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THE ASTROPHYSICAL JOURNAL, 496 : 1031õ1043, 1998 April 1
1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.
(
OBSERVATION AND MODELING OF HIGH­n IRON L­SHELL LINES FROM
INTERMEDIATE ION STAGES
B. J. WARGELIN,1,2 P. BEIERSDORFER,3 D. A. LIEDAHL,3 S. M. KAHN,1,4 AND S. VON GOELER5
Received 1997 June 23 ; accepted 1997 October 31
ABSTRACT
The spectra of highly ionized iron species between 7 and 9 have been studied using data obtained at
ñ
the Princeton Large Torus tokamak under plasma conditions similar to those present in solar and stellar
ÿares. The wavelengths of many iron lines are measured with very high accuracy (j/*j up to 4 ] 104),
along with several other lines in species such as He­like Al XII and Mg XI. Theoretical spectra that
predict both the wavelength and the intensity of Fe emission lines are compared with the observed
spectra and are used to make accurate line identiïcations. Virtually all the observed iron lines are found
to arise from n \ 4, 5, and 6 ] 2 transitions in Fe XXIõXXIV, and many lines are identiïed for the ïrst
time. Several transitions are shown to have diagnostic applications, and a detailed analysis of the density
sensitivity of Fe XXII lines is presented.
Subject headings : atomic data õ line : identiïcation õ Sun : X­rays, gamma rays õ X­rays : general
1. INTRODUCTION
Emission lines arising from n \ 4 ] 2 and n \ 5 ] 2
transitions in highly ionized iron species such as Fe XXIõ
XXIV have been observed for many years in the X­ray
spectra of solar ÿares Meekins, & Cowans
(Doschek, 1972 ;
& Feldman et al. et al.
Seely 1986 ; McKenzie 1985 ; Fawcett
and are expected to be seen in most classes of X­ray
1987)
sources by next generation X­ray spectroscopy satellite mis­
sions such as the Advanced X­Ray Astrophysics Facility
(AXAF) and the X­Ray Multi­Mirror Mission (XMM).
Many of these lines are quite prominent, and several can
be used to infer the physical parameters of the emitting
gas, including electron density, temperature, charge­state
distribution, and deviations from coronal ionization
equilibrium.
Instrumental considerations also encourage the study of
4 ] 2 and 5 ] 2 transitions. Most of these lines fall between
7 and 9 a range particularly well suited for study using
ñ,
stable and high­resolution di+raction crystals such as
ammonium dihydrogen phosphate (ADP), with lattice
spacing 2d \ 10.648 In addition, the photon energy is
ñ.
above the low­energy cuto+ below which most detectorsî
quantum efficiency rapidly declines because of photoaborp­
tion in windows or surface layers. In particular, AXAFîs
e+ective area, when using either grating/detector com­
bination, peaks in just this energy range. Likewise, for astro­
physical sources, photoabsorption by circumstellar and
interstellar material is less problematic than it is at longer
wavelengths. Finally, most 4 ] 2 and 5 ] 2 lines are well
separated, requiring a resolving power of only a few
1 Department of Physics and Space Sciences Laboratory, University of
California, Berkeley, CA 94720.
2 Present address Harvard­Smithsonian Center for Astrophysics, 60
Garden Street, Cambridge, MA 02138.
3 Lawrence Livermore National Laboratory, 7000 East Avenue, Liver­
more, CA 94550.
4 Present address : Department of Physics, Columbia University, 538
West 120th Street, New York, NY 10027.
5 Princeton Plasma Physics Laboratory, Princeton University,
Princeton, NJ 08543.
hundred for e+ective application of diagnostic line­intensity
ratios.
Clear illustrations of the importance of accurate atomic
rate data (for Fe L­shell emission in particular) in analyzing
astrophysical X­ray spectra were recently provided by the
Advanced Satellite for Cosmology and Astrophysics (ASCA).
Several observations showed that existing plasma­emission
models, or rather, the emission rates they incorporated,
could not provide adequate ïts to the spectral data for any
set of physically reasonable plasma parameters et al.
(Drake
et al. et al. Indeed, sub­
1994 ; Fabian 1994 ; White 1994).
sequent atomic modeling results showed that the intensity
of the 3 ] 2 line complex relative to that of the 4 ] 2 blend
had been underestimated by a factor of approximately 2
Osterheld, & Goldstein These errors were
(Liedahl, 1995).
discovered during an analysis of astrophysical spectra with
a resolving power of only 20 (near 10 the high­
ñ) ;
resolution spectral data expected from future missions will
provide even greater challenges for spectral modeling codes.
Using theoretical atomic models et al.
(Doschek 1972 ;
et al. et al. and comparisons
Bromage 1978 ; Fawcett 1987)
with laser plasma spectra Faenov, & Pikuz
(Boiko, 1978 ;
& Ridgeley many of the transitions seen in
Fawcett 1979),
solar spectra between 7 and 9 have been identiïed.
ñ
Several important features remain unidentiïed, however,
and very little quantitative work has been done on the diag­
nostic uses of iron lines in this wavelength band (see Mason
& Storey With adequate knowledge of relevant
1980).
atomic parameters, however, plasma diagnostics based on
4 ] 2 and 5 ] 2 lines sometimes can be more useful than
those relying on the more familiar 3 ] 2 transitions.
In this paper we present spectra of highly ionized iron
between 7.1 and 9.0 obtained at the Princeton Large
ñ
Torus (PLT) tokamak, which has temperatures and den­
sities similar to those in solar and stellar plasmas. We
compare these high­resolution spectra with results from a
detailed atomic model of Fe ions, which allows us to make
several new line identiïcations and to develop density diag­
nostics for astrophysical use. The wavelengths of many lines
are measured with unprecedented precision, and a few pre­
viously published identiïcations are corrected. We also
identify and accurately measure the wavelengths of several
1031

1032 WARGELIN ET AL. Vol. 496
lines from other common elements that occur in this wave­
length region.
In we discuss plasma conditions in the PLT tokamak,
° 2
the spectrometer used, and our analysis and calibration
procedure. In we describe the HULLAC computational
° 3
suite and the assumptions made in our calculations. In ° 4
we present our observations and line identiïcations, and
in we discuss line­intensity ratios that can be used as
° 5
diagnostics.
2. DATA COLLECTION
2.1. T he Princeton L arge Torus Tokamak
Tokamaks, designed for fusion research, have provided
abundant information about the physics of highly charged
ions Goeler et al. Stamp,
(von 1981 ; Hinnov 1982 ; Peacock,
& Silver et al. Virtually all existing
1984 ; Beiersdorfer 1989).
tokamaks have stainless steel containment vessels, so there
is always some background emission arising from highly
ionized iron, as well as from smaller amounts of chromium,
nickel, and other metals that are sputtered from the
chamber walls or limiter plate. Indeed, early tokamaks were
unable to attain their expected plasma temperatures
because so much energy was lost via radiation from
ambient iron ions. Subsequent tokamaks have been
designed to minimize sputtering from interior surfaces and
often use coatings of low­Z elements such as Be, B, and C so
that emission from sputtered ions will be at lower power
and photon energies.
Tokamaks have plasma conditions similar to those found
in stellar coronae, particularly ÿares, which have typical
densities of 1011õ1013 cm~3 and temperatures up to a few
times 107 K. As a result, spectra from a given element are
similar, and results from laboratory observations can often
be applied directly to astrophysical sources. Previous labor­
atory identiïcations of 4 ] 2 and 5 ] 2 transitions in Fe
ions have made extensive and e+ective use of laser plasmas
et al. & Ridgeley which typi­
(Boiko 1978 ; Fawcett 1979),
cally have densities of order 1020 cm~3. At such high den­
sities, however, opacity and satellite broadening e+ects are
often signiïcant, and metastable levels may be collisionally
excited to higher levels, which results in radiative tran­
sitions that rarely occur in astrophysical X­ray sources.
Another di+erence is that tokamak plasmas are much larger
than laser plasmas, which allows the e+ective use of curved
crystal spectrometers that can be used to map out detailed
dispersion curves and provide extremely accurate wave­
length measurements. Precise line positions make it easier
to identify transitions when comparing observations with
theoretical predictions, and they permit more reliable line­
intensity measurements when lines are partially blended.
The experiments described here were performed on the
PLT Goldston, & Colestock a medium­size
(Hosea, 1985),
tokamak with major and minor radii of 134 and 40 cm,
respectively. Typical central electron temperatures when
using ohmic heating are 0.8õ3.0 keV [corresponding to (1õ
3.5) ] 107 K], with temperatures falling toward the
chamber walls following a roughly Gaussian proïle. Line­
of­sightõaveraged electron densities are in the range of (0.2õ
10.0) ] 1013 cm~3, with a typical value of a few times 1013.
Densities are highest in the center of the plasma and have a
somewhat ÿattened parabolic spatial proïle. A typical
plasma discharge, or ```` shot,îî lasts about 1 s, and trace
amounts of other elements can be injected into the hydro­
gen plasma during each shot to study emission spectra,
either for wavelength calibration or for diagnosis of plasma
parameters. Temperature and density can also be measured
independently using Thomson scattering and Michelson
interferometry, respectively.
2.2. Spectrometer
We used a high­resolution vacuum spectrometer with a
Bragg crystal and Johann geometry, as described by
et al. to record the X­ray spectra pre­
Beiersdorfer (1989),
sented here. A curved ADP crystal (57.3 cm radius of
curvature) focused X­rays from the plasma onto a position­
sensitive detector according to the Bragg equation, j \ 2d
sin h, where d is the crystal plane spacing (2d \ 10.648 for
ñ
ADP) and h is the Bragg angle of di+raction. In this
geometry, di+racted X­rays having di+erent wavelengths
originate from di+erent regions of the plasma.
The ïrst element of our detector was a ÿat ```` chevron îî
conïguration microchannel plate, which was coated with
approximately 3000 of CsI to increase X­rayõtoõelectron
ñ
conversion efficiency. Secondary electrons were proximity­
focused onto a ïber­optic surface coated with about 8 km of
P­20 phosphor. Light signals then traveled down two ïber­
optic tapers to two 1024 channel Reticon photodiode
arrays. During each plasma discharge, the array was read
out every 4 ms over a period of 192 ms for a total of 48
spectra.
Ideally, the detector face would be curved to match the
Rowland circle, but since our detector was relatively small,
focusing errors did not signiïcantly degrade resolution ; the
crystal could also be slightly pivoted on its axis, and dif­
fracted lines could still be adequately focused on the micro­
channel plate face. To extend the wavelength coverage of
the spectrometer further (the bandpass for a single crystal
position was typically 1 the entire spectrometer was
ñ),
tilted, which required careful repositioning of the detector
along the Rowland circle deïned by the crystal position and
orientation.
Our data were obtained using three detector positions,
covering three partially overlapping wavelength regions
that we refer to as short­, medium­, and long­wavelength
ranges. Each of these data sets was further subdivided into
two halves by the two­piece ïber­optic taper. The result was
six sets of data, each of which required its own wavelength
calibration. Because of the nonlinear dispersion character­
istics of the spectrometer and slight spatial distortions in the
microchannel plate and optical tapers, it was necessary to
map out dispersion curves actively in order to obtain the
desired wavelength measurement accuracy.
2.3. Calibration
To calibrate the wavelengths of observed lines, we
injected very small amounts of sodium or magnesium into
the plasma by using the laser ```` blow­o+ îî method (Marmar,
Cecchi, & Cohen Approximately 15 ms after injection
1975).
and 35 ms after the start of data acquisition, the injected
ions began emitting prominent K series (1s2 np
1S 0 õ1s 1P 1 )
and Lyman series shows some typical
lines.6 Figure 1
spectra obtained before and during calibration line
emission.
Sodium and magnesium were chosen as calibrators
because a large number of their K and Lyman emission
6 We use the ```` K îî label only for He­like emission lines, in order to
distinguish them from the H­like Lyman lines.

No. 2, 1998 MODELING OF HIGH­n IRON L­SHELL LINES 1033
FIG. 1.õExample spectra taken (a) during and (b) before calibration
line emission. Each spectrum was collected over a period of 28 ms. The
calibration lines are from the Lyman series of hydrogenic Na XI. (The
intensity of Lyf is enhanced by charge­exchange recombination of bare
Na XII with trace amounts of neutral hydrogen.) Background emission
from Fe ions is present in both spectra, along with a few emission lines
from residual Al and Se.
lines fall within the 7õ9 range under study, and theoretical
ñ
calculations of their wavelengths are very accurate. A list of
the reference lines used is found in along with the
Table 1,
estimated uncertainty of each lineîs wavelength. We used
the results of & Mack for the H­like lines.
Garcia (1965)
Their calculations include the weighted contributions of
all n ] 1 components (not just the and terms)
2P 3@2 2P 1@2
and are accurate to better than 0.0001 For Mg Lya,
ñ.
which has an asymmetric line proïle and at
(Lya
1 Lya
2
8.4192 and 8.4246 are not resolved in our data), we
ñ
allowed an uncertainty of 0.0003 to account for any
ñ
errors introduced by our assumption of a 2 : 1 intensity ratio
of the two Lya components. For the He­like lines we used
the predictions of U. I. Safronova (1986, private
communication), which we believe are more accurate than
the wavelengths listed in pp. 186, 215). The
Kelly (1987,
uncertainty we assumed for each line is generally the di+er­
TABLE 1
WAVELENGTH CALIBRATION LINES
Wavelength
Ion Transition (ñ) References
Mg10‘ . . . Kv 7.2247 ^ 0.0003 1
Mg10‘ . . . Kd 7.3103 ^ 0.0002 1
Mg10‘ . . . Kc 7.4731 ^ 0.0002 1
Na10‘ . . . Lyg 7.63936 ^ 0.0001 2
Na10‘ . . . Lyf 7.67662 ^ 0.0001 2
Na10‘ . . . Lyv 7.73477 ^ 0.0001 2
Na10‘ . . . Lyd 7.83318 ^ 0.0001 2
Mg10‘ . . . Kb 7.8503 ^ 0.0002 3
Na10‘ . . . Lyc 8.02107 ^ 0.0001 2
Mg11‘ . . . Lya 8.42100 ^ 0.0003 2
Na10‘ . . . Lyb 8.45950 ^ 0.0001 2
Na9‘ . . . Kv 8.6863 ^ 0.0004 1
Na9‘ . . . Kd 8.7885 ^ 0.0003 1
Na9‘ . . . Kc 8.9830 ^ 0.0002 1
REFERENCES.õ(1) U. T. Safronova, private communication, (2)
& Mack (3) this work, measured using nearby Na10‘
Garcia 1965 ;
Lyman series lines.
ence between Safronovaîs and Kellyîs values and makes
ample allowance for the fact that the He­like calculations
are for only the 1s transitions. Weak tran­
np 1P 1 ] 1S 0
sitions from other excited levels (such as will
1s np 3P 1 )
slightly shift the centroid of the blended line, but this e+ect
is negligible for all the He­like calibration lines appearing in
our spectra except for Mg Kb. In that case, the e+ective
wavelength of the Mg Kb blend was itself calibrated using
nearby Na Lyman lines, which provided a net wavelength
accuracy of ^0.0002 ñ.
The intrinsic resolving power of the spectrometer when
perfectly focused was estimated to be 3500 et
(Beiersdorfer
al. The FWHM of the Doppler­broadened lines was
1989).
measured to be as small as 0.003 (about six detector
ñ
channels), corresponding to j/*j B 2500. Since the center
of a strong line can be measured to a small fraction of its
FWHM, the wavelength di+erences between lines can be
determined with high precision. In most cases, however, it is
impossible to exploit this potential precision fully in wave­
length measurements because the exact dispersion curve is
not well determined.
As mentioned previously, however, the crystal in our
spectrometer could rotate over a small range without sig­
niïcantly degrading the spectral resolution. Such rotations
move the di+racted spectrum across the face of the detector,
but the angular separations of line pairs (determined by the
Bragg di+raction condition) remain the same even though
their physical separation on the detector changes. We uti­
lized this fact to map out a very precise dispersion curve for
each of the six data sets (two detector halves for each of
three detector positions) by observing how the channel
spacing between pairs of calibration lines changed as those
lines moved across the detector. Deïning i as dh/dN, where
h is the Bragg angle and N is the detector channel number,
the angular separation *h between any two lines is then
*h\ h 2 [ h 1 \ P N1
N2
i(N)dN , (1)
where and are, respectively, the Bragg angle and
h 1 N 1
detector channel number corresponding to the ïrst line, and
and correspond to the second line.
h 2 N 2
Taking pairs of calibration lines with known detector
positions (channel numbers) and wavelengths (Bragg
angles), we can then determine i(N) by using linear least­
squares methods to ïnd the best polynomial ït. Once i is
known as a function of N, the wavelength of any line can be
calculated based upon the wavelength and position of a
single calibration line using the equation
j unknown \ 2 d sin (h cal ]*h) , (2)
where
*h\ P Ncal
Nunknown
i(N)dN . (3)
We determined i(N) for each data set using calibration
data that were statistically weighted according to the uncer­
tainty in each lineîs ïtted channel position (using Voigt
proïles) and wavelength (see Second­order poly­
Table 1).
nomials gave acceptable ïts to ïve of the calibration data
sets, while the ïrst half of the medium­wavelength data
required a third­order ït. That data set was exceptionally
well constrained by its numerous and strong Na Lyman

1034 WARGELIN ET AL. Vol. 496
series lines and permitted the wavelengths of several Fe
lines to be measured to 0.0002 or 0.0003 Near the ends of
ñ.
our spectral coverage, wavelength calibration was some­
what less precise for several reasons : (1) spectral resolution
was worse because the crystal was at nonoptimal angles ; (2)
calibration­line wavelengths were not as accurately known ;
(3) both calibration and Fe lines were generally weaker. It
was also observed that the positions of the longest wave­
length lines drifted slightly during the course of a shot, but
this phenomenon was very repeatable, and we minimized its
impact by comparing calibration and Fe­emission data
taken from identical time groups. As a result, a calibration
accuracy of 0.001 or better was maintained over the entire
ñ
range studied.
3. CALCULATED SPECTRA
The model spectra were calculated using the HULLAC
atomic physics package. For the problem at hand,
HULLAC was used to calculate the atomic structure of the
ions Fe XXIõXXIV, the radiative decay rates, and the rate
coefficients for electron impact excitation. These atomic
data were then used to calculate the distribution of level
populations within each charge state according to the equa­
tions of statistical equilibrium, from which the line spectrum
follows. Model spectra from Cr XXIõXXII were also calcu­
lated since those ions have some emission lines in the wave­
length range under study.
The atomic structure and radiative rates are calculated
ab initio using a relativistic, multiconïguration, parametric­
potential method in intermediate coupling et al.
(Klapisch
HULLAC was developed for optimum performance
1977).
with highly charged high­Z ions, for which intermediate
coupling using j­j basis states is most appropriate. In this
paper, L S­coupling notation is used when such a term can
be unambiguously assigned (as for all Li­like and Be­like
states, and B­like states with a 2s2 core). For B­like tran­
sitions involving a 2s electron, and for all C­like transitions,
j­jõcoupling notation has been used, along with L S terms
suggested by other authors for previously identiïed lines.
The models used in the calculations are given in Table 2.
Radiative transitions include the multipoles E1, E2, M1,
and M2. The collisional cross sections are calculated
according to the quasi­relativistic distorted wave approx­
imation Klapisch, & Oreg Collisional­
(Bar­Shalom, 1988).
rate coefficients c (units of cm3 s~1) are found by averaging
vp(v) over a Maxwellian velocity distribution. The rate coef­
ïcients for collisional excitation from all states within con­
ïgurations (2s2p)k to all excited states (2s2p)k~1nl in the
models are calculated, as well as the 2l ] 2l@ intrashell
excitations.
Coupling of excited states to levels in adjacent charge
states through inner shell ionization, dielectronic recombi­
nation (DR), and radiative recombination is ignored for
several reasons. K­shell ionization of Fe ions in their
ground states produces no emission in the spectral band
studied here. DR, on the other hand, contributes D10% of
the total line ÿux, varying with temperature and ion species
et al. For plasma temperatures of interest
(Liedahl 1995).
here, DR involving excitation of an L­shell electron is most
important. Each such recombination begins with a radi­
ationless capture of the form (2s2p)k ] e ] (2s2p)k~1nln@l@
(n, n@ º 3), which may stabilize with the emission of an
X­ray satellite line. The excited but bound state left by
stabilization, (2s2p)knl, cascades to the ground state, with
the eventual emission of another X­ray.
Of the two X­rays produced as a consequence of DR,
only the satellite is distinct from the line produced directly
through electron impact excitation and can, in principle, be
identiïed. The satellite spectrum is, however, composed of a
large number of weak lines, and except for the possibility
of detecting the long­wavelength shoulders (unresolved
satellites) of resonance lines of the recombining ion, DR­
driven lines in these ions are generally too weak to select
out from spectra measured in tokamak experiments. Ignor­
ing recombination therefore cannot lead to line misiden­
tiïcation because of satellite contamination. Likewise,
intensity enhancement of nonsatellite lines produced
through DR­initiated cascades is too small an e+ect to
isolate.
Radiative recombination is even less important than DR
in driving 4 ] 2 and 5 ] 2 line emission in these ions (under
conditions near coronal equilibrium) because the generally
small rates are dominated by capture into the n \ 2 and
n \ 3 levels, bypassing the higher n levels. Charge transfer
from neutral hydrogen, in contrast, preferentially populates
high­n levels, roughly n \ 9õ11 for the Fe charge states of
interest here. Since radiative decays tend to proceed to the
lowest energy level allowed by selection rules, most of those
high­n levels either decay directly to a ground level (e.g.,
10s ] 2p), or fall as far as they can to intermediate­n levels
with (e.g., 10h ] 5g), which then decay via
l \ l ' \ n [ 1
*n\*l\ 1 steps along the so­called Yrast chain (e.g.,
5g ] 4f ] 3d ] 2p). Such transitions are not expected to
contribute appreciably to our spectra, and charge exchange
is therefore not considered in our modeling calculations.
As shown in two C­like Fe models were used in
Table 2,
the calculations. As indicated, the 676 level model does not
include the n \ 3 or n \ 4 shells. These were omitted in the
calculations of 5 ] 2 and 6 ] 2 Fe XXI spectra simply to
keep the size of the models manageable. This introduces
TABLE 2
CHARACTERISTICS OF ATOMIC MODELS USED IN CALCULATING MODEL SPECTRA
Number of Radiative Number of Collisional
Name Isosequence Number of Levels n ' l ' Rates Ratesa
Fe XXI . . C 1004 5 4 132959 18662
C 676 6b 3 63370 12099
Fe XXII B 735 6 4 74338 10341
Fe XXIII Be 302 7 4 12034 2900
Fe XXIV Li 42 7 4 330 118
Cr XXI Be 166 7 4 12019 2911
Cr XXII Li 42 7 4 331 118
a Each rate computed on a 6 point temperature grid.
b Model does not include levels with principal quantum numbers n \ 3 or 4.

No. 2, 1998 MODELING OF HIGH­n IRON L­SHELL LINES 1035
small errors in the branching ratios of radiative transitions
from n \ 5 and n \ 6 excited states, but the resulting errors
in relative line intensities are also small and have no bearing
on the results presented here.
4. OBSERVED SPECTRA AND LINE IDENTIFICATIONS
Some 60 shots, each with 48 time­binned spectra, were
scanned for prominent features, and approximately 50 lines
of high statistical signiïcance and reproducibility were dis­
cerned, not counting the Na and Mg calibration lines. A
composite spectrum is shown in with each feature
Figure 2
labeled (see ïgure legend for labeling convention). Well over
30 Fe lines were identiïed, along with 10 lines from other
elements, including Li­like Cr XXII.
The composite spectrum combines spectra collected
using eight di+erent detector­position or crystal­angle set­
tings, which were chosen based on (1) high signal­to­noise
ratio, (2) high resolution, and (3) exclusion of lines from
elements other than Fe and Cr. In a few cases, it was impos­
sible to avoid inclusion of some weak calibration lines
below 7.5 as well as a few lines from Al and Se. Those
ñ,
lines were excised from the composite spectrum (and labeled
in parentheses) to facilitate comparison with the model
spectrum, which includes emission from only Fe and Cr
ions.
The component spectra were joined at 7.505, 7.814, 7.881,
7.958, 8.006, 8.106, 8.352, 8.413, 8.453, 8.498, 8.566, 8.851,
and 8.943 and their relative amplitudes and continuum
ñ,
levels were adjusted so that overlapping lines had approx­
imately equal strength. As mentioned in within indi­
° 2.2,
vidual spectra focused X­rays of di+erent wavelengths arise
from di+erent regions of the tokamak plasma, i.e., regions
that have di+erent temperatures, densities, and plasma
column depths. Thus it can be seen that lines near the two
ends of the composite spectrum become increasingly weak,
since the spectrometer was collecting X­rays emitted near
the edges of the tokamak plasma. Indeed, below about 7.4
only a low­temperature, short­column portion of the
ñ,
plasma can be observed, and no lines from highly ionized
Fe are seen.
The theoretical spectra used to identify transitions in the
observed data are also shown in with line widths
Figure 2,
set to 0.0063 FWHM (corresponding to j/*j \ 1270 at 8
ñ
Two such spectra are shown ; both are composed of the
ñ).
same lines with the same intensities, but one employs line
wavelengths that have been slightly adjusted (as described
later in this section) to agree more closely with the observed
spectrum, while the other uses the directly computed,
uncorrected wavelengths. This illustrates how slight di+er­
ences in line wavelengths can alter the appearance of
spectra.
As discussed in the theoretical model includes emis­
° 3,
sion from Fe XXIõXXIV and Cr XXII. Because the observed
spectrum has been assembled from several shots, each
occurring under somewhat di+erent circumstances and each
line originating from a di+erent part of the plasma, the
relative emission measure of each ion included in the theo­
retical model was adjusted ```` by eye îî to match the observed
data as well as possible. For simplicity, we set a temperature
of 1000 eV for all ionsõthe relative line strengths within a
given charge state depend only weakly on temperatureõ
and adjusted the relative ion abundances as follows :
Fe XXIV, 1.00 ; Fe XXIII, 0.78 ; Fe XXII, 0.61 ; Fe XXI, 0.063 ;
Cr XXII, 0.78. Emission from Cr XXI, although calculated,
was not included in the model spectrum because it was not
observed in the data. As will be discussed in the spectra
° 5,
of B­ and C­like Fe depend on electron density ; the spec­
trum shown assumes a density of 1013.5 cm~3. As can be
seen, the resulting theoretical and observed spectra match
very well, with generally excellent agreement in wavelengths
and relative intensities.
In we list our Fe­line identiïcations, along with a
Table 3
comprehensive compilation of previous theoretical and
observational work on Fe spectra between 7 and 9 with
ñ
wavelength accuracies of 1 or 2 The wavelengths
mñ.
reported by et al. are also included
McKenzie (1985)
(following a slight correction) even though the accuracy
they quote is only 3 Although their solar observations
mñ.
are of high quality and resolution, the measured wave­
lengths of well­studied transitions in hydrogenic and
helium­like ions for lines between approximately 7.2 and 8
are systematically 3 or 4 longer than the known
ñ mñ
values, which indicates a calibration error. We therefore
reduced their measured wavelengths by 0.003 for lines
ñ
shortward of 8 which brings their results into excellent
ñ,
agreement with other measurements.
Since our emphasis is on astrophysical applications,
does not include lines that have been observed only
Table 3
in laser plasma spectra, since many of those lines arise from
doubly excited states, which can only be excited in
extremely high density environments et al.
(Bromage 1978).
Using the same inclusion criteria as those used for Table 3,
lists unidentiïed lines that are believed to come
Table 4
from Fe based on a priori knowledge of plasma constitu­
ents. lists lines from elements other than Fe that
Table 5
were observed in our spectra, several of which are promi­
nent in solar ÿare spectra and have important diagnostic
applications.
Nearly all of our wavelength measurements are accurate
to 1 Two exceptions are included in Tables and
mñ. 3 4,
with uncertainties of 0.003 or more : line E1 (at D7.478
ñ ñ)
because of blending with residual Mg Kc emission, and line
U4 (at D9.009 because it was at the very edge of our
ñ)
spectral coverage and resolution was poor. In those cases
where a measurement is accurate to better than 1 the
mñ,
uncertainty in the last digit (tenths of 1 is indicated in
mñ)
parentheses. We are able to measure the wavelengths of 27
lines to better than 1 Five of those lines have been
mñ.
previously measured to an accuracy of 0.0007 by &
ñ Seely
Feldman and our agreement with their results is
(1985),
excellent.
No accuracy estimates are provided for the theoretically
calculated wavelengths listed in but agreement
Table 3,
between our calculations and observed values is excellent
for the Fe XXIV lines. Agreement among the Fe XXIII lines is
equally good, except for the six lines arising from transitions
to the 2s2p level (lines E11, E10, E5, E4, E2, and part of
1P 1
the E1 blend), each of which had observed wavelengths that
were approximately 0.010 shorter than those predicted by
ñ
theory. We are unable to explain this discrepancy, but note
that if the calculated energy of the level is
2s2p 1P 1
decreased from 95.1 to 93.2 eV (above the ground
2s2 1S 0
state), the wavelengths of all six lines are brought to within
0.001 of their respective observed values. It is interesting
ñ
that the calculations of et al. apparently
Fawcett (1987)
have a similar error in the energy of the level, but
2s2p 1P 1
no other Fe XXIII levels.
For transitions in B­like Fe XXII, our calculated wave­

1036 WARGELIN ET AL.
FIG. 2.õObserved and model spectra. The observed spectrum is a composite ; the di+erent sections have been adjusted in amplitude to maintain
reasonably consistent line intensities, but no other adjustments have been made to account for the instrumental response, or for the variety of plasma
temperatures and densities represented in the data. Portions of the spectrum below D7.4 and above D8.8 are of lower quality because of unavoidable
ñ ñ
instrumental e+ects. Small gaps in the data (with labels in parentheses) are where non­Fe emission lines have been excluded for clarity. The labeling
convention for Fe and Cr lines is as follows : L for Li­like Fe XXIV, E for Be­like Fe XXIII, B for B­like Fe XXII, and C for C­like Fe XXI ; Cr for Cr XXII ; U for
unidentiïed.
Model spectra are shown both with and without wavelength adjustments. For the adjusted spectrum, 0.7 eV was added to each C­like line, 1.2 eV to each
B­like line, and 1.9 eV to the six Be­like transitions having lower level (lines E11, E10, E5, E4, E2, and part of E1). As explained in the text, these few
2s2p 1P 1
systematic corrections bring virtually all model lines into excellent agreement with observed wavelengths. Calibration lines from Na and Mg are shown
across the top.
lengths are systematically about 6 or 7 longer than the
mñ
measured values ; if 1.2 eV is added to the theoretical ener­
gies of all Fe XXII lines listed in then the maximum
Table 3,
di+erence between calculated and measured wavelengths is
only 0.001 (excluding the three tentatively identiïed
ñ
B­like lines that will be discussed in The theoretical
° 4.3).
wavelengths for the C­like lines are all approximately 0.004
longer than those experimentally measured (equivalent to
ñ
a di+erence of 0.6 eV), except for line C4, which has a calcu­
lated wavelength 0.007 shorter than that observed.
ñ
On theoretical grounds we expect HULLAC predictions
to be more reliable than previous predictions, since the
HULLAC models include more energy levels or 7)
(n ' \ 6
and predict emergent line intensities rather than just oscil­
lator strengths. Intensity predictions based solely on oscil­
lator strengths can be misleading when levels are populated
by mechanisms other than direct dipole electron impact
excitation, or when they decay via forbidden transitions or
multiple branches. A good example is provided by the
Fe XXIV 4 ] 2 lines. Although the radiative rates (and thus
oscillator strengths) for 2sõ4d (*L \ 2) transitions are neg­
ligibly small, the 4d levels are populated from the 2s level by
nondipole collisional excitation and then decay via fully
allowed transitions to produce 4d ] 2p lines (L9 and L7)
that are just as strong as the 4p ] 2s lines (L5 and L6).
Our expectations are met by the excellent agreement
between measurements and theory with regard to wave­
lengths (after the few systematic adjustments described
above) and relative line intensities within each ion species.
This gives us conïdence in our line identiïcations even
when they may disagree with previous work. In the follow­
ing subsections we discuss the results in more detail, begin­
ning with emission from di+erent ion stages of Fe, followed
by unidentiïed Fe lines, and concluding with emission from
elements other than Fe.
4.1. L ithium­like Fe XXIV
Fe XXIV has 10 signiïcant emission lines between 7.1 and
9 of which we are able to observe the eight that lie above
ñ,
7.4 Agreement between observation and theory is ex­
ñ.

TABLE 3
IRON SPECTRAL LINES
Line j obs j calc
Identiïcationa (ñ)b (ñ) Fe Ion Transition
L1 . . . . . . . . . . . . . 7.169c 7.1649d,e XXIV 2s 2S 1@2 õ5p 2P 3@2,1@2 (weighted average \ 7.1664 ñ)
7.1692d,e
L2 . . . . . . . . . . . . . 7.370c 7.368d XXIV 2p 2P 1@2 õ5d 2D 3@2
7.3670e
L3 . . . . . . . . . . . . . 7.437d 7.437d XXIV 2p 2P 3@2 õ5d 2D 5@2
7.438c 7.4363e
L4f . . . . . . . . . . . . 7.457d 7.461d XXIV Tentative identiïcation : 2p 2P 3@2 õ5s 2S 1@2
7.4601e
E1g . . . . . . . . . . . . D7.478d 7.473d XXIII 2s2 1S 0 õ2s5p 1P 1
7.472c (7.489)d (XXIII) (28% from 2s2p 1P 1 õ2s6d 1D 2 )
7.475h
E2f . . . . . . . . . . . . 7.498d 7.506d XXIII 2s2p 1P 1 õ2s6s 1S 0
B1g . . . . . . . . . . . . 7.6812 (4)d 7.687d XXII 2s22p 2P 1@2 õ2s26d 2D 3@2
7.680c (7.683)d (XXIII) (dominates previously identiïed line 2s2p 3P 1 õ2s5d 3D 2 in Fe XXIIIh)
7.682i (7.680)h (XXIII)
E3 . . . . . . . . . . . . . 7.733d 7.736d XXIII 2s2p 3P 2 õ2s5d 3D 3
7.733c 7.734h
B2f . . . . . . . . . . . . 7.752d 7.757d XXII 2s22p 2P 3@2 õ2s26d 2D 5@2,3@2
B3f . . . . . . . . . . . . 7.865d 7.870d XXII 2s22p 2P 1@2 õ2s2p 1@2 5p 1@2,3@2 (J \ 1/2, 3/2)
E4f . . . . . . . . . . . . 7.9009 (5)d 7.911d XXIII 2s2p 1P 1 õ2s5d 1D 2
7.902j 7.886h
7.901c
E5f . . . . . . . . . . . . 7.936d 7.947d XXIII 2s2p 1P 1 õ2s5s 1S 0
L5 . . . . . . . . . . . . . 7.9857 (2)d 7.986d XXIV 2s 2S 1@2 õ4p 2P 3@2
7.986j 7.9862e
7.986i 7.985j
7.984k 7.986l
7.983c 7.979m
L6 . . . . . . . . . . . . . 7.9960 (4)d 7.996d XXIV 2s 2S 1@2 õ4p 2P 1@2
7.996j 7.9964e
7.996i 7.995j
7.992k 7.996l
7.993c 7.989m
B4 . . . . . . . . . . . . . 8.0904 (3)d 8.097d XXII 2s22p 2P 1@2 õ2s25d 2D 3@2
8.091j 8.074j
C1f . . . . . . . . . . . . 8.1536 (5)d 8.157d XXI 2s22p 1@2 2p 1@2 (J \ 0)õ2s22p 1@2 6d 3@2 (J \ 1)
8.153i
B5f . . . . . . . . . . . . 8.1684 (4)d 8.174d XXII 2s22p 2P 3@2 õ2s25d 2D 5@2,3@2
8.167c
C2f . . . . . . . . . . . . 8.2036 (9)d 8.206d XXI 2s22p 1@2 2p 3@2 (J \ 1)õ2s22p 1@2 6d 5@2 (J \ 2)
L7 . . . . . . . . . . . . . 8.2326 (4)d 8.234d XXIV 2p 2P 1@2 õ4d 2D 3@2
8.232j 8.232j
8.233i 8.2322e
8.231k 8.232l
8.231c 8.225m
B6f . . . . . . . . . . . . 8.274d 8.283d XXII Tentative identiïcation : 2s2p 3@2 2p 3@2 (J \ 5/2)õ2s2p 3@2 5d 1@2 (J \ 7/2) ; previous identiïcationh :
8.273c Fe XXIII 2s2p 3P 2 õ2p4p 3D 3
8.271k
L8 . . . . . . . . . . . . . 8.2850 (4)d 8.287d XXIV 2p 2P 1@2 õ4s 2S 1@2
8.2854 (7)n 8.2862e
8.285c 8.279m
8.289k 8.284l
E6 . . . . . . . . . . . . . 8.3038 (3)d 8.304d XXIII 2s2 1S 0 õ2s4p 1P 1
8.3040 (7)n 8.305j
8.305j 8.306h
8.305i 8.306m
8.303k
8.303c
L9 . . . . . . . . . . . . . 8.3161 (3)d 8.319d XXIV 2p 2P 3@2 õ4d 2D 5@2,3@2 ; also Fe XXIII 2s2s 1S 0 õ2s4p 3P 1 , at j calc \ 8.317 ;dj the shoulder on
8.3160 (7)n 8.3171e the long side is 5 ] 2 transitions in Fe XXII and Fe XXI
8.317j 8.317j
8.318i 8.317l
8.316k 8.311m
8.316c

TABLE 3õContinued
Line j obs j calc
Identiïcationa (ñ)b (ñ) Fe Ion Transition
L10 . . . . . . . . . . . 8.3761 (7)d 8.376d XXIV 2p 2P 3@2 õ4s 2S 1@2 also about 15% from Fe XXII 2s2p 1@2 2p 3@2 (J \ 3/2)õ2s2p 1@2 5s(J \ 1/2)
8.3757 (7)n 8.3758e at j calc \ 8.387 ;d the shoulder on the short side is a 6 ] 2 Cr XXII line
8.376i 8.373l
8.371c 8.368m
B7f . . . . . . . . . . . . 8.4053 (6)d 8.421d XXII Tentative identiïcation 2s2p 1@2 2p 3@2 (J \ 1/2)õ2s2p 1@2 5d 5@2 (J \ 3/2) observed intensity
8.4055 (7)n is about twice that predicted
8.406c
E7 . . . . . . . . . . . . . 8.529d 8.529d XXIII 2s2p 3P 0 õ2s4d 3D 1
8.528k 8.527h
8.529c
E8g . . . . . . . . . . . . 8.546d 8.551d XXIII 2s2p 3P 1 õ2s4d 3D 2,1
8.550j (8.547d) (XXI) [and 2s22p 1@2 2p 3@2 (J \ 1)õ2s2 2p 3@2 5d 3@2 (J \ 2, 1, 0)]
8.547k 8.552j
8.550c 8.548h
C3g . . . . . . . . . . . . 8.5740 (8)d 8.578d XXI 2s22p 1@2 2p 1@2 (J \ 0) 3P 0 õ2s22p 1@2 5d 3@2 (J \ 1) 3D 1
8.573j (8.581)d (XXI) [and 2s22p 1@2 2p 3@2 (J \ 2)õ2s22p 3@2 5d 3@2 (J \ 3)]
8.574i 8.573j
8.575c
E9 . . . . . . . . . . . . . 8.6172 (6)d 8.617d XXIII 2s2p 3P 2 õ2s4d 3D 3
8.616j 8.618j
8.619i 8.615h
8.614k
8.614c
C4 . . . . . . . . . . . . . 8.640d 8.633d XXI 2s22p 1@2 2p 3@2 (J \ 1)õ2s22p 1@2 5d 5@2 (J \ 2)
8.644j
8.643c
C5f . . . . . . . . . . . . 8.663d 8.668d XXI 2s22p 1@2 2p 3@2 (J \ 2)õ2s22p 1@2 5d 5@2 (J \ 3), 2s22p 3@2 2p 3@2 (J \ 2)õ2s22p 3@2 5d 5@2 (J \ 3)
8.660j
8.664c
B8 . . . . . . . . . . . . . 8.714d 8.720d XXII 2s22p 1@2 2P 1@2 õ2s2p 1@2 4p 3@2 (J \ 3/2)
8.715j 8.713j
8.714c
B9 . . . . . . . . . . . . . 8.720d 8.728d XXII 2s22p 1@2 2P 1@2 õ2s2p 1@2 4p 3@2 (J \ 1/2)
8.722j 8.723j
8.723c
B10f . . . . . . . . . . . 8.736d 8.744d XXII 2s22p 1@2 2P 1@2 õ2s2p 1@2 4p 1@2 (J \ 3/2)
8.734j
8.736c
B11f . . . . . . . . . . . 8.753d 8.769d XXII Tentative identiïcation : 2s22p 1@2 2P 1@2 õ2s2p 1@2 4p 1@2 (J \ 1/2) ; observed intensity is about
8.752k twice that predicted ; previous identiïcation : h Fe XXIII 2p2 1D 2 õ2p4d 1F 3 but very weak
8.752c at normal densities, and j calc \ 8.737d
E10 . . . . . . . . . . . 8.8149 (4)d 8.826d XXIII 2s2p 1P 1 õ2s4d 1D 2
8.815j 8.826j
8.811i 8.794h
8.812k
8.814c
E11 . . . . . . . . . . . 8.906d 8.918d XXIII 2s2p 1P 1 õ2s4s 1S 0
8.906j 8.919j
8.906k
8.908c
B12 . . . . . . . . . . . 8.9748 (6)d 8.982d XXII 2s22p 2P 1@2 õ2s24d 2D 3@2
8.976j 8.976j
8.975i 8.952h
8.977c
a Labeling convention : L for Li­like Fe XXIV, E for Be­like Fe XXIII, B for B­like Fe XXII, C for C­like Fe XXI, U for unidentiïed.
b Numbers in parentheses give the uncertainty of the measured wavelength in tenths of 1 When no error is listed, the uncertainty is 1 or 2
mñ. mñ.
c Laser plasma observations by et al.
Boiko 1978.
d This work.
e Theoretical calculations by & Safronova
Vainshtein 1985.
f New identiïcation.
g Clariïcation of previously published identiïcation.
h Theoretical calculations by et al.
Bromage 1978.
Solar observations (with wavelength corrections) by et al.
McKenzie 1985.
j Solar observations and theoretical calculations by et al.
Fawcett 1987.
k Laser plasma observations by & Ridgeley
Fawcett 1979.
Theoretical calculations by Edlen 1979.
m Theoretical calculations by et al.
Doschek 1972.
n Solar observations by & Feldman
Seely 1986.

MODELING OF HIGH­n IRON L­SHELL LINES 1039
cellent, except for the wavelength and intensity of L4
The measured wavelength of L4 is at
(2p 2P 3@2 õ5s 2S 1@2 ).
least 0.003 lower than predicted, and its observed inten­
ñ
sity is roughly 3 times higher than predicted. It is possible
that the ```` true îî transition is obscured by
2p 2P 3@2 õ5s 2S 1@2
the wing of Mg Kc, and that line L4 is in fact some other,
unknown transition, but we are unable to suggest any likely
candidates. We therefore label our identiïcation of L4 as
tentative.
4.2. Beryllium­like Fe XXIII
Of the 11 Fe XXIII transitions listed, four are new. They
are the 6 ] 2 and 5 ] 2 analogs of the previously identiïed
4 ] 2 transitions (E10 at 8.815 and
2s2p 1P 1 õ2s4d 1D 2 ñ)
(E11 at 8.906), and correspond to, respec­
2s2p 1P 1 õ2s4s 1S 0
tively, line E1 at D7.478 (in which the 2s2p
ñ 1P 1 õ2s6d 1D 2
transition has about one­third of the intensity of the pre­
viously identiïed transition) ; E2 at 7.498
2s2 1S 0 õ2s5p 1P 1
E4 at 7.901 (which had been incorrectly assigned to a
ñ; ñ
line at 7.883 by et al. in their study of the
ñ Bromage 1978
et al. laser plasma spectra) ; and E5 at 7.936
Boiko 1978 ñ.
The wavelength of the E1 blend is not well measured in
our data, but when the 1.9 eV correction (see is applied
° 4)
to the component, we predict a centroid
2s2p 1P 1 õ2s6d 1D 2
of 7.474 for the blend. It was found that the E8 line is also
ñ
a blend, consisting of a Be­like line and a cluster of 5 ] 2
transitions in C­like Fe.
4.3. Boron­like Fe XXII
There are several new or reidentiïcations of Fe XXII lines,
including a few density­sensitive lines whose use as diagnos­
tics will be discussed in Lines B1 and B2 are 6 ] 2
° 5.
transitions, which are quite strong in some of our spectra.
The B1 transition was found to
2s22p 2P 1@2 õ2s 26d 2D 3@2
dominate a previously identiïed but much weaker tran­
sition in Fe XXIII. Nearly as strong as B1 are lines B2 and B3
(a newly identiïed 5 ] 2 transition), but their wavelengths
could not be measured as precisely because they were par­
tially obscured by the so­called w and z lines of He­like
Al XII (see Table 5).
The identiïcation of B5 (along with the C­like line, C1)
solves a puzzle in a series of solar ÿare spectra reported 25
years ago by et al. They observed six strong
Doschek (1972).
lines or blends between 7.95 and 8.40 and were able to
ñ
correctly identify four as transitions in Fe XXIV and XXIII,
leaving two unknown features around 8.10 and 8.16 They
ñ.
correctly suggested that the ïrst line (which we label B4)
might be the transition in Fe XXII
2s22p 2P 1@2 õ2s25d 2D 3@2
but were puzzled by the second ```` doublet îî feature, which
did not weaken over time (as the ÿare cooled and the ions
recombined) like any of the other lines. That second feature
is the blend of C1 and B5 (8.154 and 8.168 respectively).
ñ,
As the ÿare cooled and B­like emission decreased, the net
intensity of the C1/B5 blend was maintained by emission
from the increasing population of C­like ions. The B5 line
itself consists of two transitions, one of which is sensitive to
density.
The only other new Fe XXII identiïcation that we con­
sider ïrm is the B10 line at 8.736 but we have also made
ñ,
three other tentative line identiïcations : B6 at 8.274 B7
ñ,
at 8.4053 and B11 at 8.753 All of these features have
ñ, ñ.
been observed in laser plasma spectra, and B7 has also been
seen quite distinctly in a solar spectrum by &
Seely
Feldman Our model calculations showed that earlier
(1986).
identiïcations of B6 and B11 by et al. were
Bromage (1978)
incorrect ; the intensities of their proposed lines are negligi­
ble at astrophysical (coronal) densities, and the expected
wavelength of their proposed B11 transition is o+ by at least
0.015 Our own identiïcations of these three lines,
ñ.
however, also must be treated with caution because of dis­
agreements between observation and calculation that are
TABLE 4
UNIDENTIFIED IRON LINES
Line j obs
Identiïcationa (ñ)b Comments
None . . . . . . . . 7.919c Weak, probably Fe XXI 2s22p 1@2 2p 3@2 (J \ 1)õ2s2p 1@2 2p 3@2 6p 3@2 (J \ 2, 1) at j calc \ 7.924 ;d
we observe a weak feature at 7.919 ñ
None . . . . . . . 7.949e We observe a weak feature at D7.950 ñ
None . . . . . . . 8.141e We observe a weak feature at 8.138 ñ
None . . . . . . . 8.2557 (7)f
U1 8.560d
U2 8.919d Always present, but usually weak in our data intensity may scale with that of U3
8.918c
8.920e
8.921g
U3 8.937d Probably from the same ion as U2
U4 D9.009d Previous identiïcation :h Fe XXII 2s2p2 4P 5@2 õ2s2p4d (3P)4D 7@2 , but very weak at normal densities
9.006c
9.006g
a Labeling convention : L for Li­like Fe XXIV, E for Be­like Fe XXIII, B for B­like Fe XXII, C for C­like Fe XXI, U for unidentiïed.
b Numbers in parentheses give the uncertainty of the measured wavelength in tenths of 1 When no error is listed, the uncertainty is
mñ.
1 or 2 mñ.
c Solar observations and theoretical calculations by et al.
Fawcett 1987.
d This work.
e Solar observations (with wavelength corrections) by et al.
McKenzie 1985.
f Solar observations by & Feldman
Seely 1986.
g Laser plasma observations by et al.
Boiko 1978.
h Theoretical calculations by et al.
Bromage 1978.

1040 WARGELIN ET AL. Vol. 496
TABLE 5
NON­IRON EMISSION LINES
Line j obs j ref
Identiïcation Ion (ñ) (ñ) Transition
Se1 . . . . Se24‘ 7.6907 (3) 7.685a 2s22p6 1S 0 õ2s22p53d 1P 1
Al w . . . . . . Al11‘ 7.7573 (2) 7.7573b 1s2 1S 0 õ1s2p 1P 1
Al xy . . . Al11‘ 7.8067 (5) 7.8065b,c 1s2 1S 0 õ1s2p 3P 2,1
Mg Kb Mg10‘ 7.8503 (2)d 7.8507e 1s2 1S 0 õ1s3p 1P 1
Al z . . . . . . . . . . Al11‘ 7.8722 (3) 7.8721b 1s2 1S 0 õ1s2s 3S 1
Se2 . . . . . . . . . Se24‘ 7.8779 (3) 7.874a 2s22p6 1S 0 õ2s22p53d 3D 1
Se3 . . . . . . . . . . . Se23‘ 7.9667 (7)
Se4 . . . . . . . . . . . Se23‘ 7.9744 (6)
Cr1 . . . . . . . . . . . Cr21‘ 8.519 8.516f,g 2s 2S 1@2 õ5p 2P 3@2,1@2
Cr2 . . . . . . . . . . . Cr21‘ 8.777 8.7749g 2p 2P 1@2 õ5d 2D 3@2
Cr3 . . . . . . . . . . . Cr21‘ 8.8444 (6) 8.8442g 2p 2P 3@2 õ5d 2D 5@2
a Measured wavelength from et al.
Boiko 1978.
b Theoretical wavelength from Drake 1988.
c Weighted average of 15% 7.8038 and 85% 7.8070 weights derived from
ñ ñ;
relative upper level populations of 5 : 3, and branching ratios of 0.107 and 1.0.
d Measured line includes small but signiïcant contributions from 1s3l levels other
than which slightly shift the centroid of the line.
1s3p 1P 1 ,
e Theoretical wavelength from U. I. Safronova 1986, private communication.
f Weighted average of 67% 8.5140 and 33% 8.5183
ñ ñ.
g Theoretical wavelength from & Safronova
Vainshtein 1985.
signiïcantly larger than for any of the other lines we have
identiïed. Speciïcally, for these lines, ranges
j calc õj obs
between 0.003 and 0.009 (after applying the systematic 1.2
ñ
eV B­likeõline energy correction), and varies
I calc /I obs
between and
1 2 1 3 .
There is one other B­like worth mentioning, even though
we cannot resolve it on our spectrum. Lying within the
B­like emission cluster between 8.70 and 8.76 is a density­
ñ
sensitive transition, (J \ 5/2),
2s22p 3@2 2P 3@2 õ2s2p 3@2 4p 3@2
which we predict lies at 8.730 (following the 1.2
ñ
eV correction). Although relatively weak in our spectrum,
the relative intensity of this transition is predicted to
increase by a factor of more than 5 between 1013 and 1014
cm~3 so that it becomes stronger than the B10 line, but
because of blending with nearby lines, it is somewhat diffi­
cult to use it as a density diagnostic. Fortunately, there is a
pair of B­like lines around 9.0 that are very strong, well
ñ
separated from other lines, and whose intensity ratio is a
function of density (see ° 5).
4.4. Carbon­like Fe XXI
All ïve of the C­like features that we identify in Table 3
have been observed in solar spectra, including the relatively
weak C2 line, which can be discerned in the spectra of
et al. Only one of those lines, however,
Doschek 1972.
has been previously (partially) identiïed : the C3 line at
8.574 ñ.
At low densities, C3 is the brightest of all the C­like 5 ] 2
features. This line is actually a blend of four transitions,
although at densities below 1014 cm~3 the density­
insensitive transition originally identiïed by et al.
Fawcett
is strongest. The other three transitions are
(1987)
(J \ 3),
2s22p 1@2 2p 3@2 (J \ 2)õ2s22p 3@2 5d 3@2 2s22p 1@2 2p 3@2
(J \ 2), and (J \ 2)õ
(J \ 2)õ2s22p 3@2 5d 5@2 2s22p 1@2 2P 3@2
(J \ 1), with relative strengths of approx­
2s22p 3@2 5d 3@2
imately 7 : 3 : 1. Between 1011 and 1013 cm~3 their intensity
increases almost 6 times faster than density, and their com­
bined strength equals that of the density­insensitive tran­
sition at around 3 ] 1013 cm~3. Like C3, the C4 and C5
lines (C5 is a blend with two dominant transitions) are also
density sensitive, and surpass C3 in intensity above approx­
imately 1014 cm~3. These and other potential diagnostic
lines are discussed further in ° 5.1.
4.5. Unidentiïed L ines
We are unable to identify a number of lines we observed.
Those lines, and any other unclassiïed lines previously seen
in solar spectra between 7.0 and 9.1 are listed in
ñ, Table 4.
The line at 7.871 seen by et al. in a solar
ñ Fawcett (1987)
ÿare spectrum is undoubtedly from Al XII 1s2 1S 0 õ1s2s 3S 1 ,
and is not listed. Although there are some features in the
model spectrum near U2, U3, and U4, they are much too
small compared to the predicted intensities of E10 and B12
to explain the relative intensities of the observed lines.
(Recall that lines near the edge of the spectrum are sup­
pressed by instrumental e+ects.)
In our e+orts to identify the lines in question, satellite
lines of iron and emission from C­, N­, and O­like nickel
were investigated using HULLAC, but no plausible candi­
dates were found. Although deïciencies in the atomic
models, exotic plasma processes in the tokamak or solar
corona, emission from trace elements, and similar explana­
tions cannot be entirely excluded, we suggest that most of
the unclassiïed lines likely come from lower ionization
stages of iron such as N­like Fe XX and O­like Fe XIX.
Because of the complexity in modeling those ions, particu­
larly with the high­n atomic levels that would be required
(n º 5), and because of uncertainties in the relative inten­
sities of the unidentiïed lines near the edge of the spectrum,
we have not pursued those investigations further.
4.6. Non­Fe Emission L ines
In addition to emission from Fe ions (and the calibration
lines from Na and Mg), we also observed lines from three
other elements that were present in the tokamak as impu­
rities : Al, Se, and Cr. The aluminum is from the housing of a
probe used to make plasma­edge measurements. The sele­
nium was left over from injection during a preceding experi­
ment and appeared only in the early stages of our
experiment. Chromium, like iron, is a component of the

No. 2, 1998 MODELING OF HIGH­n IRON L­SHELL LINES 1041
stainless­steel containment vessel and is always present,
although at only about 10% the level of iron. Nickel is also
present for the same reason, but as described above, was not
observed. The remaining few percent of the stainless steel
chamber consists mostly of manganese, which has negligible
emission at such a low concentration.
Ten emission lines from the above three elements are
listed in along with Mg Kb, a calibration line that
Table 5,
was itself calibrated using Na Lyman lines as discussed in
The Al lines are He­like Ka transitions, speciïcally the
° 2.3.
resonance line intercombination line
(1s2 1S 0 õ1s2p 1P 1 ),
blend with 85% from and for­
(1s2 1S 0 õ1s2p 3P 2,1 3P 1 ),
bidden line We believe that our wave­
(1s2 1S 0 õ1s2s 3S 1 ).
length measurements of these lines known respectively as w,
x, y, and z in the notation of are the most
Gabriel (1972)
accurate to date, and note that they are essentially in perfect
agreement with the predictions of Drake (1988).
Se1 and Se2, the two most prominent selenium lines we
observe, are from transitions in Ne­like Se XXV. These lines
are quite strong in one of our shots, allowing us to deter­
mine their wavelengths with an uncertainty of only 0.0003
The wavelengths we measure are about 0.004 longer
ñ. ñ
than those measured by et al. Based on pre­
Boiko (1978).
vious work et al. we also identiïed Se3
(Beiersdorfer 1989),
and Se4 as transitions in Na­like Se XXIV.
As discussed before, our theoretical model includes
Li­like Cr XXII and Be­like Cr XXI. Emission from chromium
is generally weak, but we are able to conïdently identify
three lines as 5 ] 2 transitions in Cr XXII. There are some
indications of 6 ] 2 and 7 ] 2 emissions at 8.365, 8.099,
8.065, and 8.041 but these features are weak and are not
ñ,
listed in the table. No emission from Cr XXI is observed.
5. DENSITY DIAGNOSTICS
The density sensitivities of Fe XXI and Fe XXII spectra
have been discussed by et al. for the 3 ] 2
Doschek (1973)
transitions, & Storey who include calcu­
Mason (1980),
lations of the 4 ] 2 lines, and et al. who
Fawcett (1987),
treat the 4 ] 2 spectrum from an experimental point of
view. In general, the density sensitivity of Fe L­shell spectra
derives from the buildup of population in low­lying meta­
stable states at densities exceeding D1012 cm~3. Each of
those low­energy excited levels can then serve as a platform
for excitation to higher energy levels via electron collisions,
often producing a set of lines that is distinct from that
observed at low densities, and whose intensity varies more
rapidly with electron density than lines produced by excita­
tion from the ground state.
At low densities (\D1011 cm~3), C­like Fe XXI lines are
excited from the (J \ 0) ground state, but at high
2s22p2
1@2
densities the upper levels of the C4 and C5 transitions are
populated primarily by collisions from the 2p
1@2 2p
3@2
(J \ 1) and (J \ 2) levels, respectively ; the upper
2p
1@2 2p
3@2
levels of the three density­sensitive transitions included in
the C3 blend are populated by collisions from both of these
metastable levels. While the C3, C4, and C5 lines may be
useful as diagnostics, a more detailed explanation is beyond
the scope of this paper, and we will concentrate instead on
B­like line diagnostics.
An illustration of the density sensitivity of B­like Fe XXII
spectra is shown in which presents model results
Figure 3,
for 4 ] 2, 5 ] 2, and 6 ] 2 transitions. The two most
prominent features are the line at 8.975 and a blend of
ñ
two lines at 9.067 and 9.070 (Wavelengths were derived
ñ.
by adding the usual 1.2 eV B­likeõion correction to our
HULLAC­calculated energies. The measured and calcu­
lated wavelengths of the 8.975 B12 line are in excellent
ñ
agreement, and although we cannot measure the wave­
lengths of the other two lines because they lie just longward
of our spectrometer limit, we expect their theoretical wave­
lengths to be accurate to within 0.001 ñ.)
A schematic of the mechanism responsible for the behav­
ior of those 4 ] 2 lines is shown in A key feature is
Figure 4.
that the ïrst excited state can decay only by a slow
2s22p 3@2
M1 transition to the ground state. Below 1012 cm~3, col­
lisional excitation rates are sufficiently low so that the decay
is still fast enough to prevent any signiïcant population
buildup in the metastable level, while at high densities the
ratio of and populations approaches its LTE
2p 3@2 2p 1@2
value of 2. Between those two limits the population,
2p 3@2
relative to the ground state population, increases from
D0.01 at 1012 cm~3 to D1.5 at 1016 cm~3. The second
essential feature is that collisional excitation from the 2p 1@2
level preferentially populates the level (at 7.5 times the
4d 3@2
rate for the level, at a temperature of 1 keV), while the
4d 5@2
level tends to populate the level (by a ratio of 5.3
2p 3@2 4d 5@2
to 1). The net result is that the population of the level
4d 5@2
increases with density faster than that of leading to an
4d 3@2 ,
increase in the relative intensity of the 9.067­ñ 4d 5@2 ]
line. Virtually the same mechanism and analogous
2p 3@2
energy levels apply for n \ 3, 5, and higher.
FIG. 3.õTheoretical spectra of B­like Fe XXII at electron temperature of
1000 eV, for densities of (a) 1012 cm~3 and (b) 1014 cm~3. Emissivity units
are arbitrary but the same for both panels. Spectra are plotted with a
FWHM resolution of 0.003 ñ.

1042 WARGELIN ET AL. Vol. 496
FIG. 4.õSchematic diagram of processes responsible for the density
sensitivity of B­like Fe XXII 4 ] 2 lines. Relative magnitudes of collisional­
rate coefficients are represented by the thickness of the solid lines. Dotted
lines indicate relevant radiative decay channels, with wavelengths (in
angstroms) and radiative branching ratios (in parentheses). At low den­
sities the dominant process is excitation of the level from ground. At
4d 3@2
high densities the level is excited from the metastable level,
4d 5@2 2p 3@2
which is fed by cascades mostly through the (J \ 1/2, 3/2, 5/2)
2s2p 3@2 2p 3@2
levels, and which decays by a slow M1 transition to ground.
Model predictions of the 4 ] 2 line ratio versus density
are shown in with the ratio rising from about 0.5
Figure 5,
at cm~3 to 1.5 at 1015 cm~3. In addition to the
n e \ 1013
plot of the ratio of the 8.975 and 9.067]9.070 lines, a
ñ ñ
second curve illustrates the e+ect of ïnite spectral
resolution, in which all nearby B­like lines are summed with
the main peaks. In the example shown, a resolution bin of
*j/j \ 1/300 has been used, centered on the primary lines.
The di+erence between the two curves is small since the
other B­like lines are relatively weak, but in a real spectrum
the contribution of lines from other ion species must also be
considered. Corresponding curves for the 5 ] 2 lines (at
8.090 and 8.168 are very similar, as one would expect,
ñ)
and are o+set vertically from the 4 ] 2 curves by 0.035 (for
the pure lines) and 0.050 (with *j/j \ 1/300).
Unfortunately, the 9.067 line is just longward of our
ñ
spectrometer limit, so we cannot apply the 4 ] 2 diagnostic
to our data. We are, however, able to use other sets of
diagnostic linesõthe 5 ] 2 analogs at 8.090 (B4) and 8.168
(B5) ; the cluster of B­like lines between 8.70 and 8.77
ñ ñ
(B8õB11) ; and the C­like C3, C4, and C5 lines between 8.6
and 8.7 deduce an electron density of 3 ] 1013 cm~3
ñõto
in the Fe XXI and XXII line­forming regions of our tokamak
plasma.
We can also apply the B­like 4 ] 2 diagnostic to the 1985
July solar ÿare spectrum reported by et al.
Fawcett (1987).
They measured a line ratio of I(9.073)/I(8.976) \ 0.54, indi­
cating a density of D3] 1013 cm~3, slightly higher than
their suggested value of D1013 cm~3, which was derived
using uncertain collision strengths and branching ratios.
Features are also seen at 8.090 and 8.168 in that ÿare
ñ
spectrum, but they are probably too weak to apply the
5 ] 2 line diagnostic e+ectively.
6. SUMMARY
We have presented results from a study of the spectrum
FIG. 5.õFe XXII 4 ] 2 line intensity ratios vs. log The solid curve is
n e .
the ratio of the intensities of the primary 9.067]9.070 and 8.976 lines,
ñ ñ
while the dashed curve is the ratio when weak nearby lines (within 0.015 ñ
of the primary lines) are included. The analogous curves for the 5 ] 2 lines
(at 8.168 and 8.090 are shifted upward by approximately 0.035 and
ñ)
0.050, respectively.
of highly ionized Fe between approximately 7 and 9 and
ñ,
conïrmed most previous line identiïcations while also cata­
loging over a dozen new lines, including transitions in
Be­like Fe XXIII, B­like Fe XXII, and C­like Fe XXI. A method
of calibrating the wavelengths of emission lines from
extended sources with very high accuracy was described,
and the results were compared with a comprehensive list of
previous theoretical work and solar and laboratory obser­
vations. Secondary products of that calibration are what we
believe to be the most accurate wavelength measurements
to date of the Al Ka complex and MgKb.
Theoretical spectra were calculated with the HULLAC
atomic modeling package and compared with observed
spectra. HULLAC employs detailed level accounting to
compute emission rates, rather than relying on scaled oscil­
lator strengths, and also uses more complete atomic models
(through n \ 6 or 7) than in previous works, so its predic­
tions of relative line intensities should be more reliable.
Agreement with observations was generally quite good with
regard to both wavelengths and intensities, although a few
systematic wavelength errors were seen and some lines
remained unidentiïed.
The use of Fe L­shell line ratios as density diagnostics
was examined, and a plot of B­like Fe XXII line ratios versus
density provided, which we used to infer a value for electron
density in a previously reported solar ÿare. The wavelength
and intensity information presented here will provide a
similar utility for the analysis of X­ray spectra from astro­
physical sources once high­resolution spectra become
available.
In addition to the Fe lines studied here, a number of
emission lines from hydrogenic and heliumlike Na, Mg, and
Al also lie in the 7õ9 wavelength regime. Several of those
ñ
lines, particularly the He­like Al XII 2 ] 1 lines (w, x, y, and
z) and He­like Mg Kb and Mg Kc, are useful as diagnostics
but may be blended with Fe L­shell emission lines. For
example, even a resolving power of 500 would be insuffi­
cient to separate the Al w­resonance line from B2, Mg Kb

No. 2, 1998 MODELING OF HIGH­n IRON L­SHELL LINES 1043
from B3, or Mg Kc from E1 and L4. (Note that the B2 and
B3 lines were not even ```` known îî until this work.) Since Fe
L­shell emission is often a prominent component of astro­
physical spectra, it is vital that any plasma codes being used
to analyze spectral data incorporate a sufficiently complete
list of reliable line emission rates, not only to account for all
the ÿux in the iron lines themselves, but also to give accu­
rate diagnostic information derived from He­like lines in
this region.
The authors wish to thank Janet Felt and Tom Gibney
for support provided in accessing the PLT data ïles. This
work was supported by the NASA X­Ray Astronomy
Research and Analysis Program under grant NAGW­4185.
Work performed at the Lawrence Livermore National
Laboratory and the Princeton Plasma Physics Laboratory
was performed under the auspices of the US Department of
Energy under contracts W­7405­ENG­48 and DE­AC02­
76­CHO­3073, respectively.
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