Total Plutonium Content Determination in Pressurized-Water Reactor Spent Fuel with the
Differential Die-Away Self-Interrogation Instrument
Alexis C. Kaplan1,2, Vladimir Henzl2, Anthony P. Belian2, Martyn T. Swinhoe2, Howard O. Menlove2, Marek
Flaska1, Sara A. Pozzi1
1
Department of Nuclear Engineering and Radiological Sciences, University of Michigan,
500 S State St, Ann Arbor, MI 48109, USA
2
Los Alamos National Laboratory, P. O. Box 1663, Los Alamos, NM 87544, USA
Abstract
The Differential Die-away Self-Interrogation (DDSI) technique for nondestructive spent fuel assay is
studied as a part of the Next Generation Safeguards Initiative project. DDSI is a passive neutron coincidence
counting technique that utilizes neutrons primarily from spontaneous fission in an assayed spent fuel
assembly (SFA) to preferentially interrogate its fissile material content. Previously, we have demonstrated by
means of high fidelity neutron transport simulations the ability of the DDSI instrument to evaluate SFA
multiplication with relatively high accuracy. Applying a recently developed concept that correlates SFA
multiplication and passive neutron count rate with total plutonium content in the SFA and first tested in
simulation space with the differential die-away instrument, we also demonstrate in this paper that with the
DDSI instrument the total elemental plutonium content can be determined with a similarly high accuracy.
The results are tested against 44 simulated SFAs from Spent Fuel Library 2a with varying initial enrichment,
burnup, and cooling time. Total Pu content is determined with a standard deviation of 2.1%, discounting
possible real life measurement errors, with respect to its true content as defined in the simulation input files.
1. Introduction
The Next Generation Safeguards Initiative Spent Fuel project (NGSI) has investigated 14 nondestructive
assay techniques over the past 5 years [1]. The techniques have been down-selected based upon simulation
results and ability to meet the needs of the international safeguards community. One of the final techniques
that have proceeded to the building stage of development is the Differential Die-Away Self-Interrogation
(DDSI) instrument. DDSI is a passive neutron coincidence counting technique that utilizes neutrons
primarily from spontaneous fission (SF) in the assayed spent fuel assembly (SFA) to preferentially
interrogate its fissile material content [2]. Coincidence counting data are collected in list-mode in order to
construct and utilize a Rossi-alpha distribution (RAD) for SFA characterization. In our previous work, we
have demonstrated by means of high fidelity neutron transport simulations the ability of the DDSI instrument
to evaluate SFA multiplication with high accuracy; i.e. within ~0.8% [3].
A novel concept that allows for determination of total elemental plutonium content (mPu) through its
universal correlation with SFA multiplication (M) and passive neutron count rate (PN) was recently
developed and first tested in simulation space with another instrument developed within NGSI-SF [4]. This
instrument is based on the Differential-Die-Away (DDA) NDA technique [5] and, unlike DDSI, relies on
active interrogation of the SFA performed by an external neutron generator. Within this paper, we adopt the
same concept, but adapt it with respect to DDSI capabilities, and demonstrate that even with the passive
interrogation-based DDSI instrument mPu can be determined in simulation space with a similarly high
accuracy.
While the method was originally tested with DDA on a variety of SFAs from Spent Fuel Library 1
(SFL1), in this work it has been tested against 44 simulated SFAs from Spent Fuel Library 2a (SFL2a) [6].
Although the difference between the two spent fuel libraries is rather subtle in terms of the fissile content, the
variation in the spontaneous fission rates is rather substantial (see section “Simulations” for details) primarily
due to different relative content of the main SF contributors such as 244Cm and 240Pu. In the simulations
within this paper, mPu was determined with standard deviation of 2.1% with respect to its true content as
defined in the simulation input files. The current results are qualitatively nearly identical to those obtained
previously for the DDA instrument and tested against a different set of SFAs, thus demonstrating the
1
robustness of the method. This apparent robustness in the simulation space makes it a promising technique
for experimental verification which, however, will be the ultimate test of the method. Within this work, we
limit ourselves to discussing the principles of operation of the DDSI instrument and total Pu determination
and present simulation results for determining plutonium content in SFL2a assemblies.
2. DDSI Instrument and its response
The simulated DDSI instrument consists of four modules, each with 14 3He detectors embedded in highdensity polyethylene (density of 0.96 g/cm3). The detectors have a 2.54 cm diameter, 40.0 cm active length,
6 atm pressure, and are each coupled to a pre-amplifier. A conceptual, cross-sectional view of the simulated
instrument is shown in Fig. 1.
Fig. 1. Cross-sectional view of the simulated
DDSI instrument.
During the envisioned assay, the SFA is lowered into the center of the instrument inside the spent fuel
pool and data are collected with both a list-mode and shift-register acquisition system. When data are
collected in the list-mode, the time of capture of every neutron in any of the 56 detectors is recorded. SF is
abundant in SFAs, primarily because of the presence of 244Cm. However, in the case of SFAs with high
cooling time (CT) and low burnup (BU), spontaneous fission of 240Pu may be the most prominent contributor
together with neutrons from (α,n) reactions initiated mostly by significant presence of 241Am. The relatively
short half-lives of Cm isotopes result in this shift of individual isotope relative contribution as a function of
CT. SF and (α,n) neutrons thermalize in the surrounding water and re-enter the fuel pins to induce additional
fissions preferentially on the fissile isotopes such as 235U, 239Pu, and 241Pu. The preferential interrogation is
the direct result of the thermal neutron induced fission cross sections, as shown in Fig. 2 [7].
2
Fig. 2. Induced fission cross sections as a function of
incoming neutron energy for some of the most abundant
isotopes in SFAs. Fissile isotopes, 235U, 239Pu, and 241Pu are
preferentially interrogated by thermal neutrons, the energy of
which is indicated with the dashed line. [7]
Depending on the multiplication of the SFA, which reflects its isotopic composition, fission chains of
various length and multiplicity will develop. While the rise and fall, i.e. die-away, of the neutron subpopulation in the fission chain induced by any individual SF or (α,n) reaction cannot be measured on a caseby-case basis, various aspects of the evolution of the entire neutron population can be determined utilizing
list-mode-based neutron coincidence counting techniques. The time of detection of each neutron is recorded
in list-mode data collection and an algorithm is implemented to produce the RAD, which is essentially a
histogram of times between the detections of any two neutrons in a pre-defined time window. In the
algorithm, the time of detection of the first neutron is treated as the trigger, and the time difference between
the trigger and any subsequent neutron in a pre-defined time window is added to the histogram. Then the
second neutron detection time becomes the trigger, and the process repeats. In this work, we use a time
window of 250 μs which is approximately three times as long as the typical die-away time observed in
simulated SFAs. This ensures that the majority of the RAD dynamic evolution is recorded and not lost by
ending the distribution prematurely. In actual measurements, the majority of this distribution consists of
accidental coincidences, defined as neutrons arriving in the time window after the trigger that are not from
the same fission or fission chain as the trigger neutron.
The RAD allows us to quantify real and accidental coincidences among neutrons as well as to observe
the die-away (and its possible dynamic evolution) of the neutron population. In the context of traditional
neutron coincidence measurements, the die-away time describes the decrease of the neutron population over
time and is typically represented by a single exponential [8].
However, due to thermalization of neutrons inside the sample, which is typically undesirable and absent
in traditional neutron coincidence counting approaches, but is necessary for self-interrogation, the real
correlation between two neutrons exhibits two distinctive modes. The first mode – fast correlation – is a
result of correlation between neutrons from the same fission event, be it spontaneous or induced fission (IF),
where the neutrons have not been moderated to thermal energies. The second mode – slow correlation – is a
result of correlation among neutrons from different fission events but within the same fission chain that have
undergone the thermal-neutron scattering time delay. The fast correlation reflects the difference in detection
times between two neutrons created in the same event, and is thus limited by the characteristic time of 3He
based neutron detectors. The slow correlation reflects the difference in detection times between two neutrons
from two subsequent fission events separated possibly by tens or even hundreds of µs due to the time
3
required for a neutron from one fission event to thermalize outside of the pin, re-enter it, or even enter
another pin and induce another fission event. As a consequence, the RAD distribution reflects both of these
correlations, each with a significantly different characteristic time constant. The sum of two exponentials
provides a sufficiently accurate description of the RAD obtained from the simulated response of the DDSI
instrument when assaying SFAs in an essentially deadtimeless mode:
( )
⁄
⁄
(1),
where N(t) is the neutron population at time t, Nfast is the initial population which will be detected in the fast
correlation mode, and Nslow the initial population that will be detected in the slow correlation mode. τfast then
represents the mean lifetime (i.e. die-away time) of an individual detected neutron in the system, while τslow
represents the mean lifetime of the entire neutron subpopulation (that consists of multiple neutron
generations [3]). The interplay of these two quantities is in the early die away time, τearly, defined as the dieaway time of a single exponential fit of the early time domain of the RAD from 4-52 μs [3]. Figure 3 is an
example of a RAD constructed from the simulated DDSI instrument response with the fast and slow
components, as well as early die-away time displayed, and accidental coincidences excluded.
Fig. 3. An example of an RAD from simulated assay of
a SFA with BU of 30 GWd/tU, 5% IE, and 5 y CT. The
two additive single exponentials - the fast and slow
components - are displayed along with the early dieaway fit.
3. Theoretical principles of determining the total Pu content
In the work of Henzl et al. [4], the total plutonium content within an assembly is found to be related to
the SFA multiplication and the detected total neutron count rate provided the CT is known or constant within
the ensemble of the SFAs that are being assayed (e.g. all SFAs from the same reactor discharge). The
multiplication reflects the competition between the fissile content and the amount and composition of the
neutron absorbers (fission products and minor actinides). It is implicitly defined by the SFA characteristic
parameters such as IE, BU, and CT. The total neutron emissions, however, reflect mass content of major
spontaneous fission isotopes in the assembly including 242Cm, 244Cm, and 240Pu, as well as the main
contributors to neutron production via (α,n) reaction (e.g. 241Am). Since the majority of these isotopes are
produced by processes that include one or more neutron captures on individual Pu isotopes, their content, and
thus the neutron emission rate, is closely correlated to the total content of elemental plutonium (i.e. mPu ) [9].
Visual representation of various production modes of individual actinides in the process of nuclear burning is
displayed in Fig. 4.
4
Fig. 4. Visual representation of the most significant actinide production modes in the spent
nuclear fuel. (Note: The alpha decay is omitted in order to focus on production of the
heaviest actinides).
In this work, we ultimately utilize the eq. (16) from [4] relating the neutron emission rate (NE),
multiplication (M), and total plutonium mass (mPu):
(
(
)(
) [(
)
)
]
(2),
with a, b, and c being instrument dependent calibration parameters, which in case of a and b may also be
functions of CT. However, as the authors of [4] modified equation (2) to include quantities measurable by the
DDA instrument (eq. (20) in [4]), we modify the same equation to include only quantities directly
measurable by the DDSI instrument. In [3] we reported our finding that the die-away time of the early time
domain (30-80 µs) of the RAD of the DDSI instrument’s response is quadratically related with the SFA
multiplication as shown in Fig. 5.
Multiplication
4.5
4.0
y = 1.82E-04x2 + 2.64E-02x + 6.38E-01
3.5
3.0
2.5
2.0
1.5
30.0
40.0
50.0
60.0
70.0
Early Die-away Time [μs]
80.0
90.0
Fig. 5. Multiplication as a function of early die-away time (τe) for 44
SFL2a assemblies. The correlation is nearly linear allowing us to use
τe in place of M to create a function only in terms of quantities
measurable with DDSI.
In the case of the DDSI instrument the singles rate (S) is identical to passive neutron count rate used in
[4], and through a simple relation with M it is then directly representative of the NE term in eq. (3):
⁄(
)
(3),
where ε is the system efficiency. Now eq. (3), i.e. the expression for determination of mPu, can be rewritten
using only quantities directly measurable by the DDSI instrument as follows:
5
(
(
)
(
)
)
(4),
where d, f, g, and h are the calibration parameters which depend on the instrument design, and in case of d
and f also on CT. It is assumed that the efficiency is included in the d parameter. Rather than expressing M
explicitly as a second order polynomial function of τe as in Fig. 5, τe alone is used instead while the calibration
constants from the polynomial are accounted for with constants g and h.
4. Simulations
All simulations were conducted with MCNP v2.7.0 [10]. Simulated RADs are created using the F8
capture type tally in which only the real coincidences can be counted and therefore accidental ones are not
included in the simulated distributions. During the simulations, the F8 capture tallies are established in
sequence with increasing pre-delay and constant gate width in order to find how many neutrons following a
trigger arrive within the time window, and when they arrived. SFAs are defined on a pin-wise basis from
material definitions developed as part of the NGSI-Spent Fuel project [6]. We simulate 44 pressurized-water
reactor assemblies from SFL2a with IE varying between 2-5%, BU varying between 15-60 GWd/tU, and CT
varying between 5-80 years. The SFAs are 17x17 assemblies with one radial region tracked through a 1/8
core using Monteburns to track isotopic changes through the burning process [6, 11]. In contrast, SFL1
which was used to simulate total Pu determination for DDA is based on infinitely reflected PWR assemblies
with four radial fuel regions simulated using MCNP burnup. The IE and BU ranges are the same as SFL2a,
however the cooling times used are 1, 5, 20, and 80 years. Due to the different simulated burning conditions
in SFL1 and SFL2a, even two SFAs with identical IE, BU and CT have generally different isotopic
composition. For most of the isotopes the absolute differences are however rather subtle with the most
prominent difference being the content of 244Cm that is up to 50% higher in SFL1 than SFL2a. Besides the
different burning conditions, the main reason for this apparent discrepancy is the choice of reaction crosssections that lead to production of 244Cm. The different content of 244Cm among the two libraries results in
differing relative contributions of individual isotopes in the total passive neutron signal and also influences
its absolute magnitude. The contributions of individual isotopes are summarized in Table I. This is
significant for the simulation of DDA and DDSI where the strength of the SF sources, as well as the
additional contribution by the (α,n) reaction dictates the frequency of fission chains and thus the measured
signal.
6
Table I. Comparison of relative contributions of the most important isotopes to the total passive neutron signal as
defined by the material composition of individual SFAs in SFL2a and SFL1.
BU
[GWd/
tU]
15
15
15
15
30
30
30
30
45
45
60
15
15
15
15
30
30
30
30
45
45
60
15
15
15
15
30
30
30
30
45
45
60
15
15
15
15
30
30
30
30
45
45
60
15
15
15
15
30
30
30
30
45
45
60
IE
[%]
CT
[y]
2
3
4
5
2
3
4
5
4
5
5
2
3
4
5
2
3
4
5
4
5
5
2
3
4
5
2
3
4
5
4
5
5
2
3
4
5
2
3
4
5
4
5
5
2
3
4
5
2
3
4
5
4
5
5
1
1
1
1
1
1
1
1
1
1
1
5
5
5
5
5
5
5
5
5
5
5
20
20
20
20
20
20
20
20
20
20
20
40
40
40
40
40
40
40
40
40
40
40
80
80
80
80
80
80
80
80
80
80
80
238
Pu
[%]
na/0.9
na/1.7
na/2.8
na/3.3
na/0.3
na/0.5
na/0.8
na/1.1
na/0.4
na/0.6
na/0.3
1.8/1.4
3.6/2.8
5.1/4.4
6.8/6.1
0.4/0.4
0.8/0.7
1.3/1.1
1.8/1.7
0.6/0.5
0.9/0.7
0.5/0.4
2.3/2.0
4.2/3.6
5.4/5.1
6.6/6.6
0.6/0.6
1.2/1.0
1.9/1.7
2.6/2.5
0.9/0.8
1.3/1.1
0.8/0.6
3.1/na
4.5/na
5.4/na
6.2/na
1.1/na
2.0/na
3.1/na
4.0/na
1.5/na
2.3/na
1.4/na
3.7/4.3
4.2/5.1
4.7/5.6
5.1/6.0
2.6/2.7
4.3/4.4
5.9/6.0
6.7/7.5
3.8/3.7
5.3/5.1
3.7/3.0
239
Pu
[%]
na/0.4
na/0.9
na/1.5
na/2.4
na/0.0
na/0.1
na/0.1
na/0.2
na/0.0
na/0.0
na/0.0
1.0/0.6
2.6/1.4
4.1/2.8
5.8/4.4
0.1/0.0
0.1/0.1
0.2/0.2
0.4/0.3
0.0/0.0
0.1/0.0
0.0/0.0
1.4/0.9
3.3/2.1
4.9/3.6
6.4/5.3
0.1/0.1
0.2/0.1
0.4/0.3
0.6/0.4
0.1/0.1
0.1/0.1
0.0/0.0
2.2/na
4.1/na
5.8/na
7.0/na
0.2/na
0.4/na
0.7/na
1.0/na
0.1/na
0.7/na
0.1/na
3.6/3.2
5.4/4.8
6.9/6.4
7.9/7.9
0.6/0.5
1.1/0.9
1.9/1.5
2.4/2.1
0.5/0.4
0.9/0.6
0.3/0.2
240
Pu
[%]
na/3.5
na/6.0
na/8.7
na/11.3
na/0.4
na/0.7
na/1.0
na/1.4
na/0.3
na/0.4
na/0.2
9.1/5.4
18.4/10.2
23.4/15.6
29.1/20.8
0.8/0.5
1.5/0.9
2.4/1.5
3.1/2.1
0.5/0.4
0.9/0.5
0.4/0.2
13.5/8.6
23.6/14.6
27.8/20.7
31.8/25.4
1.3/0.9
2.5/1.6
4.0/2.5
5.1/3.6
1.0/0.6
1.6/0.9
0.7/0.3
20.8/na
30.0/na
32.7/na
34.9/na
2.7/na
4.9/na
7.5/na
9.3/na
2.0/na
3.1/na
1.3/na
34.2/29.0
38.4/33.8
38.9/36.2
39.1/37.2
9.3/6.7
14.6/10.3
19.0/14.2
21.1/17.3
6.8/4.8
10.1/6.5
4.8/2.6
242
Pu
[%]
na/0.6
na/0.7
na/0.7
na/0.7
na/0.2
na/0.2
na/0.3
na/0.3
na/0.1
na/0.1
na/0.1
1.4/0.9
1.9/1.1
1.9/1.3
2.0/1.4
0.3/0.2
0.4/0.3
0.5/0.4
0.6/0.4
0.2/0.2
0.3/0.2
0.2/0.1
2.1/1.4
2.5/1.7
2.2/1.7
2.1/1.7
0.5/0.4
0.7/0.5
0.9/0.6
1.0/0.7
0.4/0.3
0.5/0.3
0.3/0.2
3.2/na
3.2/na
2.6/na
2.4/na
1.0/na
1.4/na
1.7/na
1.8/na
0.9/na
1.0/na
0.6/na
5.2/4.7
4.1/3.8
3.1/3.1
2.7/2.5
3.6/2.6
4.2/3.2
4.2/3.5
4.1/3.5
2.7/2.0
3.2/2.3
2.1/1.3
241
Am
[%]
na/0.3
na/0.4
na/0.6
na/0.8
na/0.0
na/0.1
na/0.1
na/0.2
na/0.0
na/0.1
na/0.0
2.2/1.4
4.5/2.7
5.8/4.2
7.3/5.5
0.2/0.2
0.4/0.3
0.8/0.5
1.0/0.8
0.2/0.1
0.3/0.2
0.1/0.1
9.2/6.3
16.2/10.9
19.3/15.2
22.2/18.5
1.0/0.7
2.0/1.4
3.4/2.3
4.5/3.5
0.8/0.6
1.4/0.9
0.6/0.3
19.0/na
27.7/na
30.5/na
32.8/na
2.62/na
5.16/na
8.49/na
10.8/na
2.2/na
3.8/na
1.6/na
33.8/30.7
38.4/36.4
39.4/38.7
39.9/39.6
9.7/7.7
16.7/13.1
23.4/19.0
27.0/24.2
8.2/6.3
13.3/9.3
6.1/3.6
242
Cm
[%]
na/23.0
na/29.8
na/34.5
na/37.2
na/8.9
na/13.3
na/17.8
na/21.8
na/8.9
na/11.7
na/6.6
0.1/0.1
0.1/0.1
0.1/0.2
0.2/0.1
0.0/0.0
0.1/0.0
0.1/0.1
0.1/0.1
0.0/0.0
0.0/0.0
0.0/0.0
0.0/0.0
0.0/0.0
0.1/0.0
0.1/0.0
0.0/0.0
0.0/0.0
0.0/0.0
0.0/0.0
0.0/0.0
0.0/0.0
0.0/0.0
0.03/na
0.05/na
0.06/na
0.07/na
0.01/na
0.02/na
0.04/na
0.05/na
0.02/na
0.03/na
0.01/na
0.1/0.0
0.1/0.0
0.1/0.0
0.1/0.0
0.0/0.0
0.1/0.0
0.1/0.0
0.1/0.0
0.1/0.0
0.1/0.0
0.0/0.0
244
Cm
[%]
na/67.8
na/56.1
na/46.2
na/38.6
na/88.4
na/83.0
na/77.2
na/71.7
na/88.4
na/85.1
na/90.9
84.1/90.0
67.8/81.4
58.3/71.4
47.0/61.3
97.6/98.1
96.3/97.3
94.2/96.1
92.6/94.5
97.6/98.1
96.9/97.7
97.8/97.1
70.8/80.5
49.1/66.7
39.0/53.3
29.0/42.1
95.4/96.4
92.6/94.8
88.6/92.2
85.5/89.0
95.6/96.4
94.0/95.7
96.0/96.5
50.7/na
29.1/na
21.4/na
14.8/na
90.3/na
84.6/na
77.2/na
71.9/na
90.8/na
87.6/na
91.7/na
18.1/27.4
8.1/15.4
5.5/9.4
3.6/6.3
67.1/72.3
54.8/63.6
42.6/53.2
35.9/43.6
68.7/73.2
61.2/69.4
71.3/74.3
246
Cm
[%]
Other
[%]
na/0.1
na/0.0
na/0.0
na/0.0
na/0.5
na/0.3
na/0.2
na/0.1
na/0.6
na/0.4
na/0.9
0.1/0.1
0.1/0.1
0.0/0.0
0.0/0.0
0.5/0.6
0.3/0.4
0.2/0.3
0.2/0.2
0.7/0.7
0.4/0.5
0.9/1.1
0.1/0.2
0.1/0.1
0.0/0.0
0.0/0.0
0.9/1.0
0.6/0.7
0.4/0.5
0.3/0.3
1.2/1.3
0.8/0.9
1.5/2.0
0.20/na
0.09/na
0.04/na
0.02/na
1.89/na
1.12/na
0.70/na
0.53/na
2.39/na
1.52/na
3.06/na
0.3/0.6
0.1/0.2
0.1/0.0
0.0/0.0
6.5/7.6
3.3/4.4
1.8/2.6
1.2/1.6
8.3/9.5
4.9/6.7
10.9/14.9
na/3.5
na/4.5
na/5.2
na/5.7
na/1.3
na/2.0
na/2.7
na/3.3
na/1.3
na/1.7
na/1.0
0.4/0.1
0.9/0.2
1.3/0.3
1.8/0.4
0.1/0.0
0.2/0.0
0.3/0.0
0.4/0.0
0.1/0.0
0.2/0.0
0.1/0.0
0.6/0.1
1.1/0.2
1.4/0.3
1.8/0.4
0.1/0.0
0.3/0.0
0.4/0.0
0.5/0.0
0.2/0.0
0.3/0.0
0.2/0.0
0.8/na
1.2/na
1.5/na
1.8/na
0.2/na
0.4/na
0.7/na
0.8/na
0.3/na
0.5/na
0.3/na
1.1/0.3
1.3/0.4
1.7/0.5
1.6/0.6
0.6/0.1
1.0/0.1
1.3/0.1
1.5/0.2
0.8/0.1
1.1/0.1
0.8/0.2
7
5. Results
Simulated results for individual SFAs from SFL2a are divided according to CT to produce four
calibration curves for 5, 20, 40, and 80 year CT assemblies. The parameters d and f are determined from the
best fit of each curve, and the constants g and h are determined as the best fit for all assemblies according to
eq.(4). Known mPu from MCNP definitions of each assembly is used along with τe, as determined from a fit
to the RAD. Therefore in an actual measurement, the mPu can be determined using only the measurable
quantities, τe and the singles rate, and a pre-established calibration curve.
When plotted on a log-log graph, the power function data forms a straight line when the proper values of
g and h are used. The values of g and h were determined to provide the best fit for SFL2a data. As in the
DDA result, g is approximately equal to 2h and this substitution could be made to simplify the equation if
there is tolerance for a small loss of accuracy. The power function for each cooling time is shown in Fig. 6.
5y
1.0E+06
S(τ+g)
1.0E+08
40 y
1.0E+03
1.0E+04
1.0E+03
1.0E+04
1.0E+04
mPu(τ+h)/(τ+g)
1.0E+04
y = 511.61x0.1572
R² = 0.9981
y = 439.33x0.1707
R² = 0.9983
1.0E+06
S(τ+g)
1.0E+08
80 y
mPu(τ+h)/(τ+g)
1.0E+03
1.0E+04
20 y
mPu(τ+h)/((τ+g)
1.0E+04
mPu(τ+h)/(τ+g)
1.0E+04
y = 353.4x0.1914
R² = 0.9978
1.0E+06
S(τ+g)
1.0E+08
1.0E+03
1.0E+04
y = 193.72x0.2476
R² = 0.99
1.0E+06
S(τ+g)
1.0E+08
Fig. 6. Simulated results for SFAs from SFL2a plotted separately for individual CT values to determine
calibration parameters d, f, g and h.
When eq. (4) for the total plutonium content is applied to 44 SFL2a SFAs using the four sets of
calibration parameters, the standard deviation with respect to the true total plutonium content is 2.1%.
However, the accuracy of the result can be improved to 1.5% should we limit the simulations to SFAs with
CT≤40 y. As shown in Fig.1 in [4], the likely reason for worse agreement in case of the SFAs with CT = 80
8
years is the different functional dependence of total neutron count rate on the total Pu content where rather
than power-like relation a logarithmic dependency may be more appropriate for description. Figure 7 shows
the relative difference between total Pu content determined based on eq. (4) and the true mPu values as a
function of the actual Pu content.
15%
Increasing BU
∆mPu[%]
10%
5%
0%
-5%
-10%
-15%
2000
3000
4000
mPu [g]
5000
6000
Fig. 7. Relative difference between the actual total Pu content and the one
determined based on eq.(4) as a function of the actual Pu content.
700
0.30
Calibration parameter,
unitless
Calibration parameter,
unitless
Despite the different material composition of individual SFAs in SFL2a and SFL1, the accuracy of the
mPu determination is very similar in the case of the DDSI instrument in the current study as it’s been in case
of the DDA instrument in [4]. In addition, the calibration parameters d and f both display a similar trend to
those obtained from the DDA instrument based study as shown in Fig. 8. While the values of d show the
same general trend as its counterpart for the DDA instrument a from eq. (20) in [4], these parameters
encapsulate the instruments’ efficiencies and are therefore expected to be different in magnitude. The value
of DDA calibration parameters seems to reverse the trend at low cooling times and the same may be true for
DDSI ones. However, due to different range of CT explored in this study the reversal of the trend in case of
the DDSI calibration parameters cannot be verified. In case of the calibration parameter f, its absolute values
seem to be very similar to b (also from eq. (20) in [4]) because these parameters reflect the physics of the
total Pu method that is based on the power relation between the total Pu content and the total passive neutron
count rate. This further supports the notion of universality of the method and makes it promising for
extension to other NDA techniques that are capable of measuring the SFA multiplication and its passive
neutron count rate.
600
0.25
500
400
0.20
300
200
0.15
100
0.10
0
1
10
Cooling Time [years]
100
1
10
Cooling Time [years]
100
Fig. 8. Comparison of values of individual calibration parameters for DDSI and DDA instrument (from [4]) and their
dependency on CT.
6. Conclusions
9
Inspired by a recently formulated concept that relates multiplication and passive neutron count rate to
total plutonium content in a spent fuel assembly we demonstrate that such concept can be adopted for the
DDSI instrument as well. The method is applied to 44 PWR assemblies in simulation space with varying IE,
BU, and CT from SFL2a. The early die-away time, as a measure of multiplication, is used in conjunction
with the singles rate to determine total plutonium content with an RMS error of 2.1% discounting any
possible errors from a real-life measurement. The results were qualitatively as well as quantitatively similar
to those obtained previously by simulation of an active interrogation based DDA technique tested against a
different SFL, providing further evidence of the robustness of the method.
7. Acknowledgements
This material is partially based upon work supported by the U.S. Department of Homeland Security
under Grant Award Number, 2012-DN-130-NF0001-02. The authors also would like to acknowledge the
support of the Next Generation Safeguards Initiative (NGSI), Office of Nonproliferation and International
Security (NIS), National Nuclear Security Administration (NNSA). The views and conclusions contained in
this document are those of the authors and should not be interpreted as necessarily representing the official
policies, either expressed or implied, of the U.S. Department of Homeland Security or the National Nuclear
Security Administration. LA-UR-13-29465.
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10