Optimization of Equipment for Tomographic Measurements of Void Distributions using Fast Neutrons

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O

PTIMIZATION OF EQUIPMENT FOR TOMOGRAPHIC MEASUREMENTS OF VOID DISTRIBUTIONS USING FAST NEUTRONS

BY

P

ETER

A

NDERSSON

Abstract

This licentiate thesis describes a novel nondestructive measuring technique for determining spatial distributions of two‐phase water flows. In Boiling Water Reactors, which compose the majority of the world’s commercial nuclear reactors, this so called void distribution is of importance for safe operation.

The presented measurement technique relies on fast neutron transmission tomography using portable neutron generators. Varying hardware options for such an instrument based on this technique and a prototype instrument, which is under construction, are described. The main design parameters are detailed and motivated from a performance point of view. A Pareto multiple objective optimization of the count rate and image unsharpness is presented. The resulting instrument design comprises an array of plastic scintillators for neutron detection. Such detector elements allow for spectroscopic data acquisition and subsequent reduction of background events at low energy by means of introducing an energy threshold in the analysis. The thesis includes two papers: In paper I, the recoil proton energy deposition distribution resulting from the interaction of the incoming neutrons is investigated for thin plastic scintillator elements. It is shown that the recoil proton losses have a large effect on the pulse height distribution and the intrinsic neutron detection efficiency is calculated for varying energy thresholds.

In paper II the performance of the planned FANTOM device is investigated using the particle transport code MCNP5. An axially symmetric phantom void distribution is modeled and the reconstruction is compared with the correct solution. According to the solutions, the phantom model can be reconstructed with 10 equal size ring‐shaped picture elements, with a precision of better than 5 void percent units using a deuterium‐tritium neutron generator with a yield of 3 · 10 neutrons per second and a measurement time of 13 h. However, it should be noted that commercial neutron generators with a factor of 10 higher yields exist and that the

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measurement time could decrease to less than a minute if such a neutron generator would be utilized.

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List of Papers

This licentiate thesis includes two papers, which are referenced to in the text by their roman number. I. Effects of proton escape on detection efficiency in thin scintillator elements and its consequences for optimization of fast‐neutron imaging P. Andersson, H. Sjöstrand, S. Jacobsson Svärd. Nuclear Instrumentation and Methods in Physics Research, Section A, 2010 My contribution: I developed the technique. I wrote the paper. II. Neutron Tomography for Void Distribution Measurements P. Andersson, S. Jacobsson Svärd, H. Sjöstrand. ENC Transactions, European Nuclear Conference, 2010 My contribution: I developed the technique. I wrote the paper.

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OPTIMIZATION OF EQUIPMENT FOR TOMOGRAPHIC MEASUREMENTS OF VOID DISTRIBUTIONS USING FAST NEUTRONS ... 1 Abstract ... 1 List of Papers ... 3 Contents ... 4 1. Introduction ... 6 1.1. Void Distributions in Light Water Reactors ... 6 1.2. Tomography ... 8 1.3. Neutron Transmission Tomography ... 9 1.4. Interactions of Neutrons with Matter and Neutron Detection ... 9 1.5. Measurement Quality ... 10 2. Neutron Tomography using Portable Neutron Sources ... 11 2.1. Portable Neutron Sources ... 11 2.2. Selection of Neutron Energy ... 12 2.3. Measurement Geometry ... 14 2.4. Collimation ... 14 2.5. Fast‐Neutron Detectors ... 16 2.5.1. Scintillator screens with CCD cameras ... 17 2.5.2. Fast‐neutron fission chambers ... 17 2.5.3. Neutron converting screens with gaseous electron multipliers (GEMs) or semiconductor flat panel detectors ... 17 2.5.4. Multichannel plates, MCP ... 18 2.5.5. Scintillator elements with photomultiplier tubes (PMTs) ... 18 3. Construction of the FANTOM device for void distribution measurements ... 22 3.1. The FANTOM device ... 22 3.1.1. Asymmetric spatial resolution requirements. ... 23 3.1.2. Axially symmetric objects ... 23

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3.2. Setting the parameters of importance for constructing an instrument setup ... 24 3.2.1. Design and performance parameters ... 24 3.2.2. Setting l ... 26 3.2.3. Setting the design parameters, F, d1, d2 ... 27 4. Summary of Paper I ... 32 5. Summary of Paper II ... 36 6. Conclusions ... 38 7. Discussion and Outlook ... 38 7.1. The Background Signals ... 38 7.2. Tomography of Dynamic Properties ... 39 7.3. Construction ... 39 8. Acknowledgements ... 40 9. References ... 42

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1. Introduction

This licentiate thesis explores an innovative non‐destructive measurement technique that addresses measurements of void distributions, which are of importance for the safety and efficiency of Boiling Water Reactors (BWRs) that is a common type of commercial reactor. The measurement technique under study is tomography using fast neutrons from portable neutron generators. Tomography means that external measurements are performed to describe the inner properties of an object. The main purpose of this technique is measurements of void distributions (see section 1.1) in full scale mock‐ups of BWR fuel bundles. Such measurements are important to perform in order to get an understanding on the void distribution and its implications on safety parameters such as Critical Heat Flux (CHF), which is limiting the power outtake of nuclear reactors.

In section 2 of this thesis, the fundamental components of a fast neutron tomography device are described. Different hardware options are briefly explained. In section 3 the FANTOM (Fast Neutron TOMography) instrument, which is under construction, is introduced. The various aspects of importance for this experimental device are described and design parameters are detailed and motivated from a performance point of view. The FANTOM instrument is intended for evaluation of the concept and methods of fast neutron tomography of void distributions. After the preparatory phase, the FANTOM device is planned to be used in investigations ,e.g., at the HWAT test loop [1] in the Royal Institute of Technology in Stockholm.

1.1. Void Distributions in Light Water Reactors

Void is defined as the volume fraction of steam in a two‐phase flow of liquid water and steam. The void distribution is of major importance in Boiling Water nuclear Reactors (BWRs), where water acts as both coolant of the fuel and moderator of the neutron flux. Therefore, good knowledge about the void distribution in reactors is important for achieving efficient and safe In Core Fuel Management (ICFM) [2].

The ability of a two‐phase flow to cool the LWR fuel decreases drastically at the critical heat flux (CHF), where a small increase of the heat flux causes a large increase of the fuel wall temperature. The reason for this is that at the CHF the heat from the fuel causes boiling of the surrounding water at such amounts that no water remains to cool the fuel wall. This is a process called dry‐out and it might cause damage of the fuel, in which case the integrity of the fuel is jeopardized. Because the integrity of the fuel is considered to be one of the barriers which protect the public from the radiotoxic fission products, great efforts are made to avoid reaching CHF. Furthermore, if the fuel is damaged, the reactor has to be shut down until the damaged fuel has been identified and possibly replaced, causing great economical loss due to loss of production.

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Two‐phase water flows develop in different flow regimes, illustrated in Figure 1, and the mechanisms leading to CHF differ as a consequence of the regimes [3]. In bubbly flows (1a) bubbles might crowd in a boundary layer close to the wall, thereby preventing liquid water from accessing the wall in the same rate as it is vaporized. In annular flows (1d) the liquid water film might dry out due to evaporation and entrainment of droplets in the steam column. Figure 1. Two‐phase flow regimes in vertical pipe: (a) bubbly flow, (b) slug flow, (c) churn flow and (d) annular flow [4]. Since knowledge about the onset conditions of overheating is essential for the safe design and operation of reactors [5], there are several thermal hydraulics test loops in the world, where critical heat flux is studied with electric heating. There are test loops both with simplified geometries, such as cylindrical or rectangular cross sections, and test loops that simulate nuclear fuel geometries. The latter test loops can consist of concentric cylinders [1] to simulate a single fuel rod or of full scale models of fuel assemblies [6]. CHF can be identified in these test loops by a sharp increase in wall temperature which is measured by thermocouples. Additional knowledge of the void distribution would be an important contribution for understanding the onset mechanisms. Furthermore, the void distribution determines the moderation in a real reactor fuel assembly, which determines the power distribution. Consequently, knowledge of the void distribution can be used to enhance the predictive capabilities of the core simulations used at nuclear power plants. Since the void distribution is a complex function of fuel geometry, fuel power distribution and spacers, it is not easily calculated. Measurements of the void distribution in thermal hydraulic test loops would be a valuable tool for evaluating and improving this type of calculations. Many techniques have been applied or suggested for measuring the distribution of the phases in multiphase flows. Some of them utilize intrusive probes such as wire‐mesh sensors [7]. There are also several non‐intrusive techniques that can be used for multi‐phase flow measurements, such as tomography using a wide range of techniques; gamma [6], X‐ray [8], NMR [9], electric

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impedance tomography [10], optical tomography [10] and neutrons [11],[12]. This thesis will not go into detail on all these techniques but rather concentrate on fast‐neutron tomography.

1.2. Tomography

The term tomography covers a variety of techniques for imaging the interior of objects by making external measurements and applying reconstruction algorithms. Tomography first found use in medicine, where a number of different tomographic techniques are available, such as Computed Tomography (CT), Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT). The first brain X‐ray CT scan was performed in 1969 [13]. The inventions in this area by G. Hounsfield and A. Cormack were awarded the 1979 Nobel Prize in Medicine. Subsequently, tomography has been exploited in other fields, such as nondestructive testing, failure search, etc.

In a CT measurement the object is probed with a beam of radiation from an external source and the intensity transmitted through the object is measured. This technique is sometimes called transmission tomography, which is more describing since all tomographic techniques require computation. Traditionally, X‐rays have been used in CT. However, neutrons are used in the technique described in this thesis.

The image reconstruction is based on the attenuation in each line of sight. This can be calculated since the penetrating intensity depends exponentially on the attenuation along the path according to Beer’s law, see Eq. 1 Eq. 1 Here, S is the signal intensity in the detector, S0 is the reference signal intensity when no object is present, the so called flat‐field intensity, is the projection of the linear attenuation coefficient, µ, of the object in the path of the radiation in the cross section plane of the object and is the position vector. A large number of data points are acquired by using many detectors at different positions and by rotating the object relative to the equipment, see Figure 2.

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Figure 2. Illustration of a fan beam measurement geometry and the recording of a projection using a large number of detector elements, Nd. Object rotation relative to the source‐detector system is required to achieve additional projections. The number of rotational increment is denoted Nф. The internal attenuation distribution is reconstructed based on the Nd * Nф data points recorded. If all possible projections are known, the internal attenuation can be reconstructed analytically using the inverse Radon transform [14]. In practice, the data is discretized and can be solved by back‐projection, convolution or iterative reconstruction methods [14]. 1.3. Neutron Transmission Tomography

Over the last decades Neutron Transmission Tomography (NTT) has been developed as an alternative to traditional x‐ray CT in nondestructive testing. One of the main advantages of NTT is the relatively large neutron cross sections of some light elements, such as hydrogen. Because of this, NTT is sensitive to hydrogen‐rich materials such as water and plastic, to which X‐rays are insensitive. This sensitivity to hydrogen makes NTT an interesting concept for void distribution measurements in two‐phase flows of water.

World leading neutron tomography facilities such as those at the Paul Scherrer Institute (PSI) [15] or Forschungsreaktor München II (FRM II) [16] utilize strong neutron sources; a spallation source or a research reactor. High‐performance neutron tomography has not yet been demonstrated using mobile neutron sources. However, in the case of void distribution measurements at the two‐phase test loops described above, the objects are immobile and thus the neutron source has to be mobile.

1.4. Interactions of Neutrons with Matter and Neutron Detection

Neutrons are uncharged particles and are not continuously slowed down in matter by the Coulomb force, such as charged particles. Therefore, neutrons may pass through many

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centimeters of material without any interaction, making the radiation difficult to shield or detect. However, occasionally, the neutrons undergo an interaction with nuclear matter due to the strong force, whereby a range of reactions can occur, including the following: • Elastic scattering (n, n) • Inelastic scattering (n, n´) • Radiative capture (n,γ) • Induced fission (n, f) • Proton emission (n, p) • Alpha emission (n, α)

For slow neutrons (energy 0.5 eV), the dominant reactions are elastic scattering (n,n) and radiative capture (n,γ). For fast neutrons (energy > 0.5 eV), the probabilities of most of the neutron‐induced reactions decrease as the energy increases. Scattering becomes the dominant reaction. When the neutron energy is high enough, inelastic scattering becomes possible, where the scattered nucleus is in an excited state after the collision. The nucleus is then de‐ excited through emission of a gamma radiation. Since the fast neutron loses energy through the scattering reaction, the flux of neutrons is gradually moderated (slowed down). As the neutron is moderated, the reactions that are dominant for slow neutrons increase in importance. [17] It should be noted that in the case of neutron detection for fast‐neutron tomography, the secondary gammas can be a source of background signals if the detector is sensitive to gamma. Furthermore, only the unscattered neutron flux is adequately treated by traditional transmission tomography techniques. Therefore, also the scattered neutron flux might be considered to contribute to the background.

For detection of slow neutrons, none of the dominant reactions are very useful since very little energy is transferred to the recoil energy in the scattering and the gamma is also difficult to detect. Other, material specific, reactions are more commonly used in slow neutron detectors where the secondary radiation is charged particles. Examples of such are protons (n,p), alpha (n,α) and fission (n,f). [17] For detection of fast neutrons, as opposed to slow neutrons, scattering might be used for detection of fast neutrons since it can give detectable amounts of energy to the recoil particle. [17]

1.5. Measurement Quality

An important aspect of measurements is the determination of the quality of the results. The quality of the results in imaging applications, such as radiography or tomography, cannot easily be expressed without an understanding of the concepts involved in imaging. Each pixel in a reconstruction of the void or other properties, such as density or attenuation, is an individual estimate of a real physical quantity, and the deviation between the real value and the estimate

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can simply be defined as the measurement error. However, it is difficult to make a general quantification of this error. Instead, three principally different sub‐categories of image quality are used in this thesis. • Accuracy • Precision • Unsharpness The accuracy is defined as the systematic, reproducible deviation between the real quantity and the estimate. The precision is defined as the irreproducible fluctuations of the estimate, due to stochastic properties, such as the counting statistics in ionizing radiation detectors. The image unsharpness causes small features in the object to be smeared out over a larger area in the image and can be quantified as the distance in the image over which a sharp edge in the object is represented. See Figure 3 for visual illustration of unsharpness. Figure 3. Attenuation profile of two concentric cylinders affected by image unsharpness. Red data points are the real physical quantities and blue data points are affected by unsharpness.

2. Neutron Tomography using Portable Neutron Sources

2.1. Portable Neutron Sources The most important component in an NTT instrument is the neutron source. Generally, there are two available types of small‐size neutron sources that can be utilized in portable devices; • radionuclides, such as 252 Cf,

• sealed tube neutron generators (NG), utilizing fusion reactions between Deuterium‐ Deuterium (DD) or Deuterium‐Tritium (DT). 0 20 40 60 0 5 10 15 Detector Position A tt enuat io n [ a .u .]

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NGs have the advantage that they can be turned off while radionuclides cannot. Therefore, NGs are more practical in a working environment. NGs using DT fusion contain the radionuclide tritium, which has a half‐life of 12 years and is hazardous if inhaled or ingested. However, the beta radiation from its decay is easily shielded in any containment. Furthermore, neutron generators are quasi‐mono energetic, which can be exploited for scattered neutron background rejection, while radionuclides emit neutrons with a wide energy spectrum.

The central component of a portable neutron generator is a linear accelerator which accelerates one of the reactant ions, normally Deuterium. The accelerated ions fuse with the other reactant (Deuterium or Tritium) embedded in a metal hydride target. The following neutron‐producing reactions take place:

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Due to the low mass of the neutrons, they carry the majority of the released energy in the reactions; 2.5 MeV from DD fusion and 14.1 MeV from DT fusion. The neutrons are emitted isotropically in the CM system of the reactants. In the Lab system, the neutrons are emitted close to isotropically, provided that the kinetic energy is low (normally ~100 keV).

The neutron yield of mobile neutron generators is typically in the range of 108 to 1011 n s‐1. At a distance of 1 m this implies a flux of 103 to 106 ns‐1cm‐1.This is very low compared to spallation and reactor sources, where a flux of 108 n s‐1cm‐2 is available [18]. Therefore, a NTT system based on a portable source needs to be constructed with a geometry and a detector system that makes efficient use of the low neutron flux. Otherwise, the low flux must be compensated for by prolonging the measurement times.

2.2. Selection of Neutron Energy

Measurements of void distributions requires high contrast of the water, which requires large reaction cross sections of the hydrogen and oxygen as compared to other materials for the selected probe. As mentioned above, NTT is often chosen when high contrast of hydrogen‐rich materials is desired. This feature of neutrons is less pronounced when fast‐neutrons are used instead of thermal, since the fast‐neutron cross sections of different materials are more uniform. As shown in Figure 4, the cross sections are also generally smaller in the fast spectrum than in the thermal. Additionally, the sensitivity to hydrogen relative to structure materials of a two‐phase test loop such as iron and zirconium is smaller for fast neutrons than for thermal neutrons. However, the sensitivity to hydrogen in an iron or zirconium environment is still better using fast neutrons than using photons, such as 667 keV gamma from the decay chain of 137

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Figure 4. Total reaction cross sections of elements 1H, 8O, 26Fe and 40Zr. (average of isotopes weighted by natural occurance)

Each circular area represents the microscopic cross section of that element. Thermal neutrons, gamma and X‐ray cross sections are added for comparison to the fast neutron cross sections. Note that because the zirconium X‐ray cross section is too large to fit in the figure, it has been excluded.

The neutrons emitted in both the DD and the DT reactions are fast. If it would be desirable, a moderator could be used to achieve a thermal spectrum. In this process, the neutrons would diffuse to a relatively large moderator volume, and a pin‐hole geometry would be needed to meet any requirements of spatial resolution in such a setup. Because this would reduce the already low flux of neutrons even further, the chosen strategy for FANTOM is to use fast neutrons as the probe, and moderation is not planned for.

Optimally, the selected probe (neutrons or gamma) interacts in the object by absorption, so that the interacting particles are removed from the penetrating flux. However, for fast neutrons, scattering is the dominant type of interaction. Therefore, the beam intensity is not following the exponential decrease predicted by Eq. 1.; there is an additional term from scattered neutrons with their origin far from the nominal lines of sight of the detector element that register them. This increases the overall count‐rate in the detector, as compared to what is expected from Eq. 1. Consequently, this additional flux would make the object appear less attenuating, unless it is effectively shielded by collimators, discriminated by the data collection system or corrected for in the analysis. Correction for background in the analysis depends on a Neutrons 2,5 MeV Neutrons 0.025 eV Gamma 667 keV Neutrons 14 MeV X‐ray 100 keV Zr O Fe H Scale 1 b 5 b 10 b

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adequate model of the background flux. Such models are associated with uncertainties and introduces inaccuracy in the measurement.

2.3. Measurement Geometry

Transmission tomography is performed using one of three common measurement geometries; parallel, fan beam or cone beam. To make efficient use of the available neutrons, a cone or fan beam geometry is a natural choice for NTT using portable generators with isotropic emission because this allows many lines of sights to be mapped simultaneously with an isotropic source. In this work focus has been put on two‐dimensional cross section images and a fan beam geometry is adequate; as illustrated in Figure 2 in the previous section.

2.4. Collimation

As stated in section 2.2, a problem of fast‐neutron imaging is the large component of scattered neutron flux. One of the suggested solutions to this is the use of collimators to shield the detectors from neutron radiation from other directions than the desired. However, because the dominant type of reaction of fast neutrons is scattering, the introduction of collimators in the setup might do more harm than good if they are not large enough for moderation and capture because of the additional scattered flux from the collimator itself. For the purpose of void distribution measurements, where a mobile setup is needed, such collimation might be too space consuming. However, since the neutrons that hit the detector after being scattered have lost part of their energy in the scattering reaction, this background can be reduced by introducing energy discrimination in the data acquisition system, i.e. only counting events with energy deposition above a certain energy threshold. A study of the signal to background (S/B) ratio in a simplified setup (see Figure 5) for different sizes of collimator has been performed with the particle transport code MCNPX [19]. The model contains only a point neutron source of 14.1 MeV, a thermal hydraulic test section represented by a cylinder of water, Ø = 10 cm, at a center distance of 10 cm from the source point and a neutron counting detector opposite of the cylinder from the source point, at a distance of 100 cm from the source point. In addition, collimators of different lengths are introduced in the space between the water cylinder and the detector. The collimator is made by borated plastic with 10% boron content.

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Figure 5. An MCNPX simulation setup for investigating the effect on the signal to background ratio of collimators of different lengths. Neutron path A represents the flux of neutrons scattered in the object, which is reduced by a collimator. Path B represents the signal neutron flux. Path C represents the background flux of scattered neutrons, which is introduced by insertion of the collimator.

The results of this study are presented in Figure 6. The introduction of a collimator increases the scattered neutron flux at the detector position when the collimator length is small. As the length increases to about 25 cm, the scattered flux decreases to a break‐even value, i.e., the same S/B ratio as that without a collimator. Further increase in collimator length gradually improves the S/B ratio.

However, it is also seen that an energy threshold in the neutron counter improves the S/B ratio much more than a collimator. In addition, the break‐even length of the collimator increases when used in combination with an energy threshold. The break‐even length is reached at 40 cm using an energy threshold of 4 MeV, if 8 MeV threshold is used, break even is not even reached at 50 cm collimator length, see Figure 6.

Neutron counter

Source

Collimator

Water cylinder

A

B

C

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Figure 6. Simulated S/B ratio in simplified measurement geometry whith different energy thresholds and collimator lengths (of borated plastic).

Since there is a need for a collimator of substantial size to improve the signal to background ratio, a better strategy in this case is to avoid collimators completely. This allows a mobile NT device with a compact and lightweight construction. Instead, an energy discrimination approach is considered for background reduction.

2.5. FastNeutron Detectors

There is a large variety of detection systems that may be used for fast‐neutron tomography. In all of them, the neutrons are converted to a secondary radiation signal, which is subsequently converted to an electric signal. In this section follows a short description of five detector concepts: • Scintillator screens with CCD cameras, [20]. • Fast‐neutron fission chambers based on 238 U or 242Pu. • Neutron converting screens with gaseous electron multipliers (GEM) or semiconductor flat panel detectors, [21]. • Multichannel plates (MCPs), [22]. • Scintillator elements with photomultiplier tubes (PMTs), [23]. 0 5 10 15 20 25 30 35 40 45 50 0 2 4 6 8 10 12 Length of collimator [cm] S/B r a ti o

Effects on S/B ratio of borated-plastic collimator Et = 0 MeV Et = 4 MeV Et = 8 MeV

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2.5.1. Scintillator screens with CCD cameras

The most commonly used detector in NTT has traditionally been scintillator screens with CCD cameras. Here, the neutrons are converted to a secondary radiation of charged particles in a thin scintillator screen. The energy of the charged particles is converted to light as they decelerate in the scintillator, which is registered in a CCD camera. Often a mirror system is used to guide the light from the screen to the camera, which is positioned in a shielded box. The long mean free paths of fast neutrons make this setup inefficient, since most neutrons simply pass through a thin screen without interacting. Increasing the thickness of the screen might compensate for this, but it also increases the complexity of the setup with a fan beam geometry [24]. Also, the thicker the scintillator screen, the larger the flux of scattered neutrons will be. Furthermore, this setup does not allow energy thresholds on an event‐by‐event basis, and thus a high degree of background must be handled in the analysis.

2.5.2. Fastneutron fission chambers

Fast‐neutron fission chambers have been suggested, where the detector material is 238U or 242

Pu. These isotopes offer some energy discrimination inherently since thermal neutrons do not induce fission. However, their energy threshold for fission is close to 1 MeV, which means that the neutrons on average have to undergo many scattering reactions before ending up below the energy threshold, especially if a DT neutron generator is used. Furthermore, the fission reaction is not the dominant type of reaction (5 ‐30 %) for the fast neutrons implying a low efficiency.

2.5.3. Neutron converting screens with gaseous electron multipliers (GEMs) or semiconductor flat panel detectors

Neutron converting screens with GEMs is an example of a detector system that utilizes a thin screen for conversion of neutrons to charged particles. The charged particles escape the converter screen and are subsequently detected in a position‐sensitive detector. For fast‐ neutron detectors the efficiency of such detectors is limited by the range of the charged particle in the converter. The converter thickness cannot exceed the charged particle range, which is typically in the order of millimeters. Therefore, the neutrons are unlikely to interact in the converter, and the efficiency is low. A detection efficiency of 0.2 % for 5 MeV neutrons has been reported in ref [21], where cascading of 25 such detectors was suggested to reach a fast neutron detection efficiency of 5%.

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2.5.4. Multichannel plates, MCP Silicone MCPs have been suggested for fast‐neutron detection. In silicone MCPs the incoming neutrons are converted to protons, deuterons or alpha particles by a number of reactions in the silicone [22]. The charged particles generate electrons in etched microscopic channels through the detector. This signal is amplified by applying an electric field over the length of the channel. Because the conversion takes place within the structure of the MCP, it does not suffer from the low efficiency associated with the conversion screens. However, the practically etchable thickness in the manufacturing process has so far been limited to 10 mm for conventional MCP glass. For fast‐neutron detection in silicone MCPs, 30 mm thickness has been suggested, with a calculated detection efficiency ranging from 2 – 15 %. [22]

The silicone MCPs offer inherent scattered neutron background discrimination due to the energy thresholds of the converting reactions, which are located at energies above ~5 MeV.

2.5.5. Scintillator elements with photomultiplier tubes (PMTs)

Matrices of scintillation fibers have previously been used to achieve space‐resolved screens with CCD cameras [25]. Larger scintillator elements have also been used with individual connection to photomultiplier tubes (PMTs) or position sensitive photomultiplier tubes (PSPMTs) for event‐to‐event pulse‐height information, [23]. Examples of setups of this type can be seen in Figure 7.

Here, the neutrons are converted to charged particles in the scintillator elements. As the charged particles slow down they excite the scintillator material, which emits light when it is deexited, promptly by fluorescence or slowly by phosphorescence. The light is transported through light guides to the photocathode of a PMT, where it is converted to electrons. Inside the PMT, the electrons are multiplied in a dynode system and the output electrical signal is collected at the anode at the back end of the PMT.

Because the scintillator light response is proportional to the charged particle kinetic energy and the PMT amplification normally is linear, the charged particle’s energy can be determined. This can be used for applying energy discrimination in order to suppress the background from scattered neutrons. However, the neutrons only deposit a fraction of their energy at each interaction in the detector. Accordingly, hydrogen‐rich scintillator materials are preferred for the detection of fast neutrons, because the neutrons deposit a relatively large fraction of their energy when scattered against a nucleus of similar mass, such as the hydrogen nucleus (proton). With the use of such a scintillator, an energy threshold can be introduced at the

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expense of lowered detection efficiency. Accordingly, a trade‐off has to be made between high detection efficiency and low sensitivity to the background of scattered neutrons.

Two available hydrogen‐rich scintillator materials are plastic scintillators and liquid organic scintillators. The plastic scintillators have the advantage that they are easy and cheap to manufacture in fibers or other shapes. The liquid scintillators also offer pulse‐shape discrimination of gamma background, which is caused by radiative capture and inelastic scattering of neutrons.

The image unsharpness is limited by the effective area of the scintillator elements. With an isotropic source, it might be advantageous to align each element with the direction of the beam to have a minimal effective area of each element. Figure 7. Detector concepts. A) Scintillator fiber matrix for imaging. Light guides to PSPMT to the right. B) Scintillator plate array. Fish‐tail light guides to PMTs or PSPMTs to the right.

The detection efficiency of the detector proportional to the ratio of the area that is covered with scintillator element. Furthermore, the intrinsic detection efficiency of each scintillator element depends on the distance travelled by the neutron in the element. This could potentially be very long to allow an almost 100 % interaction probability of the neutron. However, the intrinsic efficiency is still limited by the interactions with carbon, which are largely

A

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parasitic because of its poor conversion efficiency to light. Therefore, the intrinsic efficiency has an theoretical upper limit defined by Eq. 2. Eq. 2 Where p is the interaction probability, , is the cross section and N is the particle density. This limits the theoretical intrinsic detection efficiency to 63 % for 2.5 MeV neutrons and 36 % for 14.1 MeV neutrons. However, dimensional constraints on the scintillator elements and energy threshold in the analysis are likely to lower these efficiencies considerably. Thin plastic scintillator fibers in combination with energy thresholds in the data acquisition on an event‐by‐event basis have the fortunate side‐effect of directional discrimination, which can be exploited. As mentioned above, the energy deposited by neutrons in an organic scintillator fiber is not converted directly to light, but indirectly through a charged particle; most importantly recoil protons from elastic scattering. Furthermore, the proton energy distribution created in a mono‐energetic neutron flux is quasi‐uniformly distributed from zero (90° lab system scattering angle) to the full neutron energy (head on collision). The proton energy is converted to light as it decelerates to a stop in the scintillator. The reason for the directional sensitivity is that full neutron energy conversion to light implies a long recoil‐proton travel range in the scintillator material and a zero degree scattering angle of the proton. Using small‐ size scintillator (a thin plate or fiber with small diameter) implies that the forward‐scattered proton is likely to escape the scintillator material before depositing all its energy, unless the incoming neutron was traveling along the fiber axis.

In addition, one may note that also the gamma‐ray background is reduced according to the same principles, although even stronger because gamma radiation interacts dominantly with the electrons in the material, which have longer travel range than the secondary protons. Thus, a detector array can be dimensioned to have a sensitivity to background from arbitrary directions that is reduced compared to the sensitivity of the mono‐directional signal component of the neutron flux at an adequate energy threshold level. An example of such a detector element is seen in Figure 8. The sensitivity to neutrons, with the introduction of an energy threshold, is shown as a function of the neutron off‐axis angle in Figure 9. This might particularly reduce the background levels from walls, environment and background scattered from the detector itself, so called undercut.

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Figure 8. Direction‐sensitive detector element (here a scintillator fiber) having the largest sensitivity for neutrons entering in the material along its axis i.e. v= 0°. Figure 9. Directional sensitivity of fiber in previous figure using energy threshold at 10 MeV in mono‐energetic and mono‐ directional flux of neutrons of 14.1 MeV.

A neutron imaging equipment with high resolution requires a large number of detector channels. A disadvantage with scintillator fiber arrays with PMTs is that the detector might be costly, since each fiber require a PMT.

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3. Construction of the FANTOM device for void distribution

measurements

3.1. The FANTOM device

An NTT device called FANTOM (Fast Neutron TOMography) is currently being constructed at the Applied Nuclear Physics Division of the Uppsala University. It is intended for evaluation of fast neutron tomography methods and for use in measurements of axially symmetric thermal hydraulic test loops. The FANTOM device utilizes a DT neutron generator with a yield of 3 · 10 neutrons per second. The detector is a scintillator array of 4 plastic scintillator elements of material EJ208 with light guides to PMTs. This detector setup is chosen since it allows variable energy discrimination and a high intrinsic detection efficiency compared to the other options listed in section 2.5. However, the absolute detection efficiency is limited here because of the low number of only 4 elements, which is a consequence of the economical constraints and the available data collection equipment. Translational movement on the object relative to the source‐detector system is enabled to allow additional lines of sight to compensate for the low number of detector elements. In addition, the object can be rotated to allow for the recording of various angular projections, see Figure 10.

Figure 10. Setup including detector, with 4 sensitive elements, a test section with translational an rotational stage (for object movement) and neutron generator.

In order to reduce measurement time, adaptations have been made to the thermal hydraulic test loop that is the object under consideration for the device. Two features available that we make use of have been identified in this context:

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• Asymmetric spatial resolution requirements, i.e., different requirements on unsharpness in different axes. • Axially symmetric object. Adaptations made to the instrument for both these features can lower the measurement time as described more in detail below. 3.1.1. Asymmetric spatial resolution requirements. In the two‐phase test loops, the demands for spatial resolution are higher in the cross section of the flow than in the axial direction of the test section. Resolution in the order of mm or sub‐ mm is needed to resolve features between fuel rods, while in the axial direction resolution in the order of cm is sufficient. Due to the asymmetric resolution requirements we can use an array of plastic scintillator plates; extended along the axial direction and the neutron beam direction, see Figure 7. Thereby, the count rate in each detector element increases proportionally to the effective area, which speeds up the measurement.

3.1.2. Axially symmetric objects

In the characterization stage, the FANTOM device allows for rotational movement of the object. This makes tomography of general non‐symmetric objects feasible. However, at one of the identified two‐phase flow test loops that are of interest for void tomography, HWAT [1], the test section is axially symmetric. The water is confined by an outer cylinder and an optional inner cylinder, both with optional heating. In an object with axial symmetry, all projections of different rotational angles around the symmetry axis are equal and no rotation is required. Therefore, the required number of data points is significantly reduced for such objects. For tomography of objects which are not axially symmetric, it can be estimated that the number of rotational increments (Nф) should exceed the number of detector positions (Nd) by a factor of

/2, [14].

The inverse Radon transform reconstruction, mentioned in section 1.2, is in this case substituted by the simpler inverse Abel transform [26]. In the discretized version, the common image representation in terms of quadratic picture elements, pixels, are replaced by concentric ring‐shaped picture elements, rixels.

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3.2. Setting the parameters of importance for constructing an instrument setup

3.2.1. Design and performance parameters

In the planning of the FANTOM instrument, there are several instrument design parameters that need to be adequately selected in order to optimize the performance. Performance parameters that might be considered are listed in Table 1: Table 1. Performance parameters considered for FANTOM device. Performance parameter Acronym Count rate CR Image unsharpness U Signal to Background ratio S/B These performance parameters are connected to the quality of the image, discussed above in section 1.5. The count rate affects the statistical uncertainty, which determines the precision. A high S/B ratio is important for the accuracy of the image, since background has to be compensated for in the analysis and in that process a model error might be introduced. In this work, it is considered that the neutron source available cannot offer a yield high enough to saturate the detectors in the measurement geometries that are relevant for the current application. Accordingly, optimization of count rate means obtaining the highest count rate possible. However, a trade‐off has to be made between the count rate and the unsharpness. Important design parameters which affect the performance are seen in Table 2: Table 2. Design parameters of the FANTOM device. Design parameters Acronym Detector element width F Detector element length l Distance source‐to object d1 Distance object‐to‐detector d2 Source spot size a Neutron yield Y The measurement geometry and its important design parameters are seen in Figure 11. There are also other measurement parameters that do not need to be fixed in the design phase, but do affect the performance parameters, such as the energy threshold. It should be noted that all the design parameters listed in Table 2 could possibly be selected in the design of a device. However, in the FANTOM case the neutron yield and the spot size are not selectable but are determined by the available neutron generator.

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Figure 11. Schematic illustration of the design variables in the measurement geometry.

It can be seen in Table 3, that the majority of the design parameters affect all the performance parameters. In Table 3, the neutron yield and spot size are excluded, since they are not selectable in the FANTOM device.

Table 3. Dependency table for design parameters of the FANTOM tomographic instrument. The table illustrates if performance parameters are affected by design parameters. Count rate Image unsharpness S/B ratio

Detector element length, l yes no yes

Detector element width, F yes yes yes

Distance source‐to‐object, d1 yes yes yes

Distance object‐to‐detector, d2 yes yes yes

Energy threshold yes no yes

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It can be seen in Table 3 that with a few exceptions, all performance parameters are affected by all design parameters. Therefore, all the three listed performance parameters in Table 3 have to be simultaneously considered for a full optimization of the device. Especially the S/B, which is affected by all the listed design parameters, is difficult to evaluate for any given design. The background level is depending on additional parameters to the listed ones, such as the object size and material, the lab environment materials in walls, ceiling, the floor, the FANTOM device structures, shielding, materials and instrumentation hardware. Some of these are not known beforehand and may even change from one measurement to another. Furthermore, S/B is also strongly affected by the energy threshold which can be changed after the design of the instrument.

To simplify the design parameter selection procedure, it has been decided that the FANTOM device is optimized only with respect to a subset of the design and performance parameters. The detector length, l, is set (but not strictly optimizated) with considerations of the effects on CR and S/B, as presented in section 3.2.2.The design parameters d1, d2 and F are selected prior to the construction, by optimizing the performance parameters CR and U according to section 3.2.3. The energy threshold will be selected after the device is built also considering the CR and S/B . However, this can be optimized experimentally. It should also be noted that a preliminary assumption on the energy threshold has to be used in the optimization procedure of the count rate and the unsharpness and this might not be the same energy threshold that is eventually used. 3.2.2. Setting l

As the detector length, l, increases, the penetrating signal beam intensity decreases exponentially. Therefore, the detection efficiency and hence the count rate is enhanced with increased length, but the more the length is increased, the smaller is the enhancement, since the signal of unscattered neutrons gradually gets attenuated by the length of the detector element.

The level of background is also increasing with the detector length. Since the ambient background neutrons can rather be assumed to enter the detector element from arbitrary directions, their intensity is not attenuated but can be assumed to be proportional to the detector length.

Accordingly, l has to be set doing a tradeoff between count rate and the S/B ratio. For the FANTOM instrument, the detector element length, l, is set to one mean free path of the DT neutrons of 14.1 MeV, which is 10 cm, also known as the attenuation length. At this detector length, 63 % of the signal neutrons have interacted in the detector and further increases will

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only increase the detection efficiency to signal neutrons marginally, while the background sensitivity continues to increase proportionally to l.

3.2.3. Setting the design parameters, F, d1, d2

The remaining design parameters F, d1 and d2 all affect the performance parameters listed above. As stated above, only two of them are optimized in the design, i.e., the image unsharpness and the count rate. This is done below in this section, by determining how the performance parameters varies as functions of the design parameters, and then choosing a set of design parameters that give an optimal performance. Since there are two performance parameters to optimize, the Pareto optimal solutions are sought, where one of the performance parameters can only be improved by simultaneously worsening the other.

One additional important aspect for the optimization of the remaining parameters is the physical space limitations on the design parameters. For the FANTOM device, we constrain the total length (d1 +d2) to 1 m, which is motivated by the demands of a small size equipment. We also constrain the minimum physical space between source‐object (d1) and object‐detector (d2) to 10 cm. See all constraints of the FANTOM design in Table 4. Table 4. Constraints in the FANTOM design. ≥ 10 cm ≥ 10 cm 100 cm 1.111 10 The image unsharpness is expressed as a function of the design variables according to Eq. 3, as argued in ref [14]. Eq. 3 Where m is the magnification, defined according to Eq. 4. Eq. 4

The spot size, a, of the source is given by the distribution of the neutron emission in the tritiated titanium target which depends on the emission angle that is used, as seen in Figure 12.

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Figure 12. Conceptual view of spot sizes for neutrons emitted at 90° and 0° angle.

The radial emission distribution is Gaussian like, typically with a FWHM in the order of a few millimeters. Smaller effective spot size can be achieved by directing the accelerator perpendicular to the direction from target to detector. Thereby, the spot size extension in the cross section of the object is defined by the range of the ions in the target. The range of 100 keV deuterons in the titanium hydride target is in the order of micrometers. However, long time running test from neutron generator producers have shown that a hole is gradually created by the interaction of the ion beam with the ion target [27]. This is estimated to a = 0.2 mm, which is used here as an approximate estimate of the spot size, a. Consequently, 90 ° neutron emission angle is used in the FANTOM device. The count rate in a detector element is expressed according to Eq. 5. Eq. 5 Where CR = count rate Y = neutron yield h = detector element height ε = intrinsic detection efficiency Here it can be noted that ε depends on the detector element width and energy threshold. The calculation of the intrinsic detection efficiency is accounted for in paper I, as summarized in section 4. In these calculations a preliminary assumption of the energy threshold has to be used. Since Monte Carlo models used in Paper II indicate that most of the scattered neutron background is below half the signal neutron energy it was considered relevant to assume that

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the energy threshold will be selected at about half the signal neutron energy. Accordingly, the optimization procedure presented here is performed for thresholds of 5, 7 and 9 MeV.

The height of the detector is chosen so that the measurement represents a 10 mm axial section of the measured object, which is the desired axial resolution of HWAT, [28]. With a plate shaped detector element according to the geometry in Figure 7, the extension of measurement in the axial direction is determined by the height of the detector according to Eq. 6, [14].

Eq. 6

Where Uaxial = axial extension of measurement

h = detector element height

Insertion of Eq. 6 into Eq. 5 gives the count rate as a function of d1, d2, and F, see Eq. 7.

Eq. 7

As seen in Eq. 3, U is a function only of F and m, not of the individual distances d1 and d2,. Therefore, for every m, the d1 and d2 can be selected to maximize the count rate without affecting the image unsharpness. As seen in Eq. 7, this is done by minimizing (d1 + d2) within the limits accounted for in Table 4. The optimal sets of d1 + d2 are illustrated in Figure 13. In the figure, the sets that minimize d1 + d2 for a given value of m within the allowed range (1.111 < m < 10) are marked with a bold line.

Figure 13. For every magnification, m, the sum of the parameters d1 and d2 must be minimized for optimal count rate.

Constant m are found in straight lines through origo, where the leftmost allowed point in each line minimizes d1 + d2. The

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The result of the minimization is seen below, in Eq. 8: d , 10 , 10 , , 2 , _{10 cm , 1.111} , , 2 Eq. 8 The difference in the regions above and below magnification, m = , , is caused by the

physical space limitations, where the breaking point represents the most compact possible instrument, for FANTOM d1,min = d2,min = 10 cm gives m = 2.

As seen in Eq. 8, the optimal selections of the sum of the distances d1 and d2 can be expressed using the single variable m. Consequently, the optimization can proceed by only considering the two parameters m and F. Eq. 8 is inserted into Eq. 7, which gives an expression of the count rate that is solely dependent on the design parameters F and m: _, , 10 , , 2 _, ,1.111 , , 2 Eq. 9 Both the unsharpness U (Eq. 3) and the count rate CR (Eq. 9) have been expressed in terms of only two design parameters; F and m. As discussed previously, U and CR are conflicting and cannot be optimized separately. Sometimes, multiple conflicting objectives, such as CR and U, are converted to a single objective in a weighted function, which is then optimized. However, it requires a priori knowledge of the adequate weights, which is not easily attained. Furthermore, the trade‐off between the multiple objectives is not seen with the single objective approach. Pareto multiple objective optimization, on the other hand, shows the trade‐off and does not require a priori knowledge of the weights [29]. In this technique, the set of acceptable trade‐ offs are sought, where a design parameter set is acceptable if it is in the Pareto front, defined as the parameter sets where none of the multiple objectives can be improved unless another objective is impaired.

To find the Pareto front in the FANTOM design space, the remaining design parameters F and m are sampled in a large number of sets. For each sampled set, U and CR are calculated. M is sampled in the region (1.11 < m < 10), where it is confined due to the limitations on d1 and d2. F is sampled in the range 0.1 mm < F < 9 mm. Where F = 0.1 mm gives a count rate that is regarded too low (< 2 cps) for any magnification, and F = 9 mm gives an unsharpness that is unacceptable (> 0.9 mm) for any allowed magnification. The resulting performance parameters

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U and CR are calculated and the results assuming an energy threshold of 7 MeV can be seen in Figure 14. Figure 14. Available count rates, CR, and image unsharpness, U, in the FANTOM design, with a threshold of 7 MeV. Every dot represents one sampled design parameter set (m, F). Since low image unsharpness and high count rate is desired, only the upper, left edge (marked in red) should be considered for the instrument design, which is the Pareto front. Every dot under the Pareto front is inferior to some other set of parameters both regarding the image unsharpness and the count rate.

The Pareto optima are seen as the line to the upper left in Figure 14, i.e., the Pareto front where none of the performance parameters can be improved without worsening the other. The design and performance parameters corresponding to the Pareto front are shown for energy threshold of 5, 7 and 9 MeV in Figure 15.

Figure 15. The Pareto optimal designs parameters and their corresponding performance in count rate and image unsharpness. Calculated for 5, 7 and 9 MeV energy thresholds. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 50 100 150 200 250 300 350 400 U [mm] C R [cp s ]

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By selecting a design parameter set in the Pareto front of Figure 15, the performance parameters of FANTOM are optimized in the sense that both CR and U cannot simultaneously be improved. There are however, many such parameter sets, each representing different weighting between resolution and count rate requirements. In the trade‐off between U and CR, the design parameters have been set to m = 10, F = 5.0 mm, d1 = 10 cm and d2 = 90 cm. This gives a total image unsharpness of 0.53 mm and a count rate of 280, 210 or 150 cps corresponding to energy threshold of 5, 7 or 9 MeV. This image unsharpness allows resolution of features of sizes smaller than the typical fuel rod pitch, which is of interest in the research at the thermal hydraulic test loops [28]. The resulting geometry is visualized above in Figure 10. A consequence of our design choice can be seen in Paper II, where the statistical uncertainties on the individual rixels are too high to make rixel widths in the sub‐millimeter range useful. The low count rate corresponding to the chosen level of unsharpness can be compensated for by longer measurement times or in the future, preferably by a stronger source yield or more detector channels. Allthough 13 h measurement time is assumed in Paper II, extreme measurement times of more than 24 h are suggested as a possible way to evaluate the method for data corresponding the yields of a high‐end commercial neutron generator.

4. Summary of Paper I

As mentioned in section 2.5.5, neutron detection with plastic scintillators is impaired by the random magnitude of the energy transferred to the recoil proton in elastic scattering reactions, implying that the transferred energy can be anything from zero to the full neutron energy. Therefore, applying energy discrimination of background neutrons at low energy also decreases the detection efficiency of the signal neutrons.

If the dimensions of the scintillator are large compared to the range of the recoil proton (which is in the range of mm), the fast neutron detection efficiency in a plastic scintillator element is easily calculated, due to the quasi‐uniform energy distribution of the recoil protons. However, in neutron imaging applications the size of the scintillator elements is limited by the requirements of small receptor unsharpness. When considering scintillator plates, the width of the detector might be in the same order of magnitude as the recoil proton range and the detection efficiency is not easily calculated because the escape of recoil protons leads to lower energy depositions compared to the large dimension scintillator. Consequently, the recoil protons may escape the scintillator element through its sides before depositing all its energy. See Figure 16.

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Figure 16. Neutron undergoing elastic scattering in a thin plastic scintillator element. The recoil proton excites electrons in the material along its path. If the proton exits the scintillator the light yield is hampered.

In Paper I, the recoil proton energy deposition distribution in thin scintillator elements is calculated for 14.1 MeV and 2.5 MeV neutrons in the plastic scintillator material EJ208 using a custom‐made Monte Carlo program, where proton recoils from elastic scattering are simulated by random sampling of the following variables:

• The scattering angle, θ. (sampled from the angular differential cross sections in evaluated nuclear data file ENDF‐B VI) • The azimutal angle, ф. (sampled from a uniform distribution) • The position in the scintillator, x , i.e. the distance from walls. (sampled from a uniform distribution) The energy deposition is calculated as the integral of the of the stopping power acting on the proton, until it reaches zero energy or escapes the scintillator plate through its sides. The resulting proton energy depositions from 14.1 MeV neutrons can be seen in Figure 17.

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Figure 17. Energy deposition distribution of 14.1 MeV neutrons in scintillator plates of varied width.

The pulse height distribution is used for estimation of the intrinsic detection efficiency with the introduction of various energy thresholds. The detection efficiency of 14.1 MeV neutrons is presented in Figure 18.