plasma diagnostics using high-resolution spectroscopic techniques

16V. W. Slivinsky, H. N. Kornblum, and H. D. Shay, J. Appl.Phys. 46, 1973 (1975).

17C. Yunonaka, M. Yokoyamna, S. Nakai, T. Saualki, . Yo-shida, M. Motova, C. Yamabe, T. Tuschudi, T. Yamanaka,J. Mizui, N. Yamaguchi, and K. Nishikawa, IAEA-CN-33/F3-5, in Plasma Physics and Controlled Nuclear Fusion Re-search 1974, Fifth IAEA Conference Proceedings, Tokyo,11-15 November 1974.K. G. Estabrook, E. J. Valeo, and W. L. Kruer, Phys.Fluids 18, 1151 (1975).

19C. F. McConaghy and L. W. Coleman, Appl. Phys. Lett. 25,268 (1974).

20 L. W. Coleman and C. F. McCanaghy, Proceedings of theEleventh International Conference on High Speed Photography(Chapman and Hall, London, 1975), pp. 196-201.

21G. I. Brulchnevitch et al., Phys. Lett. (Amsterdam) 51, 249(1975).

22 D. J. Bradley et al., Opt. Commun. (Amsterdam) 15, 231(1975).

23D. T. Attwood, L. W. Coleman, J. T. Larsen, and E. K.Storm (unpublished).

25A. J. Lieber, R. F. Benjamin, H. D. Sutphin, and C. B.Webb, Nucl. Instrum. Methods 127, 87 (1975).

25V. W. Slivinsky, H. G. Ahlstrom, K. G. Tirsell, J. Larsen,S. Glaros, G. Zimmerman, and H. Shay, "Measurement ofthe Ion Temperature in Laser Driven Fusion, " Phys. Rev.35, 1083 (1975).

26W. L. Kruer, "Recent Developments in Laser Plasma Theoryand Simulations, " presented at the August 6, 1976 GordonResearch Conference, Tilton, N. H. (unpublished).

27j. H. Erkkila, "Laser Light Scattering and Absorption in

Dense, Spherically Symmetric Plasmas," Ph. D. thesis(University of California, 1975) (uwpublIshed), LawrenceLivormore Lab. Roport No. UCRL-51914.

28H. Hora, Phys. Fluids 12, 182 (1969).29H. Hora, Z. Phys. 226, 156 (1969).30 H. Hora, Opto-Electron 2, 201 (1970).31H. Hora, in Laser Interaction and Related Plasma Phenom-

ena, edited by H. J. Schwarz and H. Hora (Plenun, New York,1971), p. 383.

32R. Kidder, "Interaction of Intense Photon Beams with Plas-mas (II), " Proceedings of the Japan-U.S. Seminar on LaserInteraction with Matter, Kyoto, Japan September 25, 1972(unpublished).

33 J. W. Shearer and J. L. Eddleman, Phys. Fluids 16, 1753(1973).

34A. Bruce Langdon and Barbara F. Lasinski, Phys. Rev.Lett. 34, 834 (1975).

35 P. Kaw, G. Schmidt, and T. Wilcox, Phys. Fluids 16, 1522(1973).

36E. J. Valeo and K. G. Estabrook, Phys. Rev. Lett. 34, 1008(1975).

37C. E. Max, Phys. Fluids 19, 74 (1976).38R. A. Haas, M. J. Boyle, K. R. Manes, and J. E. Swain,

J. Appl. Phys. 47, 1318 (1976).3 9 T.P. Donaldson and I. J. Spalding, Phys. Rev. Lett. 36,

467 (1976).40 M. Born and E. Wolf, Principles of Optics (Pergamon, New

York, 1964), Chap. 3.41D. Phillion, "Evidence for Short Density Scale Heights at

the Critical Density Surface in Laser Irradiated Plasmas"(unpublished).

Plasma diagnostics using high-resolution spectroscopic techniques*t

U. Feldman and G. A. DoschekE. 0. Hulburt Center for Space Research, Naval Research Laboratory, Washington, D.C. 20375

(Received 1 December 1976)

Density-sensitive line intensity ratios measurable in high-resolution spectra are discussed for high-temperature plasmas (1.5-1300 eV). By working along isoelectronic sequences, it is possible to find density-sensitive ratios over a wide range of electron densities (10"2 to - 10"' cm-3 ). This range includes the densityof a number of laboratory plasmas of current interest. We also discuss the temperature sensitivity of some ofthe line ratios for ions formed in the colder plasmas with temperatures of 1.5-15 eV. We present a table offorbidden lines obtained from Skylab spectra of the solar corona. Lines of this type should be detectable incertain laboratory spectra. Their long wavelengths make these lines particularly suitable for measuring theion temperature or nonthermal motions. Finally, we show the feasibility of detecting megagauss magneticfields in high-temperature plasmas, from profiles of selected spectral lines.

I. INTRODUCTION

High spatial and spectral resolution can be used todetermine the physical conditions in high-temperatureplasmas. The electron density and temperature can bederived from the intensity ratios of certain spectrallines. The combined ion temperature and nonthermalturbulence can be determined from spectral line pro-files. In some cases the lines are primarily broadenedby the Zeeman or Stark effects, and analysis of the lineshapes and widths allows the strength of the magneticfield or the electron density to be inferred. The Dopp-ler shifts of the lines reveal anisotropic mass mo-tions. The absolute intensity of certain emission linesand the knowledge of the emitting volume can be used todetermine the abundance of impurity elements. Each

726 J. Opt. Soc. Am., Vol. 67. No. 6, June 1977

of these measurements involves isolating particularemission lines that are primarily sensitive to a singlephysical parameter.

The lines sensitive to a particular parameter mayfall in the x-ray, the EUV, the uv, or even in the vis-ible region of the spectrum. In this paper we show howspectral line ratios can be used to determine the elec-tron density. We will show that by working along iso-electronic sequences, it is possible to find density sen-sitive lines for a number of laboratory plasmas of cur-rent interest (1012 to - 1021 cm- 3). In the case of colderplasmas with temperatures of 1. 5-15 eV, we discusscertain line ratios that can be used to measure the elec-tron temperature. In the case of high-temperatureplasmas, some of the lines considered fall at long wave-

Copyright © 1977 by the Optical Society of America 726

- -X- 3

JN

N 1 Z )0 0 InN tO) Z

Z Z .i

- 2

o 0 0 0 Nl

a1) 4) 0, W) Nz z z z '-.

FIG. 1. Simplified energy level diagram for hypotheticalthree-level ion. The solid lines indicate the excitations anddeexcitations; the wavy lines show the radiative decay modes.

lengths (> 1000 i). Because the Doppler width of a lineis proportional to wavelength, these lines are particu-larly well suited for the determination of combined iontemperature and turbulence. Finally, we show fromprofiles of selected spectral lines the feasibility of de-tecting megagauss magnetic fields in high-temperatureplasmas. The work presented below is based partly onavailable atomic data for certain ions that are common-ly found in solar plasmas, and partly on calculations byCowan' involving heavy ions. The remainder is basedon isoelectronic extrapolations of these data to ions thatmight be expected in certain laboratory plasmas. Forthese ions, the uncertainty in the atomic data is greater.However, the main conclusions derived from the extrap-olated data are not expected to change significantly.

II. DENSITY-SENSITIVE LINE RATIOS

The basic ideas behind our calculations can be ex-plained by considering two general cases, illustratedby hypothetical three-level ions. The real ions we con-sider fall into one or the other of these cases, or intoa combination of these catagories. In all of the calcu-lations, we assume that the plasma is in ionization equi-librium. Then, for the levels considered, only elec-tron (and sometimes proton) impact excitation and de-excitation, and spontaneous radiative decay, are im-portant in determining level populations. We also as-sume that the lines are optically thin, i. e., that thepopulations of the levels are not significantly altered byradiative transfer effects.

A. Case (a)

A hypothetical three-level ion is shown in Fig. 1.Level 1 is a level in the ground configuration. Each ofthe upper levels can be excited by electron excitationfrom level 1, and can be deexcited or can radiatively

decay to level 1. Solid arrows indicate the collisionalelectron transitions; the wavy arrows show the radiativedecay modes. We assume in case (a) that level 2 doesnot decay to level 1 by an ordinary electric dipole tran-sition. For example, the transition might be spin for-bidden, or a magnetic dipole transition. The decayrate A21 is much smaller than A31. From the detailedbalance of the three levels, the photon intensity ratio121/131 (see Fig. 1) is given by

121 = n-A

131 n3A 31

[C13 C3 2 + C12C32 + C12 C31 + (C,3A 32 + C12A3 2 + C12 A3 1)/NJ]A 2 1(c12 C2 3 + C13 C2 3 + C13 C21 + C1 3A 2 1 /Ne)A 3 1

(1)

In Eq. (1), ni are the populations (cm-3) relative to lev-el 1, Aij are spontaneous decay rates (s-1), and Cij arethe excitation and deexcitation coefficients (cm 3 Sol). In

the limit of zero density, the ratio approaches

ML _ . 31 + C13 A3 2 + CIA 32131 Ne O C13A31

(2)

In the high-density limit, where NeC32 and NeC31 can nolonger be neglected, the ratio approaches

M2.1 (C13 C3 2 + Cl2C3 2 + CU2 c 30)A2 3I31 Ne (C12C23 + C13C23 + C13 C2 1 )A3 1 (

The collision coefficients for allowed transitions can beexpressed in the form2

Cij = 2.7 7 10'5 f (.gi exp(- iEii/kTe)

(Te)'''A.Eij 1 (4)

where fij is the absorption oscillator strength, (gij isthe effective Gaunt factor, AE j is the transition energy(ergs), Te is the electron temperature (0 K), and k isBoltzmann's constant. For most of the ions we con-sider, AEij/kTe <<1 and Cij is only weakly dependent onTe, i.e., Ci -c T'-1" 2. The collisional deexcitation ratesare given by

Cji = (wi/w) Cij exp(AEijj/kTe) , (5)

where wi and w, are the statistical weights of the lowerand upper levels, respectively. Note that when Eq. (4)is substituted into Eq. (5), that Cji becomes independentof the Boltzmann factor, exp(- AEij/kTe). The collisionrates for nonallowed optical transitions were obtainedfrom the literature, and are cited specifically below forthe actual transitions we consider.

Because Cij are not strongly temperature dependent,the line ratios given by Eqs. (1)-(3) depend primarilyon the density. Since usually C12 < C,3 and A3 2 =A 3 1 inEq. (2), I2?1/131 1. In the high-density limit [Eq. (3)],the collision terms in the numerator and denominatorare about equal, and therefore 121/13, =A21/A31 << 1, typi-cally several orders of magnitude. Thus the ratio 121/I3, varies by orders of magnitude, depending on the den-sity. In other cases, A3 2 <<A31 , and the ratio in the low-density limit can be approximated by C12 /C13.

B. Case (b)

In case (b), instead of assuming A2 , <<A31, we assumethat A., =A32 »A 31 . For example, the three levels

727 J. Opt. Soc. Am., Vol. 67, No. 6, June 1977 U. Feldman and G. A. Doschek 727

might be the 3s2S,1 2 , 3p 2P, and 3d2 D levels of Na-likeions. The line ratio of interest is now 132/121, and not

I

I21/I3,. We also assume that C1, «C, 3 C12 . Theratio132/I21 is given by

32- (C12C23 + C13C23 + C13 C2 1 + C13A211N,)A3--'21 [ C13C 2 + C12C3 2 + C12C3 1 + (C1 3A32 + C12A32 + C12A31)/IV, 1A1

In the low-density limit,

I32 C13A32,, C'21 NC- 0 C13 A32 + C12 A3 2 + C 12A 31 C12

In the high-density limit,

132 (C12C23+ C13 C23 + C13 C2)A32 C23A3 (8)121 N

0- C13 C3 2 + C12 C32 + C12 C3 j A 21 C3 2A21 (

and 132/121 is approximately unity. Thus, as in case (a),the ratio varies by a large factor between the low- andhigh-density limits.

In case (a), the ratio of interest is large at low den-sities, and decreases with increasing density. In case(b), the ratio of interest is small at low densities, andincreases with increasing density.

For case (b), density sensitivity occurs if N0 C12 cA21,or NC23,A32A. Because the relevant transitions are al-lowed transitions, Eq. (4) can be used to calculate Ci.Since exp(- AEij/kT 0) is usually -1, (g) is between 0. 2and 0. 8. We find from the relation N0 Cij =Aj that

N 6.1 X10 22i(Tc)1/2

where the well-known relationship between fi and Ajihas been used; and X is the approximate wavelength ofthe lines in angstroms. In Eq. (9), i and j refer to thelower and upper levels of the transition, respectively.For Tez86 eV or 106 K and wj = w, Ne 22x1017 cm- 3 at1000 A and 2x1020 cm-3 at 100 A

III. RESULTS

A. The FI isoelectronic sequence [case (a)]

Case (a) can be illustrated with the ions of the fluorineisoelectronic sequence. The actual levels are shown inFig. 2. This sequence satisfies the case (a) criterionthat A2, <<A31 . The transition 2- 1 is a magnetic dipoletransition, and A3, ;A 31.

Equation (1) was solved usingf values determined byWiese et al. 3 and Cowan, ' assuming a Gaunt factor of0. 52 The proton excitation rates, and the direct elec-tron excitation rates C12, were calculated and extrap-olated from Bely and Faucher, and Blaha, 5 respective-ly. The decay rates can be evaluated from the analyticexpression derived by Shortley. 6 The temperatures atwhich the collision coefficients Cij were calculated weretaken from Jordan7 and extrapolated from her work tothe heavier ions up to Moxxxiv. Although her calcula-tions may need modifications at high densities, thetemperatures she derives are close enough for ourpurposes. As shown, the results are not very sensitiveto temperature. (The effect of temperature on the cal-culations for the F i sequence is shown in a previous pa-per on the subject. )8

The results for the F i sequence are shown in Fig. 3.We chose ions that cover the range from Arx toMO xxxiv. The lighter ions are formed at temperaturesof :o140 eV, while MO xxxiv is formed at z3000 eV. Theuseful range of density sensitivity in the ratio is prob-ably about two orders of magnitude, i. e., from about1 to 0.01. In this range the ratio is almost inverselyproportional to density. For example, for Arx the ratiois sensitive from :2x1011 cm-3 to =4x1013 cm- 3; forMoxxxiv the ratio is sensitive from ;1017 cm- 3 to ;2X1019 cm- 3 . For the light ion Arx, the wavelengths ofthe two lines are widely separated. The forbidden lineis well into the visible. Thus two spectrographs areneeded to observe both of these lines simultaneously,and they must be calibrated with respect to each other.However, because the forbidden line is at such a longwavelength, it is easy to measure its profile and there-by determine the ion temperature and nonthermal tur-bulence. The Arx line has been observed in the spec-trum of the solar corona. 9 In contrast, the Mo xxxivlines are much nearer each other in wavelength, andboth lines could be observed using a single grazing in-cidence spectrograph. Also, the profiles of both linescould be measured using, for example, the high-resolu-tion spectrograph described by Behring, Cohen, andFeldman. ' 0 The MO xxxiv lines have not yet been ob-served in plasma spectra. Our wavelengths are extrap-olated and are believed to be accurate to within an ang-strom. Note that at the low densities found in tokamakplasmas (=1014 cm'3), all the forbidden lines of iron andabove are intense. They are as strong or stronger thanthe resonance lines.

The type of calculation done for the F i isoelectronicsequence can also be done for the 0 I, C I, and B i se-quences. In all these sequences for a particular ele-ment, there is a forbidden line that has approximatelythe same wavelength as the line in the F i sequence."

F I ISOELECTRONIC SEQUENCE

2s2p6 2 S

N

H-4

2s 22p5

J1/2

1/2

3/2

FIG. 2. Energy level diagram for the F I isoelectronic se-quence. The lines used to obtain the ratios in Fig. 3 are shown.

728 J. Opt. Soc. Am., Vol. 67 No. 6, June 1977

(6)

U. Feldman and G. A. Doschek 728

0.1 I- ArX(140eV)(4257A/l65.53A \o 2-TiXl7(320eV02ll9A/l2l.97A)

3-FeXXIIII550eV)(975A/93.93A)-- 1 -1 11 I I 1 ' 'I'IIL I'll I 1 1 I I I I I -

lo0ll 102 10I3 IO4 15O -

H -

,, 1.0 .

I- ZnXMlI950eV)5094/73.96)0.1 2-SeX(I500eV)(290A/59A) 2 3@ 4

3-Zr XXX (2000 eV)(140A/43A) -I\

4-Mo=XXX1(3000eV)(0I3A/38A)0.01 I I , I I I I I 11 '1 I

e 613 1014 I0O 1ol6 io'7 1ol8 1019

ELECTRON DENSITY (cm-3)

FIG. 3. Density-sensitive line ratios calculated for ions of the

Fi isoelectronic sequence. The intensities are expressed inphotons and not ergs.

The same is true for the allowed lines.' 2 For theseother sequences, the intensity ratio of the forbidden toallowed line in a particular element will be similar to the

ratio in the F i sequence. The main difference is that thedifferent ions of a given element are formed at differenttemperatures. For example, the B i lines are emittedat about twice the temperature of the F i lines. Theground terms of the 0 I and C I sequences are 3

P. In the0i sequence the 3 pj -

3P2 magnetic dipole transition isthe most practical one to consider for atomic numberZ S 28. The 3Pl - 3'o transition is at much longer wave-lengths and becomes an important line for still higherstages of ionization. In the C i sequence the 3pl-3Po

transition is the short wavelength line while 3P2 -3p

is the long wavelength line. "

B. The Na I and 0 I isoelectronic sequences [case (b)

Case (b) can be illustrated with ions of the sodiumand oxygen isoelectronic sequences. The pertinent lev-els are shown in Fig. 4. The lines of the Q I sequence

NaI OIISOELECTRONIC SEQUENCE ISOELECTRONIC SEQUENCE

3d

3 p, JH- 0: S H

2s22p4-4 2t3p ~

FIG. 4. Energy level diagrams for the Nai and OI isoelec-tronic sequences. The lines used to obtain the ratios in Figs.5 and 7 are shown.

729 J. Opt. Soc. Am., Vol. 67, No. 6, June 1977

10

OI0

H-

0.0l

I I 111111 1 1 1111111 1 1 I111 1i 1 11111 1 1 11111 II 1 1I I! I111111i li i

I - Mg Iii (1.3eV) Na ISOELECTRONIC SEQUENCE

2- Si DZ (6 OeV)3- S 1Z(14eV)4- Ca X (69eV)5-Fe MI(260eV) 2 6

6- Cu XIX(520eV)

-i 2I

)I I m

10 13 10 14 1015 1016 1017 1018 1019 l0eELECTRON DENSITY ( cm-3 )

FIG. 5. Density-sensitive line ratios calculated for ions of theNai isoelectronic sequence. The intensities are expressed inphotons and not ergs.

involve transitions within the 2s22p4 configuration andthe lines of the Nai sequence involve transitions withinthe 31 configuration (I -orbital angular momentum).For a particular temperature, the 0 i lines are atshorter wavelengths than the Nai ions, and are thussensitive at higher densities compared with the Naiions [see Eq. (9)]. The combined temperature range ofboth of these sequences is from 1. 3 to 3000 eV. In bothsequences, A32 ~A21 >> A31 . In the Na i sequence, A31 issmall because the 3d - 3s transition only occurs via theelectric quadrupole mode. In the 0 I sequence, the 2p6

-2s'2p 4 transitions are two-electron transitions (parity-forbidden), and are not very probable. For similarreasons, C,3 is small for both sequences. In these se-quences there are several more levels involved than inthe simplified example discussed in Sec. II. However,in principle the problem is the same as in the example.The wavelengths of the lines of the NaI sequence areknown from the literature. 13 The wavelengths of theO i lines are known from the literature up throughNi xxi. 1

4 We have extrapolated the results up to Mo xxxv.

The specific values for Mo-xxxv are from Cowan. '

The results for the Nai sequence are shown in Fig. 5.The collision rates were taken from Blaha.5 The ratiovaries by about one order of magnitude over about twoorders of magnitude in density. Thus the Nai ratiosare not quite as sensitive to density as the F i ratios.The Mgii lines have been discussed by Feldman andDoschek, 15 and the density sensitivity of the lines in theNai sequence was previously discussed by Feldmanet al. 16

The lines of the Nai sequence have one importantadvantage over the lines of the F i sequence. Becausethe energy separation between 3d and 3p is about thesame as between 3p and 3s, both lines in the line ratiofall at nearly the same wavelengths. Thus instrumentalsensitivity with wavelength is not as important as forthe F i sequence, and both lines of all the ions can be ob-served using the same spectrograph. The intensityratios for the lighter ions of the Nai sequence also ex-hibit a strong temperature dependence. In fact, for theions Mg ir through S vi, the line ratios may be used toderive the temperature rather than the density (seeFeldman and Doschek for Mg ii15). As can be seen fromEqs. (7) and (8), the line ratio is proportional to


3s 2S 1 l/2

Be I ISOELECTRONIC SEQUENCE

JIs -- 0

2p 2ID 2

FIG. 6. The temperature sen-sitivity of line intensity ratiosin the Nar isoelectronic se-quence (see text for discussion).To is the equilibrium tempera-ture of maximum emitting ef-fic iency.

'P

2s2p 3

2s 21S

exp(- AE 23/kT0 ), which is a strongly varying function oftemperature at the equilibrium temperature To at whichthe lighter ions are formed. This variation is shownfor the Nai ions in Fig. 6.

The results for the Q I sequence are shown in Fig. 7.The oscillator strengths were calculated from Cowan'and the Gaunt factors are given by Van Regemorter andDavis. 2 The coefficient C13 must be small, but its pre-cise values are not known. Thus the curves in Fig. 7should level off in the low-density limit, and not ap-proach zero. This sequence was discussed in connec-tion with laser-produced plasmas by Doschek et al. 14As for the Nai sequence, the line pairs in the Qi se-quence occur close together in wavelength, and can beobserved with a single spectrograph. For the heavierions shown in Fig. 7, the temperature dependence is notimportant. There are many possible lines 121 that maybe used to obtain the line ratio, 132/121. There is onlyone 132 line, however. It is the 2s2p8 1P1-2p6 'S0 line.

The above calculations for the Qi sequence involvelines from the configurations, 2s22p4, 2s2p8 , and 2p6.

1 0E I ' M''IIT I . I'1l 11""1 '"1 1 ' ' 1OI ISOELECTRONIC SEQUENCE

1.0

I-. I-rX07OeV)- 3 / 2-Ti=X(340eV)

Z 0.1 3-FeXIX(690eV)4-NiW(860eV)5-ZnXXKf (lOOOeV)6-Mom (3000eV) -

0.01 , 8 1 20 21 22107 108 1019 1020 1021 10 2

ELECTRON DENSITY (cm- 3 )

FIG. 7. Density-sensitive line ratios calculated for ions of theOi isoelectronic sequence. The intensities are expressed inphotons and not ergs.

FIG. 8. Energy level diagram for the Bei isoelectronic se-quence. The lines used to obtain the ratios in Fig. 9 are shown.

The same type of calculation can be generalized to otherisoelectronic sequences, i. e., 2s22pk, 2s2pk+l, and 2p+2 ,where k =1, 2, 3, 4. As mentioned in connection withthe F i lines, the advantage of using different sequencesis that for a particular element, the same density sensi-tivity can be obtained at different temperatures.

The Na i and O i sequence lines of Ti xii, Fe xvi,Fexix, and Znxxiii can be found in spectra of laser-produced plasmas. 14,16,17 We analyzed the spectracreated by focusing a 10 J pulse of 1. 06 Aum radiationon a slab target of various materials. The pulse lengthwas 0. 5-1 ns and the focal spot was 20-50 m in diame-ter. We found that the intensity ratio of the pertinentFe xix lines (see Fig. 7) is about 1.14 For Znxxiii, theratio is much less than 1. These ratios indicate a den-sity less than 1020 electrons cm-3. This result is inagreement with results we obtained from the analysis ofthe Stark effect on high members of the Lyman seriesof Bv, C vi, Nvii, and Fix. 18 In laser-produced plas-mas from slab targets, we occasionally observed re-gions in the expanding plasma that were at somewhathigher electron densities than surrounding regions. 16These density enhancements occurred at a distance ofabout 1-2 mm from the target. The Nai lines of Tixirand Fe xvr were instrumental in establishing the factthat the density is greater in these regions. It was foundthat the electron density is less than 10l8 cm-3 at a dis-tance of 1 mm from the target, but is locally greaterthan 1018 cm-3 in the density enhanced regions.

C. The Be I isoelectronic sequence

Finally, we discuss ions of a sequence that is a com-bination of case (a) and case (b). Figure 8 shows thepertinent energy levels of an ion of the beryllium iso-electronic sequence. If we define level 2 as the 2s2p 3 p,level, and level 3 as the 2s2p'Pl level, then the ionfalls into case (a). However, calculations show that the


0.1

Ti / To

0

rf)H

2

0

H

3p

1


M .0

02 0.1

c'!

C."4

CL)C-"

4 1.0

H 0.1

1015 1016 1017

ELECTRON DENSITY (cm-3)

FIG. 9. Density-sensitive line ratios calculated for ionsBeI isoelectronic sequence. The intensities are expressphotons and not ergs.

intersystem line 2s2 'SO-2s2p 3P, is about two ordeof magnitude weaker than the 2s2 1S0 -2s2p'P, resoline at all densities. A more practical ratio is obfrom the lines 2s2p 3P2 -2p2 3P2 and 2s2 'SO-2s2p 3PThis is the line pair that we consider, and we defilevel 3 as the 2p2 3P2 level. (The 2s2 iS 0 -2s2p3P2is very weak because it is a magnetic quadrupolesition. The 2S2 'SO-2s2p3P0 transition is strictly Ibidden.) We now have a situation in which A21 is s

because the transition is spin forbidden, but is stimuch greater than A,,, where level 3 is now define2p 2 3P2 . The 2s 2 'SO-2p 2 3 P2 transition is a two-ele

transition. Thus the ion is a combination of casesand (b), because of the way in which we define theels.

Figure 9 shows the results for four ions of the Isequence. The results resemble a case (a) ion; titio is largest at low densities. A considerable anof theoretical work has been done on the light ionsand Ov by workers in astrophysics.' 9 ' 20 Calculatifor Sixi are also available. We have extrapolateastrophysical results for Caxvir and Fexxrii. Bo371.06 A Caxvii intersystem line and the 263.76 .Fexxiii intersystem line have been identified in s(flare spectra by Widing.22 A list of solar flare liktween 171 and 630 A has been published by Sandliral.23 The small density sensitivity of the Fexxiiat densities less than= 2X 1014 cmm3 is due to the2s2p 3P2 - 2s2p 3P, magnetic dipole transition, whicomes important for the heavy ions.

We note that it is important to consider all typeexcitations when working with complicated ions suthe Be-like ions. Figure 10 shows the Be-like litfor CaxvII at very low densities. In one calculatetwo-electron excitation, 2s2 'S,-2p 2 3P2 is includesthe other calculation, it is set equal to zero. If t


electron coefficient were in fact zero, which it is not,the Be-like line ratio would be a good density indicatorin solar flare plasmas. The error introduced by ne-glecting the two-electron rate leads to an order of mag-nitude error in the line ratio.

IV. FORBIDDEN LINES

For case (a), one of the lines involved is either amagnetic dipole transition or a spin-forbidden transi-tion. Many lines of this type have been identified forelements abundant in the solar atmosphere. In particu-lar, the recently obtained solar spectra from Skylab(1100-4000 A) have enabled us to compile a fairly com-plete list of forbidden lines in the EUV. These linesare emitted by ions at temperatures between = 52 andX :950 eV. Because of their long wavelengths and hightemperature, these lines have enabled the nonthermal

1019 turbulence in the solar corona to be determined. Also,the identification of these lines is an important step inidentifying the forbidden lines of heavier elements in

oed in laboratory spectra. A list of the strongest forbiddenlines identified in solar plasmas is given in Tables I andII. Most of these lines are emitted at temperatures-130 eV. During flares, higher-temperature lines areobserved which we have discussed elsewhere. 2 4 Also,

rs Sandlin et at.2 5 have compiled a list of forbidden linesnance observed in the Skylab spectra. They discuss the inten-tained sity behavior of these lines in different solar regions.

L1 -

ine Figure 11 shows profiles of a few of the stronger co-line ronal forbidden lines. The x's in the figure are points,ran- on Gaussian profiles. As can be seen, the coronal linefor- profiles are well fit by Gaussians. From the ionization-mall, equilibrium calculations of Jordan,26 the ion tempera-11l ture of maximum emission of the coronal ions can bead as determined. (In the corona, the electron and ion tem-ctron peratures are most likely equal.) The profiles in Fig.(a) 11 are wider than expected for just instrumental andlev- thermal Doppler broadening in ionization equilibrium.

The excess widths of the lines are interpreted as dueeither to microscopic or macroscopic turbulence in the

3e I corona. The observation of such turbulence is impor-ie ra- tant in the theory of coronal heating, which is still aniount unsolved problem.* C IIIions)d theth theA

AarLes be-n etratio

ch be-

s oftch asLe ratioon, theL; in.le two-

I- 100"I

-9

10141012

ELECTRON DENSITY (cm'3)

FIG. 10. The effect of the double electron excitation,2p2 3p, on the indicated line intensity ratio for Caxvii.

2s 2 1 SO-

U. Feldman and G. A. Doschek

TABLE I. Forbidden lines between 1100 and 2000 A (SpectrumA). Numbers in parentheses are intensities from Spectrum B.Spectrum A and B were recorded about 40 above the solarlimb. The slit was tangent to the limb. The spectrographused was the NRL instrument flown on Skylab. Predicted andcalculated wavelengths are from Edlen,9,29 Svensson, Svens-son, Ekberg, and Edl6n, 31 and Jordan. 32 The Ovii wavelengthsare from Engelhardt and Sommer. 33 The Fe x lines were iden-tified by Smitt. 34

Ion and Transition -solar (A) S cal ( Internity atSutn S.

Mg VI] 2p3 3P, 2p2 5 S 1189.84 1189.7 1.4 0.20 1.2)6/nM3 VI 2p3 '' 12 2p3 'P3/2 1190.07 1190.1 2.4 0.20 1.2(6)Mg VI 2p

3 4S312 - 2p

3 2P,,2 1191.64 1190.6 0.8 0.19 1.1(6)

S X 2p3 4

S312 - 2p3

2D5/2 1196.26 1196.9 0.62 0.20 1.6(6)

S X 2p3 0

S3 2 -2p3 2p323 1213.00 1213.6 3. 1 0.22 1.9(6)Inc XIII 3p

2 p, - 3p

2 'So 1216.46 1217.2 (15 )a (0. 2 5,a (2.5(6))'

F. XII 3p3

'S312 - 3p3 2

P31 2 1242.03 1242.05 13.7 0.17 1.8(6)

(56) (0.20) (2.6(6))Ni XIIl 3p4

3P, - 3p

4 'S

0 1277.23 1277.0 0.42 0.18 2.0(6)Mg V 2p

4 3PI - 2p

4 ISo 1324.45 1324.4 0.26 0.17 6.8(5)

Fc XII 3P3 4

S312 - 3p3 2

P,,2 1349,38 1349.51 8.4 0.23 3.0(6)

-3p3 2( 14 1 0.20) (2.2(6))M. xi 23

3 3p 3 2

.V2 P3/2 1359.59 1359.5 0.17 0.17 1.4)6)

Ca XV 2p2 3

P2

- 2p2

ID

Ar Xl 2p4 3p

2 - 2p4

I D2

Si Vill 2p3

4S3/2 - 2p3

2D5,2

Si Vill 2p3 4

S312 - 2p3

2D)/2

Fr X

Fr Xl

Cr X

Cr X

Fe X

Fe X

Fe X

SXI

o VII

o Vil

3p4

3d 4 a 2 - 3p4

( D)3d 2

F7p2

3p4 3

P, - 3p4

I So

3p3

4S3/2 3p3 2

P3/ 2

3p3 4

S3/2 - 3p3 2pI /2

3p43d 4

F712 - 3p4

('D)3d 2F71 2

3p4

3d 4

D712 - 3p4

3d 2G712

3p43d 4D7 2 -3p

43d 2G02

2p2 3P p 2p

2 I D2

1s2n

3S2 - Is2p

3P2

Is2s 3S, - Is2p

3PO

SIX 2p4 3

P2 -2p4 1

D2

ME VI 2p3 4

S3 /2 - 2p3

'D3/2S Xi 2p

2 3P2 - 2p

2 1D2

Fe IX 3p53d 3p, - 3p

53d

3D2

Ni XIV 3p3 4

S3M2 - 3p3 2

D1/2Fe IX 3p

53d

3P2 - 3p

53dF

3

Fo X 3p4

3d 4D712 - 3p4(3

P) F`7/2

1368.84

1370.54

1375.98

1392.12

1408.66

1409.47

1428.76

1440.49

1445.76

1452.70

1463.50

1467.08

1489.04

1564.10

1582.60

1603.31

1611.7

1614.51

1623.68

1639.80

1666.94

1715.45

1717.42

1749.6?

1805.97

1826.23

1841.55

1847.25

1862.76

1866.75

1917.21

1918.27

1376.6

1390.67

1440.6

1445.78

1467.42

1488.9

1564.1

1583.5

1614.6

1623.63

1639.87

1715.1

1805.87

1826.15

1841.3

1867

1916.8

1.5?

0.15

0.15?

0.29

0.24

0.45

2.6(5.6)0.42

9.3(13)

2.0(4.4)6.2

(17)0.27

0.65

2.2

0.35

(36)0.30

2.2

0.56

1.8

1.2

1.1

2.0

2.8

5.2

0.20

0.20

0.18

0.17

0.22(0.21)0.20

0.22(0.23)

0.18

0.18(0.18)0.19

0.21

0.30

0.18

(0.37)0.16

0.26

0.20

0.26

0.22

0.16

0.26

0.25

0.27

1.3(6)

9.6(5)

1.2(6)(1.3(6))

1.1(6)

1.5(6)(1.5(6))1.5(6)

1.1(6)

(1.6(6))

1.4(6)

1.2(6)

1.4(6)

2.1(6)

1.8(6)

V. LINE BROADENING BY MAGNETIC FIELDS

Some theoretical calculations of hot and dense plas-mas, such as low-inductance vacuum spark plasmas,or laser-produced plasmas, suggest the presence ofmegagauss magnetic fields.2 7 It is possible to detectmagnetic fields of this strength in these plasmas fromthe analysis of line profiles in the EUV region. In the100-300 A region, lines from a broad range of ioniza-tion stages are emitted. For example, emission froman ion such as Fe ix arises in cold regions. Emissionfrom ions such as Fexviii arises in substantially hotterregions. 2 8

Figure 12 shows profiles of the Fe Ix 103. 566 A lineand the Fe xviii 103.94 A line. The spectra were pro-duced by a low-inductance vacuum spark and were re-corded by the NBS 10.7 m grazing incidence spectro-

I 7

e201 A63 5

20

X

TBEII. Obevdfridnlns o <20 setu

.147 AFeX[Too 1.9.106 K

81349A FeXI[Teo 1.9.-I06 K

6-

.20

4 -

I- 3

2

a

FIG. 11. Forbidden lines of highly ionized ions, recorded inspectra of the solar corona (see Table I). The x's representpoints on Gaussian profiles.

TABLE 1I. Observed forbidden lines for X >2000 A (spectrumB).

?s(A) solarIon and transition (air) Intensity" W0(A)5 "T"

Fexx 3pS3d 3P2-3p'3d3D2 2042.36 54 0.40 3. 8(6)Nixv 3p2 3P,-3p 2 'D2 2085. 610Ni xii 3p4 3

P2-3p4 1D2 2125.50 34 0.46 5. 1(6)

Si viI 2p4 3P2-2p4 1D2 2146. 67 28 0. 53 3.2(6)Si IX 2p2 3P2-2p2 1D2 2149.33 46 0. 46 2.4(6)Fexir 3p3 4

S3/2-3p3 2D1 /2 2169.03 74 0.39 3.2(6)

Ni xiv 3p3 4S3/2 -3p

3 2D,/ 2 2184.20 31 0. 42 3. 9(6)

Fexii 3p3 4S 23,2 -3p

3 2D3/2 2405. 71 216 0.40 2. 8(6)

Fe iXd 3pS3d 3F4-3p5 3d 1F3 2497. 8 ...Fe xii 3p3 2

D3/2-3p3 2P3 /2 2565.99 78 0.40 2.4(6)

2570. 14 49 0.37 ' 'Fe xiii 3p2 3p,-3p2 1D2 2578. 77 216 0.46 3. 3(6)Fe xi 3p4 3 P2-3p4 1D2 2648. 73 255 0. 42 2. 5(6)

'Units are erg cm 2 s-' st-' at the sun."Observed width including instrumental width (= 0. 06 A for X< 2000 A; = 0. 12 A for A > 2000 A.

CWeak line.dBlend.eNumbers in parentheses are powers of ten.


a J l l


graph. These profiles show structure which is prob-ably real. The width of the Fe ix line corresponds to a

temperature of 0.26 keV, which is about a factor-of-two higher than in ionization equilibrium. The widthof the Fe xviii line corresponds to a temperature of 2.6keV, which is about a factor-of-five times greater thanthe ionization equilibrium temperature. The only man-ner in which the linewidths can be interpreted as purethermal Doppler broadening is to assume that the plas-ma is in a state of transient ionization.

However, the observed structure in the profiles sug-gests that broadening mechanisms other than thermalDoppler broadening may be important. Turbulence is apossible broadening mechanism. If the linewidths areinterpreted as a combination of thermal and nonthermalDoppler broadening, the nonthermal velocities are 21km s-1 for Feix and = 94 kms-1 for Fexviii.

A second plausible broadening mechanism is the in-tense magnetic fields generated by the discharge cur-rent. The predicted strengths of these fields are in themegagauss range for the pinched regions of the plasma.Figure 13 shows the full widths at half-maximum oflines near 100 A due to both thermal Doppler broaden-ing and broadening induced by the Paschen-Back effect.In terms of the Paschen-Back effect, the width of theFexviii line corresponds to magnetic fields of about 5MG. These fields do not seem unreasonably large, ascan be seen from the equation Bo =I/5r, where I is thecurrent (I=150 000 A) and r is the radius of the pinchedregion (r = 5. 0x 10-3 cm). Stark broadening does notappear to be a likely broadening mechanism because thelevels involved are not degenerate, and therefore notsubject to first-order Stark broadening. In elementssignificantly heavier than iron, the importance of Pas-chen-Back broadening relative to Doppler broadeningwill increase. It is possible to test the hypothesis thatthe broadening is due to magnetic fields by obtaining theprofile of a line from a heavy ion that has an ionizationpotential nearly the same as the ionization potential ofFe xviIr. If the line broadening is mainly Doppler, thenthe width of the heavy ion line should be significantlyless than the Fexvnii line, while if the broadening is

.8l ll l l l

Fe ll Fe XvEII103.566 A 103.944

I.-

C-)

0-.4

.017A .054A0I-

FIG. 12. Low-inductance vacuum spark spectra of lines ofFeix and Fe xviii. The structure in the profiles is probablyreal, and some of the braodening may be due to intense mag-netic fields.


0107

F 107 X H = lo2 ( A )2( )

-X 0- 10 0

600-2 10-,

A .- X 2AHA)- (-

FIG. 13. The full width at half-maximum (AX) as a function oftemperature or magnetic field for ions of tungsten and iron at100 A. T indicates thermal Doppler broadening; H indicatesbroadening due to the Paschen-Back effect. At a given tem-perature, the thermal broadening is less for the heavier ele-ment, tungsten.

induced magnetically, the width should be the same asthe Fe xviii line. It is also possible to find an ion pres-ent in the high-temperature and magnetic field regionthat has lines in two different wavelength regions, e. g.,100 and 350 A. The relative widths of the lines will de-termine the origin of the broadening because Dopplerbroadening scales as A and broadening by magneticfields scales as X?.

*The paper is based on an invited talk by one of us (U. F. )

given at the 1976 annual meeting of the Optical Society ofAmerica, Tucson, Ariz. [J. Opt. Soc. Am. 66, 1060A(1976). ]

tWork partially supported by ERDA.FR. D. Cowan (private communication, 1976).2H. Van Regemorter, "Rate of Collisionals Excitation in Stellar

Atmospheres, " Astrophys. J. 136, 906 (1962); J. Davis(private communication, 1976).

3W. L. Wiese, M. W. Smith, and B. M. Miles, "Atomic

Transition Probabilities, I Vol. II, Nat. Stand. Ref. DataSer. Nat. Bur. Stand. 22, (1969).

4e. Bely and P. Faucher, aFine Structure Proton ExcitationRates for Positive Ions in the 2p, 2p, 3p, 3p5 series,Astron. Astrophys. 6, 88 (1970).

5M. Blaha, "Effective Gaunt factors g&ff for excitation of posi-tive ions by electron collisions in a simplified Coulomb Bornapproximation, " Astrophys. J. 157, 473 (1969); "Collisionexcitation of positive ions in configurations: Transitionsbetween levels of the P term Part II, " Astron. Astrophys. 1,42 (1969).

6G. H. Shortley, "The Computation of Quadrupole and Mag-netic-Dipole Transition Probabilities, " Phys. Rev. 57, 225(1940).

7C. Jordan, "Ionization equilibria for high ions of Fe and Ni,Mon. Not. PR. Astron. Soc. 148, 17 (1970).

8G. A. Doschek and U. Feldman, "Diagnostic Forbidden linesof highly ionized elements for tokamak plasmas, " J. of APPv.Phys. 47, 3083 (1976).


9B. Edl6n, "On the identification of Arx and Arxiv in the solarcorona and the origin of the unidenLifled coronal lines,"Solar Phys. 0, 439 (1969).

t1 W. E. Behring, Leonard Cohen, and U. Feldman, "The solarspectrum: Wavelengths and identifications from 60 to 385Angstroms, " Astrophys. J. 175, 493 (1972).

flU. Feldman, G. A. Doschek, R. D. Cowan, and LeonardCohen, "Transitions 2 si 2pM-2s2pk6 t of the N I and C x iso-electronic sequence, " Astrophys. J. 196, 613 (1975).

12U. Feldman, "Spectroscopy from laser-produced plasmas atflare temperatures," Astrophys. Space Sci. 41, 155 (1976).3R. L. Kelly and L. J. Palumbo, Atomic and Ionic EmissionLines Below 2000 Angstroms, " NRL Report No. 7599 (1973).

14 G. A. Doschek, U. Feldman, J. Davis, and B. D. Cowan,"Density Sensitive Lines of Highly ionized iron, " Phys. Rev.A 12, 980 (1975).

15U. Feldman and G. A. Doschek, "The 3s-3p and 3p-3d linesof Mg ii observed above the solar limb for Skylab, " Astro-phys. J. Lett. 212, L147 (1977).

16U. Feldman, G. A. Doschek, D. K. Prinz, and D. J. Nagel,"Space-resolved spectra of laser produced plasmas in theXUV, " J. AppL. Phys. 47, 1341 (1976).

17W. E. Behring, Leonard Cohen, G. A. Doschek, and U.Feldman, "Transitions of Znxxii, Znxxiii, Znxxiv, Gexxiv,and Ge xxv observed in laser produced plasmas, " J. Opt.Soc. Am. 66, 376 (1976).

18U. Feldman, G. A. Doschek, D. J. Nagel, W. E. Behring,and B. D. Cowan, "Laser plasma spectra of highly ionizedfluorine, " Astrophys. J. 187, 417 (1974).

19 A. K. Dupree, P. V. Foukal, and C. Jordan, "Plasmadiagnostic techniques in the ultraviolet. The C iii density sen-sitive lines in the sun, " Astrophys. J. 209, 621 (1976).

2 0H. Nussbaumer, "Spectral lines in the Be I isoelectronic se-quence, " Astron. Astrophys. 16, 77 (1972).

2'H. P. Muhlethaler and Hf. Nussbaumer, "Transition Proba-bilities within 2s2-2s2p-2p2 in the Bex sequences Be i-Ni xxv,Astron. Astrophys. 48, 109 (1976); A. H. Gabriel and C.Jordan, Case studies in atomic collision physics 2, edited by

E. W. McDaniel and M. R. C. McDowell (North-Holland,Amsterdamn, 1972), p. 210.

"KI. G. Widing, "Fe xxiii 2G3 A and Fexxiv 255 A emission insolar flares, " Astrophys. J. Lett. 197, L33 (1975).

23G. D. Sandlin, G. E. Brueckner, V. E. Scherrer, and R.Tousey, "High temperature flare lines in the solar spectrum171 A-630 A," Astrophys. J. Lett. 205, L47 (1976).

24G. A. Doschek, U. Feldman, K. P. Dere, G. D. Sandlin, M.E. VanHoosier, G. E. Brueckner, J. D. Purcell, and R.Tousey, "Forbidden lines of highly ionized iron in solarflare spectra," Astrophys. J. Lett. 196, L83 (1975).

25G. D. Sandlin, G. E. Brueckner, and R. Tousey, "Forbid-den lines of the solar corona and transition zone: 975 A-3000A," to be published in Vol. 214 (June 15) of the Astrophys. J.(1977).

26C. Jordan, "The ionization equilibrium of elements betweencarbon and nickel, " Mon. Not. R. Astron. Soc. 142, 501 (1969).

27T. N. Lee, "Solar Flare and Laboratory Plasma Phenomena,"Astrophys. J. 190, 467 (1974).

28 U. Feldman and G. A. Doschek, "Spectroscopy of highlyionized atoms produced by a low inductance vacuum spark,"to be published in the Proceedings of the Fifth InternationalConference of Atomic Physics, July 1976, Berkeley, Calif.

29B. Edl6n, "Z-Dependence of the level interval in 2S22p2,2s22p9 and 2s22p', II Solar Phys. 24, 356 (1972).

30 L. A. Svensson, "Predicted Wavelengths of Coronal Transi-tions in the Configurations 3s 23p2 , 3S23p9 and 3s23p4, " SolarPhys. 18, 232 (1971).

3 1L. A. Svensson, J. 0. Ekberg, and B. Edldn, "The Identi-fication of Feix and Nixi in the Solar Corona," Solar Phys.34, 173 (1974).

32C. Jordan, "The Identification of New Forbidden CoronalLines in the Solar EUV Spectrum, " Solar Phys. 21, 381(1971).

33W. Engelhardt and J. Sommer, "Observations of 23S-23IPTransitions in the Hei Isoelectronic Sequence," Astrophys.J. 167, 201 (1971).

34 R. Smitt (private communication, 1976).

Laws of optics at high irradiance. II. Experiments with SF6at normal incidence*

William H. Thomasont and James D. Macomber:Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803

(Received 21 May 1976; revision received 20 August 1976)

The dependence upon irradiance of the steady-state reflectance, absorptance, and transmittance of pure SF6gas and of SF6-He mixtures has been studied at normal incidence, and compared with the predictions of theprevious theoretical paper. The radiator was a CO2 laser operating at the center of the P20 line.(wavelength10.591035 jim) providing irradiances of 0.9, 1.6, 3.3, 6.2, 17, 26, 53, and 103 kWm-2. The SF6 pressuresemployed were 33, 45, 57, and 81 Pa (pure) and 40 and 74 Pa mixed with 156 and 64 Pa of He, respectively.The experimental results, averaged over several cell lengths to eliminate interference effects from the surfacesof the KCI cell windows, agreed with the theoretical predictions to within 0.0058 for reflectance and within0.028 for transmittance (68% confidence levels) over the entire range of pressures and irradiances employed.The experimental error in the measurements was estimated to be less than 0.005 for the reflectance and 0.01for the transmittance. These results constitute excellent confirmation of the theory, considering that all dataused as input to the computational algorithm were taken from the literature (or measured or calculatedindependently) with no adjustable parameters.

INTRODUCTION

In the previous paper, 1 we developed a theoretical pro-cedure for calculating the reflectance, absorptance,and transmittance of a multilayer absorbing slab athigh steady-state irradiance. In this paper an experi-


mental test of this procedure is described.

The light source employed was a continuous wave in-frared laser (CO2), operating in a single longitudinaland transverse mode (TEMOO). The sample consistedof three layers, each in the form of a plane slab. The

Copyright © 1977 by the Optical Society of America 734

plasma diagnostics using high-resolution spectroscopic techniques

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