Up: Laboratory observation and modeling
Subsections
4.1 Ionization balance
Table 4:
Observed and calculated relative line intensities in FTU tokamak
|
|
Relative Intensity
a |
|
|
Measured |
Calculated
d |
Ion |
(Å)
c |
|
HULLAC |
CHIANTI |
Ca XVI |
154.9 |
14 |
17.8 |
17.7 |
|
157.8 |
17 |
17.2 |
13.4 |
|
164.2 |
100 |
100.0 |
100.0 |
|
167.4 |
40 |
39.8 |
48.0 |
|
168.9 |
51 |
48.2 |
67.6 |
|
|
|
|
|
Ca XV |
161.0 |
100 |
100.0 |
100.0 |
|
171.6 |
34 |
19.2 |
18.2 |
|
176.0 |
18 |
12.4 |
12.1 |
|
176.9 |
46 |
31.7 |
30.4 |
|
177.3 |
35 |
23.8 |
24.2 |
|
181.9 |
98 |
97.1 |
95.9 |
|
182.9 |
28 |
20.1 |
18.3 |
|
201.0 |
48 |
41.8 |
39.5 |
|
|
|
|
|
Ca XIV |
153.2 |
13 |
9.0 |
13.5 |
|
165.3 |
27 |
38.0 |
53.0 |
|
167.0 |
46 |
51.6 |
67.4 |
|
183.5 |
15 |
32.7 |
33.9 |
|
186.6 |
62 |
65.4 |
66.0 |
|
189.0 |
12 |
10.3 |
14.0 |
|
193.9 |
100 |
100.0 |
100.0 |
|
|
|
|
|
Ca XIII |
156.7 |
37 |
34.3 |
34.1 |
|
159.8 |
17 |
23.6 |
24.5 |
|
161.7 |
100 |
100.0 |
100.0 |
|
162.9 |
14 |
18.0 |
18.0 |
|
164.1 |
23 |
22.9 |
23.0 |
|
168.4 |
53 |
30.3 |
30.5 |
|
|
|
|
|
-
aLine intensity, relative to some representative line in each isosequence.
-
bLabels refer to Fig. 7.
-
cFrom Kelly ([1987]).
-
dFor
and
values, corresponding to the
measured MA location of the ion.
![\begin{figure}
\par\resizebox{\hsize}{!}{\includegraphics[angle=90]{ms9307f6.eps}}\smallskip
\end{figure}](/articles/aas/full/2000/04/ds9307/Timg56.gif) |
Figure 6:
Synthetic line-integrated time-averaged XUV spectrum of highly ionized calcium in
the TEXT tokamak |
The LOS-integrated TEXT spectrum was modeled using
fractional abundances estimated as
described in Sect. 2.3.
Ionization and recombination rates, used for this
calculation, were taken from the recent work of
Mazzotta et al. ([1998]).
Their ionization equilibrium curves for the calcium ions
differ from those of Arnaud & Rothenflug [1985],
both in MA temperature and ionization fractions.
The difference is most pronounced, up to 200%, for
the lower ionization stages (Ca XIV - Ca XII)
due to improved dielectronic recombination rates.
Our calculated calcium ion ground state distributions closely reproduced
the measured ones (Lippmann et al. [1987]).
Using QSS emissivities, we constructed
a line-integrated time-averaged synthetic TEXT
spectrum (Fig. 6). All lines predicted by HULLAC are shown.
This includes not only the
transitions of interest,
but also a large number of
and
transitions.
These lines are grouped in two domains: 14 Å
45 Å
and 50 Å
100 Å. The calculated intensities
of these lines are typically a factor of 102 - 103 less than
the
lines.
The 50 - 100 Å domain is covered by GRITS, however, line intensities
are below the detector sensitivity limit.
As seen in Fig. 6,
these lines contribute insignificantly to
line or background intensities.
All lines were given a Gaussian shape with the FWHM of GRITS.
The agreement between wavelengths
from Kelly ([1987]) and HULLAC is
for
most lines, which, however, resulted in different
blend patterns (comp. to Fig. 3).
Good agreement between synthetic and measured spectra can be considered
as indirect validation of the new fractional
abundance calculations for calcium.
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
the stated experimental error in most cases.
In comparison
with Lippmann et al. ([1987]),
improved atomic rates
result in a better
agreement between the measured and calculated relative
line intensities.
Results for individual ions are discussed below.
The emphasis is on the
beryllium- to nitrogen-like calcium ions, due to their
plasma temperature and density diagnostic potential.
Calculated density dependence of the level populations
is shown in Fig. 7.
Both ground and excited level
populations are in corona equilibrium at
cm-3.
The ground configuration levels approach Boltzmann values at
1014cm-3, and transfer population to the
excited 2pk+1 levels at different,
-dependent, rates.
This enables utilization
of the
E1 line intensity ratios
as density diagnostics.
Forbidden (M2) transitions between ground levels of
Ca XV, Ca XIV and Ca XIII can
also be used as a density diagnostics. These
far ultraviolet lines have been observed in a
solar active region by Feldman et al. ([1998])
and used to study physical conditions of the
solar corona.
![\begin{figure}
\par\resizebox{\hsize}{!}{\includegraphics[angle=90]{ms9307f7.eps}}\smallskip
\end{figure}](/articles/aas/full/2000/04/ds9307/Timg63.gif) |
Figure 7:
Modeled relative populations
of the n=2 levels as a function of electron density
at
values given in Table 1 (basic 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 normalized to the total population per ion.
The level labels are shown in Tables 2 and 3.
The levels not shown in Tables 2, 3 are labeled
as follows: b) Ca XVII: 6 - 1s22p
P0;
c) Ca XVI: 3 - 1s22s2p
P1/2;
4 - 1s22s2p
P3/2;
5 - 1s22s2p
P5/2;
d) Ca XV: 5 - 2s22p
S0;
6 - 2s2p
S2 |
Because of the high edge tokamak plasma density
(
1012 cm-3), collisional
quenching of the upper levels of these transitions
overtakes radiative decay:
both FTU and TEXT plasma edge spectra,
recorded by the SPRED and NITS instruments, respectively,
indicated no evidence of the forbidden lines. The line
intensities, calculated for the edge tokamak densities,
are a factor of
102 - 103less than those of typical XUV lines, which is beyond
the photometric sensitivity limit of the instruments used.
Ca XVIII -
The only XUV lines identified in solar flare spectrum are
and
(see references in Lawson & Peacock [1984]).
The lines are populated according to their statistical
weights. The discrepancy between calculations and
measurements in the
TEXT tokamak is
attributed to the GRITS calibration uncertainty
above 300 Å.
Ca XVII -
An example of a persisting disagreement between calculations and
solar flare measurements is a long-standing
problem with the line intensity ratios
of the Be I-like isosequence
R = I(2s
2s2p
(2s2p
,
J'=1,2 and J''=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 observed in the solar flares by
the NRL Skylab-based S082A spectroheliograph.
The calculated line intensity ratios
have consistently implied an electron density
of
cm-3 and higher,
in contrast to the density of
cm-3,
derived from other line intensity ratios (Doschek et al. [1977];
Bhatia & Mason [1983]; Dufton et al. [1983];
McCann et al. [1989]; Harra et al. [1992]).
All six lines have been observed in TEXT.
Calculated and measured relative
intensities agree within 40%, with the two exceptions of
and
,
which are blended
with the F IV lines.
Except for the
and
lines,
all other lines are
relatively weak and the inferred densities have
larger uncertainties or unrealistic values.
We therefore investigated various CR effects on the
)
ratio.
As the number of levels, included
in the model, increase, the calculated
ratios decrease,
due to cascades to the
levels. This effect is
20%
as n = 3,4 levels are added to the model.
In particular, the R1ratio was found to be 61 (n=2 only; 10 lowest levels),
49 (
;
30 levels)
and 47 (
;
125 levels).
The ratio, measured in TEXT, is
.
Both
and
lines are primarily populated
by electron impact excitation. The
level is
populated from the ground, whereas the
levels are populated both from the ground and from the
levels.
The DWA rates for these transitions, calculated by
HULLAC, are within
15% of the R-matrix
rates calculated by Dufton et al. ([1983]), for the
400 - 900 eV temperature range (with one exception
of
,
for which the HULLAC
rate is
35% smaller than the rate from Dufton et al. [1983]).
The detailed 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
ionization equilibrium temperatures.
Direct ionization is found to be the dominating
process, the autoionization flux originating
from the
levels
of Ca XVI is negligible, and the population flux due
to inner-shell ionization
from
and
levels of Ca XVI
to
levels of Ca XVII is several
orders of magnitude
less than the flux to the ground state. Significant departure
from ionization equilibrium is required
to populate the
levels through inner-shell
ionization (Feldman et al. [1992]).
Our calculations indicate that if
,
at
cm-3 up to 50% of
the total population of
levels is due to
inner-shell ionization, and
the R1 ratio is
practically the same as at
cm-3at ionization equilibrium conditions.
We conclude, therefore, that the
R1 ratio should be a reliable density diagnostics
in the
range of
1010 - 1014 cm-3.
Intensity ratio of two
lines of the same ion can be used
as a temperature diagnostic due to the temperature
dependence of the excitation rate coefficients, if
the separation of the upper levels of these lines
is much less than
,
as in the case of
the resonant and intercombination lines of
Be I-like calcium,
R2(Ca XVII
/
(
eV).
Figure 8 presents
the calculated R2 as a function of
logarithmic electron temperature in K.
The lines have been observed in the solar flare on 09 August 1973
by the Skylab SO82A.
The ratios
are
0.05 - 0.08 (measured by Doschek et al. [1977]) and
0.027 - 0.058 (re-measured by
Dufton et al. [1983]).
Our calculations yield the logarithmic temperature between
5.9 and 7.2, derived from the latter measurement.
The Ca XVII ionization equilibrium temperature
is
(Arnaud & Rothenflug [1985])
and 6.78 (Mazzotta et al. [1998]). McCann et al. ([1989]), using
the SO82A observational data for the same flare,
measured the R2 ratio for the ions S XIII and Ar XV,
and derived the logarithmic temperatures of
(sulfur),
6.0 and 6.45 (argon). These temperatures are within
20% of the ionization equilibrium temperatures of sulfur
and argon, respectively. The temperature, inferred
from the
ratio, is
consistent with the latter measurements and is reasonable
for solar flares, although
clearly much higher accuracies in the intensity measurements
are needed to utilize this type of line ratio techniques.
Relative line intensities, calculated using
the CHIANTI database, are close to the HULLAC calculation
and consistent with the experimentally inferred intensities.
Ca XVI-
The blending problem is especially aggravated in the
150 - 170 Å domain, densely populated by
Ca XIV, Ca XV and Ca XVI lines.
We note that our calculations did not reconcile
the discrepancy between measured and calculated
intensities of the
and
lines
(upper levels
).
Lippmann et al. ([1987])
attributed them to the fact that their model did
not include collisional excitation between 2s2p2 2D levels and
the
levels, which resulted in overestimation
of the upper level populations. Recent calculations of
Keenan et al. ([1998]), which used R-matrix
collision rates and included the
levels as well,
demonstrate a similar trend. HULLAC excitation
rates between these terms are comparable to the excitation
rates from the ground. According to our calculations, however,
these excitation processes become noticeable (
% in the
level
populations) only at
1014 cm-3.
The
150 - 170 Å lines and the
and
lines were recorded
from different TEXT discharges, which could have explained
the difference. The relative line intensities
of the
150 - 170 Å lines from both TEXT and
FTU datasets are in
good agreement with HULLAC calculations. The ratio
)
= 1.3, recorded in TEXT,
also agrees well with HULLAC prediction of 1.25.
Keenan et al. ([1998]) pointed out that
CHIANTI database gives abnormally low intensity of the
latter ratio. Whereas this was due to a missing piece of data
and has been corrected in v. 2.0 (Landi et al. [1999]),
the CHIANTI relative intensities still differ from our measurements and
HULLAC calculations. The measured branching ratios of the lines originating from
the
levels agree well with computations.
Several Ca XVI line pairs are electron density sensitive,
and they have been used by Dere et al. ([1979])
and Keenan et al. ([1998]) in
application to solar flare diagnostics.
In addition to the mentioned R ratio,
the intensity ratios of
to
are also density sensitive. The R ratio,
however, seems to be a more reliable diagnostics, since
the lines are close and subject to blends to a lesser degree.
![\begin{figure}
\resizebox{\hsize}{!}{\includegraphics[angle=90]{ms9307f8.eps}}\end{figure}](/articles/aas/full/2000/04/ds9307/Timg113.gif) |
Figure 8:
Predicted Ca XVII line intensity ratio
/
as a function of electron temperature |
Ca XV-
As in the case of boron-like calcium,
many of the lines are blended, and in some
cases (150 - 170 Å) it was difficult
to measure the brightnesses accurately.
The
blend was separated to
the three components
,
(Ca XV) and
(Ca XVI) using
our model.
Ten out of fourteen recorded lines in TEXT and most of the
lines recorded at FTU
agree within the experimental error with the
measurements.
Both HULLAC and CHIANTI models include the important
configuration. The radiative cascade effects are small:
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 have been used to infer electron
densities in solar flares (Dere et al. [1979]; Keenan et al. [1992],
and references therein). Present HULLAC calculations
do not improve upon density estimates previously published.
Ca XIV-
HULLAC calculations agree within the error of measurements with both TEXT and FTU
datasets for the majority of the lines. The effect of cascades from n = 3 and n = 4levels is weak,
%. Inclusion of the
levels
affects the
relative line intensities insignificantly (
%).
CHIANTI intensities are in overall good agreement with the measurements,
however some line intensities disagree up to a factor of two.
In the same time, there is a close agreement between several
measured branching ratios and the branching ratios from HULLAC and
CHIANTI.
Diagnostics potential of Ca XIV lines
includes the density-sensitive intensity ratios of
the lines, originating from 2s2p
P to the lines,
originating from
(Feldman et al. [1980]).
The line intensity ratios of
,
,
,
to
are density sensitive up to
cm-3.
Although
is blended with a very strong
Ca XVII
line, it is possible to accurately separate them. The density predictions
for TEXT, for example, based on the intensity ratio of
and
to
are within 20% of the independently measured
value. Three most intense XUV lines (
and
)
have been identified
in the full Sun spectra (Behring et al. [1972]),
and recently in the transition region (Brosius et al. [1998]).
Ca XIII-
Both HULLAC and CHIANTI calculations agree well with the TEXT and FTU datasets.
Several line
intensity ratios, e.g.
,
to
,
can be used as density diagnostics
in the range between 1010 and 1013 cm-3.
The Ca XIII XUV lines have not been observed in solar plasmas.
Ca XII-
The two XUV lines (
and
)
have been identified in the full Sun
spectra (Behring et al. [1972]).
The lines share the same upper
level
and
their intensity ratio is simply a ratio of
the transition probabilities, known with fairly high accuracy.
As follows from Fig. 5, the
is a blend, which is the reason for a 20% difference
between the measured and calculated relative intensities.
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