZIN and V. C. RUDNEV,JQSRT 7, 345 (1967). D. M. COOPER, JQSRT 12, 1175 (1972).