Performance of the Neutron Diagnostic System for Alcator C-Mod.
C. L. Fiore and R. L. Boivin
MIT Plasma Fusion Center, 190 Albany St., Cambridge, MA 02139
Abstract
Measurement of the global neutron production from the Alcator C-Mod tokamak
has been done for all experimental operation in deuterium, which commenced
in August 1993. Up to 3× 1012 neutrons/s have
been measured for diverse plasmas, including high current (1 MA), pellet
injected, and rf heated discharges. Measurements during the initial
run period were obtained using two sets of neutron detectors housed in
polyethylene loaded moderator stations. Two more moderator stations
containing additional neutron detectors have been obtained from LLNL
and have been installed
in the Alcator C-Mod experimental cell.
The system has been calibrated using
Cf252 placed at discrete points inside the Alcator C-Mod
vacuum vessel. This paper presents a description of the
diagnostic, followed by details of the calibration method and results.
A discussion of the derivation of ion temperature from the global
measurements is included with first results from the
integrated system.
I. Introduction
The neutron diagnostic system for Alcator C-Mod is capable
of measuring the total fusion yield over the full range of
deuterium operation. The anticipated neutron source rate
will vary from 1× 1011 n/s at Ti=1 keV and
\hat ne=1× 1020 m-3, to 1× 1016
n/s for Ti= 6.5 keV at \hat ne=1× 1021
m-3. A brief description of the experimental layout
will be followed by details of the calibration. The first
results of neutron rate measurements will be presented along
with the derivation of the ion temperature from these data.
II. Experimental Layout
The global neutron detection system for Alcator C-Mod is
comprised of 12 fission chambers of varying sensitivity as
well as 4 BF3 counters and 4 He3 detectors. These
are distributed in 4 moderator stations. The first two
moderator stations, built at MIT [1,2], house 3 fission
detectors enriched 93% in U235, containing 1.68g, 0.08g
and 0.004 g of fissile material respectively, in addition to
1 BF3 counter. The remaining 2 moderator stations were
obtained from LLNL and are described in Ref. [3]. These each
contain three fission chambers enriched 93% in U235, 2
He3 detectors and 1 BF3 counter. The fission chambers
were selected to cover the entire operational regime of the
Alcator C-Mod experiment using the count rate mode, between
1× 1011 up to 1× 1016 n/s. There is
sufficient overlap between the operating ranges to allow
cross calibration between detectors.
One of the moderator stations, containing detectors 1-4,
is located directly under the
center of Alcator C-Mod, inside the borated concrete igloo
which surrounds the tokamak. This position was chosen to
minimize changes in sensitivity which can occur when large
structures (such as other diagnostic systems) are moved near
the detectors. The second station (detectors 5-8) is located near the
toroidal midplane, adjacent to the large opening in the igloo
which accommodates the buswork for the experiment. Of the
remaining moderator stations, one is attached to the cell
wall at the toroidal midplane and the other is on top of the
igloo above Alcator C-Mod.
III. Calibration
Three calibrations of the neutron detection system have been
done. A 66.5\mug source (1.56× 108 n/s) was
obtained from ORNL for the purpose of calibrating this
experiment in January, 1992. The source strength has been
adjusted to allow for the decay of the at each
calibration date. In each case, the source was placed at
discrete locations inside the Alcator C-Mod vacuum vessel.
The source position for one location has been repeated for
all three cases to establish consistency between
calibrations.
The calibration positions are shown in Fig. 1. The source
was placed inside a thin aluminum tube (0.4 mm wall) 3 m
long. This allowed the source to be moved to different
positions in the experiment while minimizing the accumulated
dose to the authors. Use of two tangential ports allowed
the source to be placed between ports as well as in port
centers. The limited number of positions used for the
calibration is due to the
long counting time (~ 2 hours) required to obtain good
counting statistics on the two most sensitive detectors
and the short time allocated for this work by the operational
schedule.
A summary of the measured efficiency for the two most
sensitive detectors (detectors 1 and 5, the 1.68 g U235 in
the original detector set) is shown in Table I. The results for
the last two calibrations on detector 1 (located underneath
Alcator C-Mod) are the same for the redundant points (F
port, KT1, and KT3). The F port efficiencies are
significantly lower than was measured in the first
calibration (1/23/92) however. This is attributed to the
addition of diagnostic equipment and cables in the F port
lower vertical ports between the first and second
calibration. Note that the B port measurements obtained on
the first and third calibrations are nearly equivalent. The
B port measurements show the highest observed efficiency
because the vertical port is unobstructed with materials.
The differences in the efficiencies measured for detector 5
(toroidal midplane at A port) are due to adjustment of the
amplifier and discriminator settings.
Since the position of the moderator containing detector 1 is centered
underneath Alcator C-Mod, it is expected that the detector response
should be insensitive to source positions on the major radius of
the device. Little difference was found between data taken with the source
placed in a port and that with source placed between ports in
the earlier calibrations, so all of the data was averaged to obtain
a calibration value for this centered detector. The exception, noted
in the previous paragraph, is the high sensitivity of the detector
to the source when it was placed in the center of B port. This port has
little material which could obstruct the free streaming of neutrons, as
opposed to most of the other ports which are filled with diagnostic
equipment and cables.
Thus a weighted average was used to determine the efficiency for this
detector in the final calibration which accounted for a somewhat higher
contribution from the exposed area of
the three unobstructed ports.
A value of 1.67× 10-9 counts/n was obtained both for the
weighted average and by averaging all of the available data points as had
been done previously. In
addition, the 3-d Monte-Carlo neutron transport code(MCNP) [5]
was used to calculate the anticipated efficiency for this
detector location to a ring source. The MCNP code was also used to
calculate the efficiency of the detectors to placed in actual calibration
positions in order to gain a normalization value for the ring source
calculation.
When this was done,
an efficiency of 1.64× 10-9 counts/n was
obtained from the MCNP calculation.
The efficiency for detector 5 was determined as a function
of the toroidal angle of the source location. A polynomial
was fit to the data, and it was integrated to determine an
overall efficiency. The MCNP calculation described above
was also used. These methods gave efficiencies of 1.70× 10-8
counts/n and 1.74× 10-8 counts/n respectively. Ultimately,
this and the remaining detectors will be calibrated relative
to detector 1 from actual plasma produced thermonuclear
neutrons. This is necessary because additional hardware was installed
between the moderator containing detector 5 and Alcator C-Mod following
the most recent calibration.
The errors in the rate measurement from known sources are
2.6% in the source rate, 14.7% from the averaging
technique, 6.7% from counting statistics, and 2.7% from
positioning uncertainty. An additional 7.7% error is used
to account for the difference between the energy
spectrum and that of the D-D fusion neutrons (from an MCNP
calculation for Alcator C-Mod detailed in Ref. [2]). This gives
an overall error in rate of 18.3%.
IV. Neutron Rate and Ion Temperature Measurements
Deuterium was introduced as a working gas in Alcator C-Mod
in August of 1993. The global neutron production rate was
measured for all deuterium discharges. The highest neutron
production rates (~ 3× 1012 n/s) were obtained
during either deuterium pellet injection experiments or ICRF
heated discharges. Examples are shown in Fig. 2.b and Fig. 3.b
The neutron production rate is related to the volume integral
of the deuterium
ion density and velocity as given by -
R = 1/2 \int dV
nD2\langle\sigma v\rangleDD/2
where \langle \sigma
v\rangleDD is the value of the deuterium fusion cross
section averaged over the velocity distribution function.
When Ti is below 25 keV, the following approximation can
be used [5]: -
\langle\sigma v\rangleDD = 2.33×
10-14Ti-2/3 exp(-18.76 Ti-1/3)
where
Ti is in keV. This expression cannot be trivially
inverted to obtain the ion temperature. Reduction of the ion
temperature from the neutron rate is done iteratively. A
trial central ion temperature is used with an assumed ion
temperature profile and integrated with the measured density
profiles over the plasma volume to obtain a calculated
neutron rate. The electron density is corrected from the
measured plasma Zeff to obtain the deuterium ion
density. The calculated rate is compared to the measured
neutron rate, and the central ion temperature is adjusted up
or down accordingly. This is repeated until the difference
between the calculated and measured neutron rates is
less than 5%.
Obtaining the ion temperature in this manner is
computationally intensive, and was beyond the resources of
prior tokamak experiments at MIT. Use of Digital Equipment
Alpha workstations reduces the computing time to several
minutes, which can be easily completed between tokamak
discharges.
The neutron rate is a strong function of the ion temperature
in the present operational range of the Alcator C-Mod
tokamak. The dependence of neutron rate on ion temperature
can be approximated as
Ti5.6 for Ti near 1 keV.
Using this form to compute the error in the calculated ion temperature,
it can be seen that
the error in the
neutron rate of 18.3% results in an error of only 3.3% in
the ion temperature at low temperatures. The error
resulting from uncertainty in
the density measurements is higher because of the
dependence of the neutron rate on the square of the deuterium
density. Unfortunately, the error in the electron density is
unavailable at this time. Trial reduction of the data in
which the assumed ion temperature profile width was varied
by 30% resulted in an 8% variation in the ion temperature.
The overall error from all sources is not expected to exceed
10% in this temperature range. Good agreement has been
found between this measurement of ion temperature and that
obtained from Doppler broadening of selected x-ray emissions
from impurities in the plasma. Examples of the ion
temperature determined from the neutron rate is shown in
Fig. 2.a and Fig. 3.a.
V. Summary and Future Work
All four planned moderator-detector stations for measuring
global neutron production on Alcator C-Mod have been
installed on the experiment. Data from the first two was
obtained for all deuterium operation to date, and ion
temperatures have been derived from the measured rates.
Data from all four systems will be available for all
subsequent operation.
Acknowledgements
The authors would like to thank Jody Miller, Bob Granetz and
Daniel Lo for assistance with the calibration of the
experiment. Data from Earl Marmar, Jim Irby, Tom Luke, and
magnetics analysis from Steve Wolfe were used in the
reduction of the ion temperature. The authors are indebted
for the use of the source to the U.S. Department of
Energy's Californium Industrial Loan Program as administered
by the Office of Nuclear Materials Production through the
facilities of the Oak Ridge National Laboratory. This work
was supported by US DOE Contract No. DE-AC02-78ET51013.
References
[1]C. L. Fiore, R.L. Boivin, R.S. Granetz, Rev. Sci. Instrum. 63,
4530 (1992).
[2]C.L. Fiore, R.S. Granetz, Rev. Sci. Instrum. 61, 3166 (1990).
[3]T. Ogawa, K. Oasa, K. Hoshino, K. Odajima, and H. Maeda, Rev. Sci.
Instrum., 61, 3181 (1990).
[4]David L. Book, NRL Plasma Formulary, (Naval Research Laboratory,
Washington, D. C., 1983).
[5]J. Briesmeister, ``MCNP--A General Monte Carlo Code for Neutron and
Photon Transport,'' LA-7396-m, Rev.2, Los Alamos National Laboratory, Sep.
1986.
Figure Captions
Figure 1. Schematic cross section of Alcator C-Mod showing source positions
during calibrations and the location of the first two neutron moderator
stations.
Figure 2. Neutron rate (a.) and ion temperature (b.)
resulting from deuterium pellet injection into a
deuterium plasma. The pellet was injected at 0.5 s. The plasma current
was 0.8 MA. The central electron density was 2.0× 1020/m3
before the pellet, and 5.0× 1020/m3 following the pellet.
The electron temperature exceeded the ion temperature by 0.4 kev prior
to the pellet injection, and was equivalent to the ion temperature
following the injection.
Figure 3. Neutron rate (a.) and ion temperature (b.)
resulting from ICRF injection into a deuterium
discharge with a small hydrogen minority. The rf injection was from 0.47 s
to 0.67 s. A deuterium pellet was injected at 0.4 s, causing the central
electron density to increase from 1.8× 1020/m3 to
5.0× 1020/m3. The electron density had decreased to 2.0×
1020/m3 by 0.52 s, when the neutron rate and ion temperature began
to reach their peak values. The central ion and electron temperatures
were equivalent prior to the rf injection at which point the ion
temperature began
to exceed the electron temperature. A 0.5 kev difference was observed
at the ion temperature
peak, and the two became equal again by 0.6 s.
The plasma current was 0.8 MA.
Table I. Calibration Data: Counts/Source Neutron
-
|
| Source Location | Detector 1 | Detector 5
|
|
3/28/94 | F | 1.45× 10-9 | 3.28× 10-9
|
|
| F(-5cm) | 1.45× 10-9 | 3.20× 10-9
|
|
| F(+5cm) | 1.51× 10-9 | 3.29× 10-9
|
|
| CTB | 2.67× 10-9 | 2.77× 10-8
|
|
| CTBC | 1.8× 10-9 | 2.77× 10-8
|
|
| CTAB | 1.62× 10-9 | 4.13× 10-8
|
|
| KT1 | 1.77× 10-9 | 6.29× 10-8
|
|
| KT3 | 1.48× 10-9 | 4.38× 10-9
|
|
8/23/93 | F | 1.54× 10-9 | 1.12× 10-9
|
|
| KT1 | 1.77× 10-8 | 3.06× 10-8
|
|
| KT2 | 1.50× 10-9 | 2.54× 10-8
|
|
| KT3 | 1.36× 10-9 | 2.12× 10-8
|
|
| KT4 | 1.41× 10-9 | 1.72× 10-8
|
|
1/24/92 | F | 2.48× 10-9 | 5.05× 10-10
|
|
| B | 2.42× 10-9 | 6.925× 10-9
|
|
| D | 2.80× 10-9 | 1.91× 10-9
|
|
| H | 3.23× 10-9 | 1.24× 10-8
|
|
| K | 2.80× 10-9 | 7.52× 10-9
|
|
|
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