PFC/JA-83-12
X-RAY LINE INTENSITIES FOR IONS OF THE HELIUM
ISOELECTRONIC SEQUENCE IN HIGH TEMPERATURE PLASMAS
E. Kaillne, J. KaIllne, and A. Pradhan
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, MA
02139
January 1983
This work was
supported
by the U.S.
Department
of Energy Contract
No. DE-AC02-78ET51013. Reproduction, translation, publication, use
and disposal, in whole or in part by or for the United States government is permitted.
By acceptance of this article, the publisher and/or recipient acknowledges the U.S. Government's right to retain a non-exclusive,
royalty-free license in and to any copyright covering this paper.
X-ray Line Intensities for Ions of the
Helium Isoelectronic Sequence in High Temperature Plasmas
E. K1une and 1. K[11ne
Harvard-Smithsonian Center for Astrophysics
Cambridge, Massachusetts
02138, USA
and
A.K. Pradhan
University of Windsor, Ontario, Canada
Abstract
Measurements are reported for the He-like X-ray spectra of
in
a
deuterium tokamak plasma with N
= 1-2 x 1014 cm-3 and T
results are interpreted with the help of computed
available
atomic
data.
The
plasma
sensitivity
excitation
argon
obtained
= 1-2 keV.
rates
and
The
other
of line intensity ratios is
discussed as well as the Z-dependence based on earlier observations of He-like S
and Cl.
1977 PACS numbers:
32.30.Rj, 32.70.Fw, 52.70.-m
Page 2
The X-ray n=2 to n=1 spectrum of ions in the helium iso-electronic sequence
consists
of four principal lines conventionally labelled w, x, y, and z.
are associated with the n=2 states 2 Pip 2
23P
state
has
no
ground
state
two-photon emission) (see Fig. 1).
are
mainly
populated
through
2 1,
and
transition
23 S,
and
respectively
21 0
the
these
Owing to
life time of the 23 S1 state, the collisional excitation 2 S
and
P
are calculable functions of
together
a rate
presence
abundance
ratio
For ion charge states in corona equilibrium, the nH:nH:nLi ratios
nH:nHenLi.
emission.
The
long
Li-like charge states in the plasma gives rise to recombination
and ionization contributions in proportion to the ground state
temperature
the
P,
with
3 P-->2
proportional to the electron density N,, must also be considered.
H-like
states
impact excitation of the ground state
1 1S0 with cascade contributions from higher exited states.
of
(the
state decays by
In a high temperature plasma,
electron
These
T
relative
J
with the ratio
to
the
T /T
expressing
(Tm)
of maximum resonance-line
=
temperature
Excitation rates have been calculated by
with
available
relative intensities for
conditions.
In
defines the
line
data
the
for
w,
other
x,
y,
order to express the T
intensity
z
and N
combinations
Pradhan
processes
and
G
=
the
ema
lines
et
electron
al. 3 ,4)
which
have been used to derive
for
different
plasma
dependences in the spectrum one
(x+y+z)/w
and
=
R
z/(x+y),
respectively, to which X = x/y can be added as the third plasma independent line
ratio.
lines
Auxiliary information on plasma
to
the
He-like
resonance
conditions
transition
electron in the 2p or 2s orbitals (see Fig. 1).
dielectronic
recombination
and
sd/w is a sensitive function of T
independent
due
is
provided
to
states with a spectator
The 2p
states
by
are
satellite
formed
the satellite to resonance intensity ratio D
in a limited temperature range for TeTm
of the ion-charge state balance.
=
but
The 2s states are formed by inner
shell excitation so the line ratio I = s /w reflects
the abundance ratio
in
by
lLi /nHe
the region of the He-like ions against which the corona equilibrium ratio at
Page 3
P can be compared 5 )
given
The intensities of both
principal
and
satellite
lines
in
the
He-like
spectrum are critically sensitive to the nuclear charge Z since the rates of the
radiative transitions depend on Z and since the ion
varies
with
Z
through
=
Tm
sensitivity of the line ratios
consideration
for
plasma
TM(Z).
will
As
state
distribution
a consequence the plasma parameter
change
diagnostics
charge
with
Z.
applications
This
is
an
important
where it is desireable to
maximize the response in the measured line ratios, for instance,
dR/dN , dG/dTe,
etc.,
or for atomic rate studies in which case the plasma condition sensitivity
might preferably be kept small.
category
where
the
M2
The
X-ratio
is
an
example
of
the
latter
rate of the ground state transition (line x) increases
rapidly with Z (in the context of excitation rates that are slowly varying
Z)
to
become
equal
between 18 and 196).
to the El rate of the competing branch 23 P2->23S., for Z
For Z >20 the departure from pure LS
manifest itself in the excitation rate for the 23 P
entails
branching
weights
decay
astrophysical
and
rates.
the
the
fine
structure
begins
to
The
present
Therefore, all 23 P
components
according
to
ratio x = x/y is entirely fixed by the radiative
Although
there
are
a
number
of
laboratory
and
observations of the line spectra of He-like ions, no experimental
study has been done of the systematic variation of
nuclear
mixing).
the spectra of ions below this limit (Z (20).
population rates divide between
statistical
coupling
level which becomes enhanced
due to interaction with the 21 P1 level (singlet-triplet
work
with
charge.
the
line
intensities
with
In this paper we present the results of such an investigation
based on new measurements for Ar and our earlier measurements for S and
similar plasma conditions.
Cl
for
Page 4
The experiment was carried out at the
Alcator C tokamak.
MIT
Plasma
Fusion
Center
counters
for
the
photon
detection
;
some
discharges were observed with the new delay line detector
(an example is shown in Fig.
of N
= 1-2 x 10
14
2).
-3
cm
and T
levels of 10-5 to 10
for
the
count
described
in
rate
ref. 8
of
discharges;
to
concentration
The plasma was practically unaffected by
measurement
plasma
could be controlled (in contrast
sensitive
The deuterium plasma with typical parameters
relative to Ne.
individual
high
= 1-2 keV was seeded with argon to
the seeding and yet allowing
statistics
the
The X-ray emission from the tokamak plasma was measured with
a Bragg crystal spectrometer of the van Hamos geometry using position
proportional
on
previous
He-like
spectra
with
good
actually, the Ar concentration
experiments
using
the
ambient
impurity species sulphur and chlorine) and adjusted up to the level permitted by
the data rate capabilities of the electronics.
GB
= 28.0
0
we
covered
a
spectrum lying in the range
bandwidth
X
=
of
3.95-4.05
At a spectrometer Bragg angle of
0
= 3.9-4.4 A with the He-like Ar
I
1.
The
plasma
conditions
were
monitored with standard diagnostic methods giving information on N and T .
e
e
In the He-like spectrum of argon (Fig. 2) we see the four
w,
x,
y, and z as well as the lines k and q representing sd and s
respectively (see Fig. 1 for definition of letter symbols).
satellites
(r
and
a,
representing
s
identified along with satellites due to
appearing
as
foothills
near
contributions were obtained
measured
principal
k
and
q
lines
the
from
+ sd
and
spectator
resonance
calculated1
)
satellites,
other
electrons
in
Estimates
intensity
n>3
ratios
as references for normalizing sd and s
z-line
intensity
to
be
determined.
orbitals
for satellite
using
the
intensities.
Hence the j-line intensity can be subtracted from the blended j+z peak
the
weaker
sd intensities) can also be
line.
9
Two
lines
allowing
Our measurements thus provide line
intensities for the x, y, z, q, r, a, and k lines relative to the resonance line
Page 5
for
individual
plasma
discharges
with
the
obtained from other diagnostic measurements.
principal
An
parameters
example
is
shown
N e and T e
in
Fig. 2
which refers to the X-ray emission collected over 100 ms of the constant current
(I
kA) portion of a plasma discharge.
= 450
several
hundred
discharges.
Our data consist of
spectra
In order to mitigate the shot-to-shot variations
(discussed in ref. 7) and to improve counting statistics, we determined
line
intensities
keV.
The results on average line intensities
results
for
representing
a plasma with N
average
= 1.5 x 1014 cm-3 and Te = 1.4
for
argon
(along
and chlorine 7 )) are given in Table 1.
sulphur
from
with
earlier
Comparison is made
with theoretical intensity ratios obtained in the following manner.
Corona equilibrium calculations for Ar
excitation
were
carried
coefficients by Pradhan et al. 3 ,4 ).
rate
included are excitations and cascades
recombination.
In
addition,
along
the to
with
out,
employing
the
The main atomic processes
radiative
and
dielectronic
z formula was used to estimate the small
inner shell ionization contribution to the z line 4) .
Line intensity ratios were
= 1.4 keV compared to T = 1.63 keV for Ar. The ratio G is a
e
m
monotonically decreasing function of T in the range Te < Tm due to the decrease
calculated
in
the
increase
for T
recombination
in
d(ln G)/dT e=
contribution,
resonance
line
-0.23 'keV
mainly
emission
for
with
for our conditions.
the
triplet states, and the
temperature.
of
which
is
about d(ln R)/dN e
principal
lines
proportional to N .
0.13 x 10
-14
3
cm .
obtain
The ratio R is most sensitive
to the plasma parameter N, because of the collisional 23 S1 -->23 P1
rate
We
transfer,
the
The plasma sensitivity in this case is
The
calculated
intensities
for
the
are found to agree with the observations (Table 1) which lends
support to the underlying theory and particularly the computed excitation rates.
Page 6
In earlier works,
an
the satellite to resonance line ratio was computed
using
approximate rate coefficient (such as with a gaunt factor) for the resonance
line.
However, accurate rates have now been computed explicitly by
al.3)
and
therefore
Pradhan
et
we derive, and employ, the following expression for these
ratios:
g Aft A] e(Eo-Es)/kT
Aa + ZAr
D = 2.4x10
T y (T)
T
where
w
is
statistical
the
Maxwellian
weight
averaged
collision
strength
factor of the satellite state.
and
Safronoval),
and
the
D
ratio
used.
The
k/w
theoretical
sensitivity is d(ln D)/dT
+150 keV
corroborating
for
ratio
charge
< Te)
in
the
spectrum
With regard
ratio
We
.
find
ratio
is
approximate
rates
calculated to be 0.058 for
0.062;
of
the
temperature
of
Fig.
2.
This
result
for
provides
to
the
I
ratio,
the
calculated
q/w
is 0.043 for Te = 1.4 keV and hence significantly smaller than
If this result were to be interpreted in terms
an
order
apparent
to
(ionization)
equate
distribution being a function of
flH/nHe
by
of
state balance, the corona equilibrium ratio (nL/nH) cor would have
to be taken at
T
9,10)
al.'
et
= 1.41 (keV)~- so the statistical uncertainty is,
the observed value of 0.061.
the
computed
evidence that the observed emission comes from He-like Ar ions in
a plasma of Te = 1.4 keV.
intensity
the
decreased by about 25% compared to earlier calculations
Te = 1.4 keV which is close to the observed ratio
instance,
Ar)
yw factor in Eq. 1, which is higher than the
because of the
previously
is
is
which in the case of Ca and Fe have been found to
agree to within a few percent with those of Bely-Dubau
that
gs
In order to calculate D, we
used the auto-ionization and radiative probabilities (Aa
Vainshtein
and
would
(q/w)cor
A
Z
temperature
and
= T /T .
z m
of
Tz = 850 eV
(i.e.,
(q/w)obs,
with the charge state
Using
c
for
0
determining
the
decrease the reccombination contributions to the excitation
Page 7
rates of the principal lines and subsequently decrease the calculated
ratios
of
Table
1
by about 9%.
of
the
tokamak (see below).
ratios
have
been
H-,
He-
found
for
are
rather
various
ions
in
our
high
tokamak
approximations
(cf. the
rates
mentioned above) giving too low values for Li-like
Therefore,
q/w
plasmas
results
on
for
relative
of sulphur, chlorine and argon.
where
R
is
intensity
as
well as
rates
to
He-like
ions.
the q/w ratio indicates the need for more accurate
In Table 1, comparison can be made between X-ray line
regime
spatial
the He-like ions
excitation rates for Li-like ions rather
than suggesting that T
spectra
the
suggest to us that the theoretical excitation
crude
R
Li-like ions in a limited size plasma of a
The fact, however, that unexpectedly
astrophysical plasmas
used
and
and
f Tz might be
The cause of the difference Te
ascribed to charge state balance effects because of differences in
distribution
G
density
dependent
#
T .
ratios, for
He-like
For all three ions we are in a density
and
(R,, the
R
low
density
limit.
Theoretically, for fixed electron density, the value of R should increase with Z
as it approaches the maximum value R (Z).
ratio
G
.G is
Ar.
temperature
dependence
of
the
is such that for most He-like ions G(Tm) lies in the range 1.0-0.7 and
>G(Tm) for T <Tm.
G(T)
The
In the present case, for a temperature of
T ~ 1.4 keV,
expected to show some increase with Z since T > T for S and T < T
~m
~m
We note in particular
the
Z-dependence
for
for
the
principal lineSwhich is predicted to be d(ln R)/dZ = 0.23, d(ln G)/dZ = 0.05 and
d(ln X)/dZ = 0.27 for constant plasra conditions.
the
data
in
Table
1
typically
experimental uncertainties.
test,
to
within
This is found to account
+15%
In order to put the
which
theory
to
is
a
not outside the
more
stringent
the plasma conditions must be better specified, particularly with respect
to radial profiles which vary with Z depending on T (Z) relative to
m
effects
for
can
be
assessed
and
the
related
T .
e
These
uncertainties in line intensities
Page 8
reduced by simultaneously measuring spectra for different ion species where
temperature of the discharge is varied around the T -values given.
Furthermore,
m
we note the predicted increase in the X ratio with Z,
observed
values in the range Z = 16-18.
which
accounts
Other data10-13)
Z<20.
for He-like ions with Z
Cr, and Fe) tend to show a less pronounced Z
signal
the
coupling
onset
effects
recombination
of
spin-orbit
in
contributions
with
to
the
The
which
in
importance
auto-ionization
excitation
computed
as
20 (for instance, Ca, Ti,
dependence
coupling.
connection
for
For Z >20, the ratio X would depend on
plasma parameters and should be lower than if the ratio were to be
for
the
rates
part
of intermediate
and
is
would
dielectronic
presently
being
investigated14) for ions up to Z=42 using extensive 9-state calculations.
In conclusion, our new measurement of the He-like spectra
with
previous
data
of
argon
along
on sulphur and chlorine exhibit line intensity ratios of a
systematic variation along the helium
isoelectronic
line
for with the help of computed (ab initio)
intensities
excitation
rates
calculated
rate
can
be
and
available
for
accounted
data
for
atomic
sequence.
decay
The
principal
rates.
Using
the
the resonance line we derive an electron temperature from
the observed dielectronic satellite to resonance line intensity that agrees with
the
independently
diagnosed
value.
Our results thus support the theoretical
atomic rates involving' the n=1 and n=2 He-like states which
for
X-ray
plasmas.
other
spectroscopic
diagnostics
of
both
laboratory
In contrast we find that the excitation rate for
medium
Z
atoms)
need
to
be
checked
and
the
basis
astrophysical
Li-like
argon
(and
before the ratio of inner shell
excitation satellite to resonance line intensities can be
measure
furnish
used
as
a
reliable
of the Li-like to He-like abundance ratio and hence an indicator of the
ion charge state balance.
Page 9
It
group
is a pleasure to acknowledge
and
experiment.
for
providing
for
the
the support of R.
argon
Parker
and
the
Alcator
seeding of the plasma need for this
This work was supported by the U.S. Department of Energy and by the
National Sciences and Engineering Research Council of Canada.
Page 10
Table 1
Intensity ratios for lines in the ile-like spectrum
experiment),
chlorine
and
sulphur
(from
of
ref. 7).
argon
The theoretical
values are for plasma conditions of N = 1.5 x 10 4cm-3 and T
ee
keV
in
the
case of Ar and N
e
= 3 x 10 1cm-3 and T
e
Cl
S
=
1.4
= 1.3 keV in the
case of S and Cl.
Ar
(present
x/w
y/w
z/w
G
R
X
Exp.
0.15
0.20
0.41
0.75
1.21
0.79
Theory
0.15
0.19
0.46
0.81
1.30
0.80
Exp.
0.17
0.25
0.39
0.81
1.04
0.69
Theory
0.16
0.24
0.43
0.83
1.08
0.65
Exp.
0.16
0.29
0.41
0.85
0.97
0.55
Theory
0.15
0.29
0.34
0.78
0.77
0.52
Page 11
References
1) L.A. Vainshtein and U.I. Safronova, Atomic and Nuclear Data
21,
Tables
49
(1978).
2) U.I. Safronova, Physica Scripta, 23, 241 (1981).
3) A.K. Pradhan, D.W. Norcross, and D.G. Hummel, Astrophys.J. 246, 246 (1981).
4)
A.K. Pradhan
Ap.J. 263,
and
J.M. Shull,
Ap.J. 249,
821
(1981)
and
A.K. Pradhan,
821 (1982).
5) A.H. Gabriel, Mon.Not.Astr.Soc. 160, 99 (1972).
6) C.D. Lin, W.R. Johnson, and A. Dalgarno, Phys.Rev. A 15,
7)
E. Kllne,
J. Kllne,
and
A.K. Pradhan,
Phys.Rev. A,
154 (1977).
March
1983,
and
E. Kllne and J. Kllne, Physica Scripta, Feb. (1983).
8) J. Kllne et al., Nucl.Instr.Meth. 203, 1155 (1982).
9) U.I. Safronova, A.M. Urnov, and L.A. Vainshtein, Lebedev Physical
Preprint
(1978)
(unpublished).
10) F. Bely-Dubau, et al., Mon.Not.R.Astr.Soc. 201, 1155 (1982).
11) C. Jordan and N.J. Veck, Solar Physics 78, 125 (1982).
12) V.A. Bsyzgunov et al., Sov.Phys.JErP 55, 1095 (1982).
13) M. Bitter et al., Phys.Rev.Lett. 43, 129 (1979).
14) A.K. Pradhan (to be published).
Institute
Page 12
Figure Captions
Figure 1:
Term diagram for the He-like n=2 to n=1 spectrum of argon showing the
X-ray. lines
seen in this experiment with the wavelengths from refs.
1
and 2.
Figure 2:
The
He-like
spectrum
characterized
by
N
field being 80 kG and
identified
by
of
= 1.7
the
conventional
argon
x 10
for
14
cm
current
letter
a
-3
and T
450 kA.
symbols
wavelength positions marked as predicted '2)
lines.
single
plasma
discharge
= 1.6 keV the toroidal
The
(see
X-ray
text)
lines
are
and their
relative to the w and
z
Is2 p
-i Is2p 33P
P
--
('P) 2 P
Is2p2s
2
Is 2p 2
P-
-
/2
Is2s 1 S
0
i3 2
T5/2
co
N~ N~ (0
0)
Y)
r~Go co
ro r
00)
-i
n
1s2
Is22p 2P is
CN
Im
C
to
K5in 0
I
,
2s 2S
Is2
1
1s
~co
(>04
0)
ly
=2
1
0
s2s 3 S
TK
I
X(A)
'I
I
'I
I
'I
I
ARGON
I
ALCATOR
#100182.15
-J
LU
z
z
4.00
3.98
3.96
3.94
qra k z
x y
200
0
N.
C/)
H
z
D
0
C-)
100
Ldw
400
300
CHANNEL
2
NUMBER
500