U.S. patent application number 15/069375 was filed with the patent office on 2016-09-15 for neutron spectrometer.
This patent application is currently assigned to MERRILL CORPORATION. The applicant listed for this patent is MERRILL CORPORATION. Invention is credited to Reinhard M. KLAASS, David M. SLAUGHTER.
Application Number | 20160266264 15/069375 |
Document ID | / |
Family ID | 47215772 |
Filed Date | 2016-09-15 |
United States Patent
Application |
20160266264 |
Kind Code |
A1 |
SLAUGHTER; David M. ; et
al. |
September 15, 2016 |
NEUTRON SPECTROMETER
Abstract
A neutron spectrometer that is more accurate, faster, and
more-portable than conventional spectrometers includes an organic
scintillator responsive to neutrons and gammas and an inorganic
scintillator that captures neutrons. A processor receives signals
representative of scintillations in the organic scintillator and in
the inorganic scintillator and discriminates neutron signals from
gamma signals. The processor also determines pulse areas for
neutron moderating signals and performs unfolding based on the
determined pulse areas to produce a neutron energy spectrum and/or
dose information.
Inventors: |
SLAUGHTER; David M.; (Salt
Lake City, UT) ; KLAASS; Reinhard M.; (Provo,
UT) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
MERRILL CORPORATION |
Clearfield |
UT |
US |
|
|
Assignee: |
MERRILL CORPORATION
Clearfield
UT
|
Family ID: |
47215772 |
Appl. No.: |
15/069375 |
Filed: |
March 14, 2016 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
13665027 |
Oct 31, 2012 |
9316753 |
|
|
15069375 |
|
|
|
|
61628474 |
Nov 1, 2011 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01T 3/001 20130101;
G01T 3/065 20130101 |
International
Class: |
G01T 3/06 20060101
G01T003/06; G01T 3/00 20060101 G01T003/00 |
Claims
1. A neutron detector comprising: an organic moderator; an
inorganic scintillator, comprising lithium gadolinium borate, that
captures neutrons; a processor which (1) receives signals
representative of scintillations in the inorganic scintillator and
identifies signals resulting from capture in gadolinium and
discriminates the signals resulting from capture in gadolinium from
other signals; and (2) using the signals that were identified as
resulting from capture in gadolinium and that were discriminated
from other signals to generate and output data of neutrons incident
on the neutron detector.
2. A neutron detector as set forth in claim 1, wherein the
inorganic scintillator comprises cerium or any other activator.
3. A neutron detector as set forth in claim 1, wherein the
processor identifies signals resulting from capture in gadolinium
and discriminates the signals from other signals based at least on
pulse shape.
4. A neutron detector as set forth in claim 1, wherein the
processor identifies signals resulting from capture in gadolinium
and discriminates the signals from other signals based at least on
pulse area.
5. A neutron detector as set forth in claim 1, wherein the
processor identifies signals resulting from capture in gadolinium
and discriminates the signals from other signals based at least on
pulse length.
6. A neutron detector as set forth in claim 1, wherein the
processor identifies signals resulting from capture in gadolinium
and discriminates the signals from other signals based at least on
scintillation in the inorganic scintillator.
7. A neutron detector as set forth in claim 1, wherein the
processor identifies signals resulting from capture in gadolinium
and discriminates the signals from other signals based at least on
scintillation in the organic moderator.
8. A neutron detector as set forth in claim 1, wherein the organic
moderator comprises poly-vinyl-toluene or other hydrogenous organic
moderator.
9. A neutron detector as set forth in claim 1, wherein the
processor performs integration to determine areas.
10. A neutron detector as set forth in claim 1, wherein the
processor curve fits decreasing edge data points to calculate a
pulse decay constant.
11. A neutron detector as set forth in claim 1, wherein the
inorganic scintillator comprises Li.sub.6GdB.sub.3O.sub.9:Ce
wherein the inorganic scintillator contains Gd-157.
12. A neutron detector as set forth in claim 1, wherein the
inorganic scintillator comprises
.sup.6Li.sub.6Gd.sup.10B.sub.3O.sub.9:Ce wherein .sup.6Li,
.sup.10B, and .sup.157Gd neutron captures are identified by the
processor by shape characteristic of Ce emission, and .sup.157Gd
captures are processed by the processor through neutron analysis
software.
13. A neutron detector as set forth in claim 1, wherein some gammas
interact with Gd and produce a scintillation, others deposit
collision energy at a Gd site in LGB crystal and produce a Ce
scintillation, which produces pulses that are identified and
separated by the processor.
14. A neutron detector as set forth in claim 1, wherein the
processor receives signals representative of scintillations in the
organic moderator and in the inorganic scintillator, the signals
including signals representative of interactions of neutrons with
.sup.157Gd.
15. A neutron detector as set forth in claim 1, wherein the organic
moderator is a scintillator.
Description
CROSS-REFERENCE TO RELATED PATENT APPLICATIONS
[0001] This application is a divisional application of U.S.
application Ser. No. 13/665,027, filed Oct. 31, 2012, which claims
priority to provisional application 61/628,474, filed Nov. 1, 2011,
whose entire contents are incorporated herein by reference for the
devices, materials, techniques, processing methods, software and
other details related to neutron spectrometry.
BACKGROUND OF THE INVENTION
[0002] The present invention relates generally to the field of
neutron spectrometers. There are many applications where accurate
measurement of neutron energy is needed; for example, to calculate
the exposure of personnel or determine the integrity of radiation
shielding or radiation containment. Unfortunately, current
spectrometers (such as Bonner Balls) have large uncertainties, have
long signal acquisition and processing times, and other
disadvantages.
SUMMARY OF THE INVENTION
[0003] This specification describes the development, design,
operation, and testing of a novel neutron spectrometer/dosimeter
that is compact, efficient, fast, and accurate. Testing at the Los
Alamos Neutron Science Center (LANSCE) and the Edwards Accelerator
Laboratory (EAL) at Ohio University has demonstrated that the
invention can produce neutron spectra over the range between 0.8
MeV and 150 MeV with an uncertainty of only +/-8%.
[0004] This spectrometer is the end result of a development program
that took 12 years, and uses some of the devices, materials, and
techniques described in U.S. Pat. No. 5,231,290, issued in 1993 and
U.S. Pat. No. 5,734,166, issued in 1998. The entire contents of
both of these patents are incorporated herein by reference for the
components, techniques, processes, and materials related to neutron
spectrometry described therein.
[0005] In one embodiment of the present invention, a 1.3 liter
detector head is a heterogeneous composite detector with a
hydrogenous plastic scintillator matrix containing uniformly
distributed lithium gadolinium borate (LGB) microcrystals. Other
materials can be used instead of or in addition to LGB such as
lithium yttrium borate. The physics of the composite detector is
quite complex and extensive research and development was required
to identify and properly characterize all the signals that result
from neutron and gamma interactions with the detector.
[0006] The plastic scintillator acts to slow impinging neutrons and
emits light related to the energy loss as the neutrons moderate in
the detector body. Moderating neutrons that have slowed
sufficiently capture in one of the Lithium, Boron, or Gadolinium
atoms in the LGB, which then releases the capture energy in a
characteristic cerium emission pulse. The light pulse resulting
from the neutron moderating in the plastic scintillator is then
paired with the LGB capture pulse to identify that the moderating
pulse was created by a neutron, and is not a pulse created by a
gamma (a gamma can create a pulse similar to a neutron moderating
pulse).
[0007] Five years of development and testing were required to
demonstrate that the characteristics of the moderating pulse varied
predictably with neutron energy. A test version of the spectrometer
was modified to permit it to record the capture of neutrons at
facilities with time-of-flight (TOF) capabilities. The inventors
were able to identify the energy of each neutron through these
time-of-flight techniques and correlate the energy from the TOF
measurements with the pulse characteristics.
[0008] The inventors discovered that about 2% of the impinging
neutrons lose all of their energy in a single collision with the
detector. There is a linear relationship between the pulse areas of
this group of neutrons and energy. However, the other 98% of
neutrons have a wide range of collision histories within the
detector body. When these neutrons are "binned" into energy groups,
each energy group contains a distribution of pulse areas. This data
was used as the basis for developing an unfolding algorithm for the
spectra. The unfolded spectra were then validated at various
facilities and matched against known spectra, both for common
neutron emitting isotopes and against the facility spectra of the
various institutions that provided a source of neutrons for this
program. Having validated the spectra, the dose equivalent and dose
rate can be determined by applying standard, regulatory damage
coefficients to the measured neutron counts for each energy bin of
the spectra.
[0009] This efficient self-contained neutron spectrometer/dosimeter
will have wide application in health physics, land-based and
sea-based nuclear power plants, scientific research, and programs
to monitor and control nuclear materials and weapons.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 illustrates a neutron spectrometer of one embodiment
of the invention.
[0011] FIG. 2 illustrates the structure of a unit cell of
.sup.6Li.sub.6.sup.natGd.sup.10B.sub.3O.sub.9:Ce with covalent
bonds indicated by bold lines and ionic bonds by thin lines, and
bonds formed by Li atoms not shown.
[0012] FIGS. 3A-3F illustrate typical pulse shapes measured in a
mixed neutron and gamma radiation field.
[0013] FIG. 4 illustrates how neutron-proton collisions in PVT
moderate the neutron energy and how gammas also attenuate in PVT
and LGB and emit pulses.
[0014] FIG. 5 illustrates a proton recoil distribution at 10
MeV.
[0015] FIG. 6 illustrates a signal analysis flow chart that depicts
major analysis steps contained in a neutron analysis software
program of one embodiment of the invention.
[0016] FIG. 7 is a schematic representation of pulse classification
parameters.
[0017] FIG. 8 illustrates a typical neutron analysis program
analysis output in the form of a moderating pulse area
histogram.
[0018] FIG. 9 illustrates a neutron analysis program plot of pulse
characteristic parameters in the form of Lambda vs. area.
[0019] FIG. 10 illustrates how time-to-capture plots can be used to
eliminate accidental pairs.
[0020] FIG. 11 illustrates a Lambda/area plot for a Cf-252
neutron/gamma field.
[0021] FIG. 12 illustrates a Lambda/area plot for a pure gamma
field.
[0022] FIG. 13 illustrates a Lambda/area plot for a Cf-252
neutron/gamma field with gamma rejection.
[0023] FIG. 14 illustrates start (moderating) pulse area plotted
versus neutron energy.
[0024] FIG. 15 illustrates TOF data acquisition of pulses with
parametric definitions.
[0025] FIG. 16 illustrates a typical calibrated response matrix
(CRM) which comprises neutron energy rows and moderating pulse area
columns.
[0026] FIG. 17 illustrates neutron detection efficiencies of a
detector of an embodiment of the invention in the high energy
neutron field at the Los Alamos Neutron Science Facility
(LANSCE).
[0027] FIG. 18 illustrates neutron detection efficiencies of a
detector of one embodiment of the invention in a test at Ohio
University's Edwards Accelerator Lab (EAL).
[0028] FIG. 19 is a flowchart for explaining how a neutron analysis
program according to one embodiment of the invention generates
displays of neutron spectrometer measured results.
[0029] FIG. 20 is a spectrum comparison at 20-800 MeV of LANSCE
detector data and detector data of an embodiment of the
invention.
[0030] FIG. 21 is a spectrum comparison at 20-200 MeV of LANSCE
detector data and detector data of an embodiment of the
invention.
[0031] FIG. 22 is a spectrum comparison between EAL (Ohio) beam
data and an embodiment of the invention using sequential least
squares (SLS) unfolding.
[0032] FIG. 23 illustrates spectrum comparisons using MAXED-FC33
unfolding code (UMG) of an embodiment of the invention, using SLS
unfolding code of an embodiment of the invention and EAL (Ohio)
beam spectra.
[0033] FIG. 24 illustrates an unfolded spectrum produced by an
embodiment of the invention for an EAL beam compared to facility
data.
[0034] FIG. 25 illustrates a sample output showing a Cf-252 source
spectrum and field strength (total neutron flux) including the
total dose rate.
DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS
[0035] The following describes the design and testing of neutron
spectrometer/dosimeters according to various embodiments of the
invention. A brief description of the LGB scintillator is
presented, followed by a discussion of the physics of a composite
detector for this system and then a detailed description of the
signal processing algorithms and calibration/validation is set
forth.
Overall Instrument Description
[0036] FIG. 1 shows one embodiment of a neutron spectrometer 100,
according to one embodiment of the invention. The spectrometer 100
includes a detector head 10, a photomultiplier tube (PMT) 20, and a
voltage divider 30 in a detector assembly light-tight enclosure 40.
The enclosure 40, along with a digitizer 50, high-voltage power
supply 60, and computer motherboard 70, together form a neutron
spectrometer assembly 80.
[0037] The instrument shown in FIG. 1 and described in further
detail below combines a number of technologies into an efficient
neutron spectrometer/dosimeter, including [0038] 1.
.sup.6Li.sub.6.sup.natGd.sup.10B.sub.3O.sub.9:Ce (LGB) scintillator
crystals [0039] 2. a composite detector composed of the LGB
scintillator crystals uniformly distributed in a poly-vinyl toluene
(PVT) scintillator, and [0040] 3. pulse shape discrimination (PSD)
algorithms/software that analyze the complex signals produced by
the LGB scintillator crystals (which contain three neutron
capturing nuclei) and the PVT scintillator.
[0041] The instrument also incorporates several commercial
off-the-shelf (COTS) components, including the photomultiplier tube
(PMT) 20, wave form digitizer, mini-computer with accessories,
high-voltage power supply 60 and voltage divider 30. A description
of each of the components follows.
LGB Detector Head
[0042] The detector head 10 incorporates an LGB/PVT scintillator.
The crystalline structure of LGB consists of oxygen polyhedra of
rare-earth and alkali ions connected by isolated boron-oxygen
triangles in a three dimensional mixed framework. A unit cell for a
single crystal .sup.6Li.sub.6.sup.natGd.sup.10B.sub.3O.sub.9:Ce,
shown in FIG. 2, is made up of both covalent bonds (bold lines) and
ionic bonds (thin lines). Further details of this structure is set
forth in Dolzhenkova, E. F., V. N. Baumer, S. I. Gordeev, "Fracture
Toughness and Crystallographic Characteristics of
.sup.6Li.sub.6.sup.natGd.sup.10B.sub.3O.sub.9 Single Crystals,"
Crystallography Reports, Vol. 48, No. 4, pp. 563-567, whose entire
contents are incorporated herein by reference for such details.
[0043] Models of LGB scintillators have shown that the crystal
structure and bonding assists in the transfer of energy resulting
from neutron capture in the Li, B, or Gd. It is the cerium, in the
correct concentration and in its +3 oxidative state, which absorbs
the energy of the emitted alpha produced by the neutron capture in
Li and B, and translates it into visible light at 370-470 nm. The
gammas emitted from neutron capture by the Gd also interact with
the LGB crystal structure, depositing energy for light that is also
subsequently emitted by the Ce. The gamma rays that escape the LGB
scintillator crystals can further interact with the PVT by electron
recoil to create additional scintillations. To a lesser extent,
gammas will interact with Gd directly resulting in scintillation at
315 nm.
[0044] The LGB crystals operate as a transparent scintillator where
the neutron absorption efficiency increases with increasing
thickness. The refractive index is 1.65, allowing the crystals to
be incorporated into plastics with similar refractive indices. The
detector head 10 is composed of 0.7-1.5 mm LGB crystal shards
uniformly dispersed in a commercially available scintillating
plastic, poly-vinyl toluene or PVT (EJ-290 made by Eljen
Technologies/Ludlum Measurements Inc.). The refractive index of the
PVT is 1.58. The 5'' (12.7 cm) diameter by 4'' (10.16 cm) long
detector head incorporates 10% LGB by weight (3% by volume).
Photomultiplier Tube
[0045] The PMT 20 is a B133D01 made by ADIT/Ludlum and receives
light from the detector head 10 and converts the light into
electrical signals. It is a 5'' (12.7 cm) diameter, 10 stage,
end-on photomultiplier with extended sensitivity in the blue
wavelength region. The peak sensitivity above 70 ma/Watt ranges
from 380 to 470 nm with a quantum efficiency above 20%. The typical
high voltage input is 1100 VDC with a recommended maximum operating
voltage of 1500 VDC. One embodiment of the invention operates in
the 1250-1450 VDC range. The current produced by incident light is
amplified by a factor of one million to one, at 1100 VDC.
Digitizer
[0046] The digitizer 50 receives the electrical signals from PMT 20
via voltage divider 30 and is a model Razor CompuScope 1422
multi-channel digitizer made by Gage Applied Technologies (Lachine,
Quebec). This waveform digitizer operates at 14 bit and a sampling
rate of 200 Mega-Samples/second (MS/s). At 200 MS/s, the time
between samples is 5 ns with a peripheral component interconnect
(PCI) 32 Bit bus interface. In this embodiment, the digitizer is
not capable of performing real-time acquisition, due to the size of
on-board memory and the low data transfer rate to a computer hard
drive memory, however real-time acquisition may be used with larger
memory and higher rates and is within the scope of the invention.
Segment width for every trigger is 592 .mu.s with non-consecutive
data segments acquired and saved to binary signal files.
Mini-Computer and Accessories
[0047] The computer motherboard 70 receives data from the digitizer
50 and is a Jetway model NC9C-550 mini-ITX board mounted in a Lian
model Li Mini-Q PC-Q08 Mini ITX chassis. The motherboard is an
expandable platform with a 1.5 GHz Intel Atom fan-less processor,
dual core N550, paired with a NM10 controller hub. It features a
dual Gb LAN, VGA, PCI, PCIe Mini Card slot for wireless capability,
GPIO, LVDS, and support for 4 USB 2.0 ports. It uses 11 watts of
power and has up to 2 GB of memory.
[0048] A 150 GB HDD hard drive from Western Digital, model
WD1500BLFS, is connected to the motherboard to manage all
operations using Microsoft Windows 7 and software described
below.
[0049] In addition, a 10.2'' (25.9 cm) LCD monitor with VGA and AV
inputs is available for operating a stand-alone instrument at
remote sites. The monitor is a Xenarc, model 1020YV unit and is
connected to the mini-computer VGA and USB connections.
High-Voltage Power Supply/Voltage Divider
[0050] The high-voltage power supply (HVPS) 60 is used to supply
high direct current voltage to the PMT 20 and is connected to the
voltage divider 30. The power supply is a model 2A12-P4 made by
Ultravolt in Ronkonkoma, N.Y. The voltage divider 30 is a model
2007 made by Canberra Industries Inc. in Meriden, Conn. A 50 ohm
terminator is connected to the dynode output and the detector
output pulse signal is connected from the anode of the voltage
divider 30 into channel 1 of the digitizer 50.
Detector Head Response to Radiation
[0051] The following series of graphs presents the signals produced
by both gamma rays and neutrons in the composite LGB/PVT detector
head 10. Due to the presence of two scintillators (the inorganic
LGB crystals and the organic PVT), both of which respond to gamma
rays, and three of the four major neutron capturing nuclei (Li, B,
and Gd), the number and types of signals produced by this system in
response to radiation is varied and complex. Fortunately, these
signals can be digitized and are sufficiently different that it is
possible to both identify them and classify them by type. As will
be described below, when a neutron interaction depicted in FIG. 3A
is followed within an appropriate time frame by capture in one of
the three nuclei (FIGS. 3B and 3C), this combination of signals
uniquely identifies a neutron and permits separation (or
discrimination) of neutron events from gamma ray events.
Neutron Interactions
[0052] FIGS. 3A through 3C summarize the signals produced by the
interaction of neutrons with the composite detector head. FIG. 3A
represents the neutron interaction with the PVT scintillator and
FIGS. 3B and 3C represent the signals produced by neutron capture
in the LGB scintillator. In FIGS. 3A to 3F, each horizontal
division is 100 nanoseconds.
[0053] FIG. 3A shows a pulse representing the sum of all neutron,
proton (n,p) collisions of a single neutron in the PVT
scintillating plastic. These pulses have a width in the range of 50
nanoseconds (ns) and variable pulse height (N.sub.0) and area
(A).
[0054] FIG. 3B shows pulses with a shape characteristic of Ce
emission from thermal neutron capture in .sup.6Li, .sup.10B, and
.sup.157Gd. The alpha emissions from .sup.6Li and .sup.10B capture
and the gamma emission from capture in .sup.157Gd are presented by
this figure. The pulses from capture in these three elements vary
from the lowest energy .sup.10B to the highest energy .sup.157Gd
resulting in different areas (A) and pulse lengths (PW10 or pulse
width at 10% of maximum height) of hundreds of ns.
[0055] FIG. 3C shows pulses produced by neutron capture in
.sup.157Gd in the LGB scintillator, that emits one or more gamma
rays which leave the crystal and interact with the PVT. Some of the
capture energy is transmitted to the Ce in the LGB scintillator,
resulting in the characteristic "tail" (long pulse length, or
PW10), while the additional gamma interaction with the PVT causes a
sharp initial pulse shape which combines with the Ce emission.
Therefore, this pulse shape is a composite or hybrid of both LGB
and PVT interactions of the neutron with the .sup.157Gd.
Gamma Ray Interactions
[0056] FIG. 3D shows a pulse representing gamma ray interactions
with the PVT plastic scintillator of variable pulse height
(N.sub.0) that very rapidly decays resulting in a very narrow pulse
(PW10).
[0057] FIG. 3E shows a pulse representing gamma ray interactions
with the LGB crystal that produce Ce emissions similar to those
produced by neutron interaction, resulting in a pulse shape with a
large pulse length (PW10) but with a clear distinction from the
neutron interaction due to the extremely small pulse height
(N.sub.0). The cerium emission pulses produced by gamma ray
interaction have a smaller area than even the .sup.10B capture
pulse and thus is easily separated (discriminated) from the neutron
induced Ce emissions by the techniques described below.
[0058] FIG. 3F shows a pulse representing gamma ray interactions
with the .sup.157Gd where the energy is not transferred to the Ce.
In this case, Gd scintillates independently of the LGB crystal,
producing a pulse shape similar to the one in FIG. 3D. These pulses
are of much smaller pulse height (N.sub.0) and area (A) and easily
identified and separated.
Pulse Shape Discrimination (PSD) Signal Analysis and Processing
[0059] The computer motherboard, along with the other components
described above, perform pulse shape discrimination (PSD) signal
analysis and processing.
Physics
[0060] The composite scintillator, which is comprised of
scintillating LGB crystals uniformly embedded in scintillating PVT
plastic, produces a pulse associated with the neutron collisions in
the detector body (moderation) and another pulse at subsequent
capture in the LGB single crystal.
[0061] FIG. 4 is a schematic of a neutron moderating and capturing
in the composite scintillator. The interaction of the fast neutrons
with the plastic scintillator produces recoil protons that can be
detected in the plastic by the emission of light. If the neutrons
continue to slow down (moderate), in the detector volume, the
probability increases that neutron capture will occur in the Li, B,
or Gd. The multi-scattering events are seen to be rapid, and their
light accumulates into a single short pulse of approximately 50 ns.
In stark contrast, another potential event is the capture of the
thermalized neutrons which results in a pulse width (PW10 in FIG.
3B) greater than 145 ns. The moderating and the capture of the
neutron occur in a reasonably short time, 12 microseconds or less.
If a moderating signal is followed by a capture signal within this
prescribed time, then it is likely that a neutron has been
identified. Even though the pulse shape of FIG. 3A (resulting from
a neutron moderating) is similar to that of FIG. 3D (resulting from
a gamma), by determining whether or not there is a subsequent
capture (FIG. 3B or 3C), neutron events are distinguished from
gamma events.
[0062] Use of the capture signal ensures the presence of a neutron.
The area associated with the moderating pulse (paired with a
capture pulse) is proportional to the energy of the impinging
neutron when it loses its energy in a single collision. However,
the inventors found, only 2% of the colliding neutrons become a
thermalized neutron from a single collision. Thus, depending on the
collision history (proton recoil, carbon, etc.) and resulting
scintillations that comprise the moderating signal, a distribution
of pulse areas can be measured for any given neutron energy. In
other words, two neutrons having the same energy may produce
moderation pulse areas that are different.
[0063] A modeling study, using MCNP5-X and the MCNP-4c/POLIMI
codes, was conducted by the inventors to simulate the response of
the LGB detector to a parallel stream of 8 different mono energy
neutrons between 1-150 MeV and to predict the number of collisions
before capture. MCNP-4c/POLIMI code tracks individual neutrons,
calculates n-p collisions and the energy loss of each collision,
until the neutron is captured.
[0064] The LGB detector head was modeled as a right circular
cylinder 12.7 cm (5'') in diameter and 10.16 cm (4'') long of the
PVT material. The LGB crystals were estimated to be spheres of
0.058 mm radius and distributed uniformly throughout the entire PVT
cylinder. The radiation source was along the cylinder's axis as a
parallel beam impinging on the entire front face of the detector
body. To limit computational time, the entire space is confined to
a spherical surface of 30 cm radius with the detector head located
at the center of the sphere.
[0065] FIG. 5 represents typical MCNP results showing the
distribution of recoils (collisions) for a single incident neutron.
The collision distribution is very similar for all the modeled
neutron energies (from 1-150 MeV), and the average number of
collisions before capture is approximately 10 collisions. The
number of single collision events (where the loss of neutron energy
was sufficient that capture was possible) is relatively small
(.about.2%). These results support the experimental data
demonstrating that different pulse areas are measured for a given
impinging neutron energy and are dependent on neutron collision
history.
[0066] It has been discovered by the inventors by extensive
time-of-flight (TOF) testing with neutrons of known energy that the
neutrons in each energy range will display a distribution of
moderating pulse areas that is different than that for other energy
ranges. For example, the distribution of pulse areas for 1000
neutrons in the 2-3 MeV range will be different than the
distribution of pulse areas for 1000 neutrons in the 80-90 MeV
range, and thus neutrons in different energy ranges will have
different characteristic pulse area distributions.
Signal Processing, Signal Analysis, and Algorithms
[0067] The neutron spectrometer/dosimeter 100 output signals are
processed through neutron identification and analysis software,
Neutron.Analyst (N.A), that automates signal analysis and
diagnostic capabilities to characterize, identify, classify and
associate (pair) pulse signals. Once paired, the software also
estimates the background and adjusts the total counts to obtain the
measured neutron count. A number of template parameters that are
used to describe and classify the signals are discussed below.
[0068] FIG. 6 illustrates an overview of the processing up to
neutron energy binning and FIG. 19 (to be discussed later)
illustrates an overview of the processing from displaying the
neutron spectra to the end. In FIG. 6, after power on, the system
uses either an EAL calibrated response matrix (a calibrated
response matrix is described in detail below) or a LANSCE
calibrated response matrix depending on whether the 0-20 MeV region
or the 20-800 MeV region is of interest. (Steps 2 and 3, FIG. 6).
The software also receives measured detector data, test ID
information, and output selection preferences as input.
[0069] Then, a recognition and classification process (step 4,
Pulse ID, FIG. 6) begins by determining a rising edge above a
threshold (above electrical noise), finds a pulse peak, and then
the decay of the signal to near zero voltage. The N.A program then
uses algorithms that correctly place each pulse in either a plastic
(e.g., gamma and moderating, FIGS. 3D and 3A, respectively) pulse
category or capture pulse category (FIGS. 3B and 3C). The
programmed algorithms in this embodiment use three distinct pulse
characteristics for pulse classification; namely, lambda (a), total
area, and pulse width (PW10) at various percentages of pulse height
(10% in this case). FIG. 7 illustrates various pulse parameters.
Several other characteristics, such as the length ratio L2/L1 and
tail area at 50% (TA.sub.50), may also be considered for various
processes in the N.A program.
[0070] Lambda is the exponential decay constant of the pulse
decreasing back edge, based on the formula:
N=N.sub.0.times.e.sup.-2t
[0071] Where N.sub.0 is the pulse height and t is the time
difference between two adjacent data points on the digitized pulse
decreasing edge. This equation is used to curve fit to the actual
decreasing edge data points and lambda (.lamda.) is the constant
for the exponential curve that best fits the data. When lambda is
very small, e.g. <0.012, the pulse has a long decay and "large
tail" and thus the program classifies it as a capture pulse, while
all other pulses having a lambda greater than 0.012 are classified
as moderating (or gamma) pulses. The total area (A) is simply the
integrated area under the shape of the pulse. The other parameters
are defined in FIG. 7.
[0072] An example of a graphical user interface (GUI) of the N.A
program is shown in FIG. 8. Various pulse characteristics can be
displayed at the GUI; in the case of FIG. 8 the moderating pulse
area distribution is shown. General analysis information on the
right hand side of the GUI shows the total number of pulses found
in the test data (1,516,552) of which 87,411 were determined to be
neutrons.
[0073] FIG. 9 shows lambda plotted against pulse area. This allows
the user to observe a separation region and select the best value
of lambda that separates neutron capture pulses in LGB (R region
pulses) from moderating (or gamma) pulses (G region pulses). Other
parameters such as PW10, late area, early area, and pulse height
can also be displayed in the development mode of the N.A
program.
[0074] Distinctive differences in pulse shape and/or pulse
characteristics (such as lambda) are the key to correctly identify
neutrons and classify them as moderating or capture pulses. These
classified pulses are then paired (step 5, Pulse Pairing, in FIG.
6) by finding the nearest moderating pulse in front of a capture
pulse. In the case of multiple capture pulses, the nearest unpaired
moderating pulse is paired with any subsequent capture pulse. All
paired pulses, that is a moderating pulse followed by a capture
pulse, are further analyzed.
[0075] Additional parameters such as tail areas at 20-50% of
N.sub.0 (see FIG. 7--TA.sub.50) as well as various area and
parameter ratios may be mapped. These mappings can be three
dimensional graphical plots of the various parameters to permit the
user to identify additional features of distinction between
moderating and gamma pulses.
[0076] In certain embodiments of the invention, various mappings or
plots are generated, for example, TA.sub.20 plotted against total
pulse area and pulse height (N.sub.0). By comparing such plots with
the same parameters of a gamma test using Co-60, the inventors
noticed that the very small pulses are a potential gamma
elimination region.
[0077] Besides the above gamma elimination methods, additional
background and/or accidental pairing removals lead to more accurate
measured counts. Accidental pulse subtraction (step 6 in FIG. 6)
involves plotting the time-to-capture of each pair, shown in FIG.
10.
[0078] The underlying principle employed is that the
time-to-capture must occur within 12 microseconds (.mu.s). The
time-to-capture (see FIG. 15) is measured from the first light
pulse from the p,n interaction in the PVT (the rising edge of the
moderating pulse) to the capture of the thermalized neutron (the
rising edge of the capture pulse). The 12 .mu.s has been validated
with Monte Carlo modeling and by experimental data such as the
example of a Cf-252 test plotted in FIG. 10. In FIG. 10, the
portion of the data designated Area A contains all pairs whose
times-to-capture are less than 12 .mu.s. These are called possible
neutrons. Then all the pairs in the portion of the data designated
Area B are counted. These pairs represent random false-pairings due
to gamma pulses or false moderating pulse identifications. Area B
pairs could also be considered the background in a measurement.
Area B must be of the same length; namely, 12 .mu.s to calculate
the correct background counts and subtract the background from the
real signal. This is based on the fact that the same background in
Area B also occurs for the first 12 .mu.s, i.e. in Area A. The N.A
algorithm subtracts the pair count in Area B from the pair count in
Area A which results in the true neutron count remaining in Area
A.
Neutron-Gamma Discrimination and Rejection
[0079] Tests were conducted by the inventors at Washington State
University (WSU) and in-house, in a "pure" gamma field, to improve
the neutron-gamma discrimination and rejection by the spectrometer
algorithms. FIG. 11 shows the lambda distribution versus area
(produced by the N.A program) for the WSU data using an LGB/PVT
detector head of dimensions 2'' (5.08 cm) diameter by 2'' (5.08 cm)
length. In one embodiment of the invention region R (capture
pulses) is red and region G (moderating pulses) is green. This test
was conducted using a Cf-252 source; i.e., a mixed neutron/gamma
source. The inventors then tested a detector head with only PVT
material to determine the regions of the FIG. 11 plot due to gamma
interactions with the PVT. FIG. 12 shows the result of this
test.
[0080] FIG. 12 shows two distinct areas that can be positively
identified as gammas in FIG. 11. One area G (green) is a vertical
area from lambdas of 0.012 to 0.12 and areas of 0.0 to 1.5. The
other area R is the horizontal area from lambdas of 0.0 to 0.012
and areas of 0.0 to 5.0. The pulses with these characteristics are
rejected as gammas and the N.A program does not even consider them
for pairing. FIG. 13 is a repeat of the neutron/gamma field test
with these gamma pulses rejected or eliminated from the N.A
analysis. Comparing the lambda versus area plot of FIG. 13 with
FIG. 11 shows the effect of this gamma elimination. The measured
neutrons without gamma rejection totaled 10836. After gamma
rejection the measured neutron total was reduced to 7489, a 31%
reduction; i.e., the rejected gammas were not mistaken as
moderating pulses which leads to greater certainty of neutron
detection.
Energy Calibration
[0081] Of the paired signals, the moderating pulse contains the
information to estimate the energy of the impinging neutron. The
neutron energy can be directly correlated with the areas of the
moderating pulses by developing and using a calibrated response
matrix (CRM) for the neutron detector and using an unfolding method
as described below.
Pulse Area
[0082] FIG. 14 is a scatter plot of all the moderating pulses
measured by the inventors at two test facilities ranging from 0.8
to 200 MeV. The energy of the neutrons in FIG. 14 was determined
based on the time the neutron takes to travel from the accelerator
beam target to the LGB detector in the time-of-flight (TOF)
experiments the inventors conducted at the Los Alamos Neutron
Science (LANSCE) facility and the Ohio University's Edwards
Accelerator Lab (EAL). The area of the moderating (start) pulse was
calculated and is plotted in relation to the TOF energy. This
scatter plot shows an almost linear relation between the energy and
pulse area of the top or highest 2% of the neutrons that lose all
of their energy in a single collision. It is also clear from this
plot that the other 98% of neutrons experiencing multiple
collisions have smaller pulse areas than the top 2%. When the
scatter plot is subdivided into narrow neutron energy ranges, or
bins, the variation in moderating pulse area represents the basis
for developing a CRM.
Time-of-Flight Data
[0083] Time-of-Flight (TOF) data was acquired with a multi-channel
digitizer at LANSCE and EAL test facilities to determine a
relationship between the moderating pulse areas and TOF neutron
energies. The neutron energy calculation is highly accurate based
on the speed of light and the time measurement between the time the
accelerator beam hits the target and the neutron enters the LGB
detector. A sample data measurement is shown in FIG. 15. The TOF
value is shown as .DELTA.t, or the time between the timing mark
(when the beam hits the target) and the rise of the moderating
pulse.
[0084] A statistically significant amount of TOF data were measured
both in the 20-800 MeV range at LANSCE and in the 0.5-13 MeV energy
range at EAL. This number of neutrons gave the assurance of
adequate data to create the CRM and complete an accurate unfolded
beam spectrum.
Calibrated Response Matrix
[0085] The inventors discovered that the time-of-flight experiments
at LANSCE and EAL demonstrated a predictable correlation between
the moderating pulse area and neutron energy. When the total number
of neutrons over the entire energy range is divided into "energy
groups," each energy group contains that fraction of pulse areas
associated with the range of energies in the group. For example,
the distribution of pulse areas for 1000 neutrons in the 2-3 MeV
range will be different than the distribution of pulse areas for
1000 neutrons in the 80-90 MeV range, and thus neutrons in
different energy ranges will have different characteristic pulse
area distributions. A response matrix is constructed that contains
all the energy groups beginning at the top with the lowest energy
and ending with the highest energy group at the bottom. An example
of such a matrix is shown in FIG. 16. In FIG. 16, each row
designates a different energy range (for example an energy range
around 1.38828 MeV) and each column is a different pulse area in
voltns (see FIG. 3). For example, in the 1.38828 MeV energy bin,
about 65% (0.645719) of the pulses have a pulse area around
1.656852 voltns. For each energy group, the pulse area fractions
(along the horizontal) sums to 1.0.
Neutron Detection Efficiency
[0086] The neutron detection efficiencies were determined as a
function of energy to ensure their accuracy and relevance. The LGB
neutron detection efficiency is defined as the ratio of the number
of neutrons measured by the instrument divided by the number of
neutrons incident to the detector's front face. The number of
incident neutrons provided by the LANSCE beam was measured by
calibration tests using U-238 foils at the exact test locations
used for the LGB detector. FIG. 17 presents the calculated LGB
neutron detection efficiencies between 20-200 MeV for the high
energy LANSCE TOF test. Also shown are the MCNP (computer model)
predictions of the efficiencies (the single data points) and their
comparison to the test measurements.
[0087] FIG. 18 depicts the neutron detection efficiency for the
0.5-13 MeV energy regime as determined by the EAL experiments. The
number of EAL beam neutrons incident to the detector was calculated
by the EAL facility team based on the beam current hitting the
target.
Unfolding Spectrum
[0088] The signal processing described above serves to eliminate
"bad" or unnecessary data such that the unfolding described below
is based on "good" data. To de-convolute the counts distributed at
different moderating pulse areas and to produce neutron spectra,
two unfolding algorithms, MAXED-FC33 and smoothed Sequential Least
Squares (SLS), were used. However, the invention is not limited to
use of such techniques and other unfolding or de-convolution
techniques may be used. The MAXED-FC33 code is part of the UMG code
(maximum entropy code UMG available from Oakridge National
Laboratory, Reginatto, Marcel, "The Few-Channel, MXD_FC33,
Unfolding Program Manual in the UMG 3.3 Package", DOE Release Date
Mar. 1, 2004, whose entire contents are incorporated herein by
reference for the algorithms, techniques, and processes related to
unfolding). The MAXED-FC33 code is used to validate the actual SLS
code used in the N.A program. The basic SLS code is available in
publications (Y. Xu, T. J. Downar, M. Flaska, S. A. Pozzi, and V.
Protopopescu, "Sequential Least Square Method for Neutron Spectrum
Unfolding from Pulse-Height Distributions Measured with Liquid
Scintillators", Joint International Topical Meeting on Mathematics
& Computation and Supercomputing in Nuclear Applications
(M&C+SNA 2007) Monterey, Calif., Apr. 15-19, 2007, whose entire
contents are incorporated herein by reference for the algorithms,
techniques, and processes related to unfolding). Both codes need
the following inputs to calculate the unfolded spectrum: a
calibrated response matrix (CRM), the neutron detector measured
data, and a default spectrum that serves as a reference point for
calculating the actual spectrum. The default spectra for both the
LANSCE and EAL tests were supplied by the facility instruments
based on standardized and well documented procedures. In order to
compare the spectrum supplied by the facility instruments with the
unfolded measured spectrum of the spectrometer 100, the default (or
facility) spectrum was multiplied times the neutron detection
efficiency of the LGB detector. The detailed calculations of both
the MAXED-FC33 and SLS codes are presented later on below.
Dosage Output
[0089] As discussed above, FIG. 19 illustrates an overview of the
processing from displaying the neutron spectra to the end. Once the
measured neutron data are unfolded, the N.A program includes a few
additional processes to display the resulting neutron spectra (step
9) on the GUI. The process steps are shown in FIG. 19 and include
calculating equivalent dose (step 10) and matching the library
which best fits the resulting measured spectrum (step 12) and
displaying each of those two results (steps 11 and 13,
respectively). The equivalent dose is based on one of the following
standards; namely, the International Atomic Energy Agency (IAEA),
the International Commission on Radiological Protection (ICRP), or
the U.S. Nuclear Regulatory Commission (NRC) damage coefficients.
The desired damage coefficient values can be selected by the user
depending on which regulatory region the instrument is being used
in.
Validation
[0090] The validation testing described below was conducted on the
spectrometer/dosimeter 100 to prove acceptable performance.
Validation of Spectrometer 100 at LANSCE High Energy Neutron
Beam
[0091] The Weapons Neutron Research Facility (WNR, LANSCE) provides
neutron beams with energies ranging from about 0.1 MeV to more than
800 MeV from an un-moderated tungsten spallation source using the
800 MeV proton beam from the LANSCE linear accelerator. For the
validation study energies above 17 MeV were needed; therefore, the
4 FP 15 L (90 meter) beam line was used. Once the neutrons are
produced they are further filtered with five centimeters (2'') of
lead and 20 centimeters (7.9'') of moderating polyethylene
(CH.sub.2) with the beam size reduced progressively to a final
aperture diameter of 8 mm in the exposure room.
[0092] Using the UMG-MAXED-FC33 and SLS unfolding programs on the
neutron measurements of spectrometer/dosimeter 100 yielded unfolded
count rates for each of 15 energy bins. Dividing the count rate by
efficiency at a specific energy results in the neutron fluence in
that energy range. A comparison of the spectra produced by the
LANSCE U-238 and the LGB methods of this embodiment is depicted in
FIG. 20. Assigning the LANSCE neutron fluence into energy ranges
similar to the calibrated response matrix allows for a direct
comparison. The results appear to be in good agreement for the
energies between 20 and 800 MeV. Specifically, examining the
neutron spectra at the lower energies, between 20 and 200 MeV,
close agreement with the neutron population as predicted from
LANSCE's U-238 detection method is exhibited (see FIG. 21).
[0093] For completeness, the uncertainty of the neutron
measurements, shown as error bars, is provided in FIGS. 20 and 21
as well. In general, the error ranged from approximately +/-8
percent variation, with the lowest/highest energies of 20 and 800
MeV indicating a +/-16 percent variation. The uncertainty of the
invention is less than the uncertainty of the LANSCE detectors.
Embodiments of the invention are also portable and much faster
(existing systems sometimes take weeks to generate a spectrum).
When evaluating the neutron fluence used in this testing, the
spectral results from the U-238 foils reported a variation of
approximately +/-20 percent. The uncertainty associated with the
neutron spectrum generated from the spectrometer/dosimeter 100 was
calculated by organizing an entire 38 hour data set obtained at the
WNR-15L beam line into seven (7) distinct experimental data groups.
The conditions of the beam were held constant during the beam's
operation resulting in minimal variation in the neutron field for
the 7 experimental groups. Evaluating the detection results in this
manner allowed the mean neutron fluence and standard deviation to
be calculated for each energy group.
Validation of Spectrometer 100 at EAL Fast Neutron Beam
[0094] The EAL located at Ohio University (Athens, Ohio) has an
active tandem Van de Graff accelerator capable of generating a 6
MeV deuteron beam. When the 6 MeV beam strikes an Al-27 target, a
spectrum of neutron energies between 1-12 MeV is emitted. The
neutrons pass through a 10.61 cm diameter collimator into a 2.1 m
diameter concrete tunnel. The spectrometer 100 was centered 7 m
from the target downstream of the collimator.
[0095] The spectrometer-measured neutron spectrum was unfolded by
using a spectral unfolding program and a CRM produced for this
energy range. The neutron fluence for MeV neutron energies
(presented in FIG. 22) was created by adjusting the unfolded count
spectrum for energy efficiency. The EAL calibration measurements
(supplied by EAL personnel and organized in similar energy bins for
ease of assessment) are provided in FIG. 22 as well. The
uncertainty of the measurement was estimated using Bayes rule as it
progressively evaluated each energy group over the entire length of
the experiment. The comparison shows good agreement between the two
measurement techniques with an average deviation of +/-7.4
percent.
[0096] FIG. 23 depicts a comparison of the referee spectrum, using
the MAXED-FC33 unfolding program, with the Ohio Beam and SLS
unfolded spectra. As can be seen in this figure, the SLS unfolding
program correlates well with the referee unfolding program and with
the Ohio beam spectrum.
[0097] A final result of the unfolding is shown in the N.A screen
of FIG. 24. This shows good correlation between the unfolded
measured spectrum and the EAL beam incident to the detector. To do
this comparison, the measured number of neutrons in each energy bin
needs to be divided by efficiency and then plotted in a histogram.
This calculation increases the measured count to a level
representing the radiation field hitting the front face of the LGB
detector. This allows a direct comparison to the EAL beam, the bold
line in FIG. 24. The data shows reasonable comparison between the
spectrum measured by one embodiment of the invention and the
facility measured spectrum.
Validation of Spectrometer 100 for Slow Neutrons at the
Lowell-Massachusetts Slow Neutron Beam
[0098] The 1 MW nuclear fission reactor at University of
Massachusetts-Lowell was also used to measure radiation fields in
the thermal and epi-thermal neutron energy regimes with an
embodiment of the invention. The beam tube was optimized for
neutron imaging, where a uniform field of thermal and epi-thermal
neutrons is required, with a low number of neutrons having energies
above the epi-cadmium cutoff. The conditioning of the neutron beam
includes passing it through 4 feet of graphite, and a 0.1 inch
aperture and a collimator with no mask filters at the beam
exit.
[0099] This experiment provided known amounts and distributions of
neutrons that possess thermal and epi-thermal energies. Because the
thermal and epi-thermal neutron energies are well below 0.5 MeV,
there are no associated moderating pulses that are recorded. The
neutron population in the Lowell beam is 100 neutrons/cm.sup.2-sec
at the end of the radiography beam line. In addition, the number of
neutrons above the epithermal is extremely small for this beam
line. Therefore, for this group, only capture pulses are
recognized. Measuring the calibrated beam with the instrument of
this embodiment yielded an efficiency of 20 percent for the
neutrons in this energy range. Results from MCNP-X calculations
yielded an estimated efficiency for the detector head at 30
percent.
[0100] The slow neutron counts were estimated for an unknown
neutron field by subtracting the portion of captures that are
associated with neutrons greater than 0.5 MeV, which are not
properly paired. Thus they are eliminated due to the inefficiency
of the pairing algorithm from the total unpaired measured captures.
The resulting counts divided by the efficiency for the slow neutron
group yield the number of slow neutrons present. The equation below
summarizes the process to determine the number of slow
neutrons:
Number of slow
neutrons=(up-pc(1-Eff.sub.association)/Eff.sub.association)/Eff.sub.Slow
neutron
[0101] Where up represents unpaired captures, pc represents paired
captures, and Eff represents the accuracy of the association
algorithm or the efficiency of detecting slow neutrons.
Spectroscopic Dosimeter Performance of an Embodiment
[0102] In certain applications such as area monitoring, radioactive
source identification, and health physics measurements, the
spectroscopic/dosimeter of this embodiment can be run in the "User"
mode. In this mode, the instrument streams data from the digitizer,
analyzes each "packet" of 0.0296 seconds of data and then displays
the spectrum, flux, fluence, and the total and rate of dose
equivalent. A sample output is shown in FIG. 25.
[0103] The example shown in FIG. 25 represents a test run in the
inventors' lab using a 490 .mu.Ci radioactive source, Cf-252, which
emulates the fission spectrum. The histogram is the measured
neutrons divided by the TOF efficiencies measured in the Ohio EAL
test. The damage coefficients used in this case are based on the
ICRP74 tables. Multiplying the neutron count in each energy bin
times the appropriate damage coefficient resulted in the total dose
equivalent and total dose rate displayed in the Neutron Data field
of FIG. 25.
Conclusions
[0104] The results above validate that the LGB/PVT composite
neutron detector does produce an identifiable capture-gated
response. The composite scintillator, which is comprised of LGB
crystals uniformly embedded in a PVT plastic, produces a pulse
associated with the neutron collisions (moderation) and, a second
pulse of its subsequent capture. To distinguish the events, the
detector uses advanced pulse shape discrimination algorithms that
are capable of classifying scintillations from neutron and gamma
collisions as well as neutron captures. Because the collected
scintillations, comprising measured pulse area signals, will (as
the inventors discovered) vary probabilistically for each neutron
due to its energy, colliding constituents, and energy loss per
collision, an unfolding algorithm such as a smoothed Sequential
Least Squares (SLS) is employed to de-convolute the measured
neutron spectrum. Using the SLS unfolding methods in an automated
N.A software package leads to good correlation with known beam
spectra and validates the performance of the LGB neutron
spectrometer/dosimeter.
[0105] The results clearly show that the detector--when exposed to
a variety of neutron sources--can reasonably measure/predict the
energy distribution of the neutron field present. The accuracy of
measurement/prediction is enhanced when the instrument is
calibrated for a narrow energy range (e.g., thermal, 1-12 MeV).
However, even when spanning from Low energy (<0.1 MeV) to 800
MeV, a good measurement/estimate of the energy spectrum is
possible. The spectrum can then easily be converted to accurate
dose equivalents.
Unfolding Program Details
MAXED-FC33 Unfolding Method
[0106] MAXED-FC33 utilizes a process that maximizes the relative
entropy and avoids the instabilities of more straight forward
methods. The required input data (files) include 1) the measured
counts at increasing pulse area, 2) the calibrated response matrix
(CRM, which relates pulse area distribution with neutron energy)
and 3) the default (first guess) neutron spectrum.
[0107] Because the unfolding process can result in large changes in
the prediction of neutron spectra for small variations in
pulse-area distributions, care must be taken in obtaining a
well-conditioned CRM. The default spectrum is used as the first
guess, which allows for the converging of the measured data to
obtain the unfolded neutron spectrum. For the best result, it is
advantageous to incorporate any understanding of the measured field
in the initial guess.
[0108] The conceptual basis of the maximum entropy algorithm used
by MAXED is discussed in detail in various publications.
Mathematically, the MAXED algorithm can be described in terms of a
set of input parameters, a set of output parameters, and the
equations relating these quantities. The algorithm requires the
following input parameters:
N.sub.k: measured counts .sigma..sub.k: estimate of the measurement
error f.sub.i.sup.DEF: default spectrum R.sub.ki: response matrix
.OMEGA.: a parameter that fixes the .chi..sup.2 of the solution
Where k=1, . . . , m and i=1, . . . , n, with m<n. The unfolding
leads to a set of parameters {.lamda..sub.k, .gamma.} that
satisfies the following set of equations:
N k + k = i R ki f i ##EQU00001## k k 2 .sigma. k 2 = .OMEGA.
##EQU00001.2## k N k .sigma. k - k , i R ki f i .sigma. k = 0
##EQU00001.3## f i = f i DEF exp { - k ( .lamda. k + Y .sigma. k )
R ki } ##EQU00001.4## k = .lamda. k .sigma. k 2 2 [ 4 .OMEGA.
.SIGMA. j ( .lamda. j .sigma. j ) 2 ] 1 / 2 ##EQU00001.5##
Sequential Least Squares (SLS) Unfolding Method
[0109] Certain embodiments use SLS to produce a neutron energy
spectrum in real time. As used herein "real time" means the
spectrum is produced in less than one hour, preferably less than 30
minutes, more preferably less than 10 minutes. A modified SLS
method is used that incorporates a Krylov subspace iteration method
to solve the least squares equations. A known effect of SLS methods
are that the results may oscillate from the correct neutron
spectrum, therefore a 5-tap Quadratic digital filter (smoothing
technique) was used to reduce the severity of these oscillations
and produce spectra that are more meaningful. Similar to MAXED, the
required input data (files) include 1) the measured counts at
increasing pulse area, 2) the CRM, and 3) the default (first guess)
neutron spectrum where all neutron values are greater than
zero.
[0110] The following Least Squares (with weighting) equation is
used to solve for the active and inactive sets to provide a
nonnegative neutron counts at different energies.
min f ( x ) = 1 2 i = 1 n w i ( N i - j = 1 m R ij x j ) 2
##EQU00002## subject to x i = 0 for i .di-elect cons. S A Subset of
S B ##EQU00002.2##
[0111] To insure nonnegative response the active set will have x
values=0. The inactive set will have x values >0, and due to
constraints on the solving mechanism there will be no x values less
than zero because of the impossibility of having negative neutron
counts.
[0112] Nomenclature for the following set of equations used in the
SLS method is given below:
w=weighting function, typically set to the sqrt(N) or set to all
values of one. N=measured neutron counts distributed among Area
bins R=the response matrix S.sub.B=The complete Set S.sub.A=The
Active Set S.sub.B\S.sub.A=The Inactive set s, g, and
.alpha.=intermediate variables that are used in solving the
algorithm
[0113] In solving for a spectrum, a feasible initial guess is
proposed, it does not need to be accurate, just a feasible starting
point to get the algorithm started. In order to solve the previous
equation and minimize the error in the Least Squares (with
weighting) analysis, the following equations are used in a
recursive manner to find the best solution with all non-negative
numbers.
[0114] Solve for s.sup.(k) using the conjugate gradient method on
normal equations (CGNE) method, from the following linear
system
.SIGMA..sub.j.epsilon.S.sub.B.sub.\S.sub.A {square root over
(w.sub.i)}R.sub.ijs.sub.j.sup.(k)= {square root over
(w.sub.i)}N.sub.i-.SIGMA..sub.j.epsilon.S.sub.B {square root over
(W.sub.i)}R.sub.ijx.sub.j.sup.(k), (1)
and then determine alpha and take a step forward by the following
equations
.alpha. = min ( 1 , min j .di-elect cons. S B \ S A s j < 0 x j
( k ) - s j ( k ) ) ##EQU00003## x j ( k + 1 ) = x j ( k ) +
.alpha. s j ( k ) ##EQU00003.2##
[0115] The j-value responsible for the given alpha is moved from
the inactive to the active set; if alpha equals 1, then no values
are moved to the active set.
[0116] The following equation is then solved
g q = i = 1 m w i R iq ( w i N i - j .di-elect cons. S B \ S A w i
R ij x j ( k ) ) for q .di-elect cons. S A ##EQU00004##
for any positive value of g.sub.q move q into the inactive set
immediately before calculating further values of g.sub.q
[0117] If the active set changes, reset k=k+1 in equation (1) and
proceed with the algorithm; otherwise, no change in the active set
terminates the algorithm.
[0118] The inventors' current understanding of the theoretical
physics of various phenomena is set forth above and this
understanding may be refined or even changed by future study. The
invention may be made and effectively used (based on the above
description) even if some of the theory set forth above is later
refined or changed. In other words, the ability to make and use the
invention does not depend on the correctness of any theory.
[0119] The invention is not limited to the particular embodiments
described above because many variations and modifications, within
the scope and spirit of the invention, are possible instead.
Accordingly, the invention is defined with reference to the
following claims.
* * * * *