Construction of a Quasi-Monoenergetic Neutron Source for Fast-Neutron Imaging

This paper presents and discusses an approach to fast-neutron imaging that will provide high-resolution detection (i.e. ≤ 1 mm) of small features such as inclusions, voids, and variations in density. The application for fast-neutron imaging centers around assessing low-Z materials in high-Z shielded configurations. For this paper we present a simple theoretical argument on the feasibility of fast-neutron imaging and present results from some of our feasibility measurements. Finally, we discuss the requirements and objectives for the fastneutron imaging system currently under construction at Lawrence Livermore National Laboratory (LLNL). Introduction Neutron imaging was first demonstrated by Hartmut Kallmann and Ernst Kuhn ca. 1935 (c.f. [1]), shortly after the discovery of the neutron by Chadwick in 1932 [2]. Neutron radiography and x-ray radiography have mutually grown in parallel as technical analogs of each other and are complementary radiographic methods. X-rays and gamma-rays (i.e. high-energy x-rays) interact with the electrons of an atom as well as the nucleus of an atom due to the electromagnetic properties of the photon. In general, this implies that photons interact (i.e. scatter) more readily with higher-Z materials. Neutrons, however, have no measurable net electric charge and can only interact with the nucleus of the atom via strong-nuclear interactions. The reduced interaction field allows the neutrons to penetrate further than photons, providing additional complementary depth to the probes of radiography. Reaction cross-sections for high-energy neutrons show only slight differences between many nuclei and can be represented by a simple model (see [3]). However, low-energy neutron reaction cross-sections vary considerably as a function of nuclei (c.f. [4]). These differences between photonand neutron-reactions with atoms provide the underpinnings for the complementary nature of their respective radiographies. Low-energy neutron radiography has been more extensively developed compared to highenergy neutron radiography because of the length scales of interest are on the order of crystalline lengths. (As a matter of reference, sample shapes have lengths approximately 29fm/√T, where T is the neutron kinetic energy in units of MeV.) Additionally, it is easier to make low-energy neutron sources, especially with moderated fission reactors. Larger reaction cross-sections with different atomic nuclei also make low-energy neutron imaging particularly enticing. Low-energy neutrons can be used to measure the crystalline structure of solids using Bragg-edge scattering, which was developed by Enrico Fermi in 1947 [5]. Bragg-edges occur at neutron energies whose deBroglie wavelengths are consistent with twice the path-length difference from the lattice spacing as a function of incident angle. For lattice spacings on the order of an Angstrom, the neutron energies are about 1-10 meV. Examples of Bragg-edge scattering with low-energy Neutron Radiography WCNR-11 Materials Research Forum LLC Materials Research Proceedings 15 (2020) 58-66 https://doi.org/10.21741/9781644900574-10 59 neutrons can be found in [6,7], and references therein. Strain mapping such as tension and torsion can be accomplished with low-energy neutron diffraction. Position-sensitive detectors that surround a sample, irradiated by low-energy neutrons register diffraction peaks (c.f. [8]). Stress is then applied to the sample and the crystal dimensions change, resulting in a different diffraction pattern. Examples of strain mapping and other techniques can be found in [9,10], and references therein. Other techniques such as attenuation-based methods are used to test for porosity in materials. High-energy neutrons (≥ 1 MeV) with ~fm-scale lengths do not have the right wavelengths necessary for applications presented above. Since fast neutrons cannot use the same techniques of diffraction, applications are limited. However, these fast neutrons have penetration power. With few exceptions, the fast-neutron total cross-sections are about 2-5 barns [3]. This crosssection range represents the lowest bounds of the slow-neutron total cross-section. (This is where the hard-sphere cross-section approximation of the nuclear size for low-energy neutrons transitions to neutron-nuclear interactions.) To first order, fast-neutron imaging can resolve mechanical defects of machined parts in heavily-shielded configurations. Fast-neutron imaging can also resolve voids in a wide variety of materials in heavily-shielded containers. Fast-neutron imaging may have sensitivity of hydride and corrosion features in heavily-shielded scenarios. Regardless of the application objective, the value of fast-neutron imaging is dependent on its resolution. In the next section, we calculate the resolution of fast-neutron imaging with Figure 1: A simple model of a step-wedge with (lengths, widths) of (L1, w1) and (L2, w2). Also included, a test pillbox of (length, width) (LD, wD). A flat distribution of neutrons is assumed and the distance from a detector array is given to be D. The detector pixels are separated by a distance s and each pixel width is p. A simple stepwedge estimate is obtained in the limit of wD goes to zero. Figure 2: Same as Fig. 1, but with rays from the step-wedge components and test pillbox representing nuclear scatter. In practical applications, the step-wedge is surround by heavy shielding for which fast neutrons are known to penetrate. Neutron Radiography WCNR-11 Materials Research Forum LLC Materials Research Proceedings 15 (2020) 58-66 https://doi.org/10.21741/9781644900574-10 60 necessary input parameters. We then show results of our feasibility tests and discuss the design requirements of our fast-neutron imaging machine, which is under construction at LLNL. Model Estimates Putting aside any tangential benefits from fast-neutron radiography, our first objective is to be able to resolve and contrast a defect of interest against background with an analytical model. To do this, we use a simple step-wedge model in two dimensions with a test pillbox in between the two steps. The analytical model we derive here is applicable to any imaging technique; the differences are in the input values for cross-sections and detector response. To begin, we define a six-step propagation (see Tab. 1) from the object plane (i.e. with the incident flux) to the digitizing plane assuming a lens-coupled CCD system. Table 1: The (reduced) flux is described by N, with subscripts denoting the n-th step in the propagation series. The variance is denoted by σ. Attenuation through the material is denoted by τ, which contains the relevant cross-sections. The other coefficients are efficiencies related to the detector. The values given are with respect to 10-MeV neutrons for scintillator response and nominal values for the CCD and ADC collections and conversions. In the context of our six-step model, contrast and fidelity is defined to be: • C ≡ ∆N6(ttttt) ∑N6(ttttt) • F ≡ ∆N6(ttttt) σN6(ttttt) , where the ∆-values are the differences in the final counts measured, the Σ-value is the total final counts, and σ is the final count uncertainty. We parallelize our model into two scenarios where one source is assumed mono-energetic and the other to be a flat uniform spectral distribution, i.e. broadband uniform. Without too much difficulty, we derive an expression for contrast to be: Neutron Radiography WCNR-11 Materials Research Forum LLC Materials Research Proceedings 15 (2020) 58-66 https://doi.org/10.21741/9781644900574-10


Introduction
Neutron imaging was first demonstrated by Hartmut Kallmann and Ernst Kuhn ca. 1935 (c.f. [1]), shortly after the discovery of the neutron by Chadwick in 1932 [2]. Neutron radiography and x-ray radiography have mutually grown in parallel as technical analogs of each other and are complementary radiographic methods. X-rays and gamma-rays (i.e. high-energy x-rays) interact with the electrons of an atom as well as the nucleus of an atom due to the electromagnetic properties of the photon. In general, this implies that photons interact (i.e. scatter) more readily with higher-Z materials. Neutrons, however, have no measurable net electric charge and can only interact with the nucleus of the atom via strong-nuclear interactions. The reduced interaction field allows the neutrons to penetrate further than photons, providing additional complementary depth to the probes of radiography. Reaction cross-sections for high-energy neutrons show only slight differences between many nuclei and can be represented by a simple model (see [3]). However, low-energy neutron reaction cross-sections vary considerably as a function of nuclei (c.f. [4]). These differences between photon-and neutron-reactions with atoms provide the underpinnings for the complementary nature of their respective radiographies.
Low-energy neutron radiography has been more extensively developed compared to highenergy neutron radiography because of the length scales of interest are on the order of crystalline lengths. (As a matter of reference, sample shapes have lengths approximately 29fm/√T, where T is the neutron kinetic energy in units of MeV.) Additionally, it is easier to make low-energy neutron sources, especially with moderated fission reactors. Larger reaction cross-sections with different atomic nuclei also make low-energy neutron imaging particularly enticing. Low-energy neutrons can be used to measure the crystalline structure of solids using Bragg-edge scattering, which was developed by Enrico Fermi in 1947 [5]. Bragg-edges occur at neutron energies whose deBroglie wavelengths are consistent with twice the path-length difference from the lattice spacing as a function of incident angle. For lattice spacings on the order of an Angstrom, the neutron energies are about 1-10 meV. Examples of Bragg-edge scattering with low-energy neutrons can be found in [6,7], and references therein. Strain mapping such as tension and torsion can be accomplished with low-energy neutron diffraction. Position-sensitive detectors that surround a sample, irradiated by low-energy neutrons register diffraction peaks (c.f. [8]). Stress is then applied to the sample and the crystal dimensions change, resulting in a different diffraction pattern. Examples of strain mapping and other techniques can be found in [9,10], and references therein. Other techniques such as attenuation-based methods are used to test for porosity in materials.
High-energy neutrons (≥ 1 MeV) with ~fm-scale lengths do not have the right wavelengths necessary for applications presented above. Since fast neutrons cannot use the same techniques of diffraction, applications are limited. However, these fast neutrons have penetration power. With few exceptions, the fast-neutron total cross-sections are about 2-5 barns [3]. This crosssection range represents the lowest bounds of the slow-neutron total cross-section. (This is where the hard-sphere cross-section approximation of the nuclear size for low-energy neutrons transitions to neutron-nuclear interactions.) To first order, fast-neutron imaging can resolve mechanical defects of machined parts in heavily-shielded configurations. Fast-neutron imaging can also resolve voids in a wide variety of materials in heavily-shielded containers. Fast-neutron imaging may have sensitivity of hydride and corrosion features in heavily-shielded scenarios. Regardless of the application objective, the value of fast-neutron imaging is dependent on its resolution. In the next section, we calculate the resolution of fast-neutron imaging with Figure 1: A simple model of a step-wedge with (lengths, widths) of (L 1 , w 1 ) and (L 2 , w 2 ). Also included, a test pillbox of (length, width) (L D , w D ). A flat distribution of neutrons is assumed and the distance from a detector array is given to be D. The detector pixels are separated by a distance s and each pixel width is p. A simple stepwedge estimate is obtained in the limit of w D goes to zero. necessary input parameters. We then show results of our feasibility tests and discuss the design requirements of our fast-neutron imaging machine, which is under construction at LLNL.

Model Estimates
Putting aside any tangential benefits from fast-neutron radiography, our first objective is to be able to resolve and contrast a defect of interest against background with an analytical model. To do this, we use a simple step-wedge model in two dimensions with a test pillbox in between the two steps. The analytical model we derive here is applicable to any imaging technique; the differences are in the input values for cross-sections and detector response. To begin, we define a six-step propagation (see Tab. 1) from the object plane (i.e. with the incident flux) to the digitizing plane assuming a lens-coupled CCD system. In the context of our six-step model, contrast and fidelity is defined to be: where the ∆-values are the differences in the final counts measured, the Σ-value is the total final counts, and σ is the final count uncertainty. We parallelize our model into two scenarios where one source is assumed mono-energetic and the other to be a flat uniform spectral distribution, i.e. broadband uniform. Without too much difficulty, we derive an expression for contrast to be: where: Here n is the density of the component (see Figs. 1 and 2), σ is the total cross-section (where the scattering component is distinct from 0-degrees), and L are the component lengths, given in Figs. 1 and 2. One important feature for the contrast is that it is explicitly independent on spectral shape, i.e. broadband uniform or mono-energetic. The implicit dependence on spectral shape is in the cross-sections.
The fidelity can be shown to be: Fidelity shows explicit spectral shape dependence. The ratio of these two is easily shown to be: Since 0 > 0 (i.e. positive-definite); this implies that > 1, making mono-energetic sources the better fidelity. Resolution is defined to be: = � − �. In the case of ~ and ≲ , = (1 + tanh ), where is the geometric (i.e. line-of-sight) resolution and is a function of step-width, pixel width, and pixel separation. For very small, where it neatly reduces to line-of-sight resolution of a step-wedge if the width of the test pillbox is zero. Using the nominal values in Tab. 1 and average cross-sections for fast neutrons, and a signal-to-noise ratio of 5%, and a flux on target of 10 9 mono-energetic 10-MeV neutrons, we estimate that the performance range is around 0.65-0.85 mm. This range is subjective to uncertainties in the cross-sections and detector efficiencies. Moreover, this simplistic model does not consider scattering from shielding materials expected to be present, which is why we are considering fast neutrons. To perform more realistic calculations, we must use Monte-Carlo techniques to consider the scattering channels, especially from shielding. Our realistic model is shown in Fig. 3. Figure 3 (Left) shows an Image Quality Indicator (IQI) consisting of concentric shells of high-Z and low-Z materials. The direction of the simulated beam is in the +z direction. Our results are based on analysis of a test pillbox (see Fig.  3 top), which is a volume, void of material. The pillboxes are placed at (x,z)= (0,0) and at the ylocations along the dashed lines shown in Fig. 3. The effective areal densities for the beam-path intersection of each pillbox are, 8.43 g/cm 2 , 137 g/cm 2 , and 191 g/cm 2 . The results of the analysis are given in table 2.  The results in Tab. 2 indicates good resolution for the areal densities denoted in Fig. 3 for the pillbox with a diameter of ~3.7 mm. It should be noted that the signal-noise-ratio for 137 g/cm 2 , is approximately equivalent to x-ray radiography using a 9-MeV bremsstrahlung source. This represents the limit for high-energy x-ray radiography for test pillboxes depicted in Fig. 3.

Feasibility Measurements
Some of our feasibility measurements have been published by a number of us [11][12][13][14][15][16]. We report on one of our feasibility measurements that was performed with 10-MeV quasimonoenergetic neutrons using the tandem Van De Graaf accelerator at the Edwards Accelerator Lab at Ohio University. The IQI used is shown in Fig. 4. It is important to note that the maximum areal density is 107 g/cm 2 . Our assessments, made for the above model (i.e. Fig. 3), is that the contrast for x-ray should be the same for 9-MeV bremsstrahlung x-rays and 10-MeV neutrons. Our results are shown in Figs. 5 and 6. In both measurements, we used a lens-coupled CCD camera and used CT techniques with the same reconstruction methods. Fig. 4.

Figure 5: Neutron CT of IQI pictured in
The smallest test pillboxes in the plastic are clearly visible, and the contrast of the interface between the Pb and plastic is excellent. Although the test pillboxes are clearly visible in both the neutron-and x-ray-CT, the contrast between the low-Z and high-Z interface is poor for the x-ray. Both of these observations are consistent with our calculations and estimates discussed above. In December 2017 we measured the above IQI, using a flat panel array, at the Los Alamos Neutron Science Center (LANSCE) at Los Alamos National Laboratory (LANL). LANSCE has a spallation source, which will provide a broadband flux. This data is still being analyzed.

Construction of the LLNL source
With the successes of our modelling and validation of our estimates, LLNL has begun construction on a 10-MeV quasi-monoenergetic neutron source at LLNL [17][18][19][20][21][22][23][24][25][26][27][28]. To meet demands of a high-brightness source, we are using a 300-µA, 100-Hz, deuteron accelerator, which consists of 2 radio frequency quadruoples (RFQ) and 1 drift tube linac (DTL). The deuterons are accelerated to 7 MeV and impinge on a pulsed, windowless deuterium gas target system. (The necessity of the windowless gas target system is that the peak power on target is expected to be at 56 kW or 2.1 kW average.) The Q-value for D(d,n) reaction then boosts the neutrons to 10-MeV. The length of the gas target is 4 cm and is maximum on the flight line at nearly 4 atm-gauge. The result is a neutron rate of 10 11 n/sr/s in the kinematically-focused forward cone of 10-degrees. The object-and image-plane will be adjustable between 1 and 5 meters for different magnifications. The source spot size (lateral area) will be around 10-mm 2 , which is necessary for the sub-mm resolution in the object plane, we are striving for.

Outlook
Our plan for December 2018 is to measure the above IQI with filled-in features, using a flat panel array, at the Los Alamos Neutron Science Center (LANSCE) at Los Alamos National Laboratory (LANL). LANSCE has a spallation source, which will provide a broadband flux. We will then remeasure the IQI at LLNL's 10-MeV quasi-monoenergetic source, currently under construction at LLNL. For the latter measurement we will use a flat panel array so that the nearly every aspect of the two measurements (LANL and LLNL) are equivalent with the exception of the source. This will validate and verify our assessments made above for broadband and monoenergetic effects on fidelity and resolution.