PFC/JA-83-4
A FAST NEUTRON SPECTROMETER FOR D-D FUSION NEUTRON
MEASUREMENTS AT THE ALCATOR C TOKAMAK
W.
A.
Fisher,
S.
H.
Chen,
D.
Gwinn,
R.
R.
Parker
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, MA
02139
May 1983
This work
was
supported
No. DE-AC02-78ET51013.
by
the U.S.
Department
of
Energy Contract
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.
A Fast Neutron Spectrometer for D-D Fusion Neutron
Measurements at the Alcator C Tokamak
W. A. Fisher* and S. H. Chen
Nuclear Engineering Department
Massachusetts Institute of Technology
Cambridge, MA 02139
and
D. Gwinn and R. R. Parker
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, MA 02139
Abstract
3
He ionization chamber
A neutron spectrometer using a high pressure
has been designed and used to measure the neutron spectrum from an ohmically heated deuterium plasma. The resolution of the spectrometer at 2.45
ParMeV is determine to be 46 keV full width at the half maximum (FWHM).
ticular attention has been paid to optimizing the detector shielding and
collimation to reject thermal and epithermal neutrons scattered from the
tokamak structure. As a result, measurements indicate that the ratio of
the number of counts in the 2.45 MeV peak to the total number of detected
For the 8 Psec amplifier time constant used, a
neutron events is 1/67.
per second has been achieved in the thermocounts
44
as
as
high
count rate
have been compared with calculated
spectra
observed
The
peak.
nuclear
Particle Transport code and they
Neutral
Carlo
Monte
MCNP
spectra using the
of neutrons produced from
evidence
is
little
There
agreement.
good
show
It has been possible to
electrodisintegration.
or
photoneutron reactions
is consistent with the
peak
thermonuclear
of
the
shape
the
that
confirm
as determined from
temperature
ion
the
that
and
Gaussian shape predicted
diagnostemperature
ion
C
Alcator
other
with
consistent
the line width is
broadline
Doppler
of
theory
the
by
tics, and follows the trends predicted
ening.
*Present Address:
National Nuclear Corp.
1904 Colony St.
Mountain View, CA 94043
Page 2
I.
The fact
the ion
that the
fusion neutron
distribution
energy
Introduction
of
since the early days
of
presented a paper
which most
Unfortunately,
in
fusion
a
could be used
thermonuclear
research.
In
The work discussed here
been
plasma has
known
1967 Lehner and Pohl
knowledge
been made of this
of the difficulty in making high resolution measurements
trons.
to study
[1]
of the theory used today was detailed.
use has
very little
spectrum
represents
a successful
because
of fusion neuattempt at
such
a measurement.
Strachan et
al.
have
[2]
Torus (PLT)
Princeton Large
to
3
a
used
He
the
measure
spectrum
neutron
at
chamber
ionization
due
the
to
a
beam heated plasma, but were unable to resolve the D-D fusion peak for an
ohmically heated plasma [3].
The measurement has been possible at Alca-
the plasma density is an order of magnitude
tor C because
in
PLT, resulting
a
ratio
of
fusion
neutrons
which is two orders of magnitude better than PLT.
improved the
ion
chamber
neutron
thermal to
fast
count rate
performance
on the design
shielding
count
and
ratio,
at the D-D peak.
of the spectrometer.
non-fusion
to
obtaining
achieving
a
The emphasis
of
Additional details
ments at Alcator C may be found in reference
neutrons
In addition, we have
collimation
thus
greater than
much
a
lower
improved
this paper
is
on the measure-
[4].
The Alcator C fusion device is a high field compact tokamak located
at and operated by the Massachusetts Institute of Technology for the U.S.
Page 3
Department of Energy.
Figure 1 shows a diagram of the machine.
The de-
sign parameters for the machine are displayed in table 1.
An important result of a neutron spectrum measurement is that it is
possible to identify the
from its
in an
energy.
Alcator
Five
physical
processes
C deuterium
electrodisintegration of
process
are
plasma
known to
be
discharge:
deuterium,
thermonuclear fusion of deuterium,
which generated the
sources
of
photoneutron
photodisintegration
neutron
neutrons
reactions,
of
deuterium,
and fusion of deuterium and tritium.
These processes have been described in detail in references [3] and [5].
Photoneutron production,
and photodisintegration
of deuterium
are pro-
cesses which occur at the ring of molybdenum blocks used to define the
plasma discharge (limiter).
but has a
cross-section
Electrodisintegration
which is several
orders
is a volume
process
of magnitude
smaller
than the D-D cross-section for the particle energies expected in Alcator
C plasmas.
All the processes except the thermonuclear D-D and D-T reac-
tions are a
result
of
some plasma conditions
these 'run-away
supra-thermal
[6].
electrons'
electrons which are
produced
for
It is possible to limit the production of
by
controlling
the plasma
discharge
condi-
tions.
Tritium produced
in the
D(d,p)T
reaction to produce 14.7 MeV neutrons.
reaction
can also
react
via D-T
These neutrons would be expected
to cause a background of neutrons above the D-D peak due to down-scattering in the room and machine structure.
Chrien
[71 has measured the D-T
rate to D-D rate ratio for PLT and found it to be between 10-
Figure 2 shows
spectrum.
how each of
the
processes
might
affect
3
and 10- 4 .
a neutron
This figure is based mainly on a spectrum measured by Stra-
Page 4
chan and Jassby
3
[3] using a
He ionization of the
same design as used
here for an ohmic discharge at the Princton Large Torus PLT.
sults were
obtained at a plasma density roughly an order of magnitude
lower than that used here
tant.
Their re-
where non-thermonuclear
processes are
impor-
As will be seen later, thermonuclear D-D reactions dominated the
neutron spectra measured here.
The D-D thermonuclear neutron rate is given by
r
n2
R =
f()
2
where n
is
the
functions of
ylm2,
Deuterium
the
and U(vrel)
neutron spectrum
f(y2 )
"(Yrel) d 3 v1 d3 v 2
lyrell
(1)
-'-'
reacting
D-D
the nuclear
can
be
f(ul),f(u 2 ) are
density,
pair,
urel is
A
cross-section.
obtained
by
the
applying
the
distribution
relative
general
the
velocity,
form
condition
for
the
that
the
3
neutron have an energy -
(0+Erel)
in the center
of mass coordinate
4
system.
result of
A general
formulation
evaluations
of
the
is
given in
spectrum
for
Lehner
the
Maxwellian ion distribution function is used here
[8].
case
of
However,
the
the isotropic
[8,9,10,111.
Williams
[10], for example, found that the three-dimensional isotropic Maxwellian
ion velocity
plasmas,
distribution,
the
expected
would produce an approximately,
distribution
Gaussian energy
for
Alcator
C
spectrum with
a mean energy given by
3
<En>
kT
bkT
+
=Q
4
2
2
2/3
7
(2)
Page 5
and the line width FWHM in keV is given by
AEn
=
82.5/kT
(3)
where kT is the plasma temperature in keV as defined by the Maxwellian
distribution.
In equation (2), b is the coefficient in the Gamow cross-
section,
E0 a(Eo)
-b/
(4)
e
a(Erel)
Erel
where EO is an energy at which the cross-section is known.
gives the line width for a spatial and time invariant
Equation (3)
plasma source.
average over
In a real measurement the line width will represent the
space and time of
the plasma distribution.
the maximum ion temperature
temperature representing
time is a more characteristic
plasma parameter
and
ion
However,
in both space and
is generally
used.
Thus a correction has to be made to obtain the peak central ion temperature from the temperature
measured
from the line width of the neutron
spectrum.
As will be seen in section IV it
is necessary to integrate over a
large portion of an Alcator plasma and also to sum the spectra of many
plasma discharges
(shots)
represents
was collected during
from the
about 11%
total
to obtain
sufficient
statistics
in
Figure 3 illustrates a typical plasma discharge.
the neutron spectrum.
The shaded area
together
the time during which the neutron
the discharge.
neutron
rate
The ion temperature can be deduced
measurement
over the shaded region.
spectrum
and
is estimated
to
vary
by
However, the effect of averaging the
Page 6
ion temperature
from a measurement
of the peak width is calculated
yield a temperature which is 0.96 the peak ion temperature
to
or a 4% cor-
rection.
The ion temperature
C is assumed to be poloidally and
in Alcator
toroidally constant but to vary with the minor radius as given by
2
r
Ti(r)
at
e
=Ti()
(5)
2
at
=
3
-a
2
qX is the limiter q [12].
-
qy
qo is central plasma safety factor and
is the limiter radius,
where a,
q0
2
A computer program was written to numerically
calculate the neutron spectrum for the Alcator C temperature and density
Table
profiles.
qj.
summarizes
2
the
correction
Ip/Bt
indicating
the
correction
slightly dependent of the major plasma parameters.
can be
understood
where the neutron
by
production is
essentially constant.
However,
examining
Fig.
function
of
the correction is quite constant.
Note that over a wide range of qZ
qZ is proportional to
as a
factor
4 and
important,
very
The reason for this
noting that
r
is
factor
< 6 cm,
for the
region
the density is
At 6.0 cm the density is 0.93 the central density.
as can be seen in Table 2 the maximum neutron rate as a function
of the minor radius does not occur at the center where the ion temperature is a maximum, but at about a minor radius of 2.3 to 4.0 cm (depending on qX)
where the
0.92 the central Ti.
ion temperature
is
essentially
constant
at about
If the ion temperature profile broadens, the region
Page 7
where the
maximum production
shifts
with it
while
the maximum production region remains constant.
derived from the half
width
of the
neutron
the temperature
of
Thus the ion temperature
spectrum is insensitive to
plasma profile effects.
Equation 5 does not however,
oscillation which
temperature.
causes
both
include
spatial
the effect
and
of the
time variations
'sawtooth'
in the
ion
The sawtooth oscillation is caused by a plasma instability.
In a short period of time the ion temperature profile flattens as in Fig.
5a.
Figure 5b shows the neutron production profile and neutron spectrum
just after a sawtooth crash.
When the effect of the sawtooth oscilla-
tion is included the correction factor for the spatial effect is 0.84.
Combining the spatial
neutron spectrum
and
width is 0.81
vary as much as 10%,
time effects,
times
the measured Ti
the peak
central Ti.
for arbitrary time limits,
from the
This might
but varied less than 5%
for the measurements presented below.
Table 3 summarizes values of the mean and dispersion for some plasma temperatures.
Clearly,
the
shift
of the mean energy is
small com-
pared to the change in the line width, and measurement of the line width
is better suited to a temperature determination.
Using the results of table 3 for Alcator C ohmically heated plasmas
for which the ion temperatures are typically 1.0 keV, a detector resolution better than 2.5% is required.
choice of
the
detector.
General
This requirement greatly limits the
discussions
can be found in references [131 and [14].
found to have a resolution better than 2%.
of
neutron
spectrometers
The ion chamber used here was
While many other techniques
Page 8
have been proposed to measure the widths for higher temperature plasmas,
[2],
[161,
[151,
[171,
[18],
[19],
no other
technique
which has a sufficient resolution without a sacrifice
several orders of magnitude.
of spectrometer,
400 msec),
As will be seen below,
has been
found
of efficiency of
the low efficiency
the short duration of the plasma discharge,
and the low neutron production rate make it
(typically
necessary to sum
spectra from many plasma discharges to obtain a useful spectrum.
[I.
The Spectrometer System
The spectrometer system shown in Figs. 6 and 7 consists of the high
pressure
3
He
ionization chamber
[20]
designed for the Alcator environment.
ber has provided
a thermal
is
in a
shielding enclosure
The manufacturer of the ion cham-
neutron shield
This assembly
ion chamber.
mounted
surrounded
which
is mounted around the
by a minimum
of
1.0
cm of
lead inside a double walled stainless steel box.
The space between the
walls of the
Li
box is
filled
with lightly packed
2
CO 3
powder
access port has been provided on one end to view the plasma.
and an
The port
is blocked by a 1 mm thick sheet of cadmium to reduce the incoming thermal neutron
thickness of
flux.
30
The stainless
cm
of
Water
steel box is
Extended
Polyester
is a mixture of 40% water,
and 60% resin,
or L1 2 CO 3 used
thermal neutrons.
to
capture
surrounded by a minimum
(WEP)
The WEP
with small amounts of boron
A
collimator,
of WEP is used to limit the view of the spectrometer
which pass through the "keyhole"
[21].
also made
only to neutrons
of an Alcator C diagnostic port.
This
port allows a view of 4.4 cm by 26.0 cm through the 20 cm thick Bitter
magnet used to provide the toroidal magnetic field.
Figure 8 is a block diagram of the spectrometer electronics.
The
Page 9
ionization chamber has an integrally mounted FET charge
amplifier.
The preamplifier
output is
An 8 psec time
shaping amplifier.
routed
sensitive pre-
via a coax
cable
to a
constant is used for pulse shaping.
The amplifier output signal is direct coupled to a multi channel analyzSpectra are
er (MCA).
gain of 4096.
of the
collected
into
2048
channels with a
conversion
A precision pulser provides a test signal onto the grid
ion chamber.
The
capacitively
coupled
signal
at
the
the ion chamber is monitored to indicate noise on the signal.
litude of
the pulser
signal
is adjusted
anode
of
The amp-
to place the pulser peak in a
channel above channel 1900, well above the range of interest for neutron
spectrum counts.
vide archival
The MCA is interfaced to a PDP-11/T55 computer to pro-
of individual
shots.
Two high voltage supplies are used
to supply the grid and anode voltages.
The grid voltage was set to 847
volts and the anode voltage was set to 3000 volts as recommended by the
manufacturer.
2.1
The Ionization Chamber
The ionization
He,
in detail
The chamber is a gridded type operating at a pressure of
291.
3
chamber has been described elsewhere
6 atm of argon and 0.5 atm of CH 4 .
neutron reacts via the
3
positive reaction energy,
3 atm of
In the detection process the
He(n,p)T nuclear reaction.
Q,
[22-
of 764.0 keV.
This reaction has a
The cross-section for this
reaction is shown as a solid line and the competing elastic scattering
cross-section is shown as a dotted line in Fig.
Fig.
9
represent
Franz et
al.
[26].
the
spectrometer
Note that the
relative
9.
The open circles in
efficiency
scattering
as
cross-section
reported by
is roughly
three times larger than the reaction cross-section at 2.45 MeV.
Further
Page 10
the reaction
cross-section increases
as the inverse square root of the
Thus the spectrometer is very sensitive to thermal
neutron energy.
and
scatter-
epithermal neutrons and will have contribution due the elastic
ing cross-section at all neutron energies.
The calibration
of the
spectrum shown
cross-sections
in Fig.
10
illustrates
the effect
response function.
on the detector
source
The
neutrons were produced by bombarding a deuterium target with a 140 keV
This source spectrum has an estimated width of 50 keV at
deuteron beam.
There is a large component of ther-
FWHM and a mean energy of 2.42 MeV.
due
mal neutrons
walls and
results
the ion chamber,
of thermalized
zero
thermal peak at
a
by a)
from
a
neutron
the
room
energy
full
their full
which deposit
from reactions
b)
neutrons
characterized
spectrum is
The
floor.
peak which
the return
to
energy
in
energy due to the
large reaction cross-section for thermal energies, c) a recoil continuum
from 0.75
times
full energy
the
on the
neutrons
Hydrogen in the
CH 4
neutron capture
and hard
gas,
total energy deposited
3
He(n,p)T reaction,
to
3
a recoil
He
gas d)
e)
and,
x-rays
keV,
interacting
and
of
the
spectrum due
to
the
y ray continuum which is
a
in the ion chamber
764
scattering
elastic
energy due
neutron
the
in
the ion
is the
incident
due
chamber.
to
The
sum of the Q of the
neutron
energy.
Thus
the thermal peak is offset by 764 keV and the signal due to gamma rays
appears below the thermal peak.
reaction cross-section
active volume
produce
but
the
do
2.4 MeV neutrons which react
not
continuum
deposit
between
their
full
energy
the full energy
via the
in
the
peak and
the first recoil feature.
Figure 11 shows a crossectional view of the known parts of the ion
Page 11
chamber.
[301.
The operationr
of a gridded ion chamber is described in Knoll
In the commercial design the preamp is mounted at one end of the
ion chamber
to minimize pickup
the preamplifier.
filling the
The
other
between the ion chamber and the FET of
end
of the
chamber through a gas fill
heater has
been
provided
to
eliminate
chamber
valve.
provides a means
of
A calcium purifier and
tritium
from
the
ion
chamber
after extended use.
The manufacturer has included a thermal neutron
of 1 mm of
shield consisting
cadmium and 3 mm of boron nitride powder around the active
This shield is claimed to have a shielding effec-
ion chamber volume.
tiveness of 200 by the manufacturer.
2.2
Shielding and Collimation
In order
shield the
code [31]
to assess
scattered
was
the amount
neutrons
used to
and type of
the Monte
Carlo
study the neutron
shielding
Neutral
transport
required
Particle
for
to
(MCNP)
the Alcator
C
machine geometry.
The machine was modeled as a torus with the surround-
ing Bitter
plates.
magnet
tallies were made
from the port.
as a
Figure
A
single diagnostic
function
12 shows
of
little
increase in
distortion
the
2.3
to
of
scattering from
copper,
The bulk of the
scattered
a
positions
cm from the plasma.
the
2.35 MeV
for
was
modeled
and
at and
away
the neutron spectrum calculated
position at a diagnostic port 50
is very
energy
port
2.45
group
major
neutrons
MeV
would
constituent
source
Note that there
group.
correspond
of
the
are at energies
for a
to
The
small
180 degree
Bitter
magnets.
less than 0.1 MeV.
Because the ion chamber is very sensitive to thermal and epithermal
Page 12
neutrons these
results
indicate
that
it
is
necessary
to
increase
the
amount of shielding over the manufacturers thermal neutrons shield.
ther,
in measurements
Fur-
done during plasma discharges with only the manu-
facturers shield the detector was saturated by the thermal and epithermal
The code predictions
neutron flux.
indicated that the
greatest number
of neutrons are in the epithermal range, where the capture cross-sections
are still ineffective.
Thus, the decision was made to design the shield
system to moderate and then capture the thermal neutrons.
A second
consideration
was
to minimize the
that the spectrometer viewed as little
flux as possible.
collimator
opening
of the machine scattered
neutron
The horizontal access to the plasma is limited by the
width of "key-hole" of the diagnostic port to approximately 4.4 cm.
vertical access
so
is limited to
26.0
cm.
It was
shown earlier
The
that the
active length of the ion chamber is 14.9 cm and that the ion chamber's
efficiency at
detecting
chamber orientation
placing the ion
neutrons
as end
opening
opening
10.2 cm vertically.
the ion
as long
MeV
chamber
neutron producing
was
This
is
20 degrees
without loss of
designed
vertical
viewed
a
large
part
of
the
insensitive
on configurations
chamber at an angle of
a minimum collimator
The collimator
2.45
to
be
opening
portion
plasma.
of
the
ion
are avoided.
By
as shown in Fig.
viewed,
or
5.3
1.2
cm
of
percent
the
of
total
the
402
5.08
cm
horizontally
was large
the
About
total
cm
7,
efficiency was obtained.
enough
radial
ninety
that
of
the
percent
of
the
The horizontal
circumference
neutron
so
and
extent
neutrons are produced inside a minor radius of 6.0 cm.
limit allows
to
producing
plasma
to
plasma.
be
The
collimator opening is blocked by a 1 mm thick sheet of cadmium to remove
thermal neutrons
from the
incoming neutron beam.
The
shield box
was
Page 13
designed so that there were no streaming paths.
Since the chamber is sensitive to gamma rays Li2 CO3 powder was used
While natu-
as a thermal neutron capture material near the ion chamber.
ral lithium in this form is not as effective as boron compounds the capture of a thermal neutron by boron leads to a capture gamma of 0.48 MeV
while the lithium capture reaction does not have a gamma ray associated
with it.
The Li 2 C0 3 powder was lightly packed between the two stainless
steel boxes.
The packing density
of the powder
is 0.76
which is
g/cc
calculated to reduce thermal neutrons by at least two orders of magnitude.
This thickness
would correspond
greater thermal
shielding
is
to a half value layer at 0.5 MeV.
required,
Li
2
CO 3
enriched
in
6
Li
If
could
be used.
Water Extended Polyester was
chosen as the moderator because:
1.
Shielding of any desired shape and size could be cast in house allowing a
modular shield system to be used,
2.
water which is trapped in resin cells,
to a 1.0 atom percent.
up to 40% of the weight
and 3.
could be
Boric acid is soluble up
Li 2 CO 3 powder could be added also but had to be
suspended in the resin making casting much more difficult.
The shielding
effectiveness of a 0.3 m thick block was tested by measuring the neutron
spectrum for PuBe and Cf252 sources with and without a shield block in
place.
The shielding effectiveness was found to be approximately 30 for
neutron energies
neutron energies.
above
1 MeV and to increase to about 100 at thermal
The WEP shield has a total weight of 1070 kg.
The ion chamber is microphonic.
To isolate the ion chamber approx-
imately 50 kg of lead shielding was tightly coupled to the ion chamber,
while the assembly was shock mounted on rubber cushions.
One inch thick
Page 14
pieces of soft
piece of
Cd
pickup.
foam rubber
blocking
the
were
used
on each
collimator
When the WEP shield
side of
port to
the
further
1
mm thick
reduce
acoustic
was in place around the shielding box no
evidence of acoustic pickup was seen during acoustic noise tests simulating shot acoustics.
Franz et al.
Acoustic
sensitivity was
studied in detail
by
[261.
III.
Spectrometer Performance
Energy Calibration with the D(D,n) 3 He Reaction
3.1
The energy calibration of the ion chamber was made with a D-D neutron generator.
The
accelerator
is
capable of
to 140 keV with a beam current of 0.3
mA.
accelerating
Under these
5.0 x 107 neutrons are produced per second.
deuterons
conditions up to
The spectrum was neasured
at a beam to neutron emission angle of 99 degrees where
the dependence
of the neutron energy on the ion beam energy is at a minimum.
angle of 99 degrees the energy of the neutrons
is 2.42 MeV.
At this
The error
in this energy is estimated to be 10 keV and due to error in the measurement of the angle.
In order
T,
on the
detector
beam angle
scan.
In
constant
to determine the effect
of
Fig.
is
resolution
99 degrees.
13,
one
can
a
series
Figures
see
of
13 and
the
decreased the response
of the amplifier time
spectra
14
qualitative
function
stant.
measured
the results
effects.
of
As the
at
a
this
time
in the vicinity of the peak
becomes more asymmetric and the FWHM increases.
fect as a plot of the increase
show
were
constant,
Figure
14 shows this ef-
in the FWHM as a function of the time con-
The data has been normalized to the 8 pisec value after which the
Page 15
relative width appears to be
constant.
To maximize the possible count
Here 8 psec
the shortest possible time constant should be used.
rate,
has been used since in most data taken to date the 8 psec time constant
has not
resulted
in excessive
pile-up.
Shorter time
constants
used if the loss of resolution is not important and if
can be
the asymmetry of
the response function is corrected for.
3.2
Energy Resolution
Calibration neutrons
Calibration using the
were
which has 0 value of -1644
keV.
provided
via
the
7
Li(p,n) 7 Be Reaction
7
Li(p,n) 7 Be
A proton beam from the Lawrence Liver-
more Laboratory's Tandem Van de Graaff Accelerator was used.
trometer was
placed
mean energy of
at a
reaction
beam angle
of
0 degrees.
4130 + 25 keV and a dispersion of
The spec-
The protons had
3 key.
a
These condi-
tions imply a neutron energy of 2450 + 25 keV for the full energy peak.
The resolution of the spectrometer mounted in the primary shielding
box was measured for neutrons incident on the spectrometer at angles of
20 degrees
(parallel
case)
70 degrees
to allow measurement
ciency of the spectrometer.
perpendicular case.
case)
to the
of
the relative
efficiency
of
the
cases and an estimate of the intrinsic effi-
parallel and perpendicular
placed at a distance of
(perpendicular
The charge of the protons striking the target
ion chamber anode wire.
was collected
and
The active center of the spectrometer was
70.2 cm for the parallel case and 113 cm in the
A LiF target
of
thickness
112 pg/cm2 (8
keV)
on
a 40 mil tantalum backing was used.
Figure 15
shows
the
calibration
spectrum for
The data has been fitted with the function:
the parallel
case.
Page 16
2
ch
1 P 2F(ch)
=
p1
2
e
P
c3
-0.707
+
P 1P4W
1 4
P2
e
ch
P5
+ P W
6
(P
1
W
=
-
i
Erfc
-
ch
(6)
-
2
3
para-
Erfc is the Complementary Error Function and the p's are fit
meters.
Note that the background and exponential are cut off by a comfunction
plementary error
spectrum shown the
full width
Gaussian is 38.2 + 3 keV.
keV.
at
the
the
of
centroid
For the
of the
component
at half maximum (FWHM)
The width of the fitted function is 45.6 + 3
The intrinsic efficiency for the parallel
be 1.7+0.5 x 10-4.
Gaussian.
case was calculated
to
The ratio of the intrinsic efficiency for the paral-
lel case to the perpendicular case was measured by normalizing the ion
chamber count rate to correct for the different
tances and total run time.
source to detector dis-
The ratio was found to be 0.98+0.05.
Thus
the orientation of the ion chamber does not seem to be critical implying
that the
detector
passing through
at either end,
of efficiency.
rate
is
the active
dependent
volume.
only
on
However,
the
number
because
of
of the
neutrons
structure
the ion chamber end configurations will result in a loss
Page 17
3.3
Figures of Merit
Because good resolution requires a long time constant
and tokamak
plasma shots are typically less than one second in duration,
portant to quantify the maximum allowable
count rate.
it
is im-
A useful
figure
of merit is the ratio of the number of counts in the full energy peak to
the total number of counts in the neutron spectrum.
Formally, the inte-
gral of the number of counts between the full width at tenth maximum is
compared with the integral of counts in the total spectrum.
It should
be noted that for all these comparisons an arbitrary cut off is used on
the low energy side.
This lower limit corresponds
the lower level discriminator
to the cutoff
on the multi channel analyzer.
from
This cut
off would correspond to an energy of less than 500 keV deposited in the
The energy
ion chamber.
could
be
The typical value for this figure
every 70
detected
pulses
recorded
from gamma
or neutron interactions.
of merit is 1/70.
in the
MCA
is
Thus,
a
full
one out of
energy
peak
pulse.
A second figure of merit is the total count
tion must
made
count rate.
between
the
The MCA count
ionization
chamber
the
facturer and various authors
rate is
104
the MCA
two rates.
there can -be signifi-
The effect
charge and gamma ray level will be discussed further
imum count
rate and
Because the number of gamma rays varies
significantly with the type of plasma discharge,
between
count
Here a distinc-
rate does not include the pulses cut off by
the lower level discriminator.
cant differences
rate.
[2,22,24,26]
counts
per
have
second.
type of
below.
dis-
The manu-
indicated that the max-
However,
tronic pulse system which limits the count rate.
the
it
is
the elec-
If the time constant
of the pulse shaping is reduced the count rate limitation will increase.
Page 18
(At a cost of resolution, as was shown in Fig.
rate is also
set.
sensitive
The MCA count
to where
13.)
This maximum count
the MCA lower level
discriminator
is
rate will not include pulses which fall below the
lower level discriminator and the number of pulses increases sharply in
the lower energy
channels.
Thus
the
count
rate at
significantly with the lower level discriminator
the MCA
setting.
can vary
Further the
number of gamma rays and hard x-rays varies significantly with the type
of plasma discharge,
and the pulse
amplitudes
for photon interactions
are generally below the discriminator level, so there can be significant
variation due to the gamma ray background.
Thus,
the MCA count rate is
always less than the rate at which radiation interacts in the ion chamber.
The
authors
above
have
all
used
settings and amplifier time constants.
pile-up on the
peaks
in the spectrum.
the MCA discriminator level.
the pile-up effects
different
lower
discriminator
More important is the amount of
This effect
is insensitive
of
For the discriminator level we have chosen,
are minimized
and the MCA dead time
is below
2%.
This would correspond to a total count rate of about 4 x 103 per second
for the 8 psec time constant used.
IV.
Measurements at Alcator C
A typical plasma discharge or shot for Alcator C is shown in Fig.
3.
For the shot shown the field was 8 T and the plasma
kA.
current was 375
The maximum electron density was 3 x 102 0 m-3 .
The neutron rate signal is derived from a bank of 14 one inch diameter
3
He proportional
operational amplifier.
counter tubes whose current is summed through an
The
shaded
which the spectrometer is gated on.
region
indicates
the
time
during
Page
Such a plasma discharge produces 1010 neutrons.
19
Unfortunately only
about one out of every 7 x 109 of the total number of neutrons produced
in the
plasma
contributes
to
the full
energy
peak due to
solid
angle
losses and the low detection efficiency of the ion chamber.
Neutron spectra were collected for individual plasma discharges and
stored on magnetic media for later analysis.
Typical 2.45 Mev peak counts
rates were only a few per shot requiring a large number of similar shots
summed together
to be
to obtain useful
spectra.
The best
single
analyzed to date had a peak rate of 2 x 1011 neutrons per second.
shot
During
the 250 msec on time there were 11 neutrons collected in the full energy
peak or a peak count rate of
44 per second.
This is very close to the
maximum rate at which the spectrometer can operate for the 8ysec amplifier time
constant
used.
The dead time was
estimated to be
shot and the thermal peak was not distorted.
time constant
and using a pile-up rejecter
2% on that
By reducing the amplifier
a count
rate as high as a
100 per second appears to be an upper limit on the count rate.
In practice,
it
is necessary to sum a large number of similar plasma
discharge spectra together
In Fig.
16,
to deduce
useful information
303 plasma discharges have been summed together in order to
understand overall
properties
of
the
spectrometer
calibration spectra and a sum of a single day,
shown.
on the plasma.
performance.
62 plasma shots are also
It is clear from Fig. 16 that there is a peak at 2.45 MeV.
ther there is little
Two
Fur-
or no contribution to the spectrum from neutrons pro-
duced by photonuclear reactions, electrodisintegration, photodisintegration or neutron down-scattering
tively,
the number
of
from the machine
counts in an integral
structure.
containing
Quantita-
the peak to an
Page 20
for both the
integral of counts in the lower channels has been compared
calibration spectrum and the shot data.
In the first case, a D(D,n) 3 He calibration, the shield
this comparison.
including the WEP was assembled in the accelerator
reaction but without the WEP moderator.
to the high level of
has one meter thick concrete
The
comparison
walls.
of
The accelerator
The nearest
these
WEP is to the shield effectiveness.
In the second
The fifty fold increase in the
room return.
vault
wall was only 200 cm
The source to detector distance
away and the floor was only 60 cm away.
was 96 cm.
room.
spectrum were taken using the D-D
case in table 2 the integrals for a
ratio is due
the results of
Table 4 shows
tests
how important
indicate
the
A further test of the shield effec-
tiveness was performed by blocking the collimator with a 10 cm polyethylene block
during
typical
plasma
discharges.
A
total
of
11
neutron
counts in the entire spectrum were recorded compared to an average of 86
counts recorded
for the unblocked
case.
Assuming
a mean
free path of
2.5 cm for fast neutrons in the polyethylene block a 6% transmission is
expected.
calibration case the WEP moderator was not used,
false floor
For the Li(p,n)Be
This. is consistent with the test results.
allowing
the
spectrometer
to be
but the facility has a
at least
500 cm from the
nearest wall or floor while the source to detector distance was
Thus the spectrum would be expected to be dominated
70 cm.
by the direct flux.
The small peak near 2.0 MeV is due to an excited state of Be.
The inte-
grals for a series of spectra sums are similar to the calibration results
and indicate that the fusion spectra are dominated by 2.5 MeV neutrons.
V.
Determination of the Ion Temperature
To deduce the ion temperature
following procedure was used:
from the line width of the peak the
Page 21
1.
The thermal and pulser peaks were examined on an individual shot basis to reject bad shots.
Plasma spectra measured under
2.
similar conditions were summed to ob-
tain sufficient statistics.
3.
The pulser and thermal peaks were fitted using a Gaussian function to
determine the noise during the set of summed shots.
4.
The full energy peak was
fitted and the error of the fit
was deter-
mined as described below.
5.
The fitted width was corrected
for the detector resolution and for
noise broadening of the peak.
6.
The average ion temperature was determined using equation 3 and corrected as described earlier to obtain the central peak ion temperature.
The primary criteria for rejecting a plasma shot was a loss of more
than 4 counts from a normal 20 counts in the pulser peak during the 200
msec spectrum measurement
of a plasma
shot.
The most probable cause of
the loss of pulser counts was the pile-up due to hard x-rays and photoneutrons produced at the limiter where the most difficulty with pileup
was encountered.
A ring of molybdenum blocks is used to limit the extent
of the plasma minor radius
at two toroidal locations at Alcator C.
level of photoneutrons
gamma
and
rays is a
strong function
of how the
gas is added to the plasma discharge at the start of the discharge.
ther,
in preliminary tests at a non-limiter port,
The
Fur-
very few shots had to
be rejected due to pile-up of gamma and photoneutron counts.
The measure-
ments reported below were done at a port with a limiter and great care
was taken in the gas programming to avoid high photo-neutron and hard xray levels.
Page 22
The summing of the data was accomplished by simply adding spectra on
a channel to channel basis.
This procedure was allowed only because the
absolute channel drift was less than one channel per day and less than 3
channels per week.
The pulser and thermal peaks were fitted in a least squares fashion
with a
single
Gaussian
function.
The
contribution
to the peak width
from ion chamber noise pick-up during the shot was typically 40 keV for
a sum of shots.
As mentioned
above,
spectra were recorded -into 2048 channels,
approximately 70 channels across the full energy peak.
procedure is to collapse
the data until only
or
While the normal
four to five
contain the
half width of the peak and then fit a function minimizing the Chi Square
statistic,
Cash
if the
original
It
[32,33]
has suggested
un-collapsed
data
is
that more
fitted
information
using
the
'C'
is
gained
statistic.
is necessary to abandon the Chi-square statistic because of the re-
quirement that
the
standard deviation
of
the number
of
counts
channel be equal to the square root of the number of counts.
in any
This is
not true when the number of counts is less than 10 as is the case here.
The 'C'
statistic is simply
N
C = 2
[ei - ni kn(ei)]
where n is the number of counts in a channel,
N is the number of channels
and e is the expected number of counts from the fitted function.
Confidence intervals are generated
around the best fitted value.
(7)
Confi-
by varying the parameter of interest
The value of
C for the minimum case is
then subtracted from the C found for varied value.
Cash has shown that
Page 23
this difference is distributed statistically as a Chi square distribution
with one degree of freedom.
AC.
Thus a confidence can be generated from the
Figure 17 shows the confidence of fit as a function of Gaussian com-
ponent sigma using the technique
August,
1982.
of
Cash for data taken
on the 6th of
Such a curve can be used to determine the range of a about
a best estimate of a given a required confidence.
A 68% confidence in-
terval has
Using
been used
for
error
analysis
here.
this
shots with as few as 20 counts in the peak have been analyzed.
it
technique
However,
was necessary to have at least 150 counts in the peak to obtain 20%
error bars on the ion temperature deduced from the width.
In order to assess whether the width could be used to deduce the ion
temperature,
two sets of plasma shots were analyzed.
tions are summarized in Table 6.
ature (low Ti)
800 eV and
case the peak
1050 eV in
The plasma condi-
Note that in the low plasma ion temper-
ion temperature
the high Ti
case.
is estimated to be about
These temperature
estimates
are based on the total neutron rate and neutral particle charge exchange
Both
diagnostics.
uncertainties on
these diagnostics
the
order
of
are
10%.
reported
The
shot
to have
to
shot
measurement
variation
of
9 channels
of
these derived temperatures was on the order of 10 to 15%.
Figure 18
shows
the two data sets
after groups
of
data have been added together for presentation purposes.- The functional
form of the fitting function is equation (6)
p5 fixed from the calibration.
normalized to the
this data which
resolution,
peak height
has not
been
The optimal fit
from the 'C'
is shown
for the low Ti case.
corrected
for
the high Ti case has
temperature is
above with parameters p4 and
the noise
a greater width.
or
statistic
Even in
spectrometer
The calculated
shown plotted against the total neutron
ion
rate and charge
Page 24
exchange derived
temperatures
ion
measurements
that
Note
agreement.
represent perfect
line
The dotted
19.
Fig.
in
would
consistent
are
with the theoretically expected result.
VI.
The neutron
Summary
here has
system described
spectrometer
measure the neutron spectrum at Alcator C.
been
used
to
The spectrometer resolution
has been measured to be 46 keV FWHM and the absolute energy calibration
By utilizing the structure of the Alcator C mag-
is accurate to 10 keV.
net in the collimator and shielding design an effective rejection of unwanted neutron and gamma ray counts has been accomplished.
Furthermore,
system is modular allowing it
to be assem-
the shielding and collimator
bled at any Alcator C horizontal diagnostic port with normal laboratory
All
lifting equipment.
materials
primary shielding material,
WEP,
used
are
readily available
the
can be cast and machined with relative
The ion chamber used is also commercially available.
ease.
While the spectrometer has very good energy resolution it
be count rate limited to less than 100 counts
second.
[2].
and
in the 2.45
appears to
MeV peak per
This is an improvement over the measurements of Strachan et al.
the count
For the measurements done here,
rate was limited by the
production rate from the Alcator C plasma and many plasma shots had to
be summed to obtain a usable spectrum.
rate in the plasma
is increased it
least several seconds of 'on' time.
discharges would be required.
several ion
relaxed.
chambers
are
used
will
Even if the neutron production
be necessary to accumulate at
Thus, at least 10 typical Alcator C
If discharge durations are extended or if
in parallel
this
requirement
could
be
Page 25
The measurements done to date at Alcator C indicate that the speceasy to use in the tokamak environment.
trometer is quite
was
magnetic shielding
50 P coaxial
standard
routed over
incorporated
cable
and
design,
special
signals
the preamplifier
from
were
to the
the plasma
noise pickup during
Nevertheless,
shaping amplifier.
the
in
No
shot
contributed only an equivalent of 40 keV to the pulser and thermal peak
widths and
could be
Table 5 provides
corrected for.
a summary of the
spectrometer performance.
By summing
shots
the
temperatures from
together
widths
it
of
has
the
been possible
thermonuclear
ion
to determine
This
peaks.
is the
case known to us in which the ion temperature has been determined
first
from the peak width for an ohmically heated discharge and also the first
systematic test of the technique
against other ion temperature diagnos-
The spectrometer is expected to be extremely useful for the study
tics.
of plasmas with non-thermal ion energy distributions.
We would like to thank the support staff of the MIT Alcator C fusion
group,
Francis Bitter Magnet laboratory,
for their assistance.
the Lawrence
Livermore
the ion chamber,
and
MIT Reactor machine
We would also like to thank Dr.
Laboratory
for his help
in
the
D.
shop
Slaughter at
calibration
of
and Frank Chmara of Peabody Scientific for his help in
conjunction with the ion chamber.
This work was supported by U.S.
DE-AC02-78ET51013.
Department of Energy Contract
No.
Page 26
REFERENCES
1.
G. Lehner and F. Pohl, "Reaktionsneutronen als Hilfsmittel der Plasmadiagnostik", Zeitschrift fUr Physik 207 (1967) 83-104.
2.
J.
D.
3.
J. D. Strachan and D.
4.
W.
A.
Strachan,
Fisher,
et
al.,
Nature
(London)
L. Jassby, Trans.
279
Am. Nucl.
(1979)
626-628.
Soc. 26 (1977)
509.
"D-D Fusion Neutron Spectra Measurements and Ion Tem-
perature Determination at Alcator
C".
M.I.T.
Plasma Fusion Center
Report PFC/RR-83-3.
5.
"Studies
of
the Photonuclear
Neutron Emission
Phase of the Alcator C Tokamak",
D.
During the
Start-up
S.
Pappas,
R.
Furnstahl,
Nucl.
Fusion
19
(1979)
G.
P.
Kochanski, PFC/RR-81-22, May 1981.
6.
H.
7.
R.E. Chrien "Measurement of Fusion Reactions from a Tokamak Plasma",
Knoepfel
and
D.
A.
Spong,
785-829.
Ph.D. Thesis, Dept. of Astrophysical Sciences, Princeton University,
1981.
8.
G.
Lehner
in
Reactions under Plasma Conditions,
Vol II,
edited
by
M. Venugapalan, John Wiley and Sons, 1971, 509.
9.
T. Elevant, Nucl. Instrum. Methods 185 (1981) 313-320.
10.
H. Brysk, Plasma Phys. 15 (1973) 611.
11.
M. M. R. Williams, J. Nucl. Energy 25 (1971), 489-501.
12.
Fairfax et al., "Energy and Particle Confinement in the Alcator Toka-
Page 27
maks", IAEA-CN-3/N-6.
13.
Calvert and Jaffee in Fast Neutron Physics, Part II edited by Marion
and Fowler, John Wiley and Sons, 1980.
14.
G.
Knoll,
Radiation Detection and Measurement chapt.
15,
John Wiley
and Sons, 1980.
15.
D.
R.
16.
H.
W.
Slaughter,
IEEE
Hendel et al.,
Trans.
Nucl.
Sci.
NS-26
(1979)
802-808.
"Tokamak Fusion Test Reactor Fusion-Reaction-
Products Diagnostics" presented at the Fourth ASTM-EURATOM Symposium
on Reactor Dosimetry, NBS, March 1982.
17.
M.
18.
TFR Group, in 8th Conf.
Chatelier
et al.,
Nucl.
Instrum.
(Unpublished)
Methods
190
(1981)
Controlled Fusion and Plasma Physics,
107-118.
1 (1977)
1.
19.
R. A. Lerche et al., Appl. Phys. Lett. 31 (1977) 645.
20.
Model FNS-1, Seforad-Applied Radiation, LTD., Israel.
21.
Manufactured by Ashland Chemical, Ohio.
22.
Instrument Manual for Seforad Fast Neutron Spectrometer, Model FNS-1
Seforad-Applied Radiation LTD. Emekhayarden, Israel.
23.
J. Cuttler, et al., Trans. Am.
24.
A.
E.
Evans,
J. D.
Nucl. Soc. 14 (1971).
Brandenberger,
"High Resolution Fast Neutron Spec-
trometry without Time-Of-Flight", LA-UR 78-2562 (1978).
Page 28
25.
S. Shalev, J. M. Cuttler, Nucl. Sci. Eng. 51 (1973) 52-66.
26.
H.
27.
W.
Franz
C.
et
Sailor,
al.,
S.
G.
Nucl.
Methods
Instrum.
Prussin,
Nucl.
144
(1977)
253-261.
Instrum. Methods 173 (1980)
511-
515.
G.
Prussin et al.,
Nucl.
Instrum.
Methods
173
(1980)
28.
S.
29.
G. Rudstam, Nucl. Instrum. Methods 177 (1980) 529-536.
30.
G.
Knoll Radiation Detection and Measurement,
p.178,
505-509.
John Wiley and
Sons, 1980.
31.
MCNP - A General Monte Carlo Code for Neutron and Photon Transport,
Version 2B, LA-7396-M revised April, 1981.
32.
W. Cash, Astron. Astrophys. 52 (1976) 307-308.
33.
W. Cash, Astrophys. J. 228 (1979) 939-947.
Page 29
Machine Parameters
to date
Design
unit
Major radius
64
58 to 71
cm
Minor radius
16.5
10 to 16.5
cm
Toroidal field
140
30 to 130
kG
Current
1000
100 to 750
kA
Density
2x10 2
lx1019-1,3x1021
M-3
1
Aux heating
4.6 Ghz Lower Hybrid
4000
0 to 750
kW
150-200 Ghz Ion Cyclotron
4-10
0
MW
Table 1.
Alcator C Operating parameters.
Page 30
Ti(rmax)
Ti from width
qlim
rmax
2.00
3.5
0.928
0.863
2.50
3.2
0.924
0.860
3.00
2.9
0.926
0.858
3.50
2.7
0.925
0.856
4.00
2.6
0.921
0.855
4.50
2.4
0.924
0.855
5.00
2.3
0.922
0.854
5.50
2.2
0.922
0.854
6.00
2.1
0.923
0.853
Table 2.
Correction factor versus qlim.
Page 31
plasma temperature
Table 3.
mean energy
width FWHM
(keV)
(keV)
(keV)
0.5
2453
58.2
1.0
2455
82.5
1.5
2456
100.8
2.0
2458
116.4
Mean neutron energy and peak line width versus the plasma
temperature.
Page 32
Notes
Case,
File
19aprc.270
D(D,n) 3 He
integral
integral
1250-1400
800-1250
ratio
1.44
2896
4166
252
13107
16139
29946
1.86
846
1174
1.39
101
114
1.13
full shield
31janc.253
D(D,n) 3 He
52.0
no WEP, high scatter
18augc.282
Li(p,n)Be
no moderator, low scatter
super6.un1
sum of 303 plasma
discharges
06augs.um5
sum of .62 plasma
discharges 8-6-82
Table 4.
Ratio of counts in peak integral to below peak integral.
Page 33
resolution
is
46
keV
FWHM
at
2450
at
keV.
1.
The
energy
2.
The
energy
3.
The contribution to the peak width due to noise pickup during
calibration is accurate
2450 keV.
to 10 keV at
a plasma shot can be measured, allowing the peak width to be
corrected for the noise
A typical
contribution.
value
at
FWHM is 40 keV .
4.
The
in the
ratio of counts
full energy
peak to total
ion
chamber counts is 1/70.
5.
The maximum count rate to date is 44 counts per second in the
full energy peak.
count rate
is
The ultimate achievable D-D neutron peak
estimated
to
be
less
than
100
counts
per
second.
6.
The intrinsic efficiency of
the ion chamber is measured to be
1.7±0.5x10~4 at 2.45 MeV.
7.
The
collimator
magnet in
its
and
shielding
design.
The
design
system
is
utilizes
modular
the
in
Bitter
design,
allowing the spectrometer to be used at any horizontal port.
The shield weight is approximately 1 metric ton.
Table 5.
Summary of Spectrometer Performance.
Page 34
"Low" Ti case
number of shots
plasma current
toroidal field
line averaged
"High" Ti case
unit
169
38
350-400
550-625
kA
110
kG
2.3x10 20
M-3
80
2.5x10 2 0
density
Ti from neutron
780
1050
eV
rate and charge
exchange
Table 6.
Plasma conditions for "low" and "high" Ti cases.
Page 35
FIGURES
1.
Fig.
The plasma is confined in
The Alcator C fusion device.
vacuum chamber by the effect of the toroidal magnetic field and
the
ohmic heating current.
A typical plasma
limiter
consisting
a
of
ring of molybdenum blocks is also shown.
Fig.
which
2.
The neutron spectrum which would
exhibits
all
the
significant
observed
for a
result
neutron
plasma
producing
reactions in an Alcator deuterium plasma discharge.
Fig.
3.
A typical high Alcator C plasma discharge as illustratTop, plasma current,
ed by three plasma diagnostics.
density from laser interferometer,
average
sents the
Fig.
spectrum
time
4.
during
which
expected
The
neutron
spectrum
was
measured.
Neutron production at a given plasma radius and neutron
after
integrating
neutron production, solid
line.
the
neutron produc-
The shaded region repre-
Toroidal field was 8.1 Tesla.
tion rate.
bottom,
middle, line
ion
line,
temperature
is
over the entire plasma.
ion
temperature
assumed
profile,
Top,
dotted
to be zero at the plasma
limiter, r = 16.5 cm.
Bottom,
obtained by subtracting
2450 keV from the calculated neutron energy.
neutron
spectrum.
The
width
is
Fig. 5a. Model of the plasma ion temperature distribution before
and after
a sawtooth
after crash.
crash.
Solid line,
before
crash,
dotted line
rs is the surface at which the plasma q = 1.
Fig. 5b. Neutron production rate versus radius and corresponding
neutron spectrum for a plasma just after a sawtooth crash.
Page 36
view
of
neutron
spectrometer
Cross-section
is
through
the
6.
Fig.
device.
Top
of
mid-plane
plasma
the total
1% of
approximately
this geometry,
next
Alcator
the
to
In
machine.
the
C
volume is viewed.
Fig. 7. Side view of the neutron spectrometer.
Fig.
8.
Spectrometer
electronics.
9.
3
(n,p)
NIM
Standard
have
electronics
been used.
Fig.
elastic,
1e
of ion chamber.
efficiency
and relative
cross-sections
[24].
Efficiency data taken from Franz et al.
Cross-section curves from ion chamber users manual [20].
Fig. 10.
produced from
target.
where the
MeV.
The
Ion
striking a deuterated
beam
keV deuterium
a 140
is 2.42
0.05
of about
with a dispersion
MeV
titanium
to the beam direction
spectrometer was at an angle of 99*
neutron energy
were
neutrons
Source
function.
response
char-ber
The pulser and thermal peak features have been reduced in
magnitude for presentation.
Fig.
chamber
11.
view
Crossectional
structure
which
ion
of
use
the
inhibits
of
the
illustrating
chamber
in an
chamber
the ion
ion
end-on configuration.
monoenergetic
MeV
2.45
Carlo Neutral Particle)
spectrum
a
spectrum
neutron
Fig. 12. Calculated
source
using
Alcator
C
distributed
code
position
is
for
13.
Qualitative
for
the
50 cm
the
MCNP
geometry.
from the plasma,
a
from
resulting
at
(Monte
The
a diagnostic
port.
Fig.
effect
of
the
pulse
amplifier
shaping
time
Page 37
were
Spectra
constant.
with a
taken
2.42 MeV and an energy dispersion of about 50 keV
beam on
deuteron
deuterated titanium
a
energy
source
neutron
140
a
using
The gain
target.
of
keV
of the
amplifier varies with the time constant.
14.
Fig.
the peak FWHM normalized to the 8 psec time constant
of
width
the
The effect of the source width (-50
case.
constant on
of the amplifier time
Quantitative effect
keV) has not been removed
and is roughly equal to the detector resolution
isec case.
for the 8
Fig. 15. Calibration peak and fit due to the Li(p,n)Be reaction.
A thin Li target was used so that the soltrce dispersion is less than
25 keV.
An 8 psec amplifier time constant was used and the
FWHM
=
46 key.
Fig. 16. Neutron spectra.
reaction.
left,
Bottom
Bottom,
of
the
62
discharges
plasma
The small peak in the Li(p,n)Be case is due to an
a single day.
excited state of Be.
that
right,
D(D,n)T
Top, right, a
due to Li(p,n)Be reaction.
sum of 303 plasma discharges.
a
from
Top left, spectrum
neutrons
indicating
Note the similarity of the spectra
from an Alcator plasma are dominated by the D-D
2.45 MeV neutrons.
Fig. 17.
Gaussian
Confidence
the fit
component of the fit.
been used here.
by using
of
the
Standard
values
(one
of a at
for a given o (width)
The method outlined by W.
sigma)
rhe
68%
uncertainty
percent
can
be
confidence
of the
Cash has
obtained
level.
Page 38
Fig.
Ti cases.
18.
Nine channel collapse of peak data for low
Note the greater width for the high Ti case (top)
even in data which has not been corrected for
tion or
is the
system
fit
and
noise.
obtained
The
using
curve
the
on
the
C-statistic
the
high
evident
detector resolu-
low Ti data, (bottom)
minimization, normal-
ized for collapsed data magnitude.
Fig.
19.
Reduced width of the 2.45 MeV fusion peak and corres-
ponding temperature
plotted
determined from
total neutron rate
the
exchange diagnostics.
against
the
central
ion
temperature
and neutral particle
charge
The dotted line shows the expected dependence.
The scale on the right can be used to convert the width to a central
ion temperature.
CP
0-
cr
0
Co
0
O
LU
Eo
cc
C0
-+-
cic
4-Q
-
97Mo
(yn)
96
MO
D (y,n)H and D (e,e',n)D
dR
dEn
D(Dn) 3 He
T(D,n)
Down Scatter of
D- T Neutrons
2I
I
3
4
5Ne
12
I2I
13
I
PFC- 8355
FIGURE 2
I
14 15 16 17
D,
k
He
/
n) ron Energy (MeV)
Neut
D
4
SPECTROMETER ON
SHOT 62
P lasm a
Current
ea k Va I ue
3 7 5 kA
ne Average
D ensity
ak Value
W
O
Ym 3
N eutrons
R elative
S ca le
ALCATOR C
B 8.1 T 6/22/82
....................
..
.
..
... ..
..
...
..
....
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..
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...
..
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.
.
..
.
I
.
..
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.
..
..
..
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.
.
...
.
..
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...
........
........
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..............
............................
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......................
....................
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....................
......................................................
.......
....
...........................................
..
..
..
....
.....
..
..
...
...
....
...
..
....
.,*...
........................................
.........................
.....
..
..
..
...
......
...
...
....
........................................
..............
..........
.............
....................................
...................... ..................
..........................
X.
.................
1:,.*.,.,.,.*.,......-.-.-.-.-..........-....-,...,............,
...
.
..
...
.
.
..
...
..
..
..
...
....
..
.
...
..
..
......
........................................
....... .............
....................
.......................................
...
...
...
...
...
.*.....
...
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..
..
..
....
............
........
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..............
..........................
...................
.....
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..
....
......
. .................
.............
. .....
............
...............
........................................
............
........................................
..
......................................
....
.....................
....................
...........................
....................
'7*:*7 --7--
'7 .-7
(155)
(355)
TIME (msec)
PFC-8118
FIGURE 3'
d Rate/ d radius for qlim 3
I
4
C
0
4-
Ti (r)
a)
4-
-o
0
2
I-
11
-.
20
15
10
5
plasma radius (cm)
1.0
Neutron Spectrum for qlim 3
0
0
10
C:
CL)
0
0.I
0.0
0
20
40
width
60
80
100
(keV)
PFC -81/6
FIGURE 4
rs
rf
-
r2,n 2
Before
Crash Tr
N=T ( ) et
2
Ti (0)
(16.5)
-1.5
at
qo
fT (0)
-- Af ter
Crash
0
f lat Profile Out
to rf, magnitude fTi(0)
Plasma Minor Radius
PFC - 8355
FIGURE 5a
dRate /d radius for qlim 3.95
I
I
I
10
15
41
C:
0
0
:3
-0
0
4-
0
a::
2
L..
O
C
5
20
plasma radius (cm)
Neutron spectrum qlim 3.95
80
4-
C
0
0
-o
0
'I) 0
4-
C-)
0
0.
'C
w
a::
60
40
-
-
20
0'
C
20
40
60
80
100
width (keV)
PFC
FIGURE 5b
-
6352
E0
.0-0
00
-oo
-o
E
ta.
0
qJ
*0
0)
VIhm
0.4-to
W>h
~~0
4-
0
.
plm
0
'0
0
C,
0)
0)
a::
w
0
w
z
z
L)0I
CL
a-
aa-
U)
Ul)
w
(0
w
0
0
0
z
_I__LU
o
w
a-
Li
C)
-z
11
________________________
(9
a-.
w
a.-
--IT
U)
z
0
D
0-
a:
w
z
w
Q9
T
LL
0
w H
.:i
1.2
2.4
-n
0
2.0
r
0.9
0.8.
E
S-1.6
1.2
uj 0.6:11
*5-0.0
ijO0.3
0
00
0
0.2 - Relative
0
1ii1
1
11
.
0.4
0
Efficiency
1
-
0
1
11
1
1
1
101
2000 3000
NEUTRON ENERGY (keV)
1000
PFC-81/3
FIGURE 9
0
0
1
1000
Thermal Peak
800
Pulser Peak
+20
+20
<600 -
4-HORci
He 3 Recoil
Full Energy
Peak
0 400
Proton
200 -20
0
Recoil
500
1000
1500
Channel
PFC- 8354
FIGURE 10
2000
w
><
c
0
cr
(D
z
z
w
(\j
w
'4-
-LJ
y
i-
(I)
z
-J
0
D
i0
C,)
4
(1)
I
WL
z
D
-J
>0 0
--N
(9I
IE
hLL
J
z
LJJ
LL.
II
II
E
<
II
wEw
F- q
-
II
w
0
II
C')
II
Sa:z w
T
w
cn
It
0-
w
cc
z
aw
a:
CL
10-
7
-
I
io- 8-
Z)
-I
II
0 0.01 0.1
I
4.-
2.3 2.35 24 2.45
1.0
MeV
FIGURE 12
PFC-8350
120
,
140
100
- 8 /isec
120
100
U) 80
F-
z
80
60-
60
0 400
40
1250
20-
1
20
0
120
0
120
I
100-
4 psec
-
4 /.sec
100
5sec
(n 80-
80
z
60 7
40
60-
0 400
20
20
0.
1050
-I
1250
1150
CHANNEL
1350
0
1050
1250
1150
CHANNEL
1350
PFC-8/22
FIGURE 13
I
I
@4 - N~
~4.
04
00
C)
.4.
.4
4.
4
co
rNO00
HIGIM BAIiV-1JH
wi
LL-
I
600
1
.
Li (p,n) Be
500400300
46 keV FWHM
200100
0
2300
2350 2400 2450 2500 2550
NEUTRON ENERGY(keV)
PFC-8/55
FIGURE 15
0~
U)cI
co
0
U)
0
0
E
00
0
0
0O
-
0
0
cc
-0
0
00
roC0
SI~noo
0
1.0
*
ILjj 0.8
-*
0
z
wOi .6
0z 0
zO4
.0
--
0
*
00
0
_
0
0
18
19
0
15
16
17
20
21
22
23
o- IN CHANNELS
PFC -8/24
FIGURE 17
24
40
I
I
I
30H
C
Co
0
20
I
C)
10
-IF~
0
2200
50
I
2400
0
0
30
/
20
74
10
"II
m4f 1<
0
2200
Thml~b
2600
I
i
40H
Co
I
I
2400
Neutron Energy
2600
(keV)
PFC
FIGURE 18
-
6356
o
z
(D
o
--.
I
co
o(
o
o0
K
0
U.
0
N
CL
0
0
0
a)
LU
0
0co
0
0
0
0
(D
Wmi
0 00
N
-0o
(A9M)
o
)
VJHMd
I
oo
o
0
(0
.
00
LqlP!M peoflp98
t-
4-
C
a)
0