WO2014179695A1

WO2014179695A1 - Spectrally matched neutron detectors

Info

Publication number: WO2014179695A1
Application number: PCT/US2014/036587
Authority: WO
Inventors: Scottie WALKER; Glenn SJODEN
Original assignee: Georgia Tech Research Corporation
Priority date: 2013-05-03
Filing date: 2014-05-02
Publication date: 2014-11-06

Abstract

A neutron detector element (200) for replacement of a ³He-based neutron detector element that includes two elongated ¹⁰B-lined (212) neutron detector tubes (210) spaced apart from each other and filled with ⁴He (214) at a predetermined pressure. The ¹⁰B-lined (212) neutron detector tubes (210) are disposed so as to have an adjoint function (310) over a predetermined spectrum of neutron energies within a predetermined bias threshold of a corresponding adjoint function of the ³He-based neutron detector element over the predetermined spectrum of neutron energies. A block of a neutron moderator material (220) surrounds the two elongated ¹⁰B-lined (212) neutron detector tubes (210). The block of moderator material has dimensions so as to be able to fit a space for the ³He-based neutron detector element (200) in a neutron detecting system (400).

Description

SPECTRALLY MATCHED NEUTRON DETECTORS

CROSS-REFERENCE TO RELATED APPLICATION(S)

[0001] This application claims the benefit of US Provisional Patent Application Serial No. 61/819,121, filed 05/03/2013, the entirety of which is hereby incorporated herein by reference.

BACKGROUND OF THE INVENTION [0002] 1. Field of the Invention

[0003] The present invention relates to neutron detectors and, more specifically, to a replacement neutron detector element that employs materials to alternative to ³He.

[0004] 2. Description of the Related Art

[0005] Neutron detectors are important in a number of applications, including homeland security and nuclear material processing control. One common type of neutron detector includes a tube filled with ³He, an isotope of helium. In such a detector, a wire passes through the tube and a voltage is applied between the tube and the wire. Neutrons striking ³He atoms in a tube cause the ³He atoms to ionize, thereby sending charged particles to the tube. This causes a momentary voltage transient between the wire and the tube, the detection of which indicates the presence of neutrons.

[0006] Helium-3 (³He) is generated as a decay product of tritium (³H). Tritium is commonly used in fusion reactions and, therefore, ³He is a byproduct of nuclear weapons. However, there is presently a very limited supply of ³He, attributed to a lack of tritium production for the nuclear weapons complex along with a significantly increased demand for the gas in various neutron detection applications. Around 2000, there were more than 200,000 liters (standard temperature and pressure) in the ³He stockpile, but today less than 45,000 liters remain, and the Department of Energy is rationing the supply to only 8,000 liters per year. A number of research efforts have been conducted to determine if existing materials could serve as an adequate substitute for ³He and additional efforts have also evaluated new materials that might serve adequately as replacements. Regardless of the effort, each study almost always focuses solely on "simple" detection cases where the overall system efficiency for one specific source (e.g. 252Cf) is the only concern (e.g. hand-held devices, backpack units, and portal monitoring systems). In these cases, inserting additional detectors and/or materials can address the issue of cumulative counts, because the spectral response is essentially irrelevant. However, in many applications such as for safeguards, non-proliferation efforts, and materials control and accountability (MC&A) programs, including fissile material assessments for plutonium and actinides, measurements are often calibrated to responses in a ³He proportional counter. In these cases, a mismatch in the neutron response function can produce serious quantification errors with potentially dire consequences. The application of a simple detector addition approach in these instances is neither appropriate nor possible due to influences resulting from the complex nature of neutron scattering in moderators, cross sections, gas pressures, geometries and structural interference. These more challenging circumstances require that a detailed computational transport analysis be performed for each specific application.

[0007] Neutron radiation detectors are an integral part of the Department of Homeland Security (DHS) efforts to detect the illicit trafficking of radioactive or special nuclear materials into the U.S. In the past decade, the DHS has deployed a vast network of radiation detection systems at key positions to prevent or to minimize the risk associated with the malevolent use of these materials. Many neutron detection systems have been equipped with ³He because of its highly desirable physical and nuclear properties.

However, a dramatic increase in demand and dwindling supply, combined with a lack of oversight for the existing ³He stockpile has produced a critical shortage of this gas with respect to detector applications. Although a number of research efforts have been undertaken to develop suitable replacements, none of these efforts are attempting to closely match the ³He detector response across different neutron energy spectra, which is critical for certain non-proliferation programs and special nuclear material (SNM) assessments.

[0008] Therefore, there is a need for spectrally matched and validated equivalent neutron detectors for the direct replacement of existing ³He detector systems. SUMMARY OF THE INVENTION

[0009] The disadvantages of the prior art are overcome by the present invention which, in one aspect, is a neutron detector element for replacement of a ³He-based neutron detector element that includes two elongated ¹⁰B-lined neutron detector tubes spaced apart from each other and filled with ⁴He at a predetermined pressure. The ¹⁰B-lined neutron detector tubes are disposed so as to have an adjoint function over a predetermined spectrum of neutron energies within a predetermined bias threshold of a corresponding adjoint function of the ³He-based neutron detector element over the predetermined spectrum of neutron energies. A block of a neutron moderator material surrounds the two elongated ¹⁰B-lined neutron detector tubes. The block of neutron moderator material has dimensions so as to be able to fit a space for the ³He-based neutron detector element in a neutron detecting system.

[0010] In another aspect, the invention is a method of designing a neutron detector element for replacement of a ³He-based neutron detector element, in which a first adjoint function over a predetermined spectrum of neutron energies for the ³He-based neutron detector element is computed on a digital computer. A proposed model of a replacement neutron detector element that is based on materials that are alternative to ³He is generated. The following steps are repeatedly executed until a second adjoint function based on materials that are alternative to ³He over the predetermined spectrum of neutron energies for the proposed model converges on the first adjoint function based on an ³He response within a predetermined bias threshold: running a simulation of the proposed model of the replacement neutron detector element on a digital computer to determine the second adjoint function over the predetermined spectrum of neutron energies for the proposed computer- aided design; comparing the second adjoint function to the first adjoint function as a function of neutron energy so as to determine the bias; and when the adjoint reaction rate bias is outside of the bias threshold, then modifying at least one dimension associated with the proposed model. The neutron detector element is built so as to correspond with the proposed model as modified once the second adjoint function over the predetermined spectrum of neutron energies for the proposed model converges on the first adjoint function within the predetermined bias threshold. [0011] These and other aspects of the invention will become apparent from the following description of the preferred embodiments taken in conjunction with the following drawings. As would be obvious to one skilled in the art, many variations and modifications of the invention may be effected without departing from the spirit and scope of the novel concepts of the disclosure.

BRIEF DESCRIPTION OF THE FIGURES OF THE DRAWINGS

[0012] FIG. 1 is a flowchart demonstrating one method of making a replacement

neutron detector element.

[0013] FIG. 2A is a top perspective view of one embodiment of a neutron detector element.

[0014] FIG. 2B is a top plan view of the embodiment of a neutron detector element shown in FIG. 2A.

[0015] FIG. 3A is a graph of adjoint function versus a spectrum of neutron energy

groups relative to the embodiment shown in FIG. 2A.

[0016] FIG. 3B is a graph of adjoint reaction rate versus a spectrum of neutron energy groups relative to the embodiment shown in FIG. 2A.

[0017] FIG. 4 is a block diagram showing one embodiment of a replacement neutron detector element in use.

DETAILED DESCRIPTION OF THE INVENTION

[0018] A preferred embodiment of the invention is now described in detail. Referring to the drawings, like numbers indicate like parts throughout the views. Unless otherwise specifically indicated in the disclosure that follows, the drawings are not necessarily drawn to scale. As used in the description herein and throughout the claims, the following terms take the meanings explicitly associated herein, unless the context clearly dictates otherwise: the meaning of "a," "an," and "the" includes plural reference, the meaning of "in" includes "in" and "on." Also, as used herein, "PVT" means polyvinyltoluene.

[0019] In one experimental embodiment, prior to developing any actual designs of replacement neutron detector elements, the fidelity of a computational approach is validated by executing radiation transport models for existing BF₃ and ³He tube and then comparing the results of these models to laboratory measurements conducted with these exact detectors. In one experimental embodiment, both tubes were 19.6 cm in height, with a 1-inch diameter, and operated at 1 and 4 atmospheres pressure respectively. The models were processed using a combination of forward Monte Carlo and forward and adjoint 3-D discrete ordinates (SN) transport methods. The computer codes MCNP5 and PENTRAN were used for all calculations with the Evaluated Nuclear Data Files Version 7 (ENDF/B- VII) continuous-energy neutron cross sections (MCNP5) and multi-group cross sections derived from the BUGLE-96 library by the GMIX utility (PENTRAN). The multi-group energy structure of the BUGLE-96 library is shown in Table 1, below:

Table 1. Forward energy group structure of the BUGLE-96 broad-group

Group Energy Group Energy Group Energy Group Energy

(MeV) (MeV) (MeV) (MeV)

1 1.73E+01 13 2.37E+00 25 2.97E-01 37 1.58E-03

2 1.42E+01 14 2.35E+00 26 1.83E-01 38 4.54E-04

3 1.22E+01 15 2.23E+00 27 l . l lE-01 39 2.14E-04

4 l .OOE+01 16 1.92E+00 28 6.74E-02 40 1.01E-04

5 8.61E+00 17 1.65E+00 29 4.09E-02 41 3.73E-05

6 7.41E+00 18 1.35E+00 30 3.18E-02 42 1.07E-05

7 6.07E+00 19 l .OOE+00 31 2.61E-02 43 5.04E-06

8 4.97E+00 20 8.23E-01 32 2.42E-02 44 1.86E-06

9 3.68E+00 21 7.43E-01 33 2.19E-02 45 8.76E-07

10 3.01E+00 22 6.08E-01 34 1.50E-02 46 4.14E-07

11 2.73E+00 23 4.98E-01 35 7.10E-03 47 1.00E-07

12 2.47E+00 24 3.69E-01 36 3.35E-03

[0021] In this experimental embodiment, once the computational methods were validated, six distinct plug-in ³He replacement models were developed via a computational adjoint SN approach. Representative examples of these designs, which match the neutron spectral importance and reaction rate of a 1-inch diameter He tube with an active length of 10 cm at 4 atm, are shown in Table 2, below, and include singular and dual detector configurations utilizing BF₃ gas, ¹⁰B lining, and/or ¹⁰B-loaded polyvinyl toluene (PVT).

[0022] Table 2. He-equivalent designs produced by computational adjoint SN evaluations.

Design Sensitive Number of Length / Cylinder Radius (cm) Pressure

Material Detectors (atm)

1 BF₃ 1 10.00 / 2.00

2 ¹⁰B lining 1 10.00 / 1.90 10 (⁴He) 3 ¹⁰B lining 2 10.00 / 1.27 (rear & forward) 10 (⁴He) 4 BF₃ 2 10.00 / 2.05 (rear) & 1.27 1

5 BF₃ 2 (forward) 1

6 PVT with 1 10.00 / 2.20 (both tubes)

4.50 / 1.27

[0023] The Parallel Environment Neutral Particle Transport (PENTRAN) Code System is a multi-group, anisotropic SN code for Cartesian geometries that was specifically designed for distributed memory and scalable parallel computing using the MPI library. This code optimizes parallel decomposition and also automatically optimizes memory allocation.

[0024] The overall design approach 100 follows an iterative process is shown in FIG. 1, in which cross section data is initially evaluated 110 and initial (proposed) PENTRAN and M CNP5 design models are developed 112. Detector dimensions are estimated and incorporated into the M CNP5 model 114. The initial M CNP5 model is executed on a digital computer 116 and the M CMP5 reaction rate is evaluated 118. If the reaction rate indicates that the M CNP5 model requires editing 120, then control is returned to block 114, otherwise the PENTRAN model is updated to incorporate any new dimensions 122. The adjoint is executed 124 and the PENTRAN is evaluated 126. If the adjoint PENTRAN model requires editing 128 then control returns to step 122, otherwise the forward models are updated 130 and evaluated 132. The models are updated as necessary 134 until they agree (converge on) the data corresponding to the existing ³He detector.

[0025] The code has demonstrated an excellent agreement with various standard deterministic transport codes such as TORT, THREEDANT and PARTISN as well as the current reference Monte Carlo code MCNP5. PENTRAN has also performed quite well in comparisons against experimental measurements that have been conducted for a variety of problems in reactor physics, radiation detection, and medical physics applications.

[0026] PENTRAN solves problems such as multi-group, isotropic/anisotropic scatter, fixed-source and criticality in Cartesian geometry. The code can operate in either the forward or adjoint transport modes, which allows for maximum flexibility in detector design.

[0027] Deterministic Adjoint Transport and the Adjoint Importance Function. In the design of a radiation detector, it is essential to account for particle importance, which reveals the specific spatial locations and corresponding energies where neutrons will contribute the most to the detector response. The solution to the adjoint form of the linear Boltzmann equation (LBE) provides such insight, which unavailable through forward deterministic or Monte Carlo methods. The adjoint form of the LBE can be derived using the adjoint identify for real-valued functions, where the Dirac brackets < > represent integration over all independent variables:

where

Ω ^■ V + a_a(f) a_{s g}'_→g {r, a ' - a ) (2)

[0028] In Equations 1 and 2, ip_g is the angular adjoint (importance) function and H is the forward transport operator. We can develop the adjoint transport operator (H^†) by applying the boundary condition that all particles leaving a bounded system have a zero importance for all groups and also requiring that a continuous importance function exists in order to arrive at:

G

f/t = -Ω ^■ V + a_g (r) - V I da' a_{s g→ g}> (f, Ω ^■ Ω ') . (³)

[0029] The minus sign on the streaming term reflects that, in the adjoint condition, particles travel in a reversed direction, where particles scatter from group g to other groups g' (groups formerly contributing to group g in the forward equation). For the case of a fixed forward detector problem, the neutron flux must satisfy the following relation: ^ΗΨ_β = · (4) because the source term (q) is purposely omitted from the forward operator (H) relation.

Likewise, the inhomogeneous adjoint equation must be satisfied with an adjoint source that is aliased to the group detector response cross section {od_,g) by

[0030] Substituting Equations 4 and 5 into Equation 1 and simplifying yields the important relation:

R = ( Pg°d,g) = <ψ]¾> < (6) where R is the detector response or reaction rate in c s^'1. This relation is valuable because it demonstrates that the detector response can be computed directly from several forward transport computations for each source or a single adjoint transport computation. Although PENTRAN provides the capability to calculate reaction rate using the angular flux shown in Equation 6, the scalar flux can be substituted in cases where they are deemed adequate. This simplification, which is shown in Equation 7 below significantly reduces the output file size and speeds the deterministic computations.

R = \ dE \ a^(x', y', z', E) q(x', y' , ζ' , E) dx'. dy'. dz' ~ Y ^ ^ (^ _j AV_j ,

^Je AV^V_d where:

V = source volume (V_q in cm³) or f¹ cell volume (AVi in cm³)

(χ', y', z¹) = spatial location of non-zero source cells (adjoint)

Φά (^χ'' y'' ^z'_> E) ^{= s}P^atial and energy dependent scalar adjoint function for detector d

q(x', y', ζ',Ε) = spatial and energy dependent source (n cm^'3 s^'1)

<P^† _d,_g,i = * cell scalar adjoint function for detector d and group g.

[0031] The ability to determine R for an arbitrary source distribution, weighted by the adjoint function, demonstrates the power of the adjoint method and its application for radiation detector design. [0032] In one experimental embodiment, the measurements for the gas-filled detectors were conducted in a secure room with a large CONEX (Container Express) that was being used for various cargo monitoring experiments. The neutron source used for the experiments was a plutonium-beryllium (²³⁹PuBe) source with a capsule density of 4.35 g

3 239 6 1 cm^" and containing 15.02 g of Pu (0.94 Ci). The stated emission rate of 1.93 x 10 n s was studied using both Monte Carlo and PENTRAN models and the average calculated emission rate of (1.925 ± 0.0001) x 10⁶ n s ¹ was within round-off of the manufacturer's claim.

[0033] One of the main objectives of any special nuclear material (SNM) detection system is to identify plutonium in cargo that is passing through a border crossing or into a port of entry (POE). The testing of such systems has been hampered over the years by a lack of (a, n) sources, security issues associated with plutonium metal, and/or the availability of another suitable source such as ²⁵²Cf due to radioactive decay or supply limitations. It has been found that a nickel scatter shield could alter a PuBe neutron spectrum to match that of subcritical multiplication in Pu metal, with average emission energy of only 2.11 MeV; therefore, the nickel-shielded source was selected as a natural fit for this experimental embodiment. The shielded source was measured in both the bare and reflected conditions inside the CONEX container, although only the bare case was used for direct comparison with the computational models. The comparisons of the computational modeling results and the experimental measurements are provided in Tables 3 and 4, below. The excellent agreement of the computational techniques confirmed the reliability of the models and established the fidelity of the computational adjoint approach toward detector design.

[0034] Table 3. Comparison of the ³He measured reaction rate recorded over a 2- minute interval for a nickel-filtered PuBe source and computational calculations of the same source with PENTRAN and the 47-group BUGLE-96 broad-group cross sections and MCNP5 with the continuous-energy ENDF/B-VII cross sections.

Method Counts Uncertainty Fractional Bias

(1.96σ)

³He Measurement 16184

PENTRAN Adioint 15780 PENTRAN Forward 16120 - -0.004

MCNP5 Forward 15582 31 -0.037

[0035] Table 4. Comparison of the BF₃ measured reaction rate recorded over a 2- minute interval for a nickel-filtered PuBe source and computational calculations of the same source with PENTRAN and the 47-group BUGLE-96 broad-group cross sections and MCNP5 with the continuous-energy ENDF/B-VII cross sections.

Method Counts Uncertainty Fractional Bias

(1.96σ)

BF₃ Measurement 3169 109

PENTRAN Adjoint 3183 0.004

PENTRAN Forward 3218 0.015

MCNP5 Forward 3273 14 0.033

[0036] General Detector Design Parameters. Although the ³He replacement detector models consisted of various materials and configurations, there were several design features common to all. For example, each detector was fitted with 2 cm of polyethylene at the rear of the detector (away from the source). This specific thickness provided the highest degree of an albedo response, (neutrons scattering backwards into the detector). Another common feature was that each detector included 2 cm of polyethylene on the front-side of the detector (toward the source), 1 cm thick walls on either side, and a common height of either 10 cm or 19.6 cm as was discussed in the introduction section.

[0037] The 1-cm sidewall thickness was simply a procurement result; however, the forward moderator thickness was determined by conducting measurements of the PuBe source using a varying thickness of polyethylene (0 - 6 cm) to establish the maximum count rate. The only variance in the sidewall thickness occurred in the multi-detector designs with dissimilar radii. In those cases, the sidewall thickness was maintained at 1 cm from the outside radius of the larger tube. Each model also utilized a uniform source of 1000 n s^'1 surrounding the entire detector assembly and vacuum boundary conditions, because an initial MCNP5 investigation revealed there was < 2% due to an albedo effect for any surface.

[0038] Although no firm constraint exists regarding the physical size of any

replacement design, serious consideration was given for detectors that would not present any undue installation issues in existing detection systems. As a general rule, the width of a detector assembly presents the greatest challenge regarding plug-in potential and an arbitrary width constraint of 7.62 cm (3 inches) was chosen in order to constrain the detector possibilities.

[0039] In one experimental embodiment the baseline detector used for design purposes was a common 1-inch diameter ³He tube pressurized to 4 atm (5.39E-04 g cm^"3) found in many detector applications. Since alternative materials such as BF₃ (1 atm), ¹⁰B-lined tubes, etc. are usually less efficient for neutron detection compared to this baseline, the only avenue for achieving an efficiency match is to increase the amount of the alternative material in a system. However, for the more difficult detection cases, the challenge of increasing the efficiency must be balanced with the requirement to maintain an overall equivalent neutron spectral response. In other words, one cannot simply insert a larger detector, obtain an acceptable cumulative count from a ²⁵²Cf source at some stipulated distance, and assume the detector will respond in equivalent fashion to a ³He spectral response.

[0040] The adjoint function over the forward air-filled course meshes (toward a source) and the adjoint reaction rate for all air-filled course meshes were plotted as a function of neutron energy in order to objectively evaluate each potential equivalent alternative design. The adjoint reaction rate, in particular, is the most important parameter that must be maintained within an acceptable range across the energy spectrum.

[0041] General findings regarding ³He-equivalent tube designs based on BF₃ gas indicate that the plug-in designs exhibited similar behavior compared with each other and ³He in some circumstances. The first of these similarities was that adjoint energy groups 20 - 41 solely accounted for the total reaction rate, because of minimal thermal emissions from the shielded PuBe source. One other similarity of the gas tube designs was the tendency for the reaction rate to gradually increase from a minimum at -Adjoint Group 20 (6.74E-02 MeV) to a maximum at -Adjoint Group 25 (4.98E-01 MeV) due to a gradual increase in the ¹⁰B (n, a) cross section versus that of ³He (n, p). There was also a tendency for positive biases to occur at -Adjoint Group 29 (1.00 MeV) to -Adjoint Group 41 (6.07 MeV) due to a rapid increase in the ¹⁰B (n, a) cross section. In fact, the magnitude exceeds that of ³He (n, p) beyond neutron energies of about 4 MeV. This disparity is tempered somewhat, however, because elastic scattering with the nucleus becomes the predominant ³He reaction for neutrons > 150 keV. Only deviations from these general tendencies will be discussed further in order to ensure a concise presentation.

[0042] Large Single BF₃ Tube Operating at 2 Atmospheres - Alternative Design 1 (referred to in Table 2, above). The overall reaction rate results for Alternative Design 1 are given in Table 5, below, and demonstrate excellent agreement with the ³He baseline. The graphical information demonstrates that this design exhibits the same overall behavior as the ³He baseline.

[0043] Table 5. Computational reaction rate comparisons for Alternative Design 1.

Method Rate (s^"1) Uncertainty Bias (%)

(1.96σ)

PENTRAN Adjoint 2.644 ~ -0.226

PENTRAN Forward 2.648 - -0.972

MCNP5 Forward 2.587 0.004 -0.805

[0044] From a discrete ordinates perspective, materials with vanishingly small dimensions, such as ¹⁰B linings, present a fine mesh size issue, because the corresponding meshes must of necessity be even smaller that the parent material. Each coarse mesh in the PENTRAN models was subdivided into fine meshes that were a maximum 0.25 cm in each direction for all the gas tube designs in this work and at least two fine meshes were desired for adequate material coverage. However, this mesh size is a factor of 2500 times larger than entire ¹⁰B lining of 1E-04 cm (1 mg cm^"2), and the 5E-05 cm thickness required for 2 fine meshes was far too small to yield accurate deterministic results (note that 1 mg cm^"2 is the range of the alpha particle reaction product in boron). Therefore, the true material density of 2.65 g cm^"3 (pi) at the fine mesh requirement of 5E-05 cm (dxi) was used to calculate the boron density (1.998E-03 g cm^"3) necessary for the use of a 0.5 cm (d¾) course mesh via Equation 8.

Pi dx₁ = p₂ dx₂

[0045] The validity of this equation has been verified by calculations with regular and modified ¹⁰B-lined tubes using MCNP5 and PENTRAN results with the modified parameters. The final plug-in designs stipulated for these tubes likely represent a minimum diameter and the actual designs will need to be adjusted for the use of a 0.28 mg cm^"2 thickness to allow for a more efficient collection of the lithium nuclei. [0046] As shown in FIGS. 2A-2B, one embodiment neutron detector element (referred to as "Design 3" in Table 2, above) for replacement of a ³He-based neutron detector element includes two spaced-apart elongated neutron detector tubes 110 that have a ¹⁰B lining 112 and that are filled with ⁴He 114 at a pressure of 10 atmospheres. Each tube 110 is 10.0 cm long and has a radius of 2.20 cm. A block of a neutron moderator material 120 (such as high density polyethylene) surrounds the neutron detector tubes 110. The block of neutron moderator material 120 has dimensions so as to be able to fit a space for the debased neutron detector element in a neutron detecting system.

[0047] The overall reaction rates for this embodiment are given in Table 6, below, and prove that this design also matches the spectral baseline ³He detector very closely. The design shown in Figure 3 (a) can be easily adapted for a 0.28 mg cm^"2 wall thickness by increasing the tube radii to ~1.84 cm. The overall behavior of this design follows a pattern similar to Design 1.

[0048] Table 6. Computational reaction rate comparisons for Alternative Design 3.

Method Rate (s ) Uncertainty (1.96σ) Bias (%)

PENTRAN Adjoint 2.738 3.321

PENTRAN Forward 2.754 2.992

MCNP5 Forward 2.625 0.004 0.652

[0049] The interface region between the tubes exhibited an increased efficiency as occurred with the other multi-tube designs. However, because of the increased ¹⁰B concentration in this region, there was a factor of 20 increase in the efficiency for Adjoint Group 29 (1 MeV) compared with Design 4 (dissimilar BF₃ tubes) and more than a 25% improvement in Adjoint Group 47 (< 0.1 eV). This concentration was also responsible for the 11% efficiency reduction when compared with the outer portions of the model on the left and right of the tubes and also produced an overall detector response that was unique among the six alternative designs.

[0050] As shown in FIG. 3A, the adjoint function 310 associated with this design conforms quite closely to the adjoint function associated with a conventional ³He design. As shown in FIG. 3B, this design had no negative bias 312 across the entire neutron energy spectrum, which resulted from a combination of the increased ¹⁰B concentration near the sidewalls of the detector and in the inner region between the detectors. The configuration of the B in these areas allowed many more lower-energy neutrons to be detected because of a smaller moderator thickness. As a result of the positive bias behavior, the dual-tube ¹⁰B-lined design represents a conservative case for criticality safety monitoring.

[0051] In an alternate embodiment a first one of the two elongated neutron detector tubes 110 has a diameter of 2.05 cm, whereas the second one of the neutron detector tubes 110 has a diameter of 1.27 cm. In this embodiment, the second tube is disposed in front of the first tube.

[0052] As shown in FIG. 4, a typical neutron detection system includes a neutron detector element 402 (which could include a conventional ³He element or a replacement element 100 of the type shown in FIG. 2A). A high voltage power supply 412 applies a voltage to the neutron detector element 402 and a pre-amplifier 410 responsive to the neutron detector element 402. A linear amplifier 414 amplifies the signal from the preamplifier 410 and a single channel analyzer (SCA) 416 processes the signal from the linear amplifier 414 for use by a timer/counter 418 and for delivery to a computer 422 through a PCI card 420.

[0053] The above described embodiments, while including the preferred embodiment and the best mode of the invention known to the inventor at the time of filing, are given as illustrative examples only. It will be readily appreciated that many deviations may be made from the specific embodiments disclosed in this specification without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is to be determined by the claims below rather than being limited to the specifically described embodiments above.

Claims

CLAIMS What is claimed is:

1. A neutron detector element for replacement of a ³He-based neutron detector

element, comprising:

(a) two elongated ¹⁰B-lined neutron detector tubes spaced apart from each other and filled with ⁴He at a predetermined pressure, the ¹⁰B-lined neutron detector tubes disposed so as to have an adjoint function over a predetermined spectrum of neutron energies within a predetermined bias threshold of a corresponding adjoint function of the ³He-based neutron detector element over the predetermined spectrum of neutron energies; and

(b) a block of a neutron moderator material surrounding the two elongated ¹⁰B- lined neutron detector tubes, the block of neutron moderator material having dimensions so as to be able to fit a space for the ³He-based neutron detector element in a neutron detecting system.

2. The neutron detector element of Claim 1 , wherein the predetermined pressure of 4He comprises 10 atmospheres.

3. The neutron detector element of Claim 1, wherein each of the two elongated ¹⁰B- lined neutron detector tubes has a length of 10.0 cm.

4. The neutron detector element of Claim 3, wherein each of the two elongated ¹⁰B- lined neutron detector tubes has a diameter of 2.20 cm.

5. The neutron detector element of Claim 3, wherein a first one of the two elongated 1⁰B-lined neutron detector tubes has a diameter of 2.05 cm and wherein a second one of the two elongated ¹⁰B-lined neutron detector tubes has a diameter of 1.27 cm, and wherein the second tube is disposed in front of the first tube.

6. The neutron detector element of Claim 1 , wherein the neutron moderator material comprises high density polyethylene.

A method of designing a neutron detector element for replacement of a ³He-based neutron detector element, comprising the steps of:

(a) computing, on a digital computer, a first adjoint function over a

predetermined spectrum of neutron energies for the ³He-based neutron detector element;

(b) generating a proposed model of a replacement neutron detector element that is based on materials that are alternative to ³He;

(c) repeatedly executing the following steps until a second adjoint function based on materials that are alternative to ³He over the predetermined spectrum of neutron energies for the proposed model converges on the first adjoint function based on an ³He response within a predetermined bias threshold:

(i) on a digital computer, running a simulation of the proposed model of the replacement neutron detector element to determine the second adjoint function over the predetermined spectrum of neutron energies for the proposed computer-aided design;

(ii) comparing the second adjoint function to the first adjoint function as a function of neutron energy so as to determine the bias; and

(iii) when the adjoint reaction rate bias is outside of the bias threshold, then modifying at least one dimension associated with the proposed model;

(d) once the second adjoint function over the predetermined spectrum of

neutron energies for the proposed model converges on the first adjoint function within the predetermined bias threshold, then building the neutron detector element so as to correspond with the proposed model as modified.

The method of Claim 7, further comprising the step of determining outward dimensions of the proposed model of a replacement neutron detector element that is based on materials that are alternative to ³He so as to be able to fit into a space for an ³He based neutron detector element in an existing neutron detection system.

The method of Claim 7, wherein the proposed model of a replacement neutron detector element that is based on materials that are alternative to ³He comprises: two spaced apart B-lined neutron detector tubes, each having a length of 10.0 cm and a radius of 1.27 cm; and

⁴He disposed in each of the ¹⁰B-lined neutron detector tubes at a pressure of 10 atmospheres of ⁴He.

The method of Claim 7, wherein the proposed model of a replacement neutron detector element that is based on materials that are alternative to ³He comprises:

(a) a ¹⁰B-lined neutron detector tube having a length of 10.0 cm and a radius of 1.9 cm; and

(b) ⁴He disposed in the ¹⁰B-lined neutron detector tube at a pressure of 10

atmospheres.

11. The method of Claim 7, wherein the proposed model of a replacement neutron detector element that is based on materials that are alternative to ³He comprises:

(a) a neutron detector tube having a length of 10.0 cm and a radius of 2.0 cm; and

(b) BF₃ disposed in the neutron detector tube at a pressure of 2 atmospheres.

(a) a first neutron detector tube having a length of 10.0 cm and a radius of 2.05 cm;

(b) a second neutron detector tube, spaced apart from and in front of the first neutron detector tube, having a length of 10.0 cm and a radius of 1.27 cm; and

(c) BF₃ disposed in each of the neutron detector tubes at a pressure of 1

atmosphere.

The method of Claim 7, wherein the proposed model of a replacement neutron detector element that is based on materials that are alternative to ³He comprises

(a) two neutron detector tubes, spaced apart from each other, each having a length of 10.0 cm and a radius of 2.20 cm; and

(b) BF₃ disposed in each of the neutron detector tubes at a pressure of 1

atmosphere.

14. The method of Claim 7, wherein the proposed model of a replacement neutron detector element that is based on materials that are alternative to ³He comprises a 1⁰B-lined PVT neutron detector tube having a length of 4.5 cm and a radius of 1.27 cm

15. The method of Claim 7, wherein the proposed model of a replacement neutron detector element that is based on materials that are alternative to ³He further comprises a block of a neutron moderator material, the block of neutron moderator material having dimensions so as to be able to fit a space for the ³He-based neutron detector element in a neutron detecting system.

16. The method of Claim 15, wherein the neutron moderator material comprises high density polyethylene, the block of high density polyethylene.