PPPL-2408

UC20-F

PPPL-2408

SATELLITE SPECTRA OF HELIUMLIKE NICKEL

By

H. Hsuan et al.

FEBRUARY 1987

PLASMA PHYSICS

LABORATORY

PPPL2408 SATELLITE SPECTRA OF HELIUMLIKE NICKEL DE87 008065

H. HSUan, M. Bitter, K. W. Hill, S. von Goeler,

B. Grek, D. Johnson, L, C. Johnson, and S. Sesnic Bm Plasma Phys'ics Laboratory, Princeton University, S 5 =- - 5 H J

P.O. Box 451 - ^ J || =- Princeton, Sew Jersey 08544

mum C.P. Bhalla and K.R. Karim ft fe I f l'-'? " I I I

Department of physics , Kansas S ta te un ive r s i t y , 5 ^ I I J I ^ .

2

I. INTRODUCTION

Heliumlike and hydrogenlike spectra of high-Z ions are of interest for

the diagnostics of tokamak plasmas and solar flares, and they are also

important for the testing of atomic theories which must include relativistic

and quantum electrodynamical effects. So far, spectra of heliumlike and

hydrogenlike ions with Z.< 26, especially Ar, Ti, Cr, and F , have been

studied in detail from tokamak plasmas. With the new generation of

tokamaks, e.g., the Joint European Torus (JET) and the Tokamak Fusion Test

Reactor (TFTR), 1 4 which are designed to obtain fusion breakeven, it is

possible to maintain plasmas of large volumes (V > 40 m J) with electron

densities, n e, in the range from 10 to 10 m and electron temperatures T e

> S keV in steady-state conditions for several seconds. Under these

conditions, elements with Z > 26 can be observed in the heliumlike and

hydrogenlike charge states.

In this paper spectra of heliumlike nickel, NiXXVII, are presented as

well as a detailed comparison of the experimental data with results from

Hartree-Fock-Slater atomic model calculations, 1 3' 1 0 and the results obtained

by the Z-expansion method. 17 - 1 The experimental results are presented in

sec. II. The identification of the observed spectral features and comparison

of wavelengths and intensities with theoretical predictions are described in

Sec. III. The analysis results and diagnostic applications ara discussed in

Sec. IV.

II. EXPERIMENT

The measurements have been performed on TFTR with a new c r y s t a l

spectrometer which cons i s t s of three c r y s t a l s and p o s i t i o n - s e n s i t i v e de tec to r s

in the Johann conf igura t ion . The instrument has been designed to record

3

spectra from three approximately vertical chords of the plasma minor section

in order to measure radial profiles of the ion temperature and plasma rotation

velocity from the Doppler broadening and Dqppler shift of X-ray lines from

metal impurity ions of Ti, Cr, Fe, and Ni. Traces (-0.1%) of these elements

are present in TFTR plasmas from the Inconel (~ 70% Ni, ~ 15% Cr, - 7% Fe,

" 2.5% Ti) bellow protective plates and the stainless steel vacuum vessel.

The resolution of the spectrometer is >/A* > 10,000. 128 spectra per crystal

are recorded during a TFTR discharge for time-resolved measurements of these

plasma parameters. The wavelength range obtained with a single spectrometer

setting covers the entire spectral range of the dielectronic satellite lines

of heliumlike ions. It is thus possible to determine the satellite to

resonance line intensity ratios accurately from a simultaneous measurement of

these lines. This is important for diagnostic applications of these intensity

ratios for measureraents of the electron temperature, the ionization

91 2 equilibrium, and ion transport.

The nickel spectra were obtained from a. central vertical chord (at a

major radius R = 249 cm? with a 2233 quartz crystal (2d = 2.028 A) of the size

of 1.5 in. x 6 in. x 0.030 in. The curvature radius was R = 1013 cm, and the

spectral resolution was VA> = 18,000. Figure 1 shows a measured spectrum of

NiXXVII. The data were obtained from the steady-state phase of a TFTR

discharge with a central electron temperature of 4 keV and a very low central

electron density, n(0) = 8 x 10 2 cm" . The radial profiles of the electron

temperature and electron density as measured by laser Thomson scattering are

shown in Fig. 2. Under these conditions the plasma electrons and plasma ions

are weakly coupled, such that the ion temperature is well below the electron

temperature. The spectral features are, therefore, well resolved and not

obscured by Doppler broadening. Moreover, the collisionally excited

4

lithiumlike and berylliumlike satellites are expected to be prominent spectral

features, since substantial deviations from coronal equilibrium occur under

these experimental conditions.

III. LINE IDENTIFICATION

The nine prominent features of the spectrum shown in Fig,1 have been

identified as the resonance line, the intercombination lines, and the

forbidden line of heliumlike nickel, NixxVII, and the associated strong

lithiumlike and berylliumlike satellites of the resonance line. The

transitions of these spectral features are listed in Table 1, The key letters

correspond to Gabriel's notation. Also listed in Table 1 are the

theoretical wavelengths and line strengths, F 2(sf), for the strong

dielectmnic satellites as obtained by Vainshtein and Safronova r 1 8 and from

our present calculations which are described below. The channel numbers, H,

in column 4 of Table 1 correspond to the center positions of the observed

spectral features. They were obtained from a least-mean-squares fit of Voigt

functions, and they were than used for determination of the experimental

wavelengths using the following relation:

x = 2d sin (a + ael o) v

o '

where fi8 (degree) = 3.719 x 10" 3(N - NQ) corresponds to the d ispers ion of the

inst rument . NQ i s the center channel number of peak 1 . Since the

spectrometer i s not absolute ly c a l i b r a t e d , the experimental wavelengths are

given in reference to the theoret ical , wavelength values for the resonance l ine

w by assigning x b e o r ' = 2d s i r 6Q to the center channel N 0 of peak 1. We

note from Table 1 tha t both s e t s of t h e o r e t i c a l wavelengths a re in good

5

agreement with the experimental values. For a more detailed comparison

between theory and experiment synthetic spectra were constructed from the

theoretical transition arrays in Table 1 as well as from the transition arrays

for the n = 3,4 lithiumlike satellites, which are given in Table 2 and in

Ref. 19. To facilitate a direct comparison with the experimental data,

channel numbers were .converted into wavelengths by using Eq. (1), and Voigt

functions were then calculated from the theoretical transitions for this

wavelength array. The synthetic spectra are shown in Figs. 3 and 4 together

with the experimental data. The calculated contributions from the different

spectral components, i. e., the heliumlike lines, the dielectronic lithiumlike

satellites, and the collisionally excited lithiumlike and berylliumlike

satellites, to the total synthetic spectrum are shown separately by the shaded

areas in subftgures (b), (c), and (d). The line intensities of the synthetic

spectrum were normalized to the intensity of the resonance line w. The

intensities of the heliumlike lines x, y, and z were obtained from the

following expression:

I c (T 1 x,y,z _ x,y,zl e> , ,

~ c (T ) ( 2 } w w l eJ

Values for the exc i t a t i on r a t e c o e f f i c i e n t s , c _ , were ca lcu la ted using

the methods described in Refs. 7 and 9 . Here, we included only the

con t r ibu t ions from d i r e c t e x c i t a t i o n , r a d i a t i v e cascade t r a n s i t i o n s , and

c o l l i s i o n a l resonances, but we neglected the con t r ibu t ion to the l ine z from

the i n n e r - s h e l l i on iza t ion . The r e l a t i v e i n t e n s i t i e s for the d i e l e c t r o n i c

s a t e l l i t e s were ca lcula ted from the following express ion:

I d i e 1 , 2 -E s i

f(2Ti ft ) i3/2 , . . , s -. , , . ~r~ = ic^i fens1 V a f ) e x pkr-J ( 3 )

w w e e e e

6

w i t h

g= A to the f ina l s t a t e | f>. In the present c a l c u l a t i o n s , the Hartree-Fock-Slater atomic model (HFS)

was employed to obtain the s i n g l e - p a r t i c l e wave func t ions . These wave

functions were then used to ca lcu la t e the r a d i a l Auger and e l e c t r i c d ipole

matrix elements. Configuration s t a t e functions belonging to the same complex

were allowed to mix. The diagonal elements of the energy matrix were

corrected for r e l a t i v i s t i c e f f e c t s . The ef fec ts due to s p i n - o r b i t i n t e r a c t i o n

were included. The energy matrices were diagonalized to obta in cor re la ted

atomic s t a t e functions and energies ; these were used in ca l cu l a t i ng t r a n s i t i o n

r a t e s . For the w, x, y, j . q, $, and z l i nes the wavelengths were ca lcu la ted using the mult i -conf igurat ion Dirac-Fock model including r a d i a t i v e cor rec t ions

of quantum electrodynamics. The dif ference between the Dirac-Fock wavelength

and the Hartree-Fock-Slater wavelength for the j - l i n e was 0.0025 A. This was added to the wavelengths of a l l o ther d i e l e c t r o n i c s a t e l l i t e l i n e s . The

syn the t ic spectrum shown in Fig. 3 was constructed from the HFS r e s u l t s . In

Ref. 17, the Z-expansion method i s used to ca l cu l a t e the atomic q u a n t i t i e s

which were used in the synthet ic spectrum shown in Fig. 4 .

The i n t e n s i t y of the c o l l i s i o n a l l y exci ted Lithiumlike (beryl l iumlike) s a t e l l i t e s was obtained from the following expression:

7

, C O l l . / , ! h _ C s T e "Hi*

( ( 4 )

Jw Cw ^Te J ViXXVII

where i\,t* (= "HixyvT o r "ilixxv' a n < ^ "NiXXVtl a r e t n e < ^ e n s i t : ' - e s l i th iura l ike

or (beryl l iumlike) and heliumlike n i c k e l . c s f T e ' * s t h e r a t e coe f f i c i en t for

e l ec t ron impact exc i t a t i on of the l i th iuml ike (or beryl l iumlike) ion from the

ground s t a t e .

The syn the t ic spectra were ca lcu la ted for the experimental ly observed

e l ec t ron and ion temperatures of T = 4 kev and Tj = 2 keV, r e s p e c t i v e l y .

Values of "uixxvi/'HUXXVII = '75 a n d "NiXXV-^NiXXVII = 0-1 &* the r e l a t i v e

abundance of hel iumlike , l i t h iuml ike , and bery l i iuml ike nickel were chosen to

obta in a bes t f i t with the observed spectrum.

IV. DISCUSSION

The detailed comparisons shown in Pigs. 3 and 4 indicate that the

predictions from both theories are in very good agreement with the

experiment. The predictions differ only slightly with respect to the

wavelength for the satellite r (feature 6), where the value of Vainshtein and

Safronova is in somewhat better agreement with the experiment than the value

obtained from the present calculations. The predicted intensities for feature

3 are in both cases slightly higher than the observed value.

The observed MiXXVII spectra confirm the trend of the charge-dependent

wavelength shifts reported in Ref, 24, in particular, we observe that the

satellite q overlaps with the y line. Similarly, the satellite 3 is very

close to the line 2. On the other hand, the dielectronic satellite k and the

collisionally excited satellite r are well separated. These charge-dependent

wavelength shifts imply that the line q is no longer appropriate for the

diagnostic of the relative abundance of the lithiumlike and heliumlike charge

states. The satellite r can be used instead.

a

The values far the abundance of NiXXV and NiXXVI relative to that of

NiXXVII, which were obtained from the analysis in Sec. Ill, are substantially

larger than the predictions for the fractional abundance of these charge

states in coronal equilibrium (see Fig. 5). Modeling calculations, such as

those described in P.ef. 9, make it possible to deduce values for the radial

ion transport coefficients from these observed deviations. The resonance

lines w of NiXXVII as well as FeXXV have been successfully used for Doppler

measurements. Doppler ion temperatures TJ > 20 keV have recently been

measured in TFTR experiments with intense neutral beam heating from these

2 6 27 impurity lines. '

ACKNOWLEDGMENTS

The technical assistance of J. Gorman, J. Lehner, P. Howard, and the TFTR

operating crew is highly appreciated. We also gratefully acknowledge the

continuing support of Dr. K.M. Young, Dr. H.P. Furth, Dr. R. Goldston,

Dr. D. Grove, Dr. D. M. Meade, and Dr. P. H. Rutherford.

This work was supported by U.S. Department of Energy contract No.

DE-AC02-76-CH0-3073. Two of us (G.P.B. and K.R.K.) were supported by the

Division of Chemical Sciences, Office of Basic Energy Sciences, Office of

Energy Research, and the U.S. Department of Energy. Computations of

excitation rate coefficients were carried out on the NAS 980 - CIKCE computer

in Orsay, France,

% 9

REFERENCES

1J. Dubau and S, Volonte, Rep. Prog. Phys. 43, 199 (1980).

2C. De Michelis and M. Mattioli, Nucl, Fusion _21_, 677 (1981).

3R. K. Janev, L. P. Presnyakov, and V.P. Shevelko, in Physics of Highly

Charged Ions, Vol. 13 of Springer Series in Electrophysics, edited by

G. Ecker (Springer, Berlin, 1985).

4 T F R Group and p. Bombarda, in proceedings of the 11th European Conference on

Controlled Fusion and Plasma Physics, Aachen, FRG,1983, edited by S.

Methfessel (European physical Society, Aachen, 1983), Vol. 7D, Part I,

p. 89. Br"

TFR Group, F. Bombarda, F. Bely-Dubau, P. Faucher, M Cornille, J. Dubau,

and M. Loulergue, Phys. Rev. A _3_2, 2374 (1985).

3E. Kallne, J. Kallne, A. Dalgarno, E. S. Marmar, J. E. Rice, and A. K.

Pradhan, Fhys. Ruv. Lett. ^ 2_, 2245 (1984).

F. Bely-Dubau, P. Faucher, L. Steenman-Clark, M. Bitter, S. von Goeler, K.

W. Hill, C. Camhy-Val, and J. Dubau, Phys, Rev. A _26^ , 3459 (1982).

P. Lee, A. J. Lieber, and S. S. Wojtowicz, Phys. Rev. A_3_1_, 3996 (1985).

M. Bitter, K. W. Hill, M. Zarnstorff, S. von Goeler, R. Hulse, L, C.

Johnson, N. R. Sauthoff, S. Sesnic, K. H. Young, M. Tavernier, F. Bely-

Dubau, P. Faucher,M. Cornille, and J, Dubau, Phys. Rev. A 32, 3011 (1985).

TFR Group, J. Dubau, and H. Loulergue, J. Phys. B J_5_, 1007 (1981).

H. L. Apicella, R. Bartiromo, F. Bombarda, and R. Giannella, Phys. Lett.

98A, 174 (1983).

10

1 2 M . Bitter, K. W. Hill, N. R. Sauthoff, P. C. Efthimion, E. rteservey,

W. Roney,S. von Goeler, R. Horton, and W. stodiek, PhyT. Rev. Lett. 43, 129

(1979).

1 3R. J. Bickerton, Plasma Phys. Controlled Fusior. 2, O e 5 (1984). 1 4 K . H. Young et al., plasma phys. controlled Fusior, J^ cj. r; (I9i4). 1 5C.p. Bhalla and K.R. Karim, Phys. Rev. A _34_, 3525 (1986).

1 6 K . R . K-.rim and C.P. Bhalla, to ba published in chys. Rev. A.

L. A. vainshtein and U. I. Safronova, At. Daca Nucl. Data Tables Z\_, 49

(1978).

U. I, Safronova, A. M. Urnov, and L. A- Vainshtein, Proc. P. N. Lebedev.

Phys.Inst. [Acad., Sci. USSR 119, 13 (1980);}

L. A. Vainshtein and U. I. Safronova, At. "Jata Nuel. Data Tables _25_, 311

(1980).

2 0 H . J a h a n n , Z. Pixys. 6 9 , 189 ( 1 9 3 1 ) . 21

M. Bitter, K. W. Hill, S. Cohen, S. von Goeler, K. Hsuan, L.C. Johnson, R,

Raftopulos, M. Reale, N. Schechtman, S. Senic, F. Spinos, J. Timberlake, s.

Weicher, N. Young, and K. M. Young, Rev. Sci. Instruin. 57, 2145 (1986). 22

M. B i t t e r , S . von G o e l e r , N. Sau tho f f , K. W. H i l l , K. Brau, D. Eames, M.

Goldman, E. S i . lver and W, S t o d i e k , i n I n n e r - S h e l l and X-Ray P h y s i c s of Atoms

and S o l i d s , e d i t e d by a. J . F a b i a n , H. K l e i n p o p p e n , and 1 . M. Watson (Plenum

P r e s s , New York, 1981) , p . 8 6 1 . 2 3 A . H. G a b r i e l , Mon. No t . R, A s t r o n . S o c . 160, 99 ( 1 9 7 2 ) . 24 TFR Group, M. Cornille, J, Dubau, and M. Loulergue, Phys. Rev. A _3_2_, 3000 ( 1 9 8 5 ) .

25 * C. B r e t o n , C. De M i c h e l i s , M. F i n k e n t h a l , and M. M a t i o l i , Fon tenay~aux-Roses Laboratory Report No. EUR-CEA-FC-948, 1978 (unpublished).

11

JH. Hsuan, M. Bitter, s. von Goeler, S. Sesnic, J. Timberlake, and S. Cohen,

Bull. Asa. Phys. Soc. _31_, 1611 {1986).

W. Bitter, K. W. Hill, S. Hiroe, H. Hsuan, S. von Goeler, S. Sesnic, and

M. Zarnstorff, Bull. Am. Phys. Soc. _31_, 1414 (1986).

12

TABLE CAPTIONS

Tab le 1 . E x p e r i m e n t a l wave l eng ths and t h e o r e t i c a l p r e d i c t i o n s Cor t h e

r e s o n a n c e , i n t e r c o m b i n a t i o n , and f o r b i d d e n l i n e s of NiXXVII, and t h e /

a s s o c i a t e d s a t e l l i t e l i n e s due t o t r a n s i t i o n s 1s 21 - \s2t'2j." * Wavelengths a r e i n A and s a t e l l i t e l i n e s t r e n g t h s F _ ( s f ) a r e i n u n i t s of 1 0 1 3 s _ 1 .

Tab le 2 . Atomic d a t a c a l c u l a t e d wi th the HFS a tomic model fo r s a t e l l i t e l i n e

t r a n s i t i o n s : 1 s 2 n - 1 s 2 l ' n " wi th n = 3 , 4 of NiXXVI. The

wave l eng ths a r e i n A. The l i n e s t r e n g t h s F 2 ( s f ) a r e i n u n i t s of 1 0 " 1 3 s " . L ines wi th F , - v a l u e s l e s s than l O ^ s - 1 a r e n o t l i s t e d ^

Peak key Transit ton H *expt 'uieor. 4^^^ 'expt. 4h'or- F 2 b ) < 3 f >

1 u la 2 ' s 0 - la 2p 'p, 116.11 1.5879" 1.5879 1.5886" 1.5886

2 x is 2 'S 0 - 1a2p 3 P 2 193.18 1.5917 1.5918 1.5921 1.5925

1a 22a 2 S ) / 2 - Is2a2p 2 P 3 / 2 1.5926 0.0106 1.5935 2.110 U 2 2 p 2 P 1 / 2 - ls2p 2 2 P 3 / 2 1.5929 0.157 1s 22p 2 P J / 2 - ls2p 2 2 S , / 2 210;21 1.5931 1.5932 6.00 1.5938 1.5910 1.98 la 22a z S 1 / 2 - )32a2p 2 P ) / 2 1.5931 12.fl 1.5910 11.12

y la 2 ' s 0 - 1s2p 3P 1.5959 1.5968 1

? S ' o 218.01 1.5962 1.5969 q 13^23 d S 1 / 2 - Ia2s2p 4 P 3 / 2 1.5965 0.172 1.5972

a 1a 22p 2 P 3 / 2 - Ia2p 2 2 P 3 / 2 1.5973 17.5 1.5981 11.10 5 k .la 22p 2 P ) / 2 - ia2p 2 2 0 3 / 2 267.17 i.5978 1.5980 38.1 1.5985 1.5987 39.32

d 1a 22p 2 P , / 2 - la2p 2 2 P , / 2 1.5980 0.166

6 r ls 22a 2 S , / 2 - I32a2p 2 P , / 2 283.50 1.5991 1.5992 6.93 1.5998 1.600? 7.19

7 J 13 22p 2 P 3 / 2 " la2p 2 2 D 5 / 2 298.31 1.6003 1.6005 58.0 1.6010 1,6011 53.19

L la 22p 2 P , / 2 - |s2p 2 2 D , 1.6021 5.73 1.6033 1.81 8 2 1 7 330.17 I.COIl) 1.6036

2 13 ' S 0 - 1s2a iSy 1.6031 1.6035

9 8 l a 2 2 a 2 lSQ - | 3 2a 2 2p ' P , 310.32 1.6037 1.6011 1.6017

The experimental wavelengths are normalized to the t heo re t i ca l values fo r the I s 2 1 S i J - l32p ' p , t r a n s i t i o n . a l lcferenoe 17, 18 b Present HKS Calu lat lona

Table 1

14

Final State I f >

Autoionizing State

|s>

1s 2p( 'pjsp 2 S s1/2 TS 2p{ 1P)4p 2 P P3/2 Is 2p< 1P>4p 2n D3/2 1s 2p( 1P)4p 2 D 5 / 2 Is 2p( 1P)3p 2 p3/2 Is 2p( 1P)3s 2 P P1/2 Is 2p( 'p)3p 23/2 Is 2p( P)3p 2

5/2 is 2p( P)4d F5/2 Is 2p( P)4d 2 D5/2 Is 2p( P)4d 2 P F7/2 1s 2p(-JP)3p

2D D5/2 1s 2p( P)3d 2u F5/2 1s 2p

15

FIGURE CAPTIONS

FIG. 1 . Satellite spectrum of NiXXVII. The data were recorded fron an

ohmically heated TFTR discharge during its steady-state phase.

FIG. 2 Radial profiles of the electron temperature and the electron

density as measured by the TFTR Thomson scattering diagnostic.

FIG. 3. Comparison of the observed NiXXVII spectrum with a synthetic

spectrum constructed from the results obtained by the present HFS

atomic model calculations. The experimental data are shown in

(a). The contributions from the heliumlike lines, the dielectronic lithiuralike satellites, and the collisionally excited

lithiumlike . and beryllium-like satellites to the synthetic

spectrum are shown by the shaded areas in (b), (c), and td), respectively. The envelope shown in (b), (c), and (d) is the total synthetic spectrum,, i.e., the sum of the various components.

FIG. 4. Comparison of the observed NiXXVII spectrum with a synthetic

spectrum calculated from the theory of Vainshtein and

Safronova. 1 ' The experimental data are shown in (a). The contributions from the helium-like lines, the dielectronic

lithiumlike satellites, and the collisionally excited lithiumlike

and berylliumlike satellites to the synthetic spectrum are shown

by the shaded areas in (b), (c), and (d), respectively, also shown in (b), (c), and (d) is the total synthetic spectrum, i.e., the sum of the various components.

FIG. 5. Fractional abundance of the ionization states of nickel for nc.

coronal equilibrium.

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EXTERNAL DISTRIBUTION IN ADDITION TO OC-20

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