ASTRONOMY & ASTROPHYSICS FEBRUARY II 2000, PAGE 95

SUPPLEMENT SERIES

Astron. Astrophys. Suppl. Ser. 142, 95–106 (2000)

Laboratory observation and modeling of extreme ultravioletspectra of highly ionized calcium

V.A. Soukhanovskii1, S. Lippmann2, M.J. May1, M. Finkenthal1,5, H.W. Moos1, K.B. Fournier3, W. Goldstein3,D. Pacella4, and G. Mazzitelli4

1 Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, U.S.A.2 2714 Fairview Ave. E. # 101, Seattle, Washington 98102, U.S.A.3 Lawrence Livermore National Laboratories, P.O. Box 808, Livermore, California 94550, U.S.A.4 Associazione EURATOM-ENEA sulla Fusione, C.R. Frascati, CP 65-00044 Frascati Roma, Italy5 Permanent address: Racah Institute of Physics, The Hebrew University, Jerusalem, Israel

Received October 8; accepted November 23, 1999

Abstract. Benchmarking and validation of atomic calcula-tions are crucial for understanding the properties of astro-physical and fusion plasmas. An extended re-evaluation ofa previous experimental study of the Ca XVIII – Ca XII

extreme ultraviolet (XUV) spectra is presented. CaF2 wasintroduced into tokamak plasmas and the spectra of thecalcium ions were recorded by a photometrically cali-brated grazing incidence time-resolved spectrometer. Thelocal plasma electron temperature and density were mea-sured independently. Nearly all features of the line-of-sightintegrated spectra were identified. Atomic data for thiswork were generated ab initio with the HULLAC suite ofcodes. The results of collisional-radiative (CR) modelingfor individual charge states agree with the measured spec-tral line intensities within the experimental accuracy formost lines, thus validating the electron temperature anddensity diagnostic potential of the L-shell lines. In addi-tion, we compare experimentally measured and calculatedline intensities with those calculated using the CHIANTIdatabase.

Key words: atomic processes, Sun: UV radiation, Sun:flares

1. Introduction

Extreme ultraviolet (XUV) solar emission lines corre-sponding to n = 2, ∆n = 0 transitions of highly ion-ized calcium, have been recorded in the past by space-born spectrometers (OSO-5, OSO-6, Skylab NRL/ATM-S082A) and sounding rocket-born instruments (Aerobee

Send offprint requests to: V.A. Soukhanovskii,e-mail: vlad@jhu.edu

150, 200 rockets), and have been used for wavelengthidentifications, temperature and density estimates in so-lar flares and for development of solar atmosphere models(Lawson & Peacock 1984; Feldman et al. 1988; Mason &Monsignori Fossi 1994 and references therein). The XUVlines emitted by L-shell calcium ions constitute a uniquediagnostic tool for studying plasma conditions in the so-lar flares. This is because many of the spectral line ra-tios due to 2s22pk − 2s 2pk+1 transitions are density andtemperature sensitive, and because of the high formationtemperature and density limits of these ions (logarith-mic temperatures between 6.25 and 6.75, electron densityrange 109 ÷ 1013 cm−3). There are few solar abundantelements which provide useful flare diagnostics based onthe XUV line ratios in this range of densities and tem-peratures. Most observed Fe ix − Fe xv XUV line inten-sity ratios are sensitive to electron density ≤ 1011 cm−3

(Dere et al. 1979; Brickhouse et al. 1995), most of theFe xvi − Fe xxiv XUV line ratios are density-sensitive atne ≥ 1013 cm−3 (Feldman et al. 1992), and their forma-tion temperatures are high. The ions of the third periodelements (Si, Mg, S) appear to be less abundant in theflares, and their observed lines, useful for Te and ne di-agnostics, are in the longer wavelength region (above 300A), inaccessible to a typical grazing incidence XUV spec-trometer. Previously, the Skylab NRL/ATM-S082A solarflare observations have been the main source of measuredcalcium line intensities. Recently flown solar missions (e.g.SERTS, SOHO) have produced a wealth of new spectro-scopic data. Its interpretation relies on the accuracy ofthe available atomic data. High quality spectra of the so-lar abundant elements, obtained from a laboratory plasmacan provide a test for the validity of atomic data andcollisional-radiative (CR) models. This is possible becausethe spectra are less contaminated by emission lines from

96 V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum

Injection

Injection

Fig. 1. Time histories of electron temperature (top) and density(bottom) spatial profiles of the FTU tokamak plasma

other elements and local plasma parameters (such as elec-tron density and electron temperature) are independentlymeasured (Finkenthal et al. 1987).

This work presents a re-evaluation of the laboratorystudy of beryllium- through oxygen-like calcium spectraperformed by our group several years ago (Lippmannet al. 1987). The spectra, recorded at the TEXT toka-mak (University of Texas, Austin), have been re-analyzed,previously unpublished lines have been added and theanalysis was extended to lithium- and fluorine-like chargestates. We also analyze new calcium spectra, recorded atthe FTU tokamak (Frascati, Italy). In the previous work(Lippmann et al. 1987; Huang et al. 1987), the difficultyin interpreting the experimental results was mainly due tothe accuracy of the available atomic data. Atomic transi-tion rates were taken from the literature, or extrapolatedfrom other ions of the same isoelectronic sequence. Thecomplexity of the model, i.e. the types of the processesconsidered and the number of levels included, was limited.In several cases these factors precluded full analysis of theexperimental data. In this work, a CR model, based on abinitio calculated transition rates, is used. For Be i-, B i- andC i-like calcium ions, a detailed model is constructed in or-der to study the role of collisional and radiative processesfrom excited states in application to electron temperatureand density diagnostic potential of these ions. We alsocompare our calculations and measurements with the pre-dictions based on the atomic data from the astrophysicaldatabase CHIANTI (v. 2.0, Dere et al. 1997; Landi et al.1999). CHIANTI contains the best available atomic datafor the ions of astrophysical interest and has been used inSERTS and SOHO data analysis (e.g. Young et al. 1978;Mason et al. 1997; Landi & Landini 1997). Throughoutthe paper, the units of eV are used for the temperaturek Te, unless noted otherwise, and line intensity ratios areexpressed in photon units.

n

T

r

e

e

qn

MAr

Te

ne

MA

MA

LOS

1

23

Tokamakcross

section

Fig. 2. Schematic view of temperature (Te), density (ne) andimpurity density (nq) profiles (upper part of the drawing). Theprocedure of obtaining Te and ne at the maximum abundance(MA) location of each ion is shown. Lower part: bold dashedline indicates different lines of sight (LOS) of the spectrometer(1) - central, (2) - MA, (3) - plasma periphery

2. Experiment and data analysis

As mentioned, data from the experiments conducted atthe TEXT and FTU tokamaks have been used in thepresent paper. The former experiment has been describedby Lippmann et al. (1987), Finkenthal et al. (1986) andFinkenthal et al. (1987). The details of both experimentswill be briefly mentioned here.

2.1. Spectroscopic instrumentation

The spectra were recorded by a 1 meter Rowland circlegrazing incidence time-resolving spectrometer (GRITS)(Hodge et al. 1984). In both experiments, GRITS had aspectral resolution of 0.8 A (full width at half maximum(FWHM) of 0.7 A). Temporal resolution (detector inte-gration time, called a frame) was 5.4 ms in the TEXTexperiment and 11 ms in the FTU experiment. A spectralrange 60 to 80 A wide was covered by the detector duringeach tokamak discharge. The wavelength calibration wasdone using resonant lines of intrinsic and seeded tokamakimpurities and is considered to be accurate to 0.2 A. Inboth experiments, GRITS image intensified photodiodearray detector was absolutely calibrated in the spectralrange of 20 − 350 A using synchrotron radiation from theNIST SURF II electron storage ring. The uncertainty inthe absolute brightness measurements was estimated tobe ∼ 30%, whereas relative brightness of two lines widelyseparated in wavelength was estimated to be ≤ 20%. Inthe TEXT experiment, the edge plasma was monitoredby a normal incidence time-resolved spectrometer (NITS)(Bell et al. 1981), covering the range between 300 and2200 A. At FTU, a SPRED (survey poor resolution ex-tended domain) spectrometer (Fonk 1982) was used formeasurements in the 200 − 1700 A range.

V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum 97

50 100 150 200 250 300 350Wavelength (Å)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Brig

htne

ss (

× 10

15 p

hoto

n / s

sr

cm2 /p

ixel

)

F V

II 11

2.98

Å F

VII

127.

78 Å

Ca

XIII

131

.22

Å C

a X

IV 1

32.9

1 Å

Ca

XIV

134

.28

Å C

a X

V 1

40.5

8 Å

Ca

XII

141.

04 Å

Ca

XV

141

.69

Å C

a X

V 1

44.3

1 Å

Ca

XII

147.

28 Å

Ca

XV

I 154

.88

Å C

a X

III 1

56.6

9 Å

Ca

XV

I 157

.79

Å C

a X

III 1

59.8

4 Å

Ca

XV

161

.01

Å C

a X

III 1

61.7

5 Å

Ca

XIII

162

.92

Å C

a X

III 1

64.1

1 Å

Ca

XV

I 164

.17

Å C

a X

IV 1

65.3

4 Å

Ca

XV

I 167

.43

Å C

a X

III 1

68.4

0 Å

Ca

XV

I 168

.87

Å C

a X

V 1

76.9

2 Å

Ca

XV

177

.25

Å C

a X

V 1

81.9

1 Å

Ca

XIV

183

.46

Å C

a X

IV 1

86.6

1 Å

Ca

XIV

188

.99

Å C

a X

VII

192.

86 Å

Ca

XIV

193

.87

Å C

a X

V 2

00.9

7 Å

Ca

XV

208

.33

Å C

a X

VI 2

08.5

9 Å

Ca

XV

215

.38

Å C

a X

VII

218.

85 Å

Ca

XV

II 22

3.03

Å C

a X

VI 2

24.5

5 Å

Ca

XV

II 22

8.74

Å C

a X

VII

232.

81 Å

F IV

243

.92

Å C

a X

VII

244.

04 Å

Ca

XV

III 3

02.2

2 Å

Ca

XV

III 3

44.7

7 Å

Fig. 3. Line-integrated, time-averaged XUV spectrum of highly ionized calcium in the TEXT tokamak. The spectrum wasobtained using six reproduceable discharges

2.2. Plasma diagnostics

TEXT was a medium-size tokamak with a central elec-tron temperature about 1 keV and central electron den-sity ' 6 1013 cm−3 (Gentle 1981). The electron temper-ature was measured in the steady state by radially re-solved Thompson scattering, and far infrared (FIR) inter-ferometry was used for electron density diagnostics. TheTEXT temperature and density profiles and other plasmaparameters are given in Lippmann et al. (1987). FTUis a compact high magnetic field, high density tokamak(Andreani 1993). Typical time histories of its density andtemperature profiles are shown in Fig. 1, as measured byFIR and electron cyclotron emission (ECE) interferome-ters, respectively. Thomson scattering measurements of Te

and ne were also available. The accuracy of Te measure-ments decreases with distance from the plasma center andis only good to ±50 eV in the plasma periphery. Calciumfluoride (CaF2) was injected into the plasma in both ex-periments using a laser blow-off (LBO) technique (Terryet al. 1983). This method caused controlled perturbationto the plasma. The central electron temperature decreasewas 14% at TEXT and 25% at FTU. The electron densityincreased by ∼ 18% at TEXT and 10% at FTU. The over-all reproducibility of the plasma parameters and those ofCaF2 injections was estimated to be within 10% in bothexperiments.

2.3. Spectra interpretation

Some of the recorded spectra are presented in Figs. 3and 4. The TEXT spectrum was composed of six overlap-ping spectra obtained from reproduceable consequent dis-charges. Emission from intrinsic tokamak impurities (suchas oxygen, carbon, iron, titanium) was integrated over sev-eral detector time frames preceding the CaF2 injection andsubtracted from the injection spectrum. This procedurealso helps to correct for the scattered light contributionto the recorded spectra. Line identifications were madeusing wavelength values compiled by Kelly (1987). Lineintensities were obtained by piece-wise fitting of a multi-Gaussian function to the data using the wavelength fromKelly (1987). Analysis of the recorded spectra included:(i) interpretation of spectral line intensities of individualcharge states and (ii) interpretation of full spectra. Line-integrated intensities are characteristic of plasma condi-tions at the maximum abundance (MA) location of eachion (Fig. 2). Therefore, local plasma conditions (Te andne) and emissivity distribution of each ion must be known.To achieve this, measurements were performed along dif-ferent LOS over a number of reproduceable discharges inthe TEXT tokamak. Line-integrated brightnesses of mostintense spectral lines were Abel-inverted and species’ ra-dial distribution profiles were inferred (Fig. 3 in Lippmannet al. 1987). Relative line intensities of the considered∆n = 0 transitions are practically temperature indepen-dent. Tables 2, 3 and 4 compare measured and calculated

98 V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum

150 160 170 180 190 200Wavelength (Å)

0

2

4

6

8

Brig

htne

ss x

1014

(ph

/sec

/sr/

cm2 /Å

)

153

.2 Å

C

a X

IV 1

54.9

Å

Ca

XV

I 1

56.7

Å

Ca

XIII

157

.8 Å

C

a X

VI

159

.8 Å

C

a X

III 1

61.0

Å

Ca

XV

161

.8 Å

C

a X

III 1

62.9

Å

Ca

XIII

164

.1 Å

C

a X

VI

164

.2 Å

C

a X

III 1

65.3

Å

Ca

XIV

167

.0 Å

C

a X

IV 1

67.4

Å

Ca

XV

I 1

68.4

Å

Ca

XIII

168

.9 Å

C

a X

VI

171

.6 Å

C

a X

V 1

76.9

Å

Ca

XV

177

.3 Å

C

a X

V 1

81.9

Å

Ca

XV

182

.9 Å

C

a X

V 1

83.5

Å

Ca

XIV

193

.9 Å

C

a X

IV 2

01.0

Å

Ca

XV

186.

6 Å

Ca

XIV

189.

0 Å

Ca

XIV

192

.9 Å

Ca

XV

II

Fig. 4. LOS-integrated Ca spectrum, recorded at FTU

05

10152025

F VII 127.8 Å

Ca XIII 131.2 Å

Ca XIV 132.9 Å

Ca XIV 134.3 Å

F VII 134.9 Å

F VI 139.9 Å

Ca XV 140.6 Å

Ca XII 141.0 Å

Ca XV 141.7 Å

Ca XV 144.3 Å

Ca XII 147.3 Å

012345

Brig

htne

ss x

1014

(pho

tons

/sec

/sr/c

m2 )

120 130 140 150 160 170Wavelength (Å)

0123456

Ca XVI 154.9 Å

Ca XIII 156.7 Å

Ca XVI 157.8 Å

Ca XIII 159.8 Å

Ca XV 161.0 Å

Ca XIII 161.8 Å

Ca XIII 162.9 Å

Ca XIII 164.1 Å

Ca XVI 164.2 Å

Ca XIV 165.3 Å

Ca XVI 167.4 Å

Ca XIII 168.4 Å

Ca XVI 168.9 Å

Fig. 5. TEXT spectra taken along three different lines of sighta) - through Ca xvi MA location b) - through Ca xiv MA lo-cation, and c) - through Ca xii MA location

line intensities, normalized to the intensity of some reso-nant representative line of the same ion. The chosen nor-malization is fairly arbitrary, and meaningful comparisonsare made on a case to case basis.

Spectral line blending presented problems in somecases. The blends can be classified as follows: calcium-specific blends (two or more close lines, emitted bycalcium ions); blends due to the limited instrumentalresolution; and blends, specific to the CaF2 injection. Thespectral blend separation techniques used were similar tothose described by Huang et al. (1987). Time behaviorof LBO-injected impurities in a tokamak plasma ischaracterized by line brightness decay time. It is thereforepossible to separate lines from different ionization stages

Table 1. Electron temperature and density at the maximumabundance location of Ca xviii - Ca xii ions in TEXT and FTUtokamaks

k Te (eV) ne (×1013 cm−3)

Ion I. P.a (eV) TEXT FTU TEXT FTU

Ca xviii 1157 1000c 650c 5.4c 3.0c

Ca xvii 1087 800b 550c 4.0b 2.8c

Ca xvi 974 650b 500c 3.3b 2.7c

Ca xv 895 450b 430c 2.9b 2.6c

Ca xiv 818 350b 360c 2.4b 2.4c

Ca xiii 727 230b 240c 1.8b 2.2c

Ca xii 657 130b 160c 1.2b 2.0c

aIonization potential, from Kelly (1987).b From measured ion emissivity profiles and measured Te

and ne profiles as described in Sect. 2.c Calculated as described in Sect. 2.

by comparing time histories of adjacent detector pixels.In the cases where the measured lines originate from thesame upper level, branching ratios of the correspondingtransitions were used to estimate blended line intensities.Also, spectra recorded at different spatial locations (andtherefore at different temperatures), were used in theanalysis. For example, Ca xii lines λ141.0 and λ147.3 arestrongly blended with the brighter lines of Ca xv andCa xiv on a spectrum recorded along the near-centralline of sight (LOS) (Fig. 5). The spectrum with the LOSpassing through the Ca xii emissivity peak was used toderive the λ141.1 and λ147.3 line brightnesses. The radialposition, according to the measured temperature profile,corresponds to ∼ 130 eV. In some cases (such as theCa xviii lines recorded at TEXT, and the FTU spectra(Fig. 4)), spatial measurements were not performed. Thepredicted ground state density distributions were usedto estimate the ion MA temperature and density, asdescribed below.

In a tokamak discharge, ground state densities ofimpurity ions are constrained by radial temperatureand density gradients and the radial particle transport.The tokamak plasma is optically thin, and the maininter-species processes are recombination (radiative,dielectronic) and ionization (direct, autoionization). In atypical ohmically heated tokamak plasma after an LBOimpurity injection, ion species evolve toward a steadystate equilibrium. This was confirmed in many experi-ments: for example, Horton & Rowan (1994) extensivelystudied transport phenomena in the TEXT tokamak,using Sc and Ti , LBO-injected into plasma. However,ion maximum abundance temperatures differ from thecoronal ionization-recombination equilibrium case dueto inward radial plasma transport. The ion fractionalabundance peaks are shifted toward higher temperatures(Table 1). Time evolution of the ground level density nq

V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum 99

of injected impurity ion species q can be obtained bysolving a set of differential equations:

dnqdt

= −1r

∂

∂rrΓq −

nqτq

+ Sq+ (1)

Iq−1nq−1 − (Iq +Rq)nq +Rq+1nq+1,

where q is ion charge (0 ≤ q ≤ 20 for calcium), Γq isradial particle flux, Sq and −nqτq are impurity source andsink terms, respectively, and Iq, Rq are total ionizationand recombination rates. To obtain fractional abundances,the set of equations was solved by the transport codeMIST (Hulse 1983). Measured Te and ne profiles wereused as input for this calculation. Transport parameters,such as diffusion and convection coefficients, which en-ter the equations through the particle flux quantity Γ,were adopted from the dedicated transport experiments(Horton & Rowan 1994).

3. Atomic data and collisional-radiative model

3.1. Details of computations

The atomic data for CR modeling was generated by theHULLAC suite of computer codes. HULLAC computesthe ab initio intermediate coupled wave functions, levelenergies and transition probabilities, using the fully rela-tivistic parametric potential code RELAC (Klapisch 1971;Klapisch et al. 1977). All double excited states with en-ergies less than or equal to the energy of the highest in-cluded resonant level were also included in the model foreach ion. The electron collision strengths were calculatedin distorted wave (DW) approximation and averaged overMaxwellian distribution to produce collisional excitationrates by the CROSS code (Bar-Shalom et al. 1988). Effectsof proton-ion collisions were not included in our model.Proton collisions can change populations of closely spacedfine structure levels, such as Ca XVI − Ca XIII groundlevels. Stratton et al. (1985) demonstrated that for theTi, Cr, Fe and Ni ions this effect is weak, with the excep-tion of carbon-like ions. Since electron impact excitationis the main source of excited level population at the typi-cal tokamak temperature and density, the accuracy of theelectron excitation rate coefficients is critical for calculat-ing accurate spectral line intensities. This especially con-cerns the ions which have metastable levels with relativelylarge populations. The DW approximation does not takeinto account scattering resonances and coupling betweenscattering channels. Finkenthal et al. (1987) pointed outthe importance of these effects for CR modeling of lower Zelements. In the described tokamak experiments electronenergies are typically much greater than collisional excita-tion thresholds of the XUV lines, and the DW approxima-tion, therefore, proves adequate. There has been a num-ber of theoretical studies which compare R-matrix and

DW calculated electron collision strengths for Ca xviii

− Ca xiii ions (for example, Huang et al. 1987; Bhatiaet al. 1986; Dufton et al. 1983; Zhang & Pradhan 1994;Bhatia & Doschek 1993; Aggarwal 1992; Baliyan & Bhatia1994). The collision strengths, calculated by the two meth-ods, agree to better than 30% for the temperature rangeconsidered (100 − 1000 eV). Therefore, the DW excita-tion rate coefficients, used in this work, are of adequateaccuracy.

Using the ab initio level energies, transition prob-abilities and collisional excitation rate coefficientsgenerated by HULLAC, quasi-steady state (QSS) levelpopulation calculations were performed for the temper-atures and densities of interest. All E1, M1 and M2radiative transitions and all collisional excitation and de-excitation transitions were included. The quadrupole (E2)radiative transitions were found to be negligible for theL-shell calcium ions and were not included in the models.For the extended detailed non-LTE calculations, whichinvolved the adjacent ion species, ionization and recom-bination rates were generated as follows: ionization rates,including inner-shell, were calculated according to theLotz formula (Lotz 1968, 1970) using the ab initio levelenergies. Autoionization probabilities were calculatedby RELAC in the DW approximation. Recombinationrates were calculated based on detailed balance principle.In particular, dielectronic recombination was taken intoaccount by calculating radiationless capture rates fromthe ab initio autoionization rates.

Atomic rates from CHIANTI database were also usedfor CR calculations of line intensities. To the extent ofour measurements, a large set of CHIANTI calcium datahas been benchmarked in the present work. CHIANTI in-cludes the best available electron impact excitation andradiative decay rates for E1 and M1 transitions of n = 2configurations of Ca XV, Ca XIV, Ca XII, n = 2, 3 config-urations of Ca XVII, Ca XVI, Ca XIII, and n = 2, 3, 4, 5configurations of Ca XVIII (Dere et al. 1997; Landi et al.1999).

3.2. Model ions

Two models were generated for each ion: a basic modeland an extended model. The basic models included areduced number of levels and basic atomic processes(collisional excitation and de-excitation and radiativedecay), and were found to be sufficient for most cases.The extended models were generated for particular testcases and therefore included greater number of levels andadditional atomic processes (such as K-shell excitation,autoionization, collisional ionization from metastable andexcited levels). The effect of radiative cascades on thepopulations of n = 2 levels is found to be ≤ 15% for thetransitions from n = 3 levels and ≤ 5% from n = 4, 5levels. For the range of plasma parameters of both exper-iments, we have checked and concluded that inner-shell

100 V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum

Table 2. Observed and calculated relative line intensities of Ca XVIII, Ca XVII, Ca XVI, Ca XV in TEXT tokamak

Relative Intensitya

Lower level Upper level Measured Calculatedd

Ion Term Labelb Term Labelb λ (A)c HULLAC CHIANTI

Ca xviii 2s 2S1/2 1 2p 2P3/2 3 302.2 100 100.0 100.02s 2S1/2 1 2p 2P1/2 2 344.8 32 51.5 51.1

Ca xvii 2s2 1S0 1 2s2p 1P1 5 192.9 100 100.0 100.02s2p 3P1 3 2p2 3P2 8 218.8 1.0 0.93 0.852s2p 3P0 2 2p2 3P1 7 223.0 1.1 0.75 0.732s2p 3P1 3 2p2 3P1 7 228.7 1.1 0.51 0.502s2p 3P2 4 2p2 3P2 8 232.8 2.0 2.15 1.952s2p 3P2 4 2p2 3P1 7 244.0 1.4 0.70 0.692s2 1S0 1 2s2p 3P1 3 371.0 · · · 2.80 2.92

Ca xvi 2s22p 2P1/2 1 2s2p2 2P3/2 10 154.9 18 17.8 17.72s22p 2P1/2 1 2s2p2 2P1/2 9 157.8 10 17.2 13.32s22p 2P3/2 2 2s2p2 2P3/2 10 164.2 100 100.0 100.02s22p 2P3/2 2 2s2p2 2P1/2 9 167.4 34 39.8 47.92s22p 2P1/2 1 2s2p2 2S1/2 8 168.9 26 48.3 67.42s22p 2P1/2 1 2s2p2 2D3/2 6 208.6 32 54.8 67.32s22p 2P3/2 2 2s2p2 2D5/2 7 224.6 40 71.3 73.5

Ca xv 2s22p2 3P0 1 2s2p3 3S1 13 137.2 20 15.8 15.62s22p2 3P1 2 2s2p3 3S1 13 140.6 42 45.7 45.72s22p2 1D2 4 2s2p3 1P1 15 141.7 51 47.9 48.82s22p2 3P2 3 2s2p3 1D2 14 144.3 107 85.5 86.22s22p2 1D2 4 2s2p3 1D2 14 161.0 100 100.0 100.02s22p2 3P0 1 2s2p3 3P1 11 171.6 35 18.9 17.92s22p2 3P1 2 2s2p3 3P2 12 176.0 8 12.2 11.82s22p2 3P1 2 2s2p3 3P1 11 176.9 47 31.3 29.82s22p2 3P1 2 2s2p3 3P0 10 177.3 20 23.5 23.82s22p2 3P2 3 2s2p3 3P2 12 181.9 60 95.9 94.22s22p2 3P2 3 2s2p3 3P1 11 182.9 15 19.8 18.02s22p2 3P0 1 2s2p3 3D1 8 201.0 29 41.2 38.82s22p2 3P1 2 2s2p3 3D2 7 208.7 82 82.3 77.92s22p2 3P2 3 2s2p3 3D3 9 215.4 95 106.0 101.4

aLine intensity, relative to some representative line in each isosequence.bLabels refer to Fig. 7.cFrom Kelly (1987).dFor Te and ne values, corresponding to the measured MA location of the ion.

ionization does not change the relative level populationssignificantly (≤ 15%), which confirms applicability ofthe steady state equilibrium. Total ionization rates fromthe n = 3, 4 resonant levels were found to be a factor of101 − 102 less than total radiative decay rates from theselevels.Ca XVIII - The basic model for lithium-like calciumincludes 67 energetically lowest levels from theconfigurations 1s22l (l = s, p), 1s23l (l = s, p, d), 1s24l(l = s, p, d, f), 1s2s2l (l = s, p), 1s2s3l (l = s, p, f),1s2s4l (l = s, p, d, f). The extended model includes levelsup to n = 5, including configurations of the type 1s2snl.A He-like calcium model with all levels up to n = 4 was

also used.Ca XVII - Our basic model for beryllium-like calcium ionincluded 125 levels of the configurations 1s22s2, 1s22snl,and 1s22l′nl′′, where n = 2, 3, 4. The extended modelcomprises configurations of the type 1s2s2nl (n = 2, 3, 4)and 1s2s2pnl (n = 2, 3, 4).Ca XVI - The configurations 2s2nl, 2s2pnl (n = 2, l = s,p; n = 3, l = s, p, d; n = 4; l = s, p, d, f) and 2s2p3 areincluded in the basic model of 147 levels. The extendedmodel, in addition to the configurations listed above,includes the 5l (l = s, p, d, f) and the 1s 2s2 2pnl (n = 2,l = p; n = 3, l = s, p, d, and n = 4, l = s, p).Ca XV - The basic model ion includes 377 levels of

V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum 101

Table 3. Observed and calculated relative line intensities of Ca XIV, Ca XIII, Ca XII in TEXT tokamak

Relative Intensitya

Lower level Upper level Measured Calculatedd

Ion Term Labelb Term Labelb λ (A)c HULLAC CHIANTI

Ca xiv 2s22p3 2D3/2 2 2s2p4 2P1/2 13 128.2 15 12.0 17.02s22p3 2D3/2 2 2s2p4 2P3/2 12 132.9 12 9.1 13.52s22p3 2D5/2 3 2s2p4 2P3/2 12 134.3 34 46.1 67.52s22p3 2P3/2 5 2s2p4 2P1/2 13 142.4 10 12.5 19.72s22p3 2P1/2 4 2s2p4 2S1/2 11 153.2 6 9.0 13.62s22p3 2D3/2 2 2s2p4 2D3/2 9 165.3 39 38.0 53.32s22p3 2D5/2 3 2s2p4 2D5/2 10 167.0 60 51.6 67.72s22p3 4S3/2 1 2s2p4 4P1/2 8 183.5 26 32.7 33.92s22p3 4S3/2 1 2s2p4 4P3/2 7 186.6 43 65.4 66.02s22p3 2P3/2 5 2s2p4 2D5/2 10 189.0 10 10.3 14.12s22p3 4S3/2 1 2s2p4 4P5/2 6 193.9 100 100.0 100.0

Ca xiii 2s22p4 1D2 4 2s2p5 1P1 9 131.2 69 63.2 68.72s22p4 3P2 1 2s2p5 3P1 7 156.7 48 34.3 34.02s22p4 3P1 2 2s2p5 3P0 8 159.8 20 23.7 24.42s22p4 3P2 1 2s2p5 3P2 6 161.7 100 100.0 100.02s22p4 3P1 2 2s2p5 3P1 7 162.9 18 18.0 18.02s22p4 3P0 3 2s2p5 3P0 8 164.1 35 22.9 22.92s22p4 3P1 2 2s2p5 3P2 6 168.4 24 30.5 30.5

Ca xii 2s22p5 2P3/2 1 2s2p6 2S1/2 3 141.0 100.0 100.0 100.02s22p5 2P1/2 2 2s2p6 2S1/2 3 147.3 40 43.6 43.1

aLine intensity, relative to some representative line in each isosequence.bLabels refer to Fig. 7.cFrom Kelly (1987).dFor Te and ne values, corresponding to the measured MA location of the ion.

the configurations 2s22p2, 2s22pnl 2s2p2nl, 2s2nl2

and 1s22p4 (n = 2, l = s, p; n = 3, l = s, p, d;n = 4; l = s, p, d, f). The extended model ioncomprised a total of 1056 levels: the configurationsmentioned above and the configurations 1s2 2s2 2p 5l(l = s, p, d, f), 1s2 2s1 2p2 5l (l = s, p, d, f), and1s 2s2 2p2nl (n = 2, l = p; n = 3, l = s, p, d; n = 4, 5, l= s, p, d, f).Ca XIV - We use the configurations 2s22p2nl, 2s2p3nl and2s2nln′l′, where n = 2, l = s, p; n = 3, l = s, p, d; n =4, l = s, p, d, f and n′ = 3, l′ = s, p, d. The total numberof levels in the basic model is 546.Ca XIII - The model ion contains 542 levels of the followingconfigurations: 2s22p4, 2s22p3nl (n = 3; l = s, p, d andn = 4; l = s, p, d, f), 2s 2p4nl (n = 3; l = s, p, d and n= 4; l = s, p, d, f), 2s 2p6, 2s22p2nln′l′ (n = 3; l = s, pand n′ = 3; l = s, p) and 2s23s23p2.Ca XII - The 267 levels of the configurations 2s22p5,2s22p4nl (n = 3; l = s, p, d and n = 4; l = s, p, d, f), 2s2p6 and 2s 2p5nl (n = 3; l = s, p, d and n = 4; l = s, p,d, f) are used in the basic model ion.

50 100 150 200 250 300 350Wavelength (Å)

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4. Results and discussion

4.1. Ionization balance

The LOS-integrated TEXT spectrum was modeled usingfractional abundances estimated as described in Sect. 2.3.

102 V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum

Table 4. Observed and calculated relative line intensities inFTU tokamak

Relative Intensitya

Measured Calculatedd

Ion λ (A)c HULLAC CHIANTI

Ca xvi 154.9 14 17.8 17.7157.8 17 17.2 13.4164.2 100 100.0 100.0167.4 40 39.8 48.0168.9 51 48.2 67.6

Ca xv 161.0 100 100.0 100.0171.6 34 19.2 18.2176.0 18 12.4 12.1176.9 46 31.7 30.4177.3 35 23.8 24.2181.9 98 97.1 95.9182.9 28 20.1 18.3201.0 48 41.8 39.5

Ca xiv 153.2 13 9.0 13.5165.3 27 38.0 53.0167.0 46 51.6 67.4183.5 15 32.7 33.9186.6 62 65.4 66.0189.0 12 10.3 14.0193.9 100 100.0 100.0

Ca xiii 156.7 37 34.3 34.1159.8 17 23.6 24.5161.7 100 100.0 100.0162.9 14 18.0 18.0164.1 23 22.9 23.0168.4 53 30.3 30.5

aLine intensity, relative to some representative line in eachisosequence.bLabels refer to Fig. 7.cFrom Kelly (1987).dFor Te and ne values, corresponding to the measured MAlocation of the ion.

Ionization and recombination rates, used for this cal-culation, were taken from the recent work of Mazzottaet al. (1998). Their ionization equilibrium curves for thecalcium ions differ from those of Arnaud & Rothenflug1985, both in MA temperature and ionization fractions.The difference is most pronounced, up to 200%, for thelower ionization stages (Ca xiv − Ca xii) due to improveddielectronic recombination rates. Our calculated calciumion ground state distributions closely reproduced the mea-sured ones (Lippmann et al. 1987). Using QSS emissivities,we constructed a line-integrated time-averaged syntheticTEXT spectrum (Fig. 6). All lines predicted by HULLACare shown. This includes not only the ∆n = 0 transitionsof interest, but also a large number of ∆n = 1 and ∆n = 2transitions. These lines are grouped in two domains: 14 A

≤ λ ≤ 45 A and 50 A ≤ λ ≤ 100 A. The calculatedintensities of these lines are typically a factor of 102 −103 less than the ∆n = 0 lines. The 50 − 100 A do-main is covered by GRITS, however, line intensities arebelow the detector sensitivity limit. As seen in Fig. 6,these lines contribute insignificantly to ∆n = 0 line orbackground intensities. All lines were given a Gaussianshape with the FWHM of GRITS. The agreement betweenwavelengths from Kelly (1987) and HULLAC is ≤ 1.5%for most lines, which, however, resulted in different blendpatterns (comp. to Fig. 3). Good agreement between syn-thetic and measured spectra can be considered as indirectvalidation of the new fractional abundance calculations forcalcium.

4.2. Individual ions

The calculated relative line intensities for Li i-like to F i-like calcium ions agree with the measured ones within thestated experimental error in most cases. In comparisonwith Lippmann et al. (1987), improved atomic rates resultin a better agreement between the measured and calcu-lated relative line intensities. Results for individual ionsare discussed below. The emphasis is on the beryllium- tonitrogen-like calcium ions, due to their plasma tempera-ture and density diagnostic potential. Calculated densitydependence of the level populations is shown in Fig. 7.Both ground and excited level populations are in coronaequilibrium at ne = 109 cm−3. The ground configura-tion levels approach Boltzmann values at ne = 1010−1014 cm−3, and transfer population to the excited 2 pk+1

levels at different, ne-dependent, rates. This enables uti-lization of the ∆n = 0 E1 line intensity ratios as densitydiagnostics. Forbidden (M2) transitions between groundlevels of Ca xv, Ca xiv and Ca xiii can also be used as adensity diagnostics. These far ultraviolet lines have beenobserved in a solar active region by Feldman et al. (1998)and used to study physical conditions of the solar corona.Because of the high edge tokamak plasma density (ne '1012 cm−3), collisional quenching of the upper levels ofthese transitions overtakes radiative decay: both FTU andTEXT plasma edge spectra, recorded by the SPRED andNITS instruments, respectively, indicated no evidence ofthe forbidden lines. The line intensities, calculated forthe edge tokamak densities, are a factor of 102 − 103 lessthan those of typical XUV lines, which is beyond thephotometric sensitivity limit of the instruments used.CaXVIII - The only XUV lines identified in solar flarespectrum are λ302.2 and λ344.8 (see references in Lawson& Peacock 1984). The lines are populated accordingto their statistical weights. The discrepancy betweencalculations and measurements in the TEXT tokamak isattributed to the GRITS calibration uncertainty above300 A.

V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum 103

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Fig. 7. Modeled relative populations of the n = 2 levels as afunction of electron density at Te values given in Table 1 (ba-sic model): a) - Ca xviii, b) - Ca xvii, c) - Ca xvi, d) - Ca xv,e) - Ca xiv, f ) - Ca xiii, g) - Ca xii. Level populations are nor-malized to the total population per ion. The level labels areshown in Tables 2 and 3. The levels not shown in Tables 2, 3are labeled as follows: b) Ca xvii: 6 − 1s22p2 3P0; c) Ca xvi: 3− 1s22s2p2 4P1/2; 4 − 1s22s2p2 4P3/2; 5 − 1s22s2p2 4P5/2; d)Ca xv: 5 − 2s22p2 1S0; 6 − 2s2p3 5S2

CaXVII - An example of a persisting disagreementbetween calculations and solar flare measurementsis a long-standing problem with the line intensityratios of the Be i-like isosequence R = I(2s2 1S0−2s2p 1P1) / I(2s2p 3PJ′ − 2p2 3PJ′′), J ′ = 1, 2 andJ ′′ = 1, 2. These intensity ratios are density sensitive(Doschek et al. 1977). The Be i-like neon, magnesium,sulfur, argon and calcium lines have been observedin the solar flares by the NRL Skylab-based S082Aspectroheliograph. The calculated line intensity ra-tios have consistently implied an electron density of∼ 1013 cm−3 and higher, in contrast to the density of≤ 1010 − 1012 cm−3, derived from other line intensityratios (Doschek et al. 1977; Bhatia & Mason 1983; Duftonet al. 1983; McCann et al. 1989; Harra et al. 1992). Allsix lines have been observed in TEXT. Calculated andmeasured relative intensities agree within 40%, with thetwo exceptions of λ228.7 and λ244.0, which are blendedwith the F iv lines. Except for the λ192.9 and λ232.8lines, all other lines are relatively weak and the inferreddensities have larger uncertainties or unrealistic values.We therefore investigated various CR effects on theR1 = I(2s2 1S0 − 2s2p 1P1) / I(2s2p 3P1,2 − 2p2 3P1,2) =I(λ192.8) / I(λ232.8) ratio. As the number of lev-els, included in the model, increase, the calculatedI(2s2 1S0 − 2s2p 1P1) / I(2s2p 3P − 2p2 3P) ratios de-crease, due to cascades to the 2p2 levels. This effectis ≤ 20% as n = 3, 4 levels are added to the model.In particular, the R1 ratio was found to be 61 (n = 2only; 10 lowest levels), 49 (n = 2, 3; 30 levels) and

47 (n = 2, 3, 4; 125 levels). The ratio, measured inTEXT, is ∼ 51 ± 5. Both λ192.8 and λ232.8 lines areprimarily populated by electron impact excitation. The2s2p 1P1 level is populated from the ground, whereasthe 2p2 3P levels are populated both from the groundand from the 2s2p 3P levels. The DWA rates for thesetransitions, calculated by HULLAC, are within ≤ 15% ofthe R-matrix rates calculated by Dufton et al. (1983), forthe 400 − 900 eV temperature range (with one exceptionof 2s2 1S0 − 2s2p 1P1, for which the HULLAC rate is' 35% smaller than the rate from Dufton et al. 1983). Thedetailed model was used for Ca xviii, Ca xvii and Ca xvi,to account for possible non-steady state contributions.The model was constructed for both tokamak and ioniza-tion equilibrium temperatures. Direct ionization is foundto be the dominating process, the autoionization fluxoriginating from the 1s2l2 levels of Ca xvi is negligible,and the population flux due to inner-shell ionization from2s22p and 2s2p2 levels of Ca xvi to 2s2p 3P levels ofCa xvii is several orders of magnitude less than the fluxto the ground state. Significant departure from ionizationequilibrium is required to populate the 2s2p 3P levelsthrough inner-shell ionization (Feldman et al. 1992). Ourcalculations indicate that if nCaXVII/nCaXVI = 1 : 10, atne = 3 1011 cm−3 up to 50% of the total population of2s2p 3P levels is due to inner-shell ionization, and the R1

ratio is practically the same as at ne = 3 1013 cm−3 ationization equilibrium conditions. We conclude, therefore,that the R1 ratio should be a reliable density diagnosticsin the ne range of 1010 − 1014 cm−3.

Intensity ratio of two ∆n = 0 lines of the sameion can be used as a temperature diagnostic due tothe temperature dependence of the excitation ratecoefficients, if the separation of the upper levels ofthese lines ∆E is much less than k Te, as in the caseof the resonant and intercombination lines of Be i-like calcium, R2(Ca xvii) = I(2s2p 3P1 − 2s2 1S0)/ I(2s2p 1P1 − 2s2 1S0) = I(λ371.0)/I(λ192.8)(∆E ' 32 eV). Figure 8 presents the calculated R2

as a function of logarithmic electron temperature inK. The lines have been observed in the solar flare on09 August 1973 by the Skylab SO82A. The ratios are0.05 − 0.08 (measured by Doschek et al. 1977) and0.027 − 0.058 (re-measured by Dufton et al. 1983).Our calculations yield the logarithmic temperaturebetween 5.9 and 7.2, derived from the latter measure-ment. The Ca xvii ionization equilibrium temperatureis log Te = 6.74 (Arnaud & Rothenflug 1985) and 6.78(Mazzotta et al. 1998). McCann et al. (1989), using theSO82A observational data for the same flare, measuredthe R2 ratio for the ions S xiii and Ar xv, and derivedthe logarithmic temperatures of ∼ 6.5 (sulfur), 6.0 and6.45 (argon). These temperatures are within 20% ofthe ionization equilibrium temperatures of sulfur andargon, respectively. The temperature, inferred fromthe I(λ371.0)/I(λ192.8) ratio, is consistent with the

104 V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum

latter measurements and is reasonable for solar flares,although clearly much higher accuracies in the intensitymeasurements are needed to utilize this type of line ratiotechniques.

Relative line intensities, calculated using theCHIANTI database, are close to the HULLAC cal-culation and consistent with the experimentally inferredintensities.

Ca XVI - The blending problem is especially aggravated inthe 150 − 170 A domain, densely populated by Ca xiv,Ca xv and Ca xvi lines. We note that our calculations didnot reconcile the discrepancy between measured and cal-culated intensities of the λ208.6 and λ224.6 lines (upperlevels 2p2 2D). Lippmann et al. (1987) attributed themto the fact that their model did not include collisionalexcitation between 2s2p2 2D levels and the 2p3 2D levels,which resulted in overestimation of the upper level popu-lations. Recent calculations of Keenan et al. (1998), whichused R-matrix collision rates and included the 2p3 levelsas well, demonstrate a similar trend. HULLAC excitationrates between these terms are comparable to the excita-tion rates from the ground. According to our calculations,however, these excitation processes become noticeable(≥ 10% in the 2s2p2 2D level populations) only at ne ≥ 51014 cm−3. The λ 150 − 170 A lines and the λ208.6and λ224.6 lines were recorded from different TEXTdischarges, which could have explained the difference.The relative line intensities of the λ 150 − 170 Alines from both TEXT and FTU datasets are ingood agreement with HULLAC calculations. The ratioR = I(λ224.6)/I(λ208.6) = 1.3, recorded in TEXT, alsoagrees well with HULLAC prediction of 1.25. Keenanet al. (1998) pointed out that CHIANTI database givesabnormally low intensity of the latter ratio. Whereasthis was due to a missing piece of data and has beencorrected in v. 2.0 (Landi et al. 1999), the CHIANTIrelative intensities still differ from our measurements andHULLAC calculations. The measured branching ratios ofthe lines originating from the 2s2p2 2P1/2,3/2 levels agreewell with computations.

Several Ca xvi line pairs are electron density sensitive,and they have been used by Dere et al. (1979) and Keenanet al. (1998) in application to solar flare diagnostics. Inaddition to the mentioned R ratio, the intensity ratios ofλ154.9, λ157.8, λ164.2, λ168.9 to λ208.6 are also densitysensitive. The R ratio, however, seems to be a morereliable diagnostics, since the lines are close and subjectto blends to a lesser degree.

Ca XV - As in the case of boron-like calcium, many ofthe lines are blended, and in some cases (150 − 170 A)it was difficult to measure the brightnesses accurately.The λ208 blend was separated to the three componentsλ208.3, λ208.7 (Ca xv) and λ208.6 (Ca xvi) using ourmodel. Ten out of fourteen recorded lines in TEXT

6.0 6.5 7.0log Te

2

3

4

5

6

7

8

Rat

io I(

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192.

9) ×

10−

2

ne = 1.0×1010 cm−3

ne = 1.0×1012 cm−3

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Fig. 8. Predicted Ca xvii line intensity ratio R2 = I(2s2p 3P1−2s2 1S0) / I(2s2p 1P1 − 2s2 1S0) = I(λ371.0)/I(λ192.8) as afunction of electron temperature

and most of the lines recorded at FTU agree withinthe experimental error with the measurements. BothHULLAC and CHIANTI models include the important2 p4 configuration. The radiative cascade effects aresmall: line intensities, calculated using HULLAC (n = 2,n = 2, 3, and n = 2, 3, 4 models) and CHIANTI data(n = 2 only), differ by ≤ 5%. Several line ratios havebeen used to infer electron densities in solar flares (Dereet al. 1979; Keenan et al. 1992, and references therein).Present HULLAC calculations do not improve upondensity estimates previously published.

Ca XIV - HULLAC calculations agree within the er-ror of measurements with both TEXT and FTU datasetsfor the majority of the lines. The effect of cascades fromn = 3 and n = 4 levels is weak, ≤ 10%. Inclusion ofthe 2 p5 levels affects the 2s22p3 − 2s 2p4 relative lineintensities insignificantly (≤ 5%). CHIANTI intensitiesare in overall good agreement with the measurements,however some line intensities disagree up to a factor oftwo. In the same time, there is a close agreement betweenseveral measured branching ratios and the branching ra-tios from HULLAC and CHIANTI. Diagnostics potentialof Ca xiv lines includes the density-sensitive intensityratios of the lines, originating from 2s2p4 4P to the lines,originating from 2s2p4 2S,2 P,2 D (Feldman et al. 1980).The line intensity ratios of λ134, λ165, λ167, λ189 to λ194are density sensitive up to ne ' 1014 cm−3. Althoughλ194 is blended with a very strong λ193 Ca xvii line,it is possible to accurately separate them. The densitypredictions for TEXT, for example, based on the intensityratio of λ165 and λ189 to λ194 are within 20% of theindependently measured value. Three most intense XUVlines (λ183.5, λ186.6 and λ193.9) have been identified inthe full Sun spectra (Behring et al. 1972), and recently in

V.A. Soukhanovskii et al.: Laboratory XUV calcium spectrum 105

the transition region (Brosius et al. 1998).

Ca XIII - Both HULLAC and CHIANTI calculationsagree well with the TEXT and FTU datasets. Severalline intensity ratios, e.g. λ131, λ160 to λ164, can be usedas density diagnostics in the range between 1010 and1013 cm−3. The Ca xiii XUV lines have not been observedin solar plasmas.

Ca XII - The two XUV lines (λ141.0 and λ147.3)have been identified in the full Sun spectra (Behring et al.1972). The lines share the same upper level 2s2p6 2S1/2

and their intensity ratio is simply a ratio of the transitionprobabilities, known with fairly high accuracy. As followsfrom Fig. 5, the λ141 is a blend, which is the reason fora 20% difference between the measured and calculatedrelative intensities.

5. Conclusions

Two CR models of highly ionized calcium have beenbenchmarked in this work by comparing their predic-tions to the line intensities, measured with an absolutelycalibrated grazing incidence spectrometer in two toka-mak experiments. The CR models are based on ab initioHULLAC and CHIANTI atomic data, which are the stateof the art in atomic structure calculations. The HULLACmodels are in a good agreement with most measured linesof lithium-like to fluorine-like calcium. CHIANTI predic-tions for several Ca xvi and Ca xiv lines are inconsistentwith our measurements and HULLAC calculations. It isshown that for the tokamak, as well as for the solar flareplasma conditions, collisional-radiative models which in-clude n = 2 and n = 3 configurations are adequate to pre-dict L-shell line intensities. At these plasma conditions,radiative or collisional cascades from n = 4, 5 levels aregenerally insignificant, and quasi-steady state approachapplies well. With the present state of atomic calculations,likely explanations for large discrepancies with experimen-tal data are transient or kinetic effects, not the atomicdata quality. Total ionization and recombination rateswhich are used by Mazzotta et al. (1998) for a new cal-cium fractional abundances calculation, have been used fora calcium L-shell spectrum simulation. A synthetic line-integrated spectrum which includes over two hundred linesin the range 50 − 360 A, predicted by HULLAC, closelyreproduces the spectrum recorded at the TEXT tokamak.Density predictions based on line ratios of beryllium-,boron-, carbon-, nitrogen-, and oxygen-like calcium arecompared with independent density measurements. Goodagreement is found in the cases with minimal experimentaluncertainties.

All computational data are available in electronic formupon request.

Acknowledgements. The authors would like to acknowledge theTEXT and FTU tokamak teams. This work was supported byU.S. DoE Grant DE-FG02-86ER53214 at JHU and ContractNo. W-7405-ENG-48 at LLNL.

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