PFC/JA-82-18
X-RAY DIAGNOSTICS OF TOKAMAK PLASMAS
E. Ksllne and J. K9llne
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, MA
02139
September 1982
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.
Ry acceptance of this article, the publisher and/or recipient acknowledoes the U.S. Government's right to retain a non-exclusive,
royalty-free license in and to any copyright covering this paper.
I
X-Ray Diagnostics of Tokamak Plasmas
Elisabeth Killne and Jan Kline
Harvard-Smithsonian Astrophysical Observatory
Cambridge, MA 02138 USA
1.- INTRODUCTION
In this review, we will venture into a new
for
arena
work
in
atomic X-ray spectroscopy which we can dub tokamak X-ray spectroscopy
diagnostics (TOXRASD).
exciting,
but
Not
does
is
the
experimental
development
explore areas of atomic and plasma
measurements
the
inaccessible
physics which have been
however,
only
until
recently.
just
This,
not mean that spectroscopy of highly ionized atoms is
lacking tradition; on the contrary, the pioneering work in this
goes
back
to the 40's and the soft X-ray studies of spark generated
Even though much of the present experimental effort
plasmas /1/.
oriented
towards
H-,
effort
He-,
has
and
ions
X-ray
with
emission
the
for
purpose
extending
highly charged heavy ions, such as
attracted
under
interest.
Here
we
laboratory
and
the
diagnostics,
shall
focus
the
molybdenum,
neon-like
reviews
Several
which
ions
are
has
also
have appeared describing the
experimental programs and we will merely refer the
/2-5/.
the
However, the emission from
their ground states excited.
and
utilizing
our understanding of the relationship between X-ray
line emission and the plasma conditions
formed
of
diagnosing
astronomical plasmas or with the aim of developing
i.e.,
well.
gone into the study of few electron systems, i.e.,
Li-like
characteristic
is
obtaining a TOXRASD for fusion conditions, the new
results touch upon some very basic atomic physics questions as
Much
area
reader
to
these
the discussion around results of the
latest vintage from the TOXRASD project at the Alcator C
tokamak
at
MIT.
2.
The plasma
source
can
PLASMA SOURCE
be
characterized
by
the
radial
and
temporal dependencies of the main parameters such as temperature (Te)
and densities (Ne,Nz) of electrons and ions.
The
plasma
source
is
I
Page 2
confined
by a toroidal magnetic field.
interactions, impurity ions
consists
are
introduced
to
determined
by
ionized
e.g.
can
be
and
distributed
equilibrium
transport phenomena.
conditions
The spatial
characterized
in
emission
and
plasma
volume
coronal)
of
these
and
impurity
shells of the individual ionization
Radial
profiles
from different ionization stages (see Fig.
dependent on plasma parameters /6-8/.
C115+
which
The impurity ions
the
distributions
by
plasma,
(e.g.
stages separated or overlapping in the plasma.
the
the
mainly of hydrogen, deuterium or helium.
successively
ions
are
However, through plasma-wall
In
Fig. 1
the
of
1) will be
profiles
of
C11 4 + at Te = 1.4 keV are shown as predicted from coronal
equilibrium and from a transport code /8/.
The radial profiles of Te
and Ne are also included.
Attempts to predict the distribution of ions in the
plasma
are
made on the assumption that the ions are in coronal equilibrium, i.e.
ionisation and recombination
knowledge
of
the
radial
processes
and
balance
temporal
each
distributions
density and temperature, it is possible to predict the
distributions
from
rate equations.
the
walls
The impurities
of electron
impurity
ion
are
transported
and a steady state distribution is achieved after a
time comparable to the energy confinement
ions
With
It is therefore crucial to know
the atomic cross sections involved.
from
other.
time
(20-30
msec).
The
are assumed to be excited and ionized from their ground states.
Atomic processes of importance are
ionization
from
electron
processes
investigation for
possible
excitation
and
the ground state followed by radiative transitions,
dielectronic and radiative recombination.
these
impact
processes
for
certain
TOXRASD.
such
plasma
The relative importance of
conditions
Furthermore,
as
the
is
a
influence
point
of
of
other
proton excitation, charge exchange and
ion-ion collisions need to be further investigated.
3.
EXPERIMENTAL TECHNIQUES
Probing the plasma conditions by means of the emitted photons in
the
X-ray region is performed with mainly four different techniques:
X-ray imaging /9,10/, X-ray continuum
measurements
/11,12/,
survey
Page 3
X-ray
spectroscopy
/2,13/
and
high
resolution,
broad
band line
spectroscopy /14-17/.
A typical time evolution of a plasma
Alcator
in Fig. 2;
C
10 ms.
is
shown
shot
in
each division along the abcissa is
The fast rise of electron density
(N.)
and
plasma
current
(Ip) is followed by a stable period in which the plasma parameters
are probed. The characteristic X-ray emission discussed in this
paper
this
is
observed
apparently
during this stable time period.
quiet
period,
there
are
However, during
internal
instabilities
developing with minor disruptions in the core of the plasma which can
be imaged with the filtered X-ray
technique,
major
m=1
diode
(cos (me)
arrays
symmetry
(SBD).
in
With
poloidal
magneto-hydrodynamical instabilities (so-called sawteeth)
observed
/18/.
Furthermore,
X-ray
information for major disruptions
discharge)
and
can
these disruptions.
give
solid
state
temperature
height
thus
on
of
the
analyzing
determined.
the
continuum
been
plasma
(terminating
the
information on the origin of
continuum.
bremsstrahlung continuum emission
superimposed
have
Emission from a pure plasma is dominated
pulse
is
angle)
imaging can provide precursory
microscopic
bremsstrahlung-recombination
this
It
can
detectors
be
by
the
measured with
and
the
electron
Departures from the pure hydrogen
occur
and
because
of
line
emission
because of effects in the high
energy tail of the electrons
causing
non-Maxwellian
These two X-ray diagnostic methods thus
shape
/19/.
an
electron
give information on the position, homogeneity and
impurity
content
electrons, etc.
region
during
as
well
as
presence
of
radial
single
plasma
Z
elements,
ionization
of
medium
stages
studied /20/.
fourth
energy
discharges,
a
the
run-away
X-ray
fast scanning crystal
With
this
diagnostic
such
Z
as
elements,
The first comparisons
with
oxygen,
and
from
technique
which
of
X-ray
is
in
diagnostics
use
at
lower
such as iron, have been
predicted
distributions,
transport effects, have shown general good agreement.
spectroscopy,
/14-16/.
high
of
of
distribution and the temporal evolution of emission from
highly ionized low
including
stability
To detect a wide wavelength range in the soft
spectrometer has been developed at PLT /13/.
the
distribution
is
high
The
resolution
several major tokamak machines
Mainly two different geometries have been
used,
focussing
I
Page 4
Rowland
circle
and
cylindrical van Hamos geometry.
the latter approach is shown in Fig. 3 /15/.
results
recent
A schematic of
We shall
discuss
some
obtained from the latter instrument at the Alcator C
tokamak at MIT and their implications for future work.
ALCATOR RESULTS
.4.
The TOXRASD experiment has been taking data for about a year and
the
efforts
AX/A
-
The
data
have
been
directed towards good wavelength resolution
1/3000, large bandwidth, high sensitivity and high count rate.
presented
here
was
taken
with a 10 cm long single wire
proportional counter which limited the bandwidth to about 5% and
count
rate
to
about
20
kHz.
Much augmented spectroscopical and
diagnostical performance can be achieved
which
we
shall
discuss
later.
by
Our
trace
element
concentrations
wavelength region 4.3-5.3 A.
detector
settings
show in Fig. 4.
from
S13+,
from
detector
improvements,
measurements of S, C1 and Mo
impurities in the Alcator C tokamak /21/
at
(where these elements
of
about
This region can
10-5 Ne)
be
in
covered
plasma.
thousand
the
three
which a composite spectrum can be formed as
This spectrum shows
characteristic
X-ray
emission
C11 4 +, and C11 5 + as indicated and a host of lines
S14+,
were
occur
cover
from molybdenum between 28+ and 32+; the plasma conditions
discharges
the
such
as
to
enhance
the
From the extensive data material
discharges,
we
shall
of
these
Mo concentration in the
of
spectra
from
several
select a few examples to illustrate
some poignant features of the results.
LINE IDENTIFICATION OF FEW ELECTRON SYSTEMS
4.1
H-Like
resonance
Spectrum.
The
at
positions
4726.1, 4731.4
spectator
transition
2S1/ 2 - 2P1 /2 , 3/2
lines
satellite lines ls2p'P 1 - 2p2
Fig. 5)
is-2p
D2 .
consistent
4783.6 mA
and
1
and
WH)
We observe these
rise
to
the
and dielectronic
for
S14+
(see
with the predicted wavelengths of
/22,23/.
Other
satellites
with
a
in a higher orbit, i.e., transitions of the type
electron
lsn -2pn, n13 are also indicated as
energy side of the
(WH
gives
2
a
small
foothill
S1 /2 -2 p1 /2 resonance line.
on
the
low
Page 5
He-like Suectra.
and
Cl
The He-like spectrum was measured for
(see examples in Figs. 6-9).
2
both
S
These spectra are dominated by
the 1s -ls2p resonance line (w)
lSo-lPl, the spin forbidden
and
lSo- 3 P 2 , (y and x, will here both be
the
intercombination line
referred to as intercombination lines).
with
letter
Appendix).
1SO 3Sl.
symbols
in
the
1
So- 3 p,
Transitions are referred
conventional
way
/23,24/
(see also
The ls-2s transition gives rise to the forbidden line (z)
Several
satellite
lines
to
the resonance line with an
extra (third) spectator electron in the 2s (lines q and r) or the
orbits
to
(lines
k
and
a)
are observed.
2p
Some other satellite lines
including the strongest, j, contribute to the spectrum but are hidden
by
the main lines (Fig. 8).
The principal lines (w, x, y and z) and
the satellite lines (q, r, a and k) are seen for both S and
wavelengths
as
predicted.
results of Vainshtein /23/.
Excellent
agreement
Cl
is found with the
Positive identification of these
lines is provided by the spectra in Figs.
satellite
lines
so
far.
states
been
observed
in
the
spectrum
Princeton PLT tokamak /14/ which
relative
satellite
to
have
escaped
They would be spread over a region of some 20 mA
on the long wavelength side of the z line /27/.
has
rise
to the w line in our S and Cl spectra,
the corresponding satellites of Be-like charge
detection
latter
6-9.
We also note that while the Li-like charge states give
significant
with
intensity
of
One
such
satellite
Fe from the plasma of the
demonstrates
the
trend
that
the
as Z4 , i.e., a factor of five
varies
increase between S and Fe when compared at
temperatures
of
maximum
emission for each atom.
The ls-3p transition in sulphur is expected to produce a line at
about
4.30 A
which
is
just outside our range of measurements, but
satellite lines to this resonance line (A) fall
wavelengths
toroidal
14
x 10
/25/.
field,
3
cm- ,
and
For
40kG,
Te
=
at
somewhat
longer
certain plasma conditions as in Fig. 6 (low
low
plasma
0.75
keV),
current,
we
300 kA,
observe
a
Ne
clear
1.5
peak
4.388+0.001 A of a width consistent with that of a single line.
at
This
peak can be identified with the strongest satellite line of the ls-3p
transition, probably the transition 1s2 2s-ls2s3p calculated to be
at
I
Page 6
4.3895 A.
observe other distinct satellite lines in this region
We
and we find a remarkable similarity with the spectrum /25/
from
the
Ne = 1019
cm- 3
and
laser
Te
=
produced
at
plasma
conditions
350 ev.
LINE IDENTIFICATION OF MANY ELECTRON SYSTEMS
4.2
In the wavelength range 4.3-5.3 A
molybdenum
from
(the
limiter
conditions (see Fig. 4).
the
of
Mo
we
observe
material)
strong
under
A point of practical
plasma
certain
consequence
is
that
impurity concentration depends strongly on plasma conditions
and becomes rapidly important for low Ne-values while
emission does not vary very much.
the
for
the
identification
S
or
Cl
Therefore we can deliberately vary
the relative intensities of spectral lines of Mo and S/Cl,
crucial
emission
which
is
of the weakest S and Cl lines, for
instance the J satellite (see Fig.
5).
calculated
identified 2p-3d, 2s-3p and 2p-3s
wavelengths,
we
have
transitions in charge states between 28+
Based
and
on 'measurements
32+
/26/.
and
The
most
interesting components of the Mo emission are the Ne-like spectrum of
Mo3 2 +, which
strongest
is
dominated
transitions
by
identifying
from
dielectronic
transitions,
each charge state.
transitions
besides dominant principal
contributions
2p1 /2 ,3 /2 -3d
in
the
Mo
and
the
We note that
spectrum,
some
recombination satellites have been
identified as well; for instance, the line at 4.837 A of Mo3 1 + /26/.
4.3
LINE INTENSITIES
Satellite line intensities (relative
Te and lie Dependences.
the
resonance
dielectronic
line)
depend
satellites,
on
this
the
electron
dependence
goes
temperature.
approximately
to
For
as
I;/Iw = '/Te and for inner shell excitation the I;'/Iw ratio follows
the abundance ratio NLi/NHe- The NLi/NHe ratio has a temperature
dependence which can be calculated assuming a certain equilibrium for
the
plasma
(coronal
equilibrium)
recombination rates /27,28/.
the
actual
certain
ionization
and
If the temperature Te is known from the
I;/Iw ratio or elsewhere, one can
determine
and
from
the
measured
I;'/Iw
ratio
NLi/NHe ratio which is the calculated NLi/NHe
Page 7
ratio for coronal equilibrium at
The
difference
Tz-Te
the
(ionization)
temperature
Tz.
expresses whether the plasma is in a state of
ionization (Tz <Te) or
recombination
(Tz >Te),
i.e.,
whether
the
considered ion of charge state Z is superheated or supercooled in the
plasma environment of given electron temperature.
An example with particularly strong satellites
spectrum
of
C1
Ik = 0.177 + 0.015,
statistical error
is
shown
Fig. 6.
From
the
the
He-like
intensity
we determine a temperature of Te = 760 eV with
of
+50 eV.
based on the most accurate
calculations
in
in
This determination of temperature is
calculations
by
Safronova
/29/,
/30/ give slightly lower values, Te = 630 eV.
other
The thus
obtained temperature is consistent with Te=650+ 150 eV measured
the
X-ray
continuum
shape
/31/.
Furthermore,
we
note
from
that
satellite ratio Ia/Ik of 0.27+0.05 agrees with the calculated one
0.23.
a
a
of
Other dielectronic satellites (see Fig. 8) are too small to be
measured except for the
estimated
/29/.
from
j line whose influence on the z line
can
be
the measured Ik and the calculated ratio Ij/Ik = 1.4
In Fig. 8 we have presented the calculated intensities of
strongest
dielectronic
recombination
satellites
line with normalization to the observed Ik.
and
r
include
Te=Tz=760 eV.
from
apart
the
inner
shell
smoothing
excitation
of
the
relative to the k
The dotted curves for
same
raw
as
data
in
Fig. 6
is
of
q
line
0.010 and that of inner-shell excitation is 14 = 0.029 /29/.
The total calculated intensity of q is 0.039 which
50%
The
points.
calculated contribution of dielectronic recombination to the
I4'
q
contribution assuming
The experimental spectrum is the
three-point
the
the
measured
ratio
of Iq = 0.073+0.015.
amounts
to
only
The situation is
similar for the r satellite where Ik + Ik' = 0.02+0.012 = 0.032
compared to a measured value of 0.053+0.017.
/29/
We have thus found that
the calculated I'' values are too low indicating that the
plasma
is
ionizing with a nominal Tz of about 420 eV with reservation, however,
for possible difference in radial profiles between
ions.
This
is
a
C11 4 +
and
C115+
general feature for most of our spectra at lower
temperatures that Iq(exp)>Iq(theor) at given Te, indicating that this
is
a
characteristic feature of the plasma we observe or perhaps one
should check for theoretical problems with
the
predicted
rates
of
Page 8
inner shell excitations.
Fig. 6
shows
but
intensities
Fig. 7.
spectra
we
is
difference.
significant
Te = 940+80 eV
continuum
measurements
reflected
in
the
the
change
1.20+0.14
(compared
/31/)
are
1.5
to
0.97+0.07
We find this ratio
corrections
after
1.37
and
0.92
where
the
for
difference
collisional population transfer between the long
3
to
the satellite
The calculated
comes
lived
from the
triplet
n=2
3
S- P, which is density dependent; the collisional and
at
comparable
are
rates
radiative
the
in going from Fig. 6 to 7, which is of interest with
and
states, i.e.
to
satellite
from
interferences as discussed above and shown in Fig. 8.
values
and
overall
density
in
regard to the line intensity ratio R = z/x+y.
be
satellite
Another reason for comparing these particular
however,
3.0 x 1014 cm- 3
with
determine
X-ray
difference
is,
example
systematically lower relative level than for
a
from
temperature
intensity
at
Ik/kw,
From
1050+150 eV
another
Ne = 3 x 1014 cm-3
densities
/32,33/.
With the above two
He-like
spectra
of
examples,
C1
(and
information on Te and Ne.
we
the
demonstrated
have
same
is
true
for
that
S)
the
contain
The statistical accuracy with which we can
measure the relative intensities of k/w and z/x+y is a matter of data
accumulation rate per single discharge, or
discharges
one can accumulate data.
question is that of reproducibility of
address
shall
below.
over
how
constant
many
In the latter case, the crucial
plasma
discharges
which
we
regard to the theory, the atomic rates
With
computed and models used appear to give a good overall description of
the
plasma
dependence
observations,
except
of
for
the
the
present
satellites
(as
due
well
to
as of previous)
inner
shell
excitation.
Comparison of ls-2y and ls-3u Transitions.
for
The He-like spectrum
sulphur of n=2 upper states appear in the X range 5.03 to 5.11 A
and is similar to that of C1 already
ls-3p
resonance
line
Since
(see
Fig. 9).
The
of the He-line S (0) is located at X z 4.30 A
/25/, which is just outside
4.31 A.
discussed
the
spectrometer
bandwidth
ending
at
this line is of diagnostics interest we can estimate
Page 9
its intensity relative to the observed satellite peak as well
the
ls-2p
as
to
resonance.
960 eV.
We use the results in Fig. 7 obtained at Te =
From the observed satellite to resonance intensity of 0.91
in
laser plasma at Te = 350 eV and the calculated Te dependence
the
/25/ we determine the relative satellite intensity to be 0.09 at Te
=
960 eV;
i.e.,
the ls-3p resonance line in Fig. 7 should be 11.4
times the satellite
measured
during
line.
other
Assuming constant
S
The
,ls-2p resonance
line
for
S
was
but similar discharges of the same run 0805.
emission,
we
determine
is- 3p
the
to
ls-2p
intensity ratio to be 0.5+0.2.
The Temperature of Electrons and Ions.
determined
the
electron
For the run 0303 we have
temperature in four ways.
Fig. 10 shows the resonance lines of H-like
and
The spectrum in
He-like
S;
these
lines are broader than normal because of larger detector contribution
at the extreme ends.
which
implies
a
We determine the
temperature
NH/NHe abundance ratio is in
satellite
ratio
in
IW/ 1 W = 0.75+0.07,
of
of Te = 2.1+0.2 keV assuming that the
coronal
the
ratio
same
equilibrium
figure,
/35/.
one
From
the
determines
as
Ij/IW = 0.040+0.012 and a temperature of 1.7+0.3 keV.
but
similar
Fig. 9.
discharge
From
this
we
single
temperature
discharge
with
equilibrium.
spectroscopic
a
to
judge
we
be improved to
can
similar
discharges.
to
a
temperature
determinations
of
ion
between
the
four
electron temperature.
atomic
physics
The results
calculations
abundance ratio relative to that of coronal
from
the
At high temperatures, the results on q suggest a plasma closer
the
case
for
lower
Te.
explore
the
would
The intensity ratios and the deduced
temperatures are a first attempt to check consistency in
and
of
different
to ionization equilibrium between Li- and He-like sulphur than
be
The
Finally, the Iq/Iw ratio
equilibrium, i.e., the ionization equilibrium or departure
same.
determine
N1 3 +/N1 4 + abundance ratio of S given by coronal
We thus find consistency
the
error
corresponds
can be used for testing the underlying
and
spectrum
is 2.3+0.5 keV.
is found to be 0.016+.006, which
1.8+0.6 keV
another
recorded the He-like S spectrum shown in
Ik/Iw = 0.014+0.01 and the statistical
0.012+0.007 by adding three consecutive,
corresponding
From
possibilities of TOXRASD.
these
data
For a complete analysis
Page 10
the radial distributions of the different ionization stages
need
to
be considered.
A parameter of crucial importance for plasma fusion is
temperature
(Ti)
can
A
be
well
used
separated
to
determine
thermal motion of the ions.
for
this
ion
or even more so is information on the relationship
between Ti and Te.
spectrum
the
purpose,
single
line
in
the
X-ray
Doppler broadening due to the
The resonance line w is a good candidate
especially for higher temperatures where the nj3
foot hill satellites are small (see Figs. 9 and 11), and the y and
lines
can
provide
complementary
information.
The
z
line width in
Fig. 9 (from run 0303) is determined to be 7.3+0.3 channels which can
be improved to 7.2+0.15 (corresponding to 3.1 mA) using an average of
three
discharges.
subtracted
630 eV.
the
From
this
estimated
we
determine
instrumental
Ti=1.4+.1 keV
resolution corresponding to
With this result, we have demonstrated that one can
simultaneous
spectroscopial
having
measurement
achieve
of Te and Ti of sufficient
statistical accuracy to see differences between the two temperatures.
With
reservation
for
not
yet
unravelled
systematic
errors, our
results suggest that the thermal coupling between electrons and
ions
is not 100% effective even for ohmically heated plasmas at relatively
high electron densities.
Ionization
predictable
Equilibrium.
function
The
line
ratio
temperature
Knowing the temperature,
dependent
because
of
a
The ratio G = x+y+z/w is
difference
in
dependence of the triplet and singlet impact excitation
has
also
too.
temperature
rates
would
of the He-like chlorine spectrum shown in Figs. 6 and 11.
temperature, we find G
of
G
reflect
We thus have two line ratios relating to Tz-Te, which we
consider for the low and high temperature, Te = 0.7 and 2 keV,
value
/32/.
been predicted to depend on Tz-Te because of the larger
recombination contribution to the triplet state, so G
Tz-Te
a
difference between experiment and calculation tells us about the
departure from coronal equilibrium (Tz-Te).
G
is
of Te for an ion abundance ratio N1 4 +/N15+ (to
choose the Cl case) in coronal equilibrium.
the
g = Iq/Iw
=0.94+.05 compared to the
= 0.96 with no recombination.
cases
At the low
predicted
/32,33/
As mentioned already, we
i
Page 11
have determined qexp >qth so both
under
equilibrium.
G=0.59+0.04
a
plasma
value
of
prediction, so that
high
we
temperature,
determine
to the predicted value of 0.45 which increases
recombination
experimental
the
At
compared
to 0.55 if
suggest
or that the N 1 4 +/N1S+ ratio is larger than that of
ionization
coronal
results
these
is
g
both
/33/.
included
(as
the
in
this
the
case,
stated above) is consistent with the
g. and
G
parameters
indicate
less
departure from ionization equilibrium at the higher temperature.
The
parameters reflecting Tz-Te and their experimental determination
are
probably
closely
to
related
ion
diffusion
i.e.,
effects,
this
transport
information has a bearing on the important question of
in
the plasma and hence confinement times.
we
identified
preliminarily
have
states from 28+ to 32+
/26/.
It
from molybdenum in charge
lines
is
wavelength,
of
On the basis
Intensity Variations of Mo Lines,
clear
that
temperature
the
intensity variation of lines will show the characteristics
dependent
of the particular charge state involved which can help
in
the
line
Assuming that we know the temperature of the plasma
identification.
in the region of the emission studied, the line ratios can aid in the
instead
Assuming
identification.
the line identification is
that
known, plasma diagnostics information can be
data
that
can
Examples
of
be used in this context are shown in Fig. 12.
The J
W resonance
which
satellite line has an intensity relative to
Te = 1.6+.4
determines
deduced.
and
the
for the cases 12a and 12b.
1.9+0.2 keV
The intensity ratio of dominant 2p-3d lines in Mo3 0 + to Mo3 2 + changes
and
0.5
between
2. It
is clear that the observed variation of the
Mo3 0 +/Mo 3 2 + intensity ratio is not consistent with the identification
the
However,
made.
temperature
given
I refers to the plasma
by
region of maximum emission from the S13+ ions (cf. Fig. 1) which
from
differ
species
can
the
be
identification
radial
distribution
the
32
+,
can
+ and the two Mo
Therefore,
the
line
for many electron systems such as Mo is a complicated
business and the temperature
Once
for Mo
too.
separated
spatially
30
identification
is
dependence
clear
must
be
used
judicially.
and a systematic of temperature
dependences emerge, we can hope to use these complicated line spectra
for detailed radial plasma mapping.
Page 12
Intensity Variations of
furthermore
measured
the
Fine
Structure
intensity
ratio
Components.
of
the
2
We
have
fine structure
2
components of the H-like resonance lines for S ( S1,/2- p 1 /2,3/ 2 )
and
of the intercombination transition of He-like S and Cl (ISO - 3p,2)The intensities are predicted to split according to statistical
weights,
i.e.,
without.preference for angular momentum of the upper
state of the transition; the predicted /32,33/ intensity
2pl/2/2P3/2 = 0.5,
and
ratios
are
w P2 / P, = 0.52 and 0.65 for S and Cl.
Our
3
3
average values for many discharges are generally not far
predictions
but
comparisons.
for
these
drastic
variations
are
observed
3
about
typical
variation
(similar for both S and Cl).
up
with
collisonal
a
10%
coupling
of
is
the
in
this
do
from
n=2
ratio
we
know
For the
0.3
to
1.3
assuming
proton
triplet states /33/.
Proton
couple
2
H-like ions and hence increase the
ratio with increasing proton
However,
nor
Theoretically we have only been able to
difference
between
range
collisons have previously been predicted to
states
here
the plasma conditions affecting these ratios.
p 2 /3p1 ratio the
come
explanations
It is neither clear which
atomic population processes could be at play
enough
these
in shot-to-shot
Examples are shown in Figs. 13 and 14 The
variations are still at large.
from
(i.e.,
also
the
2s
and
2p
p1,/2 /2 P3/ 2 intensity
electron)
density
/27/.
the proton effects appear too small to explain the observed
variations let alone that the change is only in one direction.
Here,
we
need to make simultaneous measurements of these two ratios to see
if the variations are correlated and hence answer the question
whether
there
is a common cause affecting these line ratios.
These
results are both experimentally clear and interpretationally puzzling
and should entice some stretching of the atomic physics imagination.
5.
NEXT GENERATION TOXRASD MEASUREMENTS
The results from the new TOXRASD experiment
tokamak
and
Princeton
information
those
from
tokamak
have
and
touched
the
well
already
established
yielded
at
the
Alcator
experiment
valuable
C
at the
diagnostics
upon interesting atomic physics questions.
However, they also indicate the potential for further development
probe the plasma and the atomic processes in greater detail.
to
For our
i
Page 13
project the limit
hopefully
has
on
the
detector
side
which
similar, the
Princeton
augmented with a new detector.
Bragg
is
25 cm
dominant
lines
for
single
than
simultaneously
(and
hence
the
accuracy
line
or
better
ion
of
The
several
temperature)
and
various
its
line
With the many line ratios one can then study simultaneously,
ratios.
the plasma presents a unique
excited
atomic
physics
laboratory
where
the
states involved in the transitions observed are subjected to
the same and (partially) controllable medium
which
is
sustained
atomic relaxation times.
count
of
width
correlation with the electron temperature deduced from
ions
0.2 mm
Alcator discharges.
objective here is to measure accurately the
lines
new
This will allow measurements of high resolution,
broad band spectra with an expected statistical
for
The
long and can detect about 0.8 mA of our spectrum
(<0.4 mA at 4.4 A).
3%
has
Together with a fast CAMAC data
shown in Fig. 4 at an expected resolution of better
than
now
spectrometer
acquisition we hope to achieve count rates of 0.2 to 1 MHz.
detector
we
solved with the development of a new fast delay line
have
x-y detector /36/;
been
been
rates
it
is
hot
electrons
Once the detector system
can
handle
Thanks
to
the
high
expect
light
of the van Ramos geometry of our spectrometer
(and to H. Schnopper /37/ who originated this spectrometer
we
high
natural to probe the time evolution of the line
efficiency
TOXRASD),
and
for a long period of time on the scale of
emission for single plasma discharges.
collection
of
to
achieve
idea
for
5 to 10% statistical accuracy for
strong lines for a time resolution of 10 ms, which can
be
augmented
by increasing the crystal height and the viewing solid angle into the
plasma, etc.
would
With the extended band width and time information,
one
able to measure the time correlation between the intensity
be
ratios x/y and W1 /2 /W3 /2 and determine the cause of the variations we
observe
in
these
ratios for seemingly constant shots and hopefully
reveal the atomic process
parameter
that
affecting
and
the
hidden
Results
atomic
physics
(including
interpretations)
the
heating.
states
varies for seemingly constant plasma shots.
of the type presented
are important
these
for
and
plasmas
measurements
and
realization of time resolved spectroscopy
heated
by
other
measures
than
ohmic
The Princeton group has already measured He-like Fe spectra
Page 14
for plasmas heated
conditions
one
by
neutral
surely
ion
disturbs
injection
the
plasma
simultaneous measurements of Ti, Te, and Tz as
provides
/38/.
a
are
volume.
these
equilibrium
function
of
and
time
a real challenge for time resolved TOXRASD measurements and
should be of great atomic physics interest, too.
atoms
Under
effective
sensores
distributed
The information is encoded in
line-spectra
and
we
are
making
the
rapid
over
form
The highly
the
of
ionized
whole plasma
characteristic
progress in increasing the
accuracy of the measurements and finding the formula for decoding the
TOXRASD spectra.
ACKNOWLEDGEMENTS
We have greatly benefitted from the stimulating support
Parker
and
the
sharing recent
imaging,
Alcator group.
data
with
us,
by
Ron
We also wish to thank M. Bitter for
R. Petrasso
for
results
on
X-ray
and John Rice for providing the results on radial profiles.
The work was supported by the U.S. Department of Energy.
Page 15
Appendix I
Key to 'the main lines and satellites of the' H- and He-like spectra.
All satellites are due to dielectronic recombination apart for those marked
with an asterick.
Spectrum
H-like
Letter Key
Multiplet transition
W(P
3/ 2)
2p
W(P
1/2
2
)
3/2
-
is
2 1/2
p 21/2 - is 2S 1/2
2p2 1D - ls2p
2
He-like
w
ls2p
x
ls2p
y
z
j
k
P 1 - Is 2 1 S0
1
P2 -'iss2
- 2 S0
1
ls2p 3P1 - is
S0
- is
ls2s 3S
ls2p 2D
5
/2
3/2
2
ls2p2 2D
2p 2 1/2
- Is 22p 2P
. s2p 2 2P /
- 1s 222p P
sp p3/2
- 1s
b
Is2p 2 2P3/2
C
ls2p 2 2P1/2 - is2 2p
d
ls2p 2 P1/2
q*
Is(2s2p 1 )2P3/2
r
ls(2s2p IP) 2 P1/2
n
Is2p 2 2S1/2
M
ls2p
-
-
Is 2p
1/2
2
P 1/2
s2 2p 2P /
1 2
22s 2 1/2
32
S
1 2
s
ls(2s2p P) P3/2
t
ls(2s2p 3 P)2
-
1 22s 2 S1/2
-
is 2p 2P 1 /2
-
-
___~1~~.-
2 1/2
1s2
ls2p 2D
a
P1
1/2
-1 2 2
/
1s6 2 2SP 1/ 2
.2
2
is 2s S1 /2
j
Page 16
REFERENCES
B. Edlen, Symposium on Production and Physics of Highly Charged
Ions, to appear in Physica Scripta, 1982.
2. K.W. Hill et al., AIP Proc. No. 75, 8 (1981) and PPPL-1887,
April 1982.
3. N.J. Peacock, AIP Proc. No. 75, 101 (1981).
4. C. deMichelis and M. Mattioli, Nuclear Fusion 21, 677 (1981).
5. Equipe TFR, Nuclear Fusion 18 647 (1978).
6. S.Suckewer, Physica Scripta 13, 72 (1981).
7. T. Kato et al, Institute of Plasma Physics, Nagoya, IPPJ-544,
(1981).
8. E.S. Marmar et al., MIT/PFC Report JA-82-12 submitted for
publication (1982).
(1981),
and
9. R. Petrasso et al., Nuclear Fusion 21, 881
Rev.Sci.Instr. 51, 585 (1980).
10. S. van Goeler, W. Stodiak, and N. Sauthoff, Phys.Rev.Lett 33,
1201 (1974), and N.R. Sauthoff, SPIE, Vol. 106, 40 (1977).
11. M. Bitter et al., in uInner Shell and X-ray Physics of Atoms and
Solids (Plenum Press) 1981, p.861 and PPPL-78 6492.
1645
.I. Helava, Phys.Rev. A25,
12. J.E. Rice, K. Molvig, and
(1981).
S. van Goeler et al, Bull.Am.Phys.Soc. 26, 812 (1981).
13.
14. K.W. Hill et al., Phys.Rev. A19, 1770 (1979), M.Bitter et al.,
Phys.Rev.Letter 43, 129 (1979), and M. Bitter et al., PPPL-1891,
April 1982.
15. E. Kallne and J. Kallne, submitted to Physica Scripta (1982).
16. P. Platz et al., J.Phys.E 14, 448 (1981) and J.Phys. B15, 1007
(1981).
17. M.G. Hobby, N.J. Peacock, and J.E. Bateman, Culham Laboratory,
CLM-R103 (1980).
and
(1978)
609
18,
18. G.L. Jahns et al., Nuclear Fusion
M.A. Dubois, D.A. Marty and A. Pochelon, Nucl.Fusion 20, 1355
(1980).
19. H. Knoepfel and D.A. Spong, Nucl.Fusion 9, 785 (1979).
20. E. Meservey et al., Bull.Am.Phys.Soc. 26, 981 (1981).
21. B. Blackwell et al., in Plasma Physics and Controlled Nuclear
Fusion Research Proc. 9th Int.Conf., Baltimore 1982.
22. U.I. Safronova, Physica Scripta 23, 241 (1981).
23. L.A. Vainshtein and U.I. Safronova, Atomic Data Nuclear Data
Tables 21, 49 (1978).
24. A.H. Gabriel, Mon.Not.R.Astr.Soc. 160, 99 (1972).
25. V.A. Boiko, et al., Mon.Not.R.Astr.Soc. 185, 789 (1978).
26. R.D. Cowan, Symposium on Production and Physics of Highly
Charged Ions, Physica Scripta (1982), and E. Kallne, J. Kal lne,
and #.D. Cowan, submitted for publication (1982).
27. V.A. Boiko et al., J.Quant.Spectr.Rad.Transf. 19, 11 (1978).
28. J. Dubau and S. Volonte, Rep.Prog.Phys. 43,199 (1980).
29. U.I. Safronova, A.M.Urnov, and L.A. Vainshtein, Dielectronic
Satellites for High Charged Resonance Lines, Preprint.
L.P. Presnyakov,
and
A.H. Gabriel,
30. C.P. Bhalla,
Mon.Not.R.Astr.Soc. 172, 359 (1975).
(1981)
and
Bull.Am.Phys.Soc. 26, 885
31. D.S. Pappas et al.,
J.E. Rice, private communication.
619
and Phys.Rev. A23,
32. A.K. Pradhan, Astroph.J.(in press),
(1981).
for
submitted
A.K. Pradhan,
and
J. Kallne,
33. E. Kailne,
publication (1982).
34. E. Kallne, J. Kallne, and J.E. Rice, Phys.Rev.Lett. 49, 330
(1982).
35. V.L. Jacobs et al., Astroph.J. 230, 627 (1979).
and A. Thompson,
36. J. Kallne, E. Kallne, L. Atencio, C. Morris
Nucl.Instr.Methods, Fall 1982 (to appearS and ibid Forth APS
Plasma Diagnostics, Boston,
on High Temp.
Topical Conf.
Aug. 25-27, 1982.
H.W. Schnoper and P.O. Taylor, U.S. Department of Energy Report
37.
No. E4-76-52-4021 (1977).
38. R.J. Hawryluk et al., Phys.Rev.Lett. 49, 326 (1982).
1.
Figure Captions
Fig. 1:
Radial emissivity profiles for He- and H-like S at Te = 1400 eV
and measured radial
abundancies
equilibrium
coronal
assuming
the Alcator C tokamak
are
for
distributions of Ne and Te. The results
atMIT with a plasma limiter of 16 cm radius.
Fig. 2:
Temporal development of a typical Alcator C plasma hydrogen discharge
at 60 kG magnetic field. The traces from top to bottom are plasma
current (I, = 325 kA at peak), electron density (Ne = 0.58 x
101 4 cm- 3 /fringe),
and the count rates of soft X-ray diode (E >1 keV)
and high resolution X-ray spectrometer (at C11 5 + 4.44 1).
Fig. 3:
Schematics of cylindrical crystal geometry showing slit, crystal and
59.5 cm
detector to scale. The crystal used is PET 2d = 8.742 A, f
at a Bragg angle of 33.50.
Fig. 4:
Full bandwidth spectrum composed of three different detector_ settings
each being a sum of four similar plasma discharges at Ne = 2.3 x
101 4 cm-3 and Te -1.4 keV. The Mo emission is enhanced relative to
that of S and C1 for these conditions.
Fig. 5:
H-like spectrum of sulphur showing the ls-2p resonance doublet as well
Some n3
as
the dielectronic recombination satellite line J.
satellites can also be discerned. The solid lines are fits to the
The spectrum is a surn of eight similar discharges of
peaks.
deuterium with Ne = 3.5 x 101 4 cm-3 , Te - 1.25 keV and BT = 80 kG.
Fig. 6:
He-like spectrum of Cl showing the principal lines w, x, y, and z as
well as the satellites q, r, a and k. The spectrum is a sum of twenty
discharges in deuterium with Ne w 1.5 x 101 4 cm- 3 , Te ~ 760 eV and BT =
40 kG. Also observed are satellites to the He-like ls-3p resonance in
Sulphur the strongest of which lies at 4.388 A.
Fig. 7:
Same as in Figure 6 but for a sum of twelve discharges in hydrogen
the conditions Ne = 2.9 x 101 4 cm- 3 , Te = 940 eV and BT = 80 kG.
Fig. 8:
The experimental spectrum of Figure 6 with three-point smoothing. The
strongest lines of the predicted 2 9 ) satellite spectrum of He-like C1
All
are shown with intensities normalized to the measured k line.
intensities are from dielectronic recombination except for lines q and
r where the added affect of inner shell excitation is shown by the
broken line.
Fig. 9:
Example of He-like spectra for sulphur recorded for a single plasma
discharge.
The conditions were Me = 3 x 1014cm- 3 , Te W 1.8 keV and
BT = 80 kG for a plasma of deuterium.
of
Fig. 10:
Example of detector setting selected to record the H-like and He-like
simultaneously.
Besides the is-2p resonance lines, one can see the
satellite line J and the 2p-3d line of Mo3 2 + at 4.804 A.
Plasma
discharge in hydrogen with conditions of N = 3.5 x io1 4 MkeV, and BT = 80 kG.
e
j
Fig. 11:
Example of He-like spectrum of chlorine from single plasma discharge deuterium with conditions of Ne = 3.5 x 101 4 cm- 3 and BT = 80 kG.
Fig. 12:
Example of spectrum in the region of the H-like resonance line in
sulphur
with
intensity variation in line Mo-emission.
Plasma
discharges in deuterium with Ne = 2.3 x 101 4 cm- 3 and BT = 80 kG.
The
temperature is determined to be Te = 1.6 and 1.8 keV for (a) and (b)
as discussed in the text.
Fig. 13:
Example of intensity variation in the ratio x/y for He-like Cl between
nominally
similar
(single) plasma discharge in deuterium with
conditions of Ne
3.4 x 1014cm~ , Te 0 1.4 keV, and BT = 80 kG.
Fig. 14:
Example of intensity variations in the ratio W(P1 /2 )/W(P / ) for
1 2
H-like sulphur for two consecutive, similar plasma discharges in
deuterium of the conditions of Ne = 2.5 x 101 4 cm- , Te 2 1.4 keV and
BT = 80 kG.
(,,-WO) 9N
q~Cj-
0o
o
to
0
0
0
0
0O
(A 9) '1
0
-4
E
(0:
0
to
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AIIAISSIV43
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Figure 2
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