Theoretical study of equilibrium nitrogen plasma radiation

J. Quant. Spectrosc. Radiat. Trans[er, Vol. 17, pp. 471-482. Pergamon Press 1977. Printed in Great Britain

THEORETICAL STUDY OF EQUILIBRIUM NITROGEN PLASMA RADIATIONt W. D. BARFIELD Theoretical Division,Universityof California,Los Alamos ScientificLaboratory, Los Alamos,NM 87545, U.S.A. (Received 28 May 1976)

Abstract--Newtheoreticalcalculationsof continuum and total radiationemittedby nitrogenplasmasin L~E at 9000, 11000, 13000, 13500and 15000°Kat Iatm are described and results are compared with previously reported experimentalresults derived from emissionand absorption measurements.Theoreticalwidths for selected N(1) and N(II) transitionsagree within a factor of 2 with recent measurementsand other theoretical results. "Excess continuum radiation", attributed by other authors to radiative attachment to neutral N, is probablydue to overlappingline wings.The calculatedtotal radiationis consistentwith experimentalresults.

1. INTRODUCTION RADIATIONemitted by nitrogen and air plasmas has been actively studied both experimentally and theoretically since the pioneer investigations of HXRSCHFELDERand MAGEE."~ ARMSTRONGet al., ~2~ BIBERMANand NORMAN,~3~KON'KOV et al., ~') and AVlLOVAet al. ~5) have reviewed progress as of the listed dates. HUNT and SIBULKIN~6) made a theoretical study of radiative transfer in a uniform nitrogen plasma in LTE. WILSOr~and NICOLET~7)tabulated effective total continuum cross sections and absorption/'-numbers and electron-impact widths and shifts for bound-bound transitions of neutral and singly-ionized C, N and O, GRIEMts'9~ and JOHNSTONit°) have developed methods for treating line broadening in plasmas. Line widths of N(I) and (II) emissions were measured by MORRXS and GARRISON,ctt) JALUFKA and C R A I G (12) and HELBIG et al. for temperatures in the range 9000-13600°K at I and 2 atm and by ASINOVSKY et al. ~17"t8~ for 10000-17000°K at 1 atm. When Boldt's results are corrected for an incorrect temperature measurement [AsINOVSKytt8)],the three sets of measurements at 13000°K, 1 atm are in agreement. THOMASand MENARDttg"2°) measured line and continuum radiation from bow shocks in air. These authors' continuum emission measurement ranged from a factor 2 (at 5000 A) to a factor 20 (at 1100/~) higher than the measurement of MORRIS,KREY and GARRISON.¢t*) Other shock measurements, reviewed in ASINOVSKY,°8) show fairly substantial quantitative discrepancies. The measurement of Morris, Krey and Garrison is substantially larger than their theoretical estimate; they attributed the excess radiation to the process N+e~N-+hv and deduced a photodetachment cross section for N - (tD) of the order of 2--4 x 10-t6 cm ~, substantially higher than theoretical cross sections which are more like 0.1-2x 10-t7cm2 [HENRY,~2" MOSKVI~,~22~COWAN~23q.The N - (tD) cross section as determined by Morris, Krey and Garrison was confirmed by ASINOVSKVet al., "SJ who also deduced a cross section for N - (3p) of 3-5 × 10-t7 cm 2. Most of the shock-wave measurements also point to the presence of excess radiation [AsINOVSKY,8~]. On the other hand, KON'KOV et al. ~'25) found no excess radiation in measurements on air at 50-100 atm. This paper reports new theoretical calculations of LTE nitrogen plasma radiation and absorption coefficients at 9000, 11000, 13000, 13500 and 15000°K, 1 atm. and 9000 °, 2 atm. Results are compared with the measurements of MORRIS, KREY and GARRISONtts't6) and ASINOVSKYet al. "s~ Theoretical collision widths of selected atomic and ionic lines are compared with recent measurements and other theoretical values.

fWork performed under the auspices of the U.S. Energy Research Development Administration. 471

472

w.D. BARFIELD 2. THEORETICAL CROSS SECTIONS

(a) Free-[ree transitions Analytical fitst (2~) to the neutral atom inverse bremsstrahlung absorption cross section calculations of KIVEL<27) are employed. In Kivel's calculations, the parameters in the configuration-dependent approximate exchange potentials were adjusted by comparison with Hartree-Fock type results; parameters in the polarization potential were fixed by comparison with polarizability and O- photodetachment measurements. The contribution due to absorption by neutral N2 is included, again making use of analytical fits to results of KIVEL f27) who employed a Born approximation treatment [HtlNDLEY(2*qto express the absorption cross section in terms of Maxwell-averaged momentum transfer cross section measurements of FROSTand PHELPS:~) Kivel's atomic cross sections are substantially lower than cross sections calculated by GELTMAN(3°) at 15000°K. For air at 6000°K, p/9o = 10-6, where atomic free-free absorption dominates, Kivel's absorption coefficient is 25-50% larger than that calculated by MJOLSNESSand RUPPEL:TM At g[go = 1, where molecular free-free absorption dominates, Kivel's values range between 14 and 30% of Mjolsness and Ruppel's. Gaunt factors for free-free transitions in the fields of N ions are taken from results of GREEN,~32)~vho used a screened Coulomb potential and took account of the effects of Fermi-Dirac statistics (availability of upper states). As pointed out by ARMSTRONGet al., c2) continuum lowering (see below) should result in an increase in the calculated number of free-free transitions, although this increase has not been taken into account in the present results. (b) Bound-free cross sections Cross sections for photoionization from the 3s and 3p subshell of neutral N were calculated using Dirac-Slater SCF nonhydrogenic wave functions ["HEX" code, LmEgMAN, CROMERand WABEl~;(33) "PELEC" code, BRVSK and ZERaV,~) BARFIELD, KOONTZ and HtJEBNER'] with term-splitting ignored. In the case of 3d and L-shell transitions and M and N-shell transitions of N ions interpolation between quantum defect model results near threshold and Born approximation results at higher energies is used [AI~MSTRON~ et al:2q. Comparisons with Hartree-Fock calculations of DAL~ARNOet aL (~) are given in ARMSTRONGet al: 2) for several N(I) and N(II) transitions. Due to plasma interactions, states with principal quantum number > n,i~, where n7, = 0.4107 Z~os[ 1023/pe(Cm3)]x/(kT(e V)),

are considered to be merged into the continuum ["continuum lowering", ARMSTRON637];here Zros = residual charge of passive ion (one greater than initial charge). Transitions from states below nc,, to states above are included in the photoionization calculations, and the photoionization edge is lowered accordingly (by Z~es/n2rit Ryd) with extrapolated cross section values, ncrit is restricted to be ~7. Possible autoionizing transitions are not included in the calculated absorption coefficient. Hartree-Fock confguration-interaction calculations of the cross section for photodetachment of N- were furnished by COWAN:23) Below the A27ru edge at 16.7eV, photoionization of N2 is treated in an r-centroid approximation with transition moment determined by comparison with measurements [Cook and OGAWA(38) COOKand METZGER;(39) SAMSONand CAIRNS~'°'] making use of Franck-Condon factors calculated by GENEROSAet al. (4~)Above the second edge the cross section is crudely approximated as twice the atomic cross section. (C) Bound-bound transitions The atomic line atlas included parameters for -10,000 line transitions of N(I)--N(V). Measured (WIESE et al: TM)or Hartree-Fock-Slater (for transitions between states with principal quantum numbers < 9 [ARMs~ONGet a/:2q) or hydrogenic [KA~AS and LATTER;('3) GREENet al:4"q ?For molecularnitrogen,the ratio fit/tabulatedvalue(Kivel)~0.8.

473

Theoretical study of equilibrium nitrogen plasma radiation

f-numbers are included in the atlas. Transitions to upper states with principal quantum number > nc,t are considered to be photoionizations. Contributions to the collision width due to Stark (electron and ion perturbers, GPJEM,<8)pp. 85, 91-93), Van der Waals and resonance (GPJEM,(8>pp. 95-100) broadening mechanisms are included. In the case of absorption lines of neutral atoms, broadening by electrons is treated in the impact approximation (dipole-monopole interaction, "strong" + "weak" collision termst). In the strong collision term, which dominates at low temperatures (kT ~ ho~jk), the minimum impact parameter Pm~. for the integration over dp is taken as 3

"/1".3 ~ E -- -3 A + ~ik ~Oj k _

p j , rain

[JOHNSTONet at.; ('°) BARANGER(~)] with A = h/my = wave length of electron with energy E before scattering, hoJjk= energy difference of states ] and k, Rik = [ ( k l r l j ) l 2 = square of radial integral (atomic units) averaged and summed over magnetic substates. The sum is over all states connected with state ./by allowed transitions. In the weak collision term, which dominates at high temperatures (h~ojk< kT), p m ~ . is determined from

2 ~ O}.rain -~-3 A Rjk [JouNsTON:"°> B~NGER~'~q. (The inconsistency of using different values for Or~. in the same expression is ignored.) The a (Z) function ("Gaunt factor") of Griem is thermally averaged.t The Lorentz electron impact profile in the far wing (kTl((r~)lao2) " 2 - hAto,o < [Aho[) is augmented by the Holtsmark profile, representing the effect of ion perturbers ("quasi-static" approximation, GRIEMtS)), for Ata of the same sign as the quadratic Stark effect. The "one electron" theory [BARANCER:~> JOXNSTONet a/. "°>] was also used to calculate the intermediate portion of the line profile (Wo't~< IhAo, I < ha~oco), for several lines (Wo~t2= impact theory line core half-width; hAto = energy displacement from line center). The resulting asymmetric profile is described by the Lorentz expression with a variable width. Since it was found that this width varies only slightly from the impact theory line core width Wo~2 (Fig. 1), the simpler Lorentz profile with constant width is used in the intermediate frequency range.* Terms describing interference between overlapping lines with common initial or final states (GRIEMc9>)were not included. 1.2

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474

W.D. BARFIELD

The contribution of molecular perturbers to the Van der Waals broadening is neglected. The semi-empirical treatment of GPOEM~9~is used for the Stark broadening of absorption lines of ions. The collision width is given by the thermal average for n, electrons h

w,,2 = ~
o-,(,,) = ~ o-,_~(,:) = ~ 8~'2(RYd)2 x/(3)~ h~,~ h,,g(~'~, ~)ao 2 (¢ = incident electron energy, [jk = absorption oscillator strength if 0 < hvjk or emission oscillator strength if hz,~k<0.). The Gaunt factor is interpolated between ~ ~0(g~-0.2) and k T ~ ¢(g ~ gco~o,.b) limiting forms (JOHNSTONet al."°>). An additional broadening due to perturbing ions (quadrupole interaction GIUEU~9)) was found to be a small effect. Calculated half-intensity half-widths for sixteen N(I) lines and ten N(II) lines agree with other theoretical estimates [GREIM;ts'9'6°'62) JONES;~ssJ WILSON and NICOLET;~7) HEY t4s)] and with measurements on N(I) at 11700 and 14700°K (HELBIG tl3>) and at 13500°K (MORRISand GARRISON"") and on N(II) at approx. 2 eV [JALUFKAand CRAm;tm POPOVlCet al."7q generally within a factor 2.t Pressure and Doppler widths are combined in a Voigt profile in the line core. The resulting profile is approximately~ normalized. Line shifts are ignored. A check was made as to how well the f-number computed by numerical integration of the profile for each line agreed with the atlas value: Table 1 gives the distributions according to the ratio pnumber by numerical integration atlas value ~with Holtsmark wing for the cases [ no Holtsmark wing "Ratio values ,~ 1 result from truncation of the profiles at the limits of the frequency range used (i.e. hv = 0, 1000 eV). Truncation of the line profiles at the frequencies where the contribution of the line becomes less than 0.0001 × continuum results in substantial loss of •-number for the weaker lines (Table 1: C, D) but has only a small effect on the total radiation. The contributions of the first and second positive and Birge-Hopfield band systems of N~ and the first negative, Meinel and Meinel* systems of N2- are taken from an atlas of - 5 x 106 transitions of N2, 02, NO, etc. In most cases the band strengths were computed in an r-centroid Franck-Condon factor (GENEROSAet aL"') approximation making use of electronic transition moments determined by comparison with measurements. Broadening of molecular lines is ignored, i.e. the full strength of a line is added to the spectral mesh interval in which the (unshifted) line center falls. Table 1. Distribution of lines according to ratio (f-number by numerical integration/atlas value) A, with Holtsmark wing; B, without Holtsmark wing; C, line profile cut off at 0.0001 x continuum (without Holtsmark wing); D, full profile (0--1000eV) (without Holtsmark wing) < 0.5 A B C D

22 0 104 8

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tExceptions are N(1) transitions with A = 1412 and 1135/~ for which the measured values of Re[. (I I) are substantially lower and higher, respectively, than the author's values, which agree with the theoretical results of Re[. (7) within a factor 2. Half-widths for four N(II) transitions (5700, 3838, 672, 3007/~) as tabulated in Re[. (8) are substantially smaller than the values of Re[. (9), which tend to agree (factor 2) with the author's results. ~:The correction factor for the normalization is exact for the limiting case Doppler width,~ collision width.

Theoretical Study of equilibrium nitrogen plasma radiation

475

3. ABUNDANCES

Species abundances are calculated by minimizing the total free energy (McCHEsr4~Y and MOLLER¢49)),with free energy data from GILMORE,¢5°) JANAFtables, °~) G ~ r 4 et al., ¢s2) WOOLEY,~') and other sources. The chemistry was checked by comparison with results of GILMORe,°') HILSENRATH and KLEIN, ~55)DRELLISHAK et al.,<5~)and P LESHANOV.¢57)There is some uncertainty about the small electron affinity of neutral nitrogen.t Table 2 demonstrates the sensitivity of the calculated abundance to this datum. The value -0.45 eV was employed for the calculations of N plasma radiation reported hereAt Fractional populations of excited states of N2 and N2÷ were calculated by GILMORE. (~4)

The equilibrium emission is given by

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(erg/cm ~ sr)

(1)

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k T , \ 112f AE\3

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13000"11atm

9000°/1atm

9000°/2 atm

0 -0.45 - 1.0 - 1.45

0.113+14 0.756+ 13 0.464 + 13 0.34+ 13

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where AE is the energy of the lowest resonance transition, a nitrogen plasma at 13000°/1 atm with Ne = 1.07 x 10'2/cm 3 is in LTE, whereas at 9000 ° LTE requires Ne > 1.3 x 10 '6 (N(II)), 3.6 x 10 '6 (N(IV)). Results obtained in this study for 9000 °, 2 atm, correspond to an electron density Ne = 1.0 × 101~/cm3. 4. R E S U L T S : C O M P A R I S O N W I T H M E A S U R E M E N T S

Calculated theoretical local emission spectra at 13000°/1 atm are shown in Figs. 2 and 3, in which the various curves give the (cumulative) contributions of the several contributing processes. The atomic lines contribution was calculated with and without the Holtsmark wing. Also shown are selected measurements of the "continuum emission" reported by MORRISet al., ( ' ) and from the composite of ASINOVSKYet al. "s) The experimental spectra reproduced from Morris

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480

W.D. BARF1ELD

et al. are given to facilitate comparison (Fig. 2). The theoretical absorption coefficient

rv (cm-') = ~ Nikv~jk ijk

[Compare (1)] at 13500°, 1 atm, is shown in Fig. 4, which also includes selected values derived from absorption and emission measurements by MORRISet al. " ~ at 13600°. The calculated continuous and total emissions for the wavelength range 2000-60000 A are shown in Fig. 5, which also shows measurements reported by KREYand MORRIS." ° As discussed Table 3. Most important lines contributing to the iniensity at Several wavelengths. Tabulated are the fractional contribution of each line to the total intensity, transition energy (hT,o), collision half-widths (cw), transition quantum numbers and atlas sequence number (NOL). Fract. Contr.

h~,o

cw

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(eV)

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NOL

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N(I) N(I) N(I) N(I) N(I) N(I) N(I) N(I) N(1) N(1) N(I) N(I)

5d~2p4S 6d--)2p4S 4d-)2p'S 5d-) 2p2D 7d---)2p2D 3s:p~2p~D 6d:-)2p2D 3s2P->2p2P 5d-~2p2D 4d~ 2p2D 3s'P~2p'S 6d--)2pZD

102 156 58

104 351

1 323

2 285 59

0 157

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N(I)

7d~2p4S

N(I)

7s-)3p4P

N(I)

6d-*3p'P

102 156 58 351 323 104 285 205

137 102 148 156 58 351 323 104

~7O-7~5A 0.034 0.019 0.016 0.011 0.011 0.011 0.010 0.112 0.114 0.064 0.030 0.019 0.018 0.014 0.012 0.271

1.84 1.79 0.062

0.0044 0.0016 0.017

N(I) N(I) N(1)

4d~ 3p4p 5s~ 3p4p 7g-~,6f

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33500-35400 A 0.0023 0.015 0.016 0.0032 0.0011 0.0051 0.0023

N(1) N(1) N(1) N(1) N(1) N(1) N(1)

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6d~5p 5g~4f

4po4s 4d-~4p 5s-~4p

102 156 58 62 50 213 35 i

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60 252

Theoretical study of equilibrium nitrogen plasma radiation

481

by the latter authors, the measurements represent lower bounds for the total emission (per cm 3) since no correction was made for self-absorption of the more intense lines. The calculated contributions at I atm due to N + e recombination radiation in the wavelength range 900/~ < A are: 4.48 (13000°); 1.51 (11000°); 0.170 (9000°) watt/cm3-sr. Table 3 identifies the lines which make the largest contributions to the intensity at several energies (13000°, 1 atm, without Holtsmark wing). Factor 2 uncertainties in line widths result in comparable uncertainty in the contribution of overlapping line wings to the intensity. 5. DISCUSSION OF RESULTS

Theoretical widths for selected N(I) and N(II) lines agree within a factor of 2 with recent measurements and other theoretical results. Although the theoretical total emission in the wavelength range > 900° A is essentially the same1 with and without the Hoitsmark wing, inclusion of the wing results in a distribution with substantially more radiation in the range 2000-60000~, as compared with measurement. Calculated total radiation is consistent with experimental results. It seems likely that the "excess radiation" attributed to formation of N- by MORRISet al. °5~ and ASlNOVSKY"~ is mainly due to overlapping line wings. The theoretical spectra indicate that it is unlikely that the true continuum could have beem measured at wavelengths> 1160/~,. It is unnecessary to assume an extraordinarily large cross section for N- photodetachment to account for the observed radiation. Acknowledgements--Numerous persons at several organizations contributed to the development of the computer program ("ABSCO" code) used for the theoretical calculations reported here. The Air Force Weapons Laboratory group under Captain Richard Harris played a major role in the development of the code and molecular band systems atlas. The atlas of atomic line transitions was furnished by Lockheed Palo Alto Laboratory (R. JOHNSTOn). Configuration-interaction calculations of cross sections for photodetachment of N- were carried out by R. CowAN(LASL). Atomic line broadening and the contributions of N- photodetachment and photoionization from the 3s and 3p subshells of neutral N were added by the author. The author thanks Drs. W. F. HUEBNERand R. D. COWANfor reading the manuscript.

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W . D . BARFIELD

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