On the slowing down of 14 MeV neutrons

Abstract

An experimental procedure is assessed to obtain moderated neutron fields starting from almost monochromatic 14 MeV neutrons generated by means of an accelerator-driven D-T source. The use of a metallic pre-moderator and a standard hydrogen-containing moderator is effective in producing neutron spectra featuring a thermal peak and an epithermal slowing down tail extending up to 14 MeV. The performance of proposed moderation system was investigated by means of MCNP Monte Carlo calculations, benchmarked against experimental measurements using an explorative set up, assembled at the Frascati Neutron Generator. The benchmarked calculations allow at making predictions about the brilliance of a 14 MeV neutron moderator in view of possible applications in neutron science.

Keywords

Fusion neutrons neutron moderators Monte Carlo simulations neutron sources

1. Introduction

Neutrons produced in fission rectors and accelerator-driven facilities (proton/electron LINACS and/or synchrotrons) typically span energies over many orders of magnitudes (tens of meV-hundreds of MeV) [1,2]. Together with these extended-range neutron sources, monochromatic beams for a restricted field of applications, e.g. those related to fusion reactors are also found. These are for example the Deuterium-Tritium (D-T) sources that produce 14 MeV neutron beams following the fusion reaction $D + T \to n +^{4} He + Q (17.1 MeV)$ . Although 14 MeV neutron sources worldwide are mostly involved in fusion related activities, very intense neutron emission rates may open also other types of investigations, if an effective moderation of the source neutrons is performed.

A.D. Taylor et al. [3] pointed out (at a speculative level) how a 14 MeV neutron fusion source (in the specific case relying on inertial fusion) could be the brightest source conceivable given the present technological knowledge. At present, accelerator-driven D-T sources rely on past and still operating fusion sources. The Rotating Target Neutron Source (RTNS) at the Livermore Laboratory [4], the Frascati Neutron Generator (FNG) [5] are just two indicative examples that inspired the project “New Sorgentina Fusion Source (NSFS)” designed to provide a 14 MeV neutron emission rate in the order of 10¹⁵ s⁻¹ [6,7]. As a matter of fact, the development of neutron sources of increasing power and brightness always followed a step-by-step approach as indicated in Fig. 1.

Fig. 1.

Historical development of the main neutron sources in the last century (source: Ref. [8]); the perspective point (red star) is expected for an inertial fusion source following A.D. Taylor et al. [3].

In all kinds of neutron sources, the neutrons used for scattering purposes are the result of the slowing down of the high-energy source neutrons generated via the different nuclear reactions (fission, spallation, photo-neutron emission) by means of proper moderators [9,10]. Moderators at pulsed spallation and/or photo-production neutron sources should provide a maximized brilliance, maintaining the time correlation of the neutron beam to the primary charged particle current. This permits to reconstruct the scattering event kinematics by means of the time-of-flight technique [11]. Typically, hydrogen-containing materials are recognized as effective moderators, embedded into a reflector blanket (beryllium, or graphite or heavy water, depending on the source) that redirect towards the moderator (and then to the beam line) the neutrons scattered with angular distributions characteristic of the physical processes that generate the source neutrons. Moderation of 14 MeV neutrons is not an easy task. Indeed, the scattering cross section is lower by almost a factor of 6 as compared to the energy around 1 MeV (the typical reference energy for the so-called evaporation peak in spallation reactions and the main energy of the fission spectrum). This reflects in a less effective lethargic process. A different approach must be thought to effectively moderate fusion neutrons, trying to maximize moderator performances.

A possible approach, based on the use of a combined metallic pre-moderator coupled to a standard hydrogenated material as moderator device, is presented. The study has been carried out using the Monte Carlo N-Particle (MCNP) code version 5, release 1.6 [12].

2. Experiment

2.1. The Frascati Neutron Generator

The Frascati Neutron Generator (Fig. 2) is an accelerator-driven fusion source operating in both D-D and D-T mode. A D⁺ beam, 300 keV energy, is directed onto a 2-cm diameter 4 μm-thick titanium target layer, where D or T is implanted, that is coated onto a 1-mm thick copper substrate. The whole Ti-Cu target is water cooled. The current of the beam can be varied up to about 1 mA. In D-T mode, a neutron emission of 10¹¹ s⁻¹ is achieved, while in D-D mode this is 10⁹ s⁻¹, owing to the lower cross section.

Fig. 2.

Software reconstruction of the of the Frascati Neutron Generator assembly; a blow up of the target section is shown on the right side of the picture.

Figure 3 shows the energy spectra in D-T mode at different neutron emission angles, measured with respect to the incident deuteron beam direction. Moreover, the iso-flux contours calculated for a 10¹⁰ s⁻¹ neutron emission rate are shown in the right panel.

Fig. 3.

(right) Neutron spectra at different emission angles: 0° refers to the direction of the incident deuteron beam; (left) iso-flux contours for a source neutron emission rate of 10¹⁰ s⁻¹.

2.2. Experiment setup and simulations

The experiment performed at FNG relies upon a moderation systems composed of a copper pre-moderator placed in front of the FNG target (see Fig. 4) and a polyethilene moderator placed after the pre-moderator [13,14].

Fig. 4.

(left) Schematic drawing of the experimental setup at FNG; (right) picture of the FNG target and of one of the 12 Bonner spheres used in the measurements.

The pre-moderator has the scope of reducing the initial energy of the neutrons and to produce a multiplication effect with $(n, 2 n)$ reactions, provided that neutron absorption is small enough. Copper has been selected as pre-moderator material due to its availability in the facility. The experimental set-up has been accurately reproduced in an MCNP model. The spectral neutron fluence at the Bonner Spheres position has been calculated. All the relevant components of the FNG device and bunker hall have been included in the MCNP model: the concrete walls of the bunker, the final part of the deuteron accelerator tube with the tritiated titanium target and cooling system, the 100 mm thick Cu block (pre-moderator), the 20 mm thick polyethylene moderator and all the supporting structures. According to the MCNP code, the average neutron fluence in a volume is estimated by summing up all the neutron tracks inside it and normalizing for the volume. In this case the track lengths have been estimated in a 5 cm radius sphere, located at the centre of the Bonner Sphere.The JEFF3.2 [15] nuclear data library was used for the transport. Steel components have been represented using SS-316 material. Supports are made of pure Al. The moderator has been represented as impurity-free polyethylene, (C₂H₄)_n with a density of 0.95 g cm⁻³. The effect on thermal neutrons of the chemical bond C–H has been extrapolated from the JEFF3.3 [16] library. The pre-moderator is made of high-purity oxygen free copper (99.9% Cu) accordingly to the chemical analysis. The walls of the experimental hall has been described as standard concrete with 2.6 g cm⁻³ density, as in previous benchmark experiments [17]. The neutron source, that has been tested in many benchmark experiments, is simulated describing a 260 keV deuteron beam impinging the titanium hydride tritiated target [17,18].

A previously characterized Bonner Sphere neutron Spectrometer (BSS) was chosen for the experimental validation of the computational model. This type of device is well suited for the specific purpose, as it offers unrivalled energy span of the response (from thermal neutron domain up to tens–hundreds of MeV), very high accuracy and established methods to infer the neutron spectrum from the raw data. The main limitation is the limited energy resolution, especially in the intermediate energy domain (1 keV to 100 keV), caused by the similarities and overlaps in the response functions [19]. The spectrometer used in this work, in use at INFN-LNF, consists of 11 mm (diameter) × 3 mm (thickness) ⁶LiI(Eu) scintillator in the centre of twelve high-density polyethylene spheres with diameters ranging from 60 mm to 300 mm. The response matrix is known with overall accuracy better than 2% [20]. The process of inferring the neutron spectrum from the sphere counts and the response matrix is called “unfolding” and is done by iterative unfolding codes [21]. Modern unfolding methods guarantees reliable results, provided minimal a priori information on the neutron field (typically obtained with a simplified Monte Carlo simulation), and an exerimentally verified response matrix. Bonner Spheres have already been successfully used to benchmark irradiation assemblies based on D-T sources [22]. During the current experiment, FNG operated at about 2 × 10¹⁰ s⁻¹. The spheres were sequentially positioned at 0.98 m distance from the target, after the pre moderator+moderator assembly. Their counts were normalized to the FNG monitor signal, obtained with the so-called associated-particle technique [23]. These normalized sphere counts, together with the BSS response matrix and related uncertainties, were introduced in the FRUIT unfolding code [24] operated in the Special Gradient Mode [25]. The MCNP-simulated spectrum was used as pre-information (guess spectrum). The unfolded spectrum and the MCNP simulation are compared in Fig. 5. Small differences arise from uncertainties in nuclear cross sections data, materials compositions, BSS positioning and BSS response matrix. A small discrepancy observed in the thermal domain can be ascribed to approximate knowledge of the chemical composition of the concrete. Indeed, neutrons scattered by the walls contribute to about 20% of the total fluence at the detector position and up to 26% if only the thermal region is considered.

Figure 5 shows in the same plot the calculated and experimentally measured neutron spectra in the equi-lethargy representation.

Fig. 5.

Calculated (dashed line + dots) and measured (continuous line + dots) neutron spectrum at the detector position (see Fig. 3).

3. Preliminary comparison among materials

After a benchmarking experiment and simulations, an investigation was performed about a possible optimized configuration of pre-moderator and moderator for FNG, considering different materials. The geometrical configuration is shown in Fig. 6. The simulation geometry was such that the Beryllium pre-moderator has a maximum thickness of 4 cm at the center, while the water moderator features a square surface area of 2304 cm² and 2 cm thickness. As a preliminary investigation, the material of the pre-moderator and of the reflector were chose to be the same (i.e. beryllium, copper, tungsten and lead), while the moderator was liquid water at room temperature.

Fig. 6.

(left) Schematic model of the moderation assembly for FNG: T is the FNG target, PM the pre-moderator, M the water moderator and R the reflector; (right) plot of the MCNP model with the scoring surface used for calculating the moderator brilliance.

The cross sections of the chosen pre-moderator (PM) and reflector (R) materials for the $(n, 2 n)$ reactions are plotted in Fig. 7 in the range up to 20 MeV from ENDF-6 database, together with the calculated water moderator’s brilliance in the configuration sketched in Fig. 6 left picture, using the same material for PM and R (with the fixed dimensions indicated above). Brilliance, (i.e. the number of neutrons per second, per unit surface, per solid angle and per energy) is calculated by scoring the neutron flux in a spherical surface, with center in the center of the moderator, delimited by a cone of a known solid angle with vertex in the center of the moderator (see Fig. 6, right picture).

Fig. 7.

(left) $(n, 2 n)$ cross sections of the materials chosen for the calculations; (right) water moderator’s brilliance corresponding to the chosen materials for R and PM.

The spectra feature a thermal peak at about 30 meV and an epithermal neutron tail extending up to 14 MeV were a peak is found due to the un-collided neutrons emitted from the source. The epithermal tail has the typical $E_{n}^{- α}$ trend with α is about 0.93 in all cases. In the case of the beryllium PM+R assembly, the thermal peak is found to be higher by a factor between 6 and 10, depending on the material, with respect to the other cases considered. Thus, this choice seems to be the most adequate to maximize moderator’s brilliance in the configuration chosen for the simulations (Fig. 6).

4. Conclusions and perspectives

In the best configuration provided by choosing a beryllium PM+R (see Fig. 6) an estimation was done by mimicking FNG as operating at a neutron emission rate of 10¹⁵ s⁻¹.

Figure 8 shows the moderator brilliance in the geometrical configuration considered in the simulations and that of the thermal moderator supplying the S8 beam line at the SINQ spallation neutron source.

Fig. 8.

Moderator’s brilliance in the configuration sketched in Fig. 5 for FNG operating at an emission rate of 10¹⁵ s⁻¹. In the same plot it is reports the thermal moderator brilliance of the SINQ spallation neutron source as seen by the S8 beam line [26].

It can be noted that the thermal peak in the specific SINQ case is a factor of about 3 higher than the one of the FNG case, while the epithermal tail is softer than the one calculated for FNG.

Table 1 reports the area of three different spectral regions for the two cases in consideration.

Table 1

Integral of the neutron spectra in Fig. 8 over three different energy intervals

Energy range (MeV)	I_FNG (cm⁻² s⁻¹ sr⁻¹)	I_S8(cm⁻² s⁻¹ sr⁻¹)
1 × 10⁻¹⁰–5 × 10⁻⁷	5.6 × 10¹¹	1.9 × 10¹²
5 × 10⁻⁷-1	2.2 × 10¹²	1.5 × 10¹¹
⩾ 1	1.8 × 10¹²	3.8 × 10¹¹
Total	4.6 × 10¹²	2.4 × 10¹²

As a matter of fact, the epithermal/fast neutron components of the spectrum introduce a higher background in the FNG case as compared to SINQ. This not only for the absolute value of the intensity in the energy region above 500 meV (see Table 1) but also for the ratio of the thermal-to-epithermal intensity. Depending on the specific application this may deserve proper strategies to allow for an effective operation of an instrument, but this issue is out of the specific scope of this introductory study.

Anyway, from the table it can be thought that with a proper choice of materials and geometry the epithermal tail of the FNG spectrum can be made softer (i.e. the slope can be slightly changed) promoting some fast neutrons into the thermal region. In this respect, as the New Sorgentina Fusion Source (that is supposed to feature a neutron emission rate above 10¹⁵ s⁻¹) is of the continuous type, the over-moderation of the neutron may be not detrimental. A further study to assess this possibility is foreseen in the next future. Going back to Fig. 1, and trusting the perspective of a future inertial fusion source as the brightest one ever built, it seems reasonable that this approach may follow the same historical development of the other types of neutron facilities (see Fig. 9): i.e. starting from a prototypical source where all the engineering and physical aspects concerning the use of 14 MeV neutrons are addressed, to reach the desired performances.

Fig. 9.

Following the approach schematized in Fig. 1, the brightest 14 meV fusion source should be developed starting from a lower power D-T source.

Footnotes

Acknowledgements

The authors are thankful to L. Quintieri and G. Skoro from the neutronics group of the ISIS spallation source (STFC, UK) for precious discussions. One of the authors (AP) warmly acknowledges J. M. Carpenter (Argonne National Laboratory) for interesting and precious indications.

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