HighNESS conceptual design report: Volume I

1.1.List of acronyms

See the list of acronyms in the Table 1.

1.2.The European Spallation Source

The European Spallation Source (ESS) is a cutting-edge scientific research facility currently under construction in Lund, Sweden. When completed to full specifications, it will be the world’s most powerful accelerator-based source of neutrons for scientific research [71]. This unparalleled capability will open new scientific avenues across various disciplines, including materials science, life sciences, energy research, environmental technology, and fundamental physics.

Currently, the ESS is actively constructing 15 instruments, which represent a subset of the envisioned 22-instrument suite essential for fulfilling the facility’s scientific mission, as outlined in the ESS statutes. Notably, the ESS mandate encompasses a fundamental physics program and the absence of a dedicated beamline for fundamental physics has been identified as a critical gap [60].

The remarkable neutron flux produced by ESS is due to its housing the world’s most powerful linear accelerator and the high beam power directed on target. At full design capability, the proton beam operates at a current of 62.5 mA and is accelerated to 2 GeV, employing a 14 Hz pulse structure, with each pulse lasting 2.86 ms. Consequently, this configuration yields an average power of 5 MW and a peak power of 125 MW.

Once the proton beam reaches its final energy, it impacts a rotating tungsten target (see Fig. 1), inducing spallation and primarily generating evaporation neutrons with energies around 2 MeV. The high-energy spallation neutrons are decelerated within the neutron moderators situated inside the moderator-reflector plug, as described in Section 1.2.1 and shown in Fig. 2.

Fig. 1.

The ESS target monolith with key components indicated: moderator and reflector plug, spallation target, and one of the 42 neutron beam ports.

Fig. 2.

The ESS target-moderator system. The picture depicts the proton beam, the spallation target, the structure housing the moderator, and the neutron beam ports.

Fig. 3.

Cross-sectional view of the ESS target/moderator area and inner shielding. The figure displays the location of the ESS moderator above the spallation target, referred to as the “upper moderator”, and the moderator below the spallation target, referred to as the “lower moderator”. The NNBAR experiment (see Section 1.2.2) will utilize both moderators.

The target area is encircled by a cylindrical steel structure with an 11-meter diameter. This structure, consisting of 6000 tons of steel shielding, is known as the ‘monolith’. The monolith is designed to absorb most of the beam power and is capable of withstanding the heat generated during operations. Additionally, the monolith includes a cooling system that utilizes pressurized helium gas. This cooling system effectively reduces the peak temperature by 150°C between successive beam shots. This structure also houses the neutron beam ports, which are essential for extracting thermal and cold neutrons from the moderators. ESS has positioned its beam port system around the moderators, allowing for neutron extraction both above and below the target as shown in Fig. 3.

Beyond the ESS monolith, the beamlines reside in the bunker, as referenced in [224]. The bunker serves as a crucial shielding area, enveloping the ESS monolith and shielding the instrument area from the significant ionizing radiation generated during operation. The shielding structure of the bunker consists of 3.5-meter-thick walls (see Fig. 4) constructed from heavy magnetite concrete, complemented by a roof of variable thickness, also composed of heavy concrete.

Figure 5 shows the completed bunker in one of the instrument hall. After the bunker, the neutron beamlines reach the instrument halls, as shown in Fig. 6. Figure 7 shows the complete layout of the facility. The instrument hall areas are located in the D01, D03, and E01 buildings.

Fig. 4.

CAD drawing of the ESS bunker, depending on the sector, the bunker has different lengths.

Fig. 5.

Overview of the complete bunker area in the ESS D03 instrument hall.

Fig. 6.

Overview of the 15 instruments currently under construction at the ESS and the instrument halls.

Fig. 7.

ESS layout and building description.

1.2.1.The ESS current moderator system

Initially, the spallation source will be equipped with a single compact, low-dimensional moderator specifically designed to produce high-brightness neutron beams for condensed matter experiments. This design is optimized for small samples and offers flexibility for parametric studies. In Fig. 2, the left side showcases the high-brightness moderator, while the right side illustrates the current configuration of the ESS target-moderator-reflector system.

The core neutron production at ESS happens in the upper and lower moderator, two moderator-reflector systems positioned both above and below the spallation target, as shown at the center of Fig. 8. A cylindrical steel structure (shown in dark red) located above the target houses the moderator and reflector, from which neutrons are extracted for the beamlines. A similar container (depicted in yellow) is positioned below the target.

Figure 2 shows the openings in the shielding, which are the beam extraction channels and are present above and below the spallation target. These channels allow for the extraction of neutrons from either or both moderators. The space shown in Fig. 3 below the spallation target is presently occupied by a steel plug and currently un-utilized. This space has the potential to accommodate an additional moderator-reflector system. The design of such a system constitutes one of the primary objectives of the HighNESS project.

Fig. 8.

Schematic view of the ESS target-moderator-reflector system. The proton beam impinges on a rotating target consisting of tungsten (purple target in the figure). A cylindrical steel structure (dark red) placed above the target contains the moderator and reflector from which neutrons are extracted to the beam lines (red arrows). A similar container (yellow) is placed below the target, and is the intended location for the placement of the high-intensity moderator in the HighNESS project. These two structures and the shaft (light blue) form the so-called twister (cf. Section 2.1).

1.2.2.The ESS upgrade area

In addition to utilizing the space beneath the spallation target for the placement of a second moderator system, the HighNESS project will take advantage of the availability of extra beam ports. Fig. 9 shows the available sectors of experimental zones, the distribution of the 15 instruments of the initial suite, and the additional beam ports and areas for additional future instruments that can be fed by a second moderator system. These areas, highlighted in green in Fig. 9, serve as the primary locations for designing instruments and experiments that will utilize the moderators developed in the HighNESS project.

ESS is also equipped with a special beam port located in the monolith for neutron extraction. This beam port, often referred to as the Large Beam Port (LBP), due to its size, is equivalent in size to three standard ESS beam ports and is illustrated in Figs 10 and 11. This infrastructure has been installed in anticipation of the neutron-antineutron oscillation experiment NNBAR [3,16], to allow the experiment to achieve its design goals. At the time of this writing, no other existing or planned neutron facility will have a beam port of similar dimensions, making ESS the best possible facility worldwide for the NNBAR experiment. The LBP also serves a broader purpose beyond the NNBAR experiment, since it can be used for various potential designs of Ultracold Neutron (UCN) sources, as detailed in Section 6.

Fig. 9.

The ESS facility. The location of the instruments of the initial suite is shown. In green the upgrade areas, where the HighNESS instruments and experiments could be placed, are highlighted.

Fig. 10.

Photograph of the monolith beam ports around the ESS Large Beam Port. An overlaid drawing shows the visible surface of the upper and lower moderators, with a shielding block in between.

Fig. 11.

(A) side view of opening in correspondence of NNBAR. (B) top view of the large beam-port opening for NNBAR.

Figures 12 and 13 depict how the NNBAR experiment will require an extension of the instrument hall. The current building perimeter extends approximately 21 meters away from the moderator. This area is available for future upgrades and will be used by the NNBAR experiment described in HighNESS Conceptual Design Report Volume II.

Fig. 12.

Overview of the NNBAR beamline extension from the current ESS building.

Fig. 13.

The NNBAR beamline and the detector hall located 200 m from the source.

1.3.HighNESS objectives

The HighNESS project, [171,172], is an EU-funded 3-year project, that commenced in October 2020. The primary objective of the project is to develop a second cold neutron source at ESS that complements the first source located above the spallation target. For the initial instrument suite, the emphasis was on creating a source capable of providing a high brightness of thermal and cold neutrons. In contrast, the new sources, designed as part of the HighNESS project, focused on two distinct aspects:

The second source was designed as a liquid-deuterium (LD₂) moderator, based on proven technology. One of the main results of this work is a complete engineering design of the LD₂ moderator, taking into account the actual layout of the ESS target station. In addition to this, the project has explored several designs for VCN and UCN sources. These design possibilities are described in Section 4, and Section 6 respectively. Furthermore, the project has successfully developed a set of neutron scattering instruments (see Section 8) and conducted a conceptual design study for the NNBAR experiment.

As mentioned previously, the first 15 instruments for the user program of ESS will view the top moderator. The start of operation of ESS will be at low power, which will be increased stepwise to finally reach the time average power of 2 MW. It is planned to reach 2 MW power around 2028. Beyond 2030, a second moderator system, like the one proposed herein, could become available. Around that date the facility would ideally be equipped with two separate neutron sources with the following features:

Thus, in this scenario of separate moderators optimized for different neutron characteristics, ESS would offer, with respect to the single-moderator case, a versatile neutron source of outstanding performance, spanning a larger neutron wavelength range, and delivering high brightness and intensity to the instruments according to their requirements. This will enable a plethora of multi-disciplinary activities which fit the original plan for ESS but offer many more possibilities beyond, for which there is strong topical scientific demand.

At the time of the writing, it is challenging to predict whether this moderator will be installed before ESS reaches the 5 MW design power. As a consequence, the majority of the findings presented in this work have been developed with consideration of both the 2 MW and 5 MW options.

1.4.The HighNESS project in the neutron landscape

Some examples of instruments and experiments HighNESS aims to make possible are already given in this introduction, but more are outlined in Section 4, Section 8, and in the HighNESS Conceptual Design Report Volume II that describes the NNBAR experiment. There is currently no alternative source with comparable parameters to ESS to enable the experiments mentioned. There are two other high-power, MW-class, pulsed spallation sources in the world, J-PARC in Japan and SNS in the USA. Both facilities have upgrade plans for the implementation of second target stations, and in both cases, the focus is on using low-dimensional high-brightness moderators, similar to the approach of the ESS first source.

These upgrades aim to achieve peak brightness superior to that of the ESS first source, with a potential increase of up to a factor of 5. However, the time-average brightness is expected to remain approximately 5 times lower than that of the first ESS source when operating at 5 MW, and for the majority of applications targeted by the HighNESS project, a high time-average intensity is essential. Furthermore, it is worth noting that the upgrades at SNS and J-PARC primarily focus on cold neutron ranges. Neither of these facilities have plans to install a VCN source near the spallation target. As a result, ESS, with its intense source and focus on delivering longer wavelengths, could provide intensities in the long-wavelength regime that are more than one order of magnitude higher. The installation of a long-wavelength facility at the ESS is uniquely favorable due to the high proton power and long-pulse time structure.

Finally, it is worth highlighting that no other facility houses a feature akin to ESS’s Large Beam Port, which opens exceptional opportunities not only for the NNBAR experiment but also for the development of world-leading UCN sources.

1.5.HighNESS project structure

Fig. 14.

HighNESS project work package structure.

The HighNESS project is organized into ten distinct Work Packages (WPs), as illustrated in Fig. 14. WP1, titled “Project Coordination”, serves as the central hub for coordinating all project activities. WP2, known as “Software Development”, focuses on creating the necessary computational tools required for the analysis and design of high-intensity moderators.

The computational tools developed in WP2 rely on experimental measurements conducted in WP3, titled “Material Characterization with Neutrons”. This work package provides material-property data, essential for generating thermal-neutron scattering kernels and validating the required models.

WP4 and WP6, designated as “Moderator Design” and “Advanced Reflectors”, respectively, serve as the foundation for neutron design efforts, specifically the development of cold sources (CN), very cold neutron sources, and ultracold neutron sources. These two work packages require inputs and specifications from the scientific-oriented WPs, WP7 (“Condensed Matter Science”) and WP8 (“Fundamental Physics”). The inputs from these scientific WPs ensure that the source designs deliver the necessary neutron fluxes and spectra, enabling groundbreaking scientific experiments at ESS that are beyond the capabilities offered by the upper moderator. WP5 (“Engineering”) is responsible for handling all the engineering aspects related to the different sources.

The objective of WP9 (“Computing Infrastructure”) is to make software and data developments carried out by WP2 and WP6 accessible to the public through the creation of cloud computing resources. Subsequently, WP10 manages the distribution of all scientific content generated as part of this project.

2.1.General description of the ESS moderator area

Figure 15 shows a horizontal cut in the geometry of the monolith, highlighting the available space below the target for the neutron extraction, consisting of two areas, each with an angle of 120°. These openings allow for the diffusion of slow neutrons towards beamlines starting outside the monolith, and arranged in four sectors which are conventionally labelled with their cardinal directions (cf. Fig. 6).

Fig. 15.

Horizontal cut in the geometry of the target monolith in correspondence to the center of the lower moderator, courtesy of R. Holmberg. The grey circle inside the twister represents the maximum available space for a Be reflector (maximum diameter 72 cm). The blue circle inside represents the location of the lower moderator. One of several candidate UCN source locations is indicated in the pciture by the red dotted circle. For more details see Section 6.

The lower moderator system will be installed inside the so-called twister, a steel structure containing the upper and lower moderator-reflector assemblies. Its name is derived from the fact that it is rotated around its shaft during the periodic exchange procedures. The coordinate system used to describe the geometry is the so-called TCS (Target Coordinate System) which has the origin inside the spallation target, with the vertical axis (X,Y=0) passing through the centre of the upper moderator. We have the following constraints for the liquid deuterium moderator and reflector: 40 cm in height, and 72 cm in diameter. This corresponds to between −7.8 cm and −47.8 cm along the Z-TCS axis. The twister starts at −61 cm with respect to Z-TCS, hence we have 13.2 cm between the maximum size of the liquid deuterium moderator and the inner shielding. However, some of this space, depending on the engineering design, must be reserved for the structural support of the lower moderator-reflector plug.

In addition to the space inside the twister structure, which contains the moderator and reflector below the spallation target, another potential location for a moderator system was identified during the early stages of the HighNESS project: the Moderator Cooling Block (MCB). The MCB, shown in Fig. 16, is essentially a removable and replaceable block of shielding material that is positioned adjacent to the twister and is water cooled. Its location has been considered for the placement of a secondary source, such as a UCN source (see Section 6). The placement of a source in that location would require a modification of the MCB. This possibility has been discussed with the ESS Target engineering team and is considered as feasible. It has therefore been explored, along with a variety of other UCN source candidate locations, as part of the HighNESS project (see Section 6). Figure 16 and Fig. 17 show the twister and the MCB next to each other. Such a source embedded in the MCB would be best suited to beamlines placed in the North sector.

Fig. 16.

Twister and moderator cooling block (MCB). Drawing courtesy of C. Jones, ESS. See explanation in the text.

Fig. 17.

Twister (left block) and moderator cooling block (MCB, right block), top view. The twister is the location for both the upper high-brightness bispectral moderator and the lower liquid deuterium moderator. The MCB is a potential location for a UCN in-pile source.

2.2.Figures of merit

It is important to define the wavelength ranges for the three groups of neutrons of interest in HighNESS (Table 2). Cold Neutrons (CN) are defined in the range from about 2 Å to about 20 Å, which is the typical range for the instruments using the cold neutrons from the upper moderator [7]. VCNs, as defined in [34], are neutrons in the range between about 10 Å and 120 Å. It is worth noting that the lower range, 10–40 Å, is of particular interest for condensed matter research, while the upper range, 40–120 Å, is more applicable to fundamental physics experiments. Finally, UCNs are defined as neutrons with wavelengths above 500 Å. The present section reports on the design and optimization of the lower moderator in terms of cold neutron intensity; the neutronic design was performed using the Monte Carlo code MCNP version 6.2 [78]. The design of the VCN and UCN sources are discussed in Section 4 and Section 6, respectively. Finally, in Section 7 options for the integration of the different sources, aiming at providing the best possible solutions to deliver CNs, VCNs and UCNs to the users, are discussed.

The whole process from the neutron moderation to the neutron transport to an experimental area needs to be taken into account when designing a neutron source. This is because the sensitivity of an experiment is proportional to the count rate of neutrons in a given wavelength and divergence range at the location of experiment. Consequently, the design of the source must be done considering the initial cold neutron flux calculations at the emission surface of the source provided by MCNP as well as the subsequent neutron transport using ray-tracing Monte Carlo simulations using the McStas code [116].

The two processes are done at different stages. In the case of the HighNESS project, MCNP simulations are done by the neutronic team (Work Package 4 of the HighNESS project, see Section 1.5), while the McStas ones are mainly performed by instrument designers for both condensed matter instruments and fundamental physics experiments. In order to link the two parts, MCNP must provide a source file to be used in McStas. This can be done in several ways, such as by fitting neutron spectra from the moderator, or by writing individual neutron trajectories in a text file (MCPL format [104]), which is then read by McStas. The latter is the preferred option within HighNESS.

There is however an additional factor that complicates the work of the source designers in HighNESS, which is the use of advanced reflectors that are intended to increase the flux from the source to the instruments. Various options have been investigated, such as the use of nanodiamond layers at the exit of the moderator, which increase the flux towards the neutron guides via quasi-specular reflection. Other materials have also been considered. To investigate these options, thermal scattering libraries were developed and included in the MCNP simulations, as well as in other particle transport tools (see Section 10).

To optimize the moderator design it is necessary to define a metric, or figure of merit (FOM). Several FOMs are needed to accommodate the needs of the various instruments. Table 3 provides the summary of the FOMs used for the design of the moderators in WP4.

2.2.2.Figures of merit for fundamental physics

The NNBAR experiment will search for baryon number violation (BNV) via neutron (n) – antineutron (n¯) oscillation. The full experiment and its scientific motivation are described in the HighNESS Conceptual Design Report Volume II. In Fig. 18 a schematic overview of the planned NNBAR experiment [3] is depicted. Neutrons that are generated in the target are moderated and traverse the LBP. A system of elliptically shaped neutron guides is placed in the region after the LBP’s exit to focus the neutrons in the direction of the detector located downstream. After having passed the optics, neutrons fly free to the detector region at the end of the instrument. The moderator-to-detector distance is 200 m.

Fig. 18.

Schematics of the NNBAR experiment (not to scale).

The probability of an oscillation is proportional to the (uninterrupted) flight time squared t2 of the neutrons. The FOM of the NNBAR experiment is then defined as ∑iNiti2 with Ni being the number of neutrons with a specific flight time ti. Thus, slower neutrons are favored.

In the lower plot of Fig. 19, the distribution of wavelengths and how they contribute to the FOM is shown for a representative simulation result. The upper plot displays the wavelength distribution in the LD₂ source for comparison.

A possible FOM for the moderator optimization can therefore be the wavelength intensity distribution that covers the solid angle defined by the exit of the LBP in the range above 5 Å (or alternatively, 2.5 Å) at the detector weighted with λ2. We note that there will be a natural cutoff at λ of about 15 Å, due to the effect of gravity on neutrons with longer wavelengths. For example, for neutrons of wavelength 12.5 Å the vertical drop due to gravity would already be 2 m. Thus, neutrons with wavelengths that are too long will not be able to reach the detector, which has a radius of 1 m. Moderator designs that perform better under this criteria should lead to a higher FOM for NNBAR.

The FOM used for the moderator design for NNBAR is therefore the intensity of neutrons, weighted with λ2, for two ranges of neutrons: above 2.5 Å and above 5 Å, with an upper cut of 15 Å.

Fig. 19.

Wavelength spectrum of the LD₂ source (upper plot) and the distribution of wavelength contribution to FOM for NNBAR (lower plot).

2.3.Neutronic design

The purpose of the cold moderator is to provide cold neutrons to beamlines for fundamental physics and neutron scattering instruments. The “NNBAR opening” is intended for fundamental physics experiments in general and the NNBAR experiment in particular, while the opening for one or more neutron scattering instruments is referred to as the “WP7 opening”.

2.3.4.First iteration

For the first baseline model, a box-shaped geometry was selected, which was found to have better neutronic performance than the cylindrical-shaped moderator. Two box-shaped geometries were initially investigated, giving a similar neutronic performance. The geometry with the lower heat load was selected in the continuation of the project.

For the selection of the dimensions, among the three optimization criteria chosen for input into the optimization code Dakota [2] (sum of intensities, sum of brightness, and NNBAR intensity), the sum of brightness for the two openings was selected. The reason for this choice is that, for a fixed dimension of the emission window (as was the case in all these optimizations), the sum of brightness gives equal weights to NNBAR and WP7, and is the de facto equivalent to optimizing for intensity for each of the two emission windows. However, among the many results provided by Dakota, with the criteria of maximization of the sum of brightness, in this first iteration a preference was given to the ones giving more intensity to NNBAR, while still having a high enough intensity to WP7.

The Be filter was introduced into the model adjacent to the NNBAR and WP7 emission surfaces as an efficient reflector of neutrons with wavelengths below about 4 Å, leading to a considerable gain in cold neutron intensity (see Section 2.3.7).

Below is the description of the “first iteration” model of the LD₂ moderator. This model is illustrated in Fig. 20.

Fig. 20.

Graphical representation of the baseline design for the LD₂ moderator submitted to WP5 for engineering studies. The color codes are the following: orange: steel (twister frame, inner shielding, etc); dark blue: liquid ortho-deuterium; blue: light water; light blue: beryllium; green: aluminum. Note that cold Be filters and ambient Be reflector are shown using the same color; the same note applies to Al. The direction of the incoming proton beam is indicated in the upper and lower left figures (for the upper left figure, the dashed arrow means that the proton beam is at a different vertical level).

A. The LD₂ moderator is represented by a rectangular vessel made of aluminum. Its inner dimensions are:

• - 45 cm long in the proton beam direction (“width”),

• - 47 cm long in the direction transverse to proton beam direction (“length”),

• - 24 cm long in the vertical direction (“height”).

In neutronics calculations, the thickness of the vessel Al walls is set to 0.3 cm for the sake of consistency and comparison with work on the upper moderator. The vessel itself is filled with liquid ortho-deuterium at 20 K and the cold Be filters are immersed in deuterium.

B. There are two openings, both perpendicular to the incoming proton beam, but in opposite directions:

• - NNBAR opening serving the North–West (NW) sector (see Fig. 6);

• - WP7 opening serving the defined South–East (SE) sector.

The NNBAR opening has an emission surface of 40 cm width by 24 cm height, while the WP7 opening has an emission surface of 15 cm width by 15 cm height. The geometric centers of both emission surfaces and of the LD₂ moderator are situated at the same level, −23.7 cm below the center of the spallation target.

The emission surfaces are covered from the inside by rectangular cold Be filters. The filters are 110 mm thick each, while their widths and heights correspond to those of their respective emission surfaces. Cold Be filters are in direct contact with deuterium, however, it is important to note that the bulk temperature of cold Be filters is not required to be 20 K: as long as their temperature is kept below about 80 K, they will provide the expected performance increase.

C. The LD₂ moderator is placed inside a standard moderator-reflector plug, thus, surrounded by the following layers:

• - 0.3 cm thick Al vessel around LD₂ and Be filter at the same temperature as LD₂;

• - 0.5 cm vacuum gap between the Al vessel and premoderator (engineering constraint);

• - 0.3 cm thick Al walls at ambient temperature surrounding the H₂O premoderator and Be reflector;

• - 1.0 cm thick layer of H₂O at ambient temperature below and on the sides to serve as a premoderator;

• - 2.5 cm H₂O layer at ambient temperature above (between the moderator and the target);

• - Be at ambient temperature below and on the side to serve as reflector, with as much volume as possible.

The summary of the expected performances, integrated over various wavelength ranges, is shown in Table 4.

Table 4

Neutronic performance and characteristics of the model from the first iteration of the design of the cold moderator. Brightness and intensity are integrated over different wavelength ranges (NNBAR and WP7 openings) and compared with the upper moderator. The values for the upper moderator are from ref. [222]. To calculate the intensity we considered the following size of the emission windows: NNBAR – 960 cm² (40 cm × 24 cm); WP7 – 225 cm² (15 cm × 15 cm); upper moderator – 42 cm² (sum of two openings of the butterfly moderator of 7 cm × 3 cm for the beamline perpendicular to the proton beam, I.e., in the NNBAR direction, cf. also [222]). All values are for 5 MW average beam power. The heatload on Be filters accounts for both the contribution at NNBAR and WP7 openings. The moderator volume is the sum of the volumes of the LD₂ box and Be filters

	Brightness [n/cm2/s/sr]
	>2 Å	>4 Å	>10 Å
NNBAR	9.11×1012	7.04×1012	5.51×1011
WP7	1.45×1013	1.08×1013	8.13×1011
Upper moderator	5.3×1013	1.7×1013	9.9×1011

	Intensity [n/s/sr]
	>2 Å	>4 Å	>10 Å
NNBAR	8.74×1015	6.76×1015	5.29×1014
WP7	3.26×1015	2.42×1015	1.83×1014
Upper moderator	2.2×1015	7.0×1014	4.2×1013
NNBAR FOM	3.00×1017 [n/s/sr × λ2]
WP7 FOM	2.96×1015 [n/s/sr]
Heatload on LD2 moderator	29.3 [kW]
Heatload on Be filter	20.0 [kW]
Heatload on Al vessel	7.1 [kW]
Total heatload	56.4 [kW]
Moderator volume	50.8 [liters]

2.3.6.Third iteration

The third iteration of neutronic optimization of the moderator was performed using Dakota with the model from the second iteration updated by the engineering constraint of requiring a 2.5% volume of aluminium in LD₂ to account for flow guides and support structures. Moreover, the third neutronic optimization was also motivated by an attempt to reduce the heat load in the moderator while preserving or even improving its performance. The temperature of LD₂ in the moderator vessel was increased from 20 K to 22 K, following indications from the engineering team about the expected temperature of the liquid deuterium in the moderator.

For the purpose of the third iteration of optimization, a parametric model of the moderator was used with the following variable parameters:

• - Moderator length;

• - Moderator width;

• - Be filter thickness;

• - Reentrant hole depth.

The height of the moderator was fixed at 24 cm. The listed parameters (see Fig. 21) were optimised with respect to NNBAR and WP7 FOMs. A multi-objective genetic algorithm (MOGA) [135] was implemented resulting in a set of solutions over a wide range of NNBAR and WP7 FOMs. These values were compared to the baseline model from the second optimization iteration; however the baseline model was modified adding 2.5 vol% Al in the liquid deuterium, and increasing the temperature of LD₂ from 20 K to 22 K. In Fig. 22 the gains made over the second iteration FoMs for WP7 are shown as a function of gains for NNBAR. A Pareto front was fitted through points closest to Utopia point, an idealized point with highest possible NNBAR and WP7 gains. In the subsequent analysis of possible solutions, these gains in NNBAR and WP7 FOMs were analyzed with regards to moderator length (see Fig. 23), moderator width (see Fig. 24), Be filter thickness (see Fig. 25) and the depth of the reentrant hole (see Fig. 26). The following limits on variable parameters used in the optimisation to maximize NNBAR and WP7 FOMs were defined:

• - 45 cm ⩽ moderator length ⩽ 50 cm;

• - 40 cm ⩽ moderator width ⩽ 45 cm;

• - 11 cm ⩽ Be filter thickness ⩽ 15 cm;

• - 9 cm ⩽ depth of reentrant hole ⩽ 15 cm;

• - Gain wrt to the model from second iteration (“baseline”) ⩾ 1.

Fig. 21.

Graphical representation of the design for the LD₂ moderator after the third iteration. The color codes are the following: orange: steel (twister frame, inner shielding, etc); dark blue: liquid ortho-deuterium; blue: light water; light blue: beryllium; green: aluminum. Note that cold Be filters and ambient Be reflector are shown using the same color; the same note applies to Al.

Fig. 22.

Third iteration of optimization: each point represents the gain in FoMs for NNBAR and WP7 with a given set of parameters with respect to the baseline model obtained in the second iteration. The Pareto front was fitted through points closest to Utopia point, an idealized point with highest possible NNBAR and WP7 gains. The aim was to select a model that lies as close as possible to the Utopia point. The moderator volume was calculated as the sum of volume of LD₂ box and Be filter. The red circles depict models after applying the limits on moderator parameters.

Fig. 23.

Performance of models with respect to moderator length. (A) gain in NNBAR and WP7 FOMs with respect to the baseline model. (B) average gain in NNBAR and WP7 FOM with respect to the baseline model.

Fig. 24.

Performance of models with respect to moderator width. (A) gain in NNBAR and WP7 FOM with respect to the baseline model. (B) average gain in NNBAR and WP7 FOM with respect to the baseline model.

Fig. 25.

Performance of models with respect to Be filter thickness. (A) gain in NNBAR and WP7 FOM with respect to the baseline model. (B) average gain in NNBAR and WP7 FOM with respect to the baseline model.

Fig. 26.

Performance of models with respect to the reentrant-hole depth. (A) gain in NNBAR and WP7 FOM with respect to the baseline model. (B) average gain in NNBAR and WP7 FOM with respect to the baseline model.

Fig. 27.

Comparison of neutron spectra for the lower and upper moderators for the third iteration of optimisation. (A) time-averaged intensity. (B) time-averaged brightness.

A smaller subset of solutions was filtered out based on these limits (represented as red circles in Fig. 22). The goal was to select a solution that is close to the Utopia point, and which also minimizes the moderator volume in order to reduce heatload. In the end, this combination of parameters was selected for the LD₂ moderator:

• - Moderator length = 48 cm;

• - Moderator width = 41 cm;

• - Be filter thickness = 13 cm;

• - Reentrant hole depth = 10 cm.

The volume of LD₂ in the moderator is 32.2 l. For reference, we can also compare the intensity of the lower cold moderator from this neutronic optimization with the model of the upper moderator. The upper moderator has a higher brightness; however, because of the smaller size, its intensity is lower. This can be seen in Fig. 27(a) and (b) which show the time-averaged brightness and intensity respectively for the thermal and cold neutrons measured at the NNBAR and WP7 openings including the time-averaged brightness and intensity calculated for the upper moderator. For the upper moderator, the size of the emission window depends on the angle of extraction: at the NNBAR location, an emission window with a surface of about 42 cm² would be available,22 and this give an intensity of the upper moderator above 4 Å of 7 × 10¹⁴ n/s/sr (i.e. 10 times lower than for the NNBAR opening of the lower moderator).

After completion of the third iteration of optimisation, the model of the cold moderator was delivered to the engineering team, WP5, where a thorough engineering study was conducted.

A summary of the expected performances, integrated in different wavelength ranges, is shown in Table 6. There is a decrease in NNBAR and WP7 FOMs in comparison to the model from the second iteration of neutronic optimisation (see Table 5) due to the increase in temperature of LD₂ from 20 K to 22 K and the presence of 2.5 vol% Al in LD₂.

Table 6

Neutronic performance and characteristics of the model from third iteration of cold moderator. Brightness and intensity integrated over different wavelength ranges (NNBAR and WP7 openings) and compared with the upper moderator. The values for the upper moderator are from [222]. To calculate the intensity we considered the following size of emission windows: NNBAR – 960 cm²; WP7 – 225 cm²; upper moderator – 42 cm². The moderator volume is the sum of volume of the LD₂ box and Be filter

	Brightness [n/cm2/s/sr]
	>2 Å	>4 Å	>10 Å
NNBAR	7.89×1012	6.07×1012	4.46×1011
WP7	1.60×1013	8.76×1012	6.89×1011
Upper moderator	5.3×1013	1.7×1013	9.9×1011

	Intensity [n/s/sr]
	>2 Å	>4 Å	>10 Å
NNBAR	7.57×1015	5.83×1015	4.28×1014
WP7	3.60×1015	1.97×1015	1.55×1014
Upper moderator	2.2×1015	7.0×1014	4.2×1013
NNBAR FOM	2.51×1017 [n/s/sr × λ2]
WP7 FOM	3.22×1015 [n/s/sr]
Heatload on LD2 moderator	28.5 [kW]
Heatload on Be filter	19.5 [kW]
Heatload on Al vessel	7.3 [kW]
Total heatload	55.3 [kW]
Moderator volume	45.0 [liters]

2.3.8.Shape of the reentrant hole

The development of the cold moderator continued with a study of the impact of different shapes of reentrant holes. More specifically, the initially rectangular shaped reentrant hole was replaced by, for example, a wedge-shaped reentrant hole with variable depth (see Fig. 28). Subsequently, the neutronic performance on the WP7 side was estimated with this shape of reentrant hole for the beamport S11 (“S” stands for South Sector, and “11” refers to the number of the beamport; it is the beamport perpendicular to both the incoming proton beam and the emission surface of the moderator at the WP7 side) and the beamport S9 with an offset of 12° with respect to S11 (see Fig. 29 for a depiction of the beamport positions). The calculated values of the WP7 FOM at various reentrant hole depths are shown in Fig. 30. The maximal gain with respect to the rectangular reentrant hole at the S9 beamport was of about 5%, but with a penalty to the WP7 FOM for the S11 beamport of about 3%. Other shapes of reentrant holes were investigated, but with a consistent result that the gain for the off-axis beamport S9 was only marginal with a small loss for the on-axis S11 beamport at the same time. Therefore, the shape of the reentrant hole was kept rectangular in this round of optimization.

Fig. 28.

Model of the wedge-shaped reentrant hole. (A) horizontal view. (B) vertical view.

Fig. 29.

Horizontal view of the wedge-shaped reentrant hole, the on-axis S11 beamport, and the off-axis S9 beamport.

Fig. 30.

Performance of a wedge-shaped reentrant hole at different depths.

2.3.9.Moderator characterization

The model of the cold moderator from the second neutronic iteration was used to perform a comprehensive moderator characterization. Given the similarity of the designs from the different iterations, the results presented in this section also apply to the design from the third iteration.

Intensity spectra from the two moderator openings are shown in Fig. 31. Spectra are shown for two proton energies of 2 GeV and 800 MeV, which for an average current of 2.5 mA correspond to operation at average power of 5 MW and 2 MW, respectively. For both openings, intensity spectra per unit power are almost equivalent, indicating that the results presented in most of this work, which are for 5 MW average power, can be directly scaled to the 2 MW average power (the initial operating power of ESS) dividing by a factor of 2.5.

Fig. 31.

Spectra comparison between the NNBAR and the neutron scattering instrument (WP7) sides of the LD₂ using MOGA optimization for protons impinging on the target at 2 GeV and 800 MeV, per unit power.

The main feature of the spectral brightness distribution on the NNBAR side is the very sharp cut-off at 4 Å due to the Be filter. The enhanced peak between 1 Å and 2 Å is a feature introduced by the filter. A smoother spectral distribution is observed on the neutron scattering instruments (WP7) opening with the thermal and cold peaks clearly visible.

The spatial distribution of neutrons coming out of the surface of the moderator was studied with a pinhole-camera tally integrated in MCNP. The pinholes are placed 2 m away from the center of the moderator along the central axis for both openings, while the detector arrays are 2 m away from the pinholes on the same axis and have dimensions of 50 cm × 50 cm and 30 cm × 30 cm for the NNBAR and WP7 sides, respectively. The results are shown in Fig. 32 (NNBAR on the left and WP7 on the right) for three wavelength ranges: λ<4Å, λ>4Å, and λ>9Å.

Fig. 32.

Pinhole images of the 24 cm × 40 cm NNBAR opening (left) and the 15 cm × 15 cm WP7 opening (right) with filters for neutrons at different energies. The pinholes are placed 2 m away from the center of the moderator along the central axis, while the detector arrays are 2 m away from the pinholes on the same axis and with the dimensions 50 cm × 50 cm and 30 cm × 30 cm for NNBAR and WP7, respectively. The pictures have the same scale and appear inverted along the vertical direction due to the camera obscura effect.

The distribution of the neutrons is quite different between the two openings. The bigger NNBAR opening has a non-uniform profile along both axes, with a central hot-spot slightly off-centered toward the top of the moderator (the pinhole images appear inverted in the vertical direction). The smaller opening for the neutron scattering instruments is a more uniform source. Although the integrated intensity is higher on the NNBAR side, the effective contribution of the neutrons from the corners is quite limited due to current optics design [206]. In any case, the advantage of having such a large opening in the moderator has been established, but further improvement can be made to increase the intensity farther from the center.

Finally, in Fig. 33 the pulse shape of the neutrons coming out of the moderator at 2 Å, 4 Å, and 9 Å is presented. The curves were obtained by recording the neutrons leaving the moderator by crossing the surface on the NNBAR side through a SSW card [78]. The neutrons were then filtered in energy using the Monte Carlo Particle Lists (MCPL) interface [104] and binned in elapsed time in ms. The histograms were normalized in order to be comparable and smoothed with Gaussian kernel density estimation. The pulse width is significantly broader than the proton pulse (2.86 ms). This is due to the slow LD₂ thermalization time and will likely impact neutron scattering experiments. In particular, the use of choppers in conventional neutron scattering experiments will certainly lead to a reduction in peak fluxes. On the other hand, for NNBAR there is no foreseen impact since the quantity of interest is the time-averaged flux.

Fig. 33.

Pulse spectra of neutrons from the moderator at 2, 4, and 9 Å wavelength. The proton beam impinging on the target lasts 2.86 ms, indicated by the shaded region on the left. Histograms are normalized to probability density functions (a.u.) for comparison. The smoothed curves are obtained with Gaussian kernel density estimation.

2.3.10.Effects of engineering design on neutronic performance

An engineering design was made based on the optimized neutronic model (see Section 3). In this section, the impact of various engineering solutions on the neutronic performance is analyzed. Two features of the engineering design were found to particularly affect the neutronic performance: first, the large thickness (0.8 cm) of the Al vessel required for the engineering design of a vessel with flat walls; second, the relatively complex design of the Al flow channels, due to the presence of a reentrant hole on the neutron scattering side.

Additionally, on recommendation from the engineering team, the beryllium was placed outside the LD₂ vessel. This was done to solve two issues: 1) there is a significant reduction of the heat load which has to be handled by the LD₂ flow inside the moderator when the beryllium is not inside; 2) there was an issue with film boiling between beryllium blocks in the thermomechanical simulations when the blocks are inside the LD₂.

To simplify the flow structure and to reduce the amount of Al inside the vessel, a change in the shape of the reentrant hole was implemented: the original square-shaped REH was replaced by a U-shaped one of the same width (15 cm) but with the height of the moderator vessel (24 cm).

To quantify the effects of these design changes, a set of tests was performed with the following modifications of the third iteration model, starting from the original optimized model (Fig. 34):

• LD₂ with Al flow guides modeled explicitly and wall thickness increased from 0.3 cm to 0.8 cm (Fig. 35).

• Be filter separated from LD₂ moderator (Fig. 36).

• U-shaped reentrant hole with a few parameters slightly changed to streamline the model (Fig. 37).

• LD₂ with Al flow guides modeled explicitly and wall thickness increased from 0.3 cm to 0.4 cm (Fig. 38).

• Tapered rectangular REH (Fig. 39).

The conclusions from this analysis are that a thickness of 0.8 cm of Al gives too much neutronic penalty and should be reduced. On the other hand, moving the Be filter outside the Al vessel (and envisaging a separate cooling) and using a simplified U-shaped reentrant hole do not give a large penalty.

Fig. 34.

Original optimized design for the LD₂ source.

Fig. 35.

As in Fig. 34, but Al flow guides modeled explicitly, while the wall thickness increased from 0.3 cm to 0.8 cm.

Fig. 36.

As in Fig. 34, but Be filter separated from LD₂ moderator.

Fig. 37.

As in Fig. 36, but with an alternative reentrant hole shape and a few parameters slightly changed to streamline the model.

Fig. 38.

As in Fig. 37, but Al flow guides modeled explicitly, while the wall thickness increased from 0.3 cm to 0.4 cm.

Fig. 39.

As in Fig. 38, but rectangular REH is tapered and the geometry is slightly changed to increase the overall performance.

2.3.11.Rounded shape model

Table 7

Impact of engineering refinements on neutronic performance, normalized to the optimized LD₂ baseline

	NNBAR	WP7
Fig. 34	100	100
Fig. 35	75	77
Fig. 36	92	98
Fig. 37	91	93
Fig. 38	94	93
Fig. 39	94	94

As a final step of the design of the liquid deuterium moderator, we investigated a model with separated LD₂ box and Be filter, U-shaped reentrant hole and rounded walls of the LD₂ box based on new preliminary engineering studies. As shown in the previous section, a 0.8-cm thick Al vessel and additional Al flow guides would be required for a vessel with flat walls (see model on Fig. 35) leading to a significant drop in NNBAR FOM of about 25 % (see Table 7). To reduce the negative impact on the neutronic performance of the cold moderator, rounded walls were proposed for the moderator. Moreover, as stated in the previous section, the Be filter and LD₂ box were separated and the shape of reentrant hole was simplified to an U-shape. This allowed reducing the thickness of the Al vessel to 0.4 cm.

The WP5 team provided a detailed CAD model of the LD₂ moderator vessel (Figs 40a and 40b). An MCNP model designed according to this CAD model is shown in Figs 41 and 42.

Fig. 40.

Design of LD₂ moderator with rounded shape, developed by the engineering team. (A) full model. (B) horizontal cut.

We note that there was no time available in the project to perform a full engineering study of this option. Nevertheless, we report these results in this document since it should be further investigated in the future. The summary of the expected performances, integrated in different wavelength ranges, is shown in Table 8.

Fig. 41.

Graphical representation of the final design for the LD₂ moderator with an U-shaped reentrant hole, separated Be filter and LD₂ and rounded walls. The color codes are the following: orange: steel (twister frame, inner shielding, etc); dark blue: liquid ortho-deuterium; blue: light water; light blue: beryllium; green: aluminum. Note that cold Be filters and ambient Be reflector are shown using the same color; the same note applies to Al.

Fig. 42.

MCNP model of the cold moderator with rounded shapes according to the technical drawing from the engineering team. This view shows the outer surface of cold moderator covered by the Al vessel.

2.4.Summary of the cold moderator design

We have successfully designed a cold neutron source with a neutron intensity above 4 Å exceeding the one from the upper moderator by a factor of 10. This accomplishment aligns with one of the primary objectives of HighNESS, which aimed to create a complementary source capable of supporting various experiments where neutron intensity holds greater significance than brightness. This has been achieved using the proven technology of liquid deuterium moderators which are the workhorses at high power research reactors and continuous sources like SINQ.33

The design of the cold moderator has been refined throughout the whole duration of the project, with several iterations with the engineering team. Details on the engineering design are provided in the next section. Although an engineering design of the rounded-shape model has not been performed due to time constraints, there are strong indications that this design could be the best one for the cold source and should be further investigated.

3.1.Introduction

The first generation ESS moderator system consists of two liquid parahydrogen low-dimensional moderators, located above the tungsten target wheel. As mentioned previously, the moderator support structure, the twister, also allows for the use of the space below the target wheel for future moderator upgrades. Figure 43 shows the isometric view of the ESS Target Monolith. The colored components are subjects of the planned upgrades of the ESS Target station [172].

Fig. 43.

ESS target monolith, isometric cutaway view.

The major engineering challenge here is to handle the enormous heat load into the LD₂ moderator of around 60 kW resulting from the spallation process of a 5 MW accelerator-driven neutron source. Following the several iterations discussed in the previous section, the following preliminary engineering design of the LD₂ moderator was developed. The moderator vessel consists of high-strength Aluminum alloy EN AW-6061 T6, which allows local stresses up to 87 MPa and will be filled with approximately 30 L of liquid deuterium. The cold moderator is surrounded by a vacuum jacket followed by a light water premoderator and a warm beryllium reflector. In addition, one cold beryllium filter (⩽80 K) is installed inside the cold moderator vessel on the NNBAR side serving the large beam port (see Fig. 44 blue block) [171].

Fig. 44.

Pre-design of the LD₂ moderator. Engineering design based on the third neutronic iteration (Fig. 21).

The fluid guides ensure that flow separation, dead areas, and swirls do not occur. The extension rods ensure additional mechanical stability since the vessel walls are flat and need to be as thin as possible to minimize neutron losses. The moderator will be milled and partially Electrical Discharge Machining (EDM) machined from a solid block of aluminum EN AW-6061 T6, and the cover will be finally welded to the main body with “low-distortion” electron beam welding. In addition to the usual structural and fluid mechanics issues, the integrability must also be checked, since the components must be installed into an existing source. Originally, the twister was designed for low-dimensional hydrogen moderators only. The integrability is critical, since the LD₂ volume moderator has a substantially larger volume and thus dissipates significantly more heat. Therefore, larger supply and dissipation cross-sections are required. All supply lines must be routed through the twister shaft. However, the diameter of the shaft cannot be increased because it is surrounded by non-replaceable shielding elements. Figure 45 shows the twister with the upper moderator on the left-hand side and on the right-hand side the integrated volume LD₂ moderator in the lower moderator plug. [171]

Fig. 45.

Integration of LD₂ moderator: 1. Upper moderator plug; 2. Upper moderator plug in the moderator support structure; 3. Moderator plug with LD₂ moderator; 4. And 5. Moderator plug in the moderator support structure near the outer reflector [171].

Fig. 46.

Definition of fluid parameters for the moderator LD₂ volume.

3.2.Definition of fluid parameters and cooling process concept design

The fluid parameters of liquid deuterium are defined in the following section, since these are required for the following designs and calculations of the new cold moderator system. Figure 46 shows a simplified representation of LD₂ (blue line) at the chosen operation pressure of 5 bar. It can be seen that the deuterium solidifies at a temperature of ≈19 K and vaporizes at ≈30 K, which defines the temperature range in the liquid phase for the moderator system. In order to avoid freezing during operation, the minimum temperature at the outlet of the heat exchanger is set to 20 K. In addition, it is assumed that additional heat load from the circulation pumps and insulation losses will increase the deuterium temperature by 1 K before it arrives at the moderator inlet. The average temperature increases in the moderator due to particle heating of 59.8 kW will be up to 3 K, which means that the average outlet temperature will be around 24 K. As a result, there is still a contingency factor for local temperature peaks of approximately 6 K before the deuterium evaporates.

Fig. 47.

Piping and instrumentation diagram for the LD₂ moderator system.

The mass flow can now be estimated by using the chosen operating pressure, the inlet- and outlet- temperature, and the heat load. A mass flow of at least 3400 g s⁻¹ liquid deuterium is needed to remove the enormous particle heat and to keep the average temperature increase below ⩽3 K. Assuming a flow velocity of up to ⩽5 m s⁻¹, an inlet/outlet pipe diameter of 70 mm would be required, which has to fit into the existing twister structure. A summary of the critical design parameters can be found in Table 9.

With the defined fluid parameters, a first piping and instrumentation diagram (P& ID, see Fig. 47) was created, and a working CAD design of the lower moderator plug was completed for use in structural mechanical simulations and fluid dynamic simulations. The P& ID in Fig. 47 is a simplified system flow diagram of the cryogenic deuterium moderator system (CDMS), consisting of the helium refrigeration system (TMCP II) with 75 kW cryo-power at 20 K, the helium transfer lines (HTL), the deuterium liquefaction cryostat (CDMS Cold Box), the deuterium transfer lines (DTL), and finally the twister with the lower moderator plug.

The helium refrigeration system is responsible for providing the required cryo-power to the deuterium cryostat to liquify the gaseous deuterium and to remove the heat load of the moderator system during operation. For this, gaseous helium is pumped in a closed loop at a minimum temperature of 20 K via the helium transfer lines to the deuterium cryostat heat exchanger and back to the helium refrigeration system. The main components of the deuterium cryostat itself are the heat exchanger, the circulation pumps, the ortho–para converter and the pressure control buffer. The circulation pumps are installed in the deuterium cryostat to supply the moderator with the liquefied deuterium in a closed circuit. In addition, the para-deuterium content is converted into almost 100% ortho deuterium by using a catalyst in the cryostat, since this has better moderator properties. An active heated pressure-control buffer is also installed in the cryostat to compensate pressure changes caused by the pulsed proton beam and beam trips.

The cryostat provides the needed liquid deuterium to the moderator via the deuterium transfer lines, where the deuterium is heated up by particle interactions and returned to the heat exchanger of the cryostat to cool the deuterium down again. In addition, a storage tank for the deuterium will be necessary since deuterium produces tritium under irradiation. Therefore, the deuterium cannot be vented like hydrogen, for example, when maintenance work or similar actions have to take place. For this reason, in case of maintenance work, the deuterium will be heated and then fed into the storage tank using a heater and compressor. Then, completing maintenance, the deuterium would be reused.

This is also advantageous, because of the high cost of deuterium. The size of the storage tank is determined by the total inventory of the circuit, cryostat and moderator, which must be kept as small as possible for safety and costs reasons. Therefore, it is very important to place the cryostat as close as possible to the moderator to reduce the total amount of deuterium. Since selecting a final location of the components was not within the framework of the HighNESS project, this will be necessary in the final design phase.

3.3.Costs estimation of LD₂ infrastructure

The rough cost estimation shown in Table 10 is based on the cost of the existing ESS hydrogen system and is scaled up according to the heat load of the deuterium moderator system (ca. 75 kW) compared to the hydrogen moderator system (ca. 30 kW). In addition, a storage tank system is considered because of the issue mentioned above that deuterium can not be vented in maintenance cases due to tritium production. In addition, significantly higher costs for deuterium itself are considered as well. Since the location of the needed new building for the helium refrigeration system and the location of the deuterium cryostate inside the Target Station building are unknown, the distance to each other is estimated in order to be able to estimate the costs for the respective transfer lines.

The real costs can deviate significantly upwards or downwards from the estimated ones if the locations (distance) of components change and if the heat load is lower or higher, for example.

3.4.Selection of materials and overall design

For the newly designed moderator, the moderating medium of LD₂ is kept at 20 K. The structural material for the moderator vessel is required to be tolerant to radiation damage, as transparent for neutrons as possible, and suitable for cryogenic temperatures. The chosen structural material shall also be sufficiently ductile for the fast load changes caused by the pulsed proton beam and sufficient in terms of strength to withstand the internal pressure of the LD₂.

Aluminum is nearly transparent for cold and thermal neutrons and is therefore typically selected as a moderator vessel material. However, the strength of pure aluminum is much too low to keep the stress from inner pressure within the allowable range, especially for large volumes as in the case of the LD₂ moderator. Therefore, heat treatable aluminum alloys (6000 series) or non-heat treatable (5000 series) are the preferred choice [61].

There is no ideal aluminum alloy, with each choice having advantages and drawbacks. Many facilities use EN AW-6061 T6, for example at SNS, J-PARC, and for the liquid hydrogen moderator of ESS. In addition, sufficient data of irradiated samples are available to evaluate the radiation-related lifetime of the moderator vessel [61]. Because of its well-known radiation properties, the high strength values and wide application fields in the frame of spallation sources, it was ultimately decided to use EN AW-6061 T6 for the lower moderator.

3.5.Design overview of the lower moderator plug

The new moderator is located in the frames of the twister just below the target wheel, as can be seen is Fig. 45. All details about the integration of the LD₂ moderator assembly into the already existing ESS twister can be found in Section 3.11. The lower moderator plug consists of the inner LD₂ moderator and a cold beryllium filter, that are surrounded by an insulation vacuum, a warm beryllium reflector, and a water premoderator on the top side, facing the target wheel. On each side of the outer vacuum vessel there are actively helium-cooled neutron windows (part of the vacuum vessel) where the cold neutrons exit the moderator (see Fig. 48).

Fig. 48.

3D cross section illustration of the lower moderator plug.

Figure 49 shows the overall box dimensions of the lower moderator plug without the media supply pipes and a horizontal cross-section of the assembly with the parts inside the plug. In principle, the LD₂ moderator sits within the surrounding vacuum vessel with a 5 mm insulation vacuum gap to the adjacent aluminum walls. A layer of water and the warm beryllium reflector segments surround the moderator, with the reflector segments also placed inside a closed aluminum vessel.

Fig. 49.

Dimensions and layout of the lower moderator plug.

The lower moderator plug has two openings on the front and the back side, one smaller neutron window A (WP7 side) and a larger neutron window B (NNBAR side). Both neutron windows are actively cooled by a transversal helium flow and are therefore designed with a thin double-wall design, as shown in Fig. 50.

Fig. 50.

3D cross-section of the neutron windows.

3.6.Assembly and welding of the moderator

A cold beryllium filter is embdedded within the LD₂ moderator on the NNBAR side, adjacent window B. This filter element is divided into two pieces for installation purposes. Three stiffening rods are also needed to support the structural integrity of the vessel. The flow guides and restrictors ensure a defined flow of the liquid deuterium from the inlet to the outlet. The whole moderator is milled and eroded from a single piece of EN AW-6061 T6 aluminum. The openings on the top and the bottom side are necessary for inserting the cold beryllium filter parts and for manufacturing reasons. The box dimensions of the moderator vessel with a wall thickness of 8 mm are shown in Fig. 51.

Fig. 51.

Detailed view of the LD₂ moderator structure within the moderator plug.

The assembly sequence of the LD₂ moderator is shown in Fig. 52 and Fig. 53. First, the parts of the cold beryllium filter are inserted through the top cut-out into the base body of the moderator. Then the 3 stiffening rods are put into the base body and into their grooves in the cold beryllium filter parts, ensuring the correct positioning. Afterwards, the moderator vessel is closed with the case plates.

Fig. 52.

Assembly of the LD₂ moderator vessel – parts overview.

Fig. 53.

Assembly of the LD₂ moderator vessel – assembly sequence.

One challenge when manufacturing the inner LD₂ moderator vessel is the welding process of the case plates, because of the high structural loads that result from the interior operating pressure of the liquid deuterium of 5 bar and the unusual box shape for a pressurized vessel. Figure 54 shows a close-up of the welding area of one of the case plates. To determine the ideal weld-in depth of the filler material, that is needed to avoid heat cracks during the welding process of the EN AW-6061 T6 aluminum alloy, detailed pre-tests of the welding geometry will be necessary in the future before building of such a vessel can be realized.

Fig. 54.

EB-welding of the LD₂ moderator vessel.

3.7.Structural mechanical calculations

Structural strength simulations with a design pressure of 7 bar (operation pressure 5 bar) following the design rules of RCC-MRx 2012 code were performed to analyze the static behavior of the LD₂ moderator, which basically behaves as a pressure vessel. Figure 55 illustrate that the large flat wall on the front-facing side – where the cold beryllium filter is placed (not included in the simulation) – the stress is particularly high due to the unusual box shape. In this area, the stress exceeds the limit of 1.5·Sm for EN AW-6061 T6, with Sm = 87 MPa and 1.5·Sm = 130.5 MPa.

Fig. 55.

Equivalent primary stress at design pressure.

To further optimize the design and meeting the strength criteria regarding the allowable stress, optimizations on this large wall were performed. At first, the wall was shaped cylindrically, which reduced the bending stresses compared to a flat wall. Nevertheless, the sum of the local membrane and bending stress PL+Pb‾ on the fillet at the boundary of the rear wall still slightly exceeded the limit of 1.5·Sm.

Finally, the large and originally flat surface was transformed into a perfectly plastic membrane, which is deformed by pressure to create a shape capable of bearing the load with reduced bending stress. This derived shape is used as a contour for the geometry of the rear wall. This free-formed, or “membrane-shaped” wall under pressure is shown in Fig. 56, shown with a 10× magnification of the deformation for visualization. To limit the extent of the free-forming effect, the membrane shape was selected with a maximum deformation of 10 mm.

Fig. 56.

Shape of membrane under pressure, magnified 10× for visualization purpose.

Fig. 57.

Updated equivalent primary stress at design pressure.

Fig. 58.

Results for membrane stress on the NNBAR-side outer wall.

Figure 57 shows the updated equivalent primary stresses at a design pressure of 7 bar. Here, it is indicated that the stress only exceeds the maximum of 130.5 MPa by 0.92 MPa at a single spot in a rounded corner. However, the linearized stresses at surfaces with σeqv⩾Sm shown in Fig. 58 demonstrate that the local primary membrane stress (left) and the primary membrane plus bending stress (right) completely satisfy the allowed strength criteria of Pm‾⩽PL‾⩽Sm(Θm) = 87 MPa and PL+Pb‾⩽1.5·Sm(Θm) = 130.5 MPa.

In summary, a free-shaped rear wall significantly reduces the sum of local membrane and bending stress compared to a flat rear wall or a cylindrical rear wall with identical offset of 10 mm. The sum of local membrane and bending stress PL+Pb‾ on the fillet at the boundary of the rear wall is below the limit of 1.5·Sm. With this design modification the strength criteria are met.

3.8.Analysis of weld seams

In principle, all moderator vessels are welded. Depending on the number of welds, the distance to each other and the welding process itself (TIG, Laser, Electron-Beam, etc.) the entire vessel can lose the additional strength gained by the selected tempered material. The TIG welding process requires a pre-heating of the vessel, which will often damage the previous heat treatments that have been made to achieve the high material strength, such as T6. This can be avoided to a large degree by using electron beam welding (with no pre-heating necessary) and a carefully planned welding design.

Nevertheless, reduced strength must be expected in the area around a weld. Thus, by putting the welds in a low stress area where possible, it is still possible to benefit from the T6 conditions. On the other hand, electron beam (EB) welding requires a very high manufacturing tolerance.

Another issue with using EN AW-6061 T6 is the need of a welding filler to avoid heat crack formation. These heat cracks occur during the rapid solidification of the melt (thanks to the high thermal conductivity of aluminum) and can be mitigated by the alloy composition of the EN AW-6061 T6, particularly owing to the silicon and magnesium content. Therefore, a good choice of filler would have, for example, a relatively high silicon content, which is offered by EN AW-4047A with 12% silicon. Increasing the content of magnesium is not helpful in this case since it evaporates when the aluminum melt is produced.

The filler material needs to be set precisely into the welding area. Also, the weld-in depth is a very sensitive value. For EB welding, it is ideal that there are no gaps between the welded parts and the filler material, because even small gaps > 0.1 mm will result in irregularities in the weld seam and a faulty welding process. This is very challenging for the manufacturing process of the welded parts in terms of accuracy and the manufacturing strategy. The loss of the T6 condition of the aluminum alloy and its influence on the strength of the weld seams and the heat affected zone (HAZ) around them was investigated by simulation. For this purpose, all material within 15 mm of weld seams is assumed to be heat affected and therefore loses the T6 condition, with a significant corresponding loss in strength values which must be considered. This was approximated by conservatively upscaling the observations from previously tested components with lower wall thicknesses. An overview of the heat affected zones of the LD₂ moderator is given in Fig. 59.

Fig. 59.

Heat affected zones of the LD₂ moderator.

Fig. 60.

Linearized stresses at the weld seams of cover plates.

The structural strength simulations with a static design pressure of 7 bar following the design rules of RCC-MRx 2012 code showed that the linearized stresses at the weld seams of the cover plates did satisfy the strength criteria of Pm‾⩽PL‾⩽Sm(Θm) = 47 MPa at all locations, but the criteria of PL+Pb‾⩽1.5·Sm(Θm) = 70.5 MPa was not satisfied for one weld of one cover plate. These results are visualized in Fig. 60.

A further simulation was performed with the same boundary conditions, but an updated design model. In this case the position of the weld seam of the former, unsatisfactory cover plate was moved 6 mm toward a less stressed region of the vessel. Figure 61 shows that the criteria of Pm‾⩽PL‾⩽Sm(Θm) = 47 MPa as well as the criteria of PL+Pb‾⩽1.5·Sm(Θm) = 70.5 MPa are satisfied for the welds of all cover plates.

Fig. 61.

Updated linearized stresses at weld seams of cover plates.

The weld seams at the three stiffening rods were also subject of the structural strength simulation. The results overview in Fig. 62 shows that the nominal stresses at the weld seams of the stiffening rods all satisfy the strength criteria of Pm‾⩽Sm = 27.5 MPa and PL+Pb‾⩽1.5·Sm = 41.3 MPa.

Fig. 62.

Nominal stresses on the weld seams of the stiffening rods.

In conclusion, it can be stated that all requirements from a structural mechanical point of view are met, considering the RCC-MRx code.

3.9.Thermohydraulic simulations

The fluid parameters and cooling concepts have been verified by full-scale fluid dynamic simulations. Here, the fluid modeled is the subcooled moderating media LD₂ with an average inlet temperature of approximately 21 K. The heat input by neutrons is pulsed, with a 14 Hz pulse frequency and 2.86 ms pulse length based on the ESS proton beam parameters. The allowed temperature increase of deuterium by neutron heat is limited in order to avoid boiling and particularly film boiling. Therefore, the goal for the fluid dynamical simulation is that the fluid temperature does not exceed the boiling temperature at any time.

This goal could not be achieved for the 5 MW load case with the given design and requirements. Further details on this issue and remedial measures are discussed in Section 3.12. The simulations were thus carried out using the design shown at reduced beam power of 2 MW, since ESS will run at this power in the initial operations phase. A corresponding total heat deposition of 28.4 kW was therefore considered in the simulations, using distribution functions derived for the design of the liquid hydrogen moderator of ESS.

The reentrant hole on the WP7 side (window A) of the moderator, opposite to the cold beryllium filter requires special consideration, since it is fully surrounded by LD₂ on the interior faces of the moderator. To achieve this, a complex flow pattern of the liquid deuterium through the moderator vessel is needed. The deuterium is guided from the inlet to the outlet via flow distributors and restrictors to ensure a homogeneous flow inside the vessel. In the area of the reentrant hole the flow is split, so that the deuterium can flow above and below it (see Fig. 63).

Fig. 63.

Flow pattern of LD₂ through the moderator vessel, below and above the reentrant hole on window A.

Figure 64 shows the velocity streamlines of the liquid deuterium inside the moderator vessel that result from the CFX analysis [94]. Time-averaged results confirm a pressure drop of 0.15 bar in the moderator and a maximum fluid velocity of 7.26 m s⁻¹ at an inlet velocity of 5.16 m s⁻¹.

Fig. 64.

Velocity streamlines of LD₂ inside the moderator vessel.

The temperature difference from the inlet to the outlet is 1.4 K with an outlet temperature of 22.4 K (time averaged). The boiling temperature of deuterium at a pressure of 5 bar is 30.6 K. This temperature is reached locally at the inner interface layer between the deuterium and the cold beryllium filter and in the small gap between the cold beryllium filter parts, as shown in Fig. 65, but the main flow is still sufficiently subcooled. Therefore, there is no risk of film boiling.

Fig. 65.

Time-averaged fluid temperatures for the LD₂ moderator.

In summary, it can be said that the fluid mechanical requirements for the 2 MW load case are met, if local boiling at the beryllium filter – fluid inner interface is allowed. So, there are no concerns from an operational safety point of view.

3.10.Design solution of the vacuum vessel

Fig. 66.

Assembly of outer vessel for the lower moderator.

The outer vessel shown in Fig. 66 consists of multiple parts that are combined inside a vessel made of EN AW-6061 T6 aluminum alloy. This vessel and the involved reflector parts also enable the water cooling of the beryllium (Be) reflector. Between the Be-reflector and the inner LD₂ moderator there is an insulation vacuum gap of 5 mm to minimize the heat transfer between the cold and warm parts.

Figure 67 shows the different parts of the assembly, that consists of the center LD₂ moderator, the warm beryllium reflector parts, and the outer aluminum vessel.

Fig. 67.

Assembly of the lower moderator plug – parts overview.

Fig. 68.

Flow pattern of water through the premoderator.

The water disc on top of the moderator plug assembly works as a premoderator for the fast neutrons released by the tungsten target. Figure 68 shows the flow pattern of water through the premoderator, that is located on top of the lower moderator plug.

It is assembled as shown in Fig. 69. Above the bigger neutron window B, also warm beryllium reflector parts are inserted and the milled and eroded water channels inside the water disc are closed via electron-beam welding.

Fig. 69.

Assembly and EB-welding detail of the premoderator.

Figure 70 to Fig. 76 show the flow pattern of water through the warm beryllium reflector parts inside the outer vessel, shown in progressive vertical cross-sections. At first the water enters through the inlet on the bottom side of the outer vessel and is afterwards distributed to the bottom part of the warm beryllium reflector.

Fig. 70.

Flow pattern of water through the warm beryllium reflector parts, section A.

Fig. 71.

Flow pattern of water through the warm beryllium reflector parts, section B.

In this bottom part, the flow is separated into two parallel flows that go upwards along each side of the NNBAR opening (Fig. 71).

Fig. 72.

Flow pattern of water through the warm beryllium reflector parts, section C.

Fig. 73.

Flow pattern of water through the warm beryllium reflector parts, section D.

Fig. 74.

Flow pattern of water through the warm beryllium reflector parts, section E.

Fig. 75.

Flow pattern of water through the warm beryllium reflector parts.

Fig. 76.

Flow pattern of water through the warm beryllium reflector parts.

While flowing toward the top, the water is also distributed alongside the side pieces of the warm beryllium reflector, as shown in Fig. 72.

When the smaller neutron window A opening is reached in Fig. 73 and Fig. 74, the water flows downwards again.

Next, the water flow is guided below the smaller neutron window A opening, through the warm beryllium filter parts underneath it (Fig. 75).

Finally, the flow is guided to the outlet pipe at the bottom side of the lower moderator plug, as shown in Fig. 76.

The assembly sequence of the outer vessel is then shown in Fig. 77 to Fig. 83. At first, the water disc premoderator is welded to the top of the outer vessel via electron-beam welding (Fig. 77).

Fig. 77.

Assembly and EB-welding of the vacuum vessel (premoderator).

The vessel is then flipped upside down and the LD₂ moderator in inserted. After this is complete, the inner bottom plate of the vacuum vessel is welded on via electron-beam welding (Fig. 78).

Fig. 78.

Assembly and EB-welding of the vacuum vessel (inner bottom plate).

Figure 79 shows how the moderator is positioned inside the insulation vacuum. It will rest on titanium pins on the top and the bottom of the moderator vessel. Titanium as a material is chosen for the positioning pins, because of its relatively low thermal conductivity – to minimize the heat transfer between the moderator and the vacuum vessel – and for its radiation resistance.

Fig. 79.

Positioning of the LD₂ moderator inside the vacuum vessel.

When the insulation vacuum around the moderator is successfully closed, the side segments of the warm beryllium reflector are inserted and the outer vessel is closed with the vacuum vessel closing discs via electron-beam welding (Fig. 80).

Fig. 80.

Assembly and EB-welding of the vacuum vessel (Be reflector side segments).

Then the warm beryllium reflector parts above the WP7 window A (Fig. 81) and the large bottom reflector part below the moderator (Fig. 82) can be mounted and afterwards covered and sealed via electron-beam welding.

Fig. 81.

Assembly and EB-welding of the vacuum vessel (Be reflector segment above WP7 window A).

Fig. 82.

Assembly and EB-welding of the vacuum vessel (large Be reflector below the moderator).

In a final step, the cover plates for the actively cooled neutron windows A & B can be welded on via electron-beam welding, as shown in Fig. 83.

Fig. 83.

Assembly and EB-welding of the vacuum vessel (cover plates for beam windows).

At this point, the pre-assembly is ready for integration into the twister, which will be described in the following section.

3.11.Integrability into the ESS twister

The newly designed moderator and reflector plug must fit into the existing twister frame below the target wheel. Also, all media supply for the moderators and the reflectors needs to be guided through the existing design of the twister shaft, since the surrounding shielding elements are not exchangeable and therefore a larger twister shaft diameter is not possible. In addition to the supply media for the first generation LH₂ moderator and its beryllium reflector above the target wheel, the lower moderator plug needs an additional supply lines for liquid deuterium, water for the premoderator, helium for the cooling of the neutron windows, water for the warm beryllium reflector, and vacuum for insulation. The designated location of the different media and the supply-pipe routing through the existing twister shaft are shown in Figs 84 and 85.

Fig. 84.

Media interfaces on the lower moderator plug.

Fig. 85.

Twister integration and interface description.

The attachment and integration of the lower moderator plug into the twister, underneath the target wheel, is illustrated in Figs 86 and 87. The outer vessel has three assembly pins radially installed on the outer cylindrical surface. The corresponding part in the twister is the lower mounting socket, where three slots with a bayonet-catch shape are implemented.

Fig. 86.

Assembly of the lower moderator plug to the twister (mounting details).

With this mechanism, the moderator plug can be inserted into the mounting socket from below and then is aligned to its final position by turning. After the plug is fixed in the mounting socket, the lower frame can be assembled to the twister shaft and welded to the mounting socket, to complete the stainless-steel shielding in this area.

Fig. 87.

Assembly of the lower moderator plug to the twister (insertion and turning).

In summary, it can be stated that the integration of the new LD₂ moderator system into the existing twister is a very complex process, but feasible.

3.12.Summary and outlook: Engineering implementation of deuterium moderator

In general, it can be concluded that a LD₂ moderator system for ESS appears to be feasible from an engineering point of view. It was demonstrated that a volume moderator, including all necessary process lines, can be integrated into the existing twister structure under the given restrictions. Furthermore, the detailed design shows that the moderator system can withstand all mechanical loads and that the manufacturing and welding, although very complex, is feasible.

The conceptual design for the cooling process describes all the additional infrastructure needed to realize such a moderator upgrade. A key point is to reduce the deuterium inventory as much as possible. On one hand, this can be accomplished by choosing a location for the cryostat as close as possible to the moderator and, on the other hand, by reducing the heat load.

The reduction of the heat load is also decisive from a thermo-mechanical point of view in order to be able to use the moderator at full beam power of 5 MW. Without further optimization, the proton beam power is currently limited to 2 MW. However, the first optimizations have already shown that the separation of the cold beryllium filter already leads to significant improvements. In contrast to the demonstrated box-shaped moderator (worst case), slightly shaped vessel walls would allow for a reduction in the wall thickness, which means in turn that less heat is generated and the neutronic performance of the moderator is improved as well. However, the following recommendations should be examined more closely in a follow-up project, before a final decision for the moderator upgrade will be made:

4.1.VCN: A long-wished-for source

An intense VCN source has been a desire of the neutron community for at least 20 years. A dedicated workshop [33] was held in 2005 to discuss ideas for sources and applications. While several ideas on possible materials for VCN were raised (cf. Section 4.6), it was clear at that time that the lack of knowledge of the properties of the candidate materials, and, in particular, the thermal scattering libraries, constituted a major problem for realistic design studies. It is worth recalling that at this workshop a program to study VCN sources was outlined, including topics such as: 1) experiments on selected moderator types; 2) development of scattering kernels for candidate materials; 3) benchmark measurements of VCN production; 4) investigations of thermal and superthermal production of VCN. The HighNESS project has taken on most of these tasks, thus offering for the first time the concrete possibility of designing realistic VCN sources.

4.2.VCN neutrons: A brief introduction

Very cold neutrons cover a wide spectral range within the long-wavelength tail of cold neutron sources,44 with energies ranging from below 1 meV (9 Å) to few hundreds of neV (>several 100 Å), the domain of UCN. A VCN source offers new possibilities in neutron scattering applications [63] and fundamental physics research. Extended neutron wavelengths (λ) inherently enhance the capabilities of diverse instrument categories. This impact can be observed in the λ dependencies of the gains in instrumental resolution at fixed geometry and in intensity at fixed resolution. For example, gains in resolutions proportional to λ−1, λ−3 and λ−3 are expected for reflectometers, time-of-flight instruments and neutron spin echo (NSE), respectively, while gains in intensity at fixed resolution are expected to be proportional to λ2, λ2 and λ3 for these three classes of instruments [33].

Particle physics experiments can benefit from enhanced VCN fluxes, including the search for neutron-antineutron oscillations (described in HighNESS Conceptual Design Report Volume II), beam experiments looking for a non-zero neutron electric dipole moment and search for novel fundamental forces (discussed in Section 4.3).

In this section, we first provide an overview of the scientific case for VCNs and later describe the different design concepts that have been developed in the course of the HighNESS project.

4.3.Fundamental physics with VCN

The primary advantage of VCNs in fundamental physics experiments is their extremely low energy, which results in long interaction times with the experimental apparatus. Unlike UCNs, VCNs can still be considered as beams, allowing for the application of beam optics and related methods. Consequently, VCNs enhance the sensitivity of most fundamental physics experiments that utilize beams of slow neutrons or exploit the wave-optical properties of these beams.

4.4.VCNs in condensed matter research

In condensed matter research with neutrons, the momentum and energy transfer of scattering events is measured to probe the structure and dynamics of a sample material. Very cold neutrons hold significant potential for advancing this field of study. While low-energy neutrons provide the highest sensitivity to low momentum and energy transfers (and are therefore well suited for maximizing resolution) their usage is hindered by the low available flux in the VCN regime. The flux of VCNs in the tail of a Maxwellian spectrum typically available from conventional cold neutron moderators exhibits a wavelength dependence of λ−5.

High-resolution techniques that are expected to gain using longer wavelength neutrons are small-angle neutron scattering (SANS), time-of-flight spectroscopy, and neutron spin-echo (NSE) [64]. Moreover, a real-space technique like neutron imaging might benefit in some cases from improved fluxes in the VCN range.

In small angle scattering, the resolution of small angles enables studying large-scale structures on the nanometer scale, i.e. from a few to a few thousand nanometers. Because of flux limitations it is usually not possible to probe larger structures up to the micrometer scale using a conventional pinhole SANS instrumentation. Other instrumentation exploring even smaller momentum transfers, and thus giving access to the low-micrometer scale, are typically limited to one dimension and require separate measurements. It is therefore desirable to increase the resolution of conventional SANS instruments.

A simple analysis [33] shows that a λ−5 slope of the long wavelength tail of the neutron spectrum of a cold moderator marks the break-even for gaining either efficiency or resolution at longer wavelengths with SANS. The momentum transfer is q=2π/λsinθ, and therefore larger wavelengths enable lower collimation and larger sample sizes in both dimensions across the beam to achieve the same angular resolution. Together with the increase of dλ for a constant dλ/λ, the gain is proportional to λ5. Hence, for a long-wavelength tail of the neutron spectrum that decays at a rate lower than λ−5 there will be a performance gain, either in data rate or resolution, or a balanced gain in both.

It is however important to point out some downsides that can be expected with VCNs, in particular the increased probability of absorption, and the effect of gravity. Increased absorption increases the requirements on all materials used in the neutron beam, in particular neutron beam windows of sources, guides, and sample cells and environments. The increased absorption probability along with an increased scattering probability will favor the use of thin samples to avoid absorption losses and multiple scattering. Effects from gravity can in principle be countered by instrument design but might increase the complexity and lead to additional absorption issues.

Considering experimental methods that probe energy transfers and thus dynamics, the same break-even principle is found for time-of-flight spectroscopy probing inelastic scattering. Simple estimates take into account that the energy change dE is proportional to dt/λ3, where dt is the time resolution. The estimated gains, taking into account a lower repetition rate, and thus scaling with λ5 again, imply a wavelength-independent performance at constant resolution for a long wavelength tail of a Maxwellian spectrum decaying with λ−5 [33,64], keeping in mind the corresponding relaxation of instrument requirements for monochromatization – initial pulse length – and neutron pulse length at the sample. However, in time-of-flight spectroscopy, the momentum transfer resolution would increase, and relaxing collimation and increased sample size could result, corresponding to the previous considerations for SANS, with gains proportional to λ4. Only the required momentum-transfer range limits such gains, where for example, for quasi-elastic measurements the wavelength must be limited to λ<4π/kmax, where kmax denotes the maximum momentum transfer.

In NSE, the use of longer wavelengths allows improving the energy resolution based on the relation dE∝dt/λ3, however without being able to profit from relaxing the requirements on incoming wavelength resolution, divergence, or increased beam size, like in the cases discussed above. Results from high-resolution NSE instruments such as IN15 at ILL indicate that the current technology of magnetic field configurations does not allow for further gains above about 25 Å [64].

For neutron imaging, different considerations need to be taken into account. Currently, thanks to progress in detector technology, neutron imaging can reach resolutions of a few micrometers. However, in the range of single micrometers, the technique meets two limitations. The first one is related to contrast, since only a few materials would provide sufficient image contrast on a thickness scale of micrometers. A colder spectrum would be beneficial, since absorption increases with longer wavelengths, enabling the resolution of smaller structures. The second limitation is neutron flux. Current resolutions and the utilization of the entire white beam spectrum already indicate a limitation in flux, suggesting that a decay in flux close to λ−5 prevents the effective use of very cold neutrons for high-resolution imaging. An VCN source with a decay in intensity lower than λ−5 would then be beneficial.

Novel lens systems for neutrons promise gains of the order of 104 [91], and long wavelengths are advantageous for lenses due to the refractive index increasing with λ2, the focal length increasing with λ−2, and the critical angle proportional to λ. The concern about increased absorption makes reflective focusing optics, like Wolter optics [130], a very attractive choice, and, by using shorter focal lengths, the impact of gravity can be minimized. However, it is important to take into account and address any potential aberrations that may arise and require correction [113]. The potential of true neutron microscopy to unlock unexplored applications and fields of study is particularly promising in soft matter and biology, where deuteration can provide unique opportunities for neutron imaging. Moreover, efficient neutron lenses designed for long wavelengths can also have a significant impact, especially in techniques such as SANS.

Finally, in [150] the possible advantages of using VCNs in reflectometry techniques are discussed for several configurations. Gains are expected for a shift of the neutron spectrum towards colder energies, provided that the brightness is preserved. The use of VCNs for reflectometry is also considered promising for compact sources; new compact sources could be designed aiming at optimizing the VCN flux, having more freedom in the advanced VCN moderator and reflector materials used in the design, with respect to existing facilities.

4.5.VCN design options

In the original proposal of the HighNESS project, two approaches were considered for the design of a VCN source. One is based on a dedicated VCN source using a suitable material that would provide a high flux of VCNs, while another one, similarly to the PF2 beamline 88 at the ILL, extracts VCNs directly from the cold source. At the dedicated workshop in 2022 [173], an additional concept was suggested, that can be considered a merger of the two approaches [141].

4.6.Solid ortho-D₂

In the first workshop dedicated to applications of a Very Cold Neutron Source [33], the designs proposed for a VCN moderator already made use of solid materials like Be, graphite, D₂ and D₂O in the configuration of a bed of small pellets between 5 and 10 K with liquid helium at 2 K flowing through the gaps as a coolant. During the workshop, it was acknowledged that deuterium-based materials are expected to be generally better than graphite and beryllium, whose total cross sections have no incoherent contribution and a steep fall for energies below the lowest Bragg edge (5 meV in Be and 2 meV in graphite). However, the higher heat capacities of beryllium and graphite left open the possibility that they might be favored when optimizing the source for the neutron flux weighted on the heating during the accelerator pulse. At the end of the workshop, there was a consensus that the lack of neutron scattering kernels and measurements was hindering the design of a VCN source based on calculations.

As mentioned above, a more recent study by Gallmeier et al. [70] looked for a VCN source option for the second target station at SNS. The set of materials investigated was chosen based on the thermal scattering libraries available. In particular, para-H₂, water ice, beryllium [23,24], ortho-D₂ [80], CH₄ [185], and neon, all solid at cryogenic temperatures of 4–6 K, were compared. The figure of merit in that study was the time-integrated pulse brightness over a liquid para-H₂ moderator at 20 K. The authors indicated that solid ortho-deuterium (SD₂) and solid methane are the most promising material for delivering a higher VCN production than liquid hydrogen, with the former able to outperform a conventional cold source by a factor 2, at the expense of a pulse five time longer. While solid CH₄ is generally considered a good candidate material for a VCN source due its high hydrogen content, it is likely not suitable in a high-power spallation facility like ESS. Irradiation of methane leads to the formation of radiolysis-induced radicals -(CH₂)_n-, followed by polymerization into carbon-based deposits and release of H₂, both of which have been observed to accumulate in the moderator vessel [18,90]. On the other hand, solid ortho-deuterium, well-established as an in-pile converter medium for UCN sources [12,29,111,115,134,182], has no physical impediment to the VCN production in high radiation fields, despite the many challenges related to keeping such a source at low temperature.

In this work, a new scattering kernel was used to model the interactions of slow neutrons with SD₂. The library, developed by the Spallation Physics Group at ESS, follows the physics of the thermal scattering model from Granada [80,81], and uses the new mixed-elastic scattering format to correctly include both the coherent and incoherent components of elastic scattering [161]. The cross section and the benchmark against experimental data [12,115] can be seen in Fig. 88. The related files are available in the ESS Gitlab repository [59].

Fig. 88.

Total scattering cross section per atom for SD₂ as a function of incident energy. Here, NJOY + NCrystal is the new library, CAB is the evaluation generated by Centro Atomico Bariloche [80,81], and IKE is the evaluation from Institut für Kernenergetik und Energiesysteme [23]. Also the more recent model developed in [121] is shown for comparison. Models are also validated with measurements from SINQ/PSI [12] and LANL/LANSCE [115]. Only every fourth data point is shown for clarity.

Fig. 89.

MCNP model of the full SD₂ moderator (a) vertical cut, perpendicular to the proton beam direction. (B) cut parallel to the target plane with the proton beam impinging from the left.

4.7.Dedicated SD₂ source

Neutronic simulations for this analysis used MCNP 6.2 [209]. Our first tests involved a moderator which had a similar total volume to the baseline LD₂ source, where the total LD₂ moderator volume was partially displaced by SD₂. Different configurations were tested, varying the relative amounts of SD₂ and LD₂. The highest intensity in the VCN region was obtained for SD₂ completely replacing the LD₂. Therefore, the focus in this section is on the properties and performance of a full SD₂ moderator. Additionally, we have investigated the effect of surrounding the SD₂ with a layer of nanodiamonds (NDs), see Section 9.2.2. The ND layer, separated from the SD₂ by a 0.5 mm Al sheet, has a thickness of 5 mm and a density of 0.6 g/cm³. Figure 89 presents the MCNP modelling of the geometry of the SD₂ moderator.

In comparison to the LD₂ baseline, the SD₂ moderator vessel has thinner Al walls (2 mm), which is possible because of the lower pressure exerted by the solid block, and due to the simpler geometry, as no reentrant hole is considered in that design. The design benefits from further improvement by the addition of a 20 K beryllium filter on the left-hand side, facing the NNBAR experiment. Unlike the design of the LD₂ moderator, the Be filter would be added outside the vessel, thus avoiding the need to remove moderator material. The addition of that filter leads to an increase of the performance on the NNBAR side in the range from 4 Å to 10 Å of about 40% in comparison to the case in which no filter is considered, while sacrificing 70% of the intensity in the range from 2.5 Å to 4 Å and 20% above 40 Å. The addition of such a filter on the opposite side would also be beneficial for the scattering instruments’ opening as this would lead to a flux increase of 5% in the CN and VCN ranges.

Table 11 summarizes the gain factors for the best performing SD₂ model (Fig. 89) over the baseline LD₂ design for the different wavelength ranges of interest.

Fig. 90.

Brightness spectra comparison for VCNs emitted by lower-moderator designs using LD₂, SD₂, and SD₂ + ND reflection layer. Tallies are taken for neutrons traveling ±2° from the normal of the emission surface; the recording surface is placed at the twister exit in the direction of the beam port for neutron scattering instruments.

Figure 90 presents the comparison of the spectral brightness, calculated for the cases with and without ND, with the LD₂ design. To obtain the absolute brightness this procedure was followed:

Fig. 91.

Thermal scattering cross section per atom for ortho-SD₂ used in this study. The elastic, both coherent and incoherent, and inelastic contributions are shown. The fall of the upscattering cross section at low energy makes SD₂ an excellent moderator for the VCN range.

Two factors contribute to the improved performance of the SD₂ moderator with respect to LD₂. The first factor is the high VCN yield of the ortho-D₂ crystal arising from the very small value of the upscattering cross-section for energies lower than 20 meV (λ> 2 Å) in comparison with LD₂, as seen in Fig. 91. This results in a longer mean free path for upscattering and thus in a significant deviation from a Maxwellian thermalization spectrum at long wavelengths (an estimated ∝λ−3.5, compared with the Maxwellian λ−5). The second factor yielding an additional gain in the VCN range is the addition of ND. Thanks to their high albedo for VCNs, NDs limit losses and trap neutrons in the moderator material. Figure 92, presenting the different moderators’ time response at the twister exit for CNs and VCNs, shows that NDs are effective in increasing the neutron travel path. The neutron count values recorded are normalized to the peak value in the cold energy range. The VCN counts, already much higher in SD₂ than in LD₂, start to drop after 7.5 ms. The addition of reflective layer increases the number of reflections of VCNs, thus the outgoing flux increases. In the cold energy range, NDs are transparent and therefore no significant difference in the time response is observed.

Fig. 92.

Temporal response of the moderator for CNs in the range 4<λ<20Å (dashed lines) and VCN λ>20Å (solid lines) for the LD₂ baseline and the SD₂ moderator with and without NDs. The recording surface is placed at the twister exit in the direction of the beam port for neutron scattering instruments.

As another interesting result, it was found that the addition of a thin ND layer to the LD₂ baseline did not produce the same relative gains described for SD₂. On the NNBAR side, a significant 40% increase was calculated for λ>40Å, but at the expense of lower wavelength neutrons, which are the most relevant for the current NNBAR design. However, no gain was found on the WP7 side, while the same losses at lower wavelengths were observed. These findings suggest that in LD₂ the good VCN reflective properties of ND are most likely not sufficient to counterbalance the upscattering from the medium.

For neutrons in the λ>40Å range, it was challenging to obtain good statistics and MCNP simulations were very time consuming in comparison with shorter wavelengths, especially when modelling the full geometry of the ESS target monolith and shielding. In order to improve the statistics, the energy-splitting variance reduction technique was introduced. Despite the use of biasing, the relative error for this energy range remains at roughly 10% – even performing the simulations on the ESS computing cluster using 400+ cores.

It should be noted that these basic simulations are not taking into account the following parameters that could have a negative effect on the gains:

Before giving more details about the effects of those three parameters in the next sections, it should be mentioned that a full optimization of the moderator’s dimensional parameters (size, shape, position, etc.) has not yet been performed. This is expected to have a positive impact the final VCN yield. For example, substantial gains are observed when adding NDs as reflector in the extraction. Similarly, reducing the thickness of the 0.5 mm Al sheet located between the D₂ crystal and the ND layer and/or using a different low-absorbing material like beryllium or magnesium can also contribute to better performance [42]. A full optimization which accounts for such engineering considerations requires a wider effort and is outside the scope of this preliminary study. Nevertheless, possible detrimental factors can be assessed and, when possible, their impact is estimated at the best of the author’s knowledge.

4.7.1.Internal cooling structure

The most critical aspect to cover to assess the feasibility of a large-volume solid deuterium moderator is the cooling of the system made by the crystal and its aluminum vessel, which is on the scale of tens of kilowatts. When the SD₂ temperature is exceeding 5 K, the VCN flux is predictably decreasing with respect to its optimum; however, it was estimated that SD₂ still outperforms the LD₂ baseline by roughly a factor of 5 at wavelengths greater than 10 Å at 15 K, near its melting point. Nevertheless, considering greater thermal stresses, there is a greater likelihood for defect formation, and the thermal conductivity of the SD₂ itself drops between 5 and 12 K [9] from approximately 30 to 1 W m⁻¹ K⁻¹, indicating the imperative need of keeping as much of the SD₂ bulk as possible at a temperature below roughly 10 K.

Preliminary steady-state thermal simulations done by the HighNESS engineering team in FZJ showed that, for pure solid ortho-D₂ at 2 MW beam power, it could be feasible to keep the moderator at the foreseen operating temperature even within the ESS environment, by implementing an embedded cooling structure. The simulations assumed a cooling structure made of two main components. First, a metallic (aluminum or beryllium) or graphite foam inlay to increase the thermal conductivity of the solid block; and second, an additional system of inner cooling pipe (or pipes) with flowing liquid helium that would extract heat from both the outer surfaces and the very deep core of the solid.

Considering both neutronic and thermal conductivity aspects, three possible material options for the inlay can be considered: aluminum, beryllium, or graphite [69,93,101,108,227]. Those foams are known to have very high effective thermal conductivities [43,109,132,217], performing comparably with their bulk counterparts at cryogenic temperatures [20,200,208,211,212]. More complex materials presenting exceptional thermal conductivity, such as diamond/copper composites [40] or aluminum/beryllium alloys, may also be worth studying but are not considered further in the context of this work.

The steady-state thermal simulation tool of Ansys^® Workbench 19.2 was used for a preliminary assessment. Material data for deuterium with variable ortho-para concentrations, helium, aluminum (99.994% and 6061-T6) and beryllium, taken from the MPDB Material Property Database v7.91, were considered in the simulation as a function of the temperature [98] except for the deuterium data [167]. The combined thermal conductivity λeff of solid deuterium with the foam made of pure aluminum (99.994%), aluminum alloy 6061-T6 or beryllium was calculated as follows:

(4)λeff=fA(Φλ1+(1−Φ)λ2)+1−fAΦλ1+1−Φλ2,

where fA=0.33 is the Bhattacharya correlation factor, Φ=0.85−0.95 the porosity of the foam, λ1(T) the thermal conductivity of solid deuterium and λ2(T) the thermal conductivity of the foam. Table 12 shows the effective thermal conductivity, calculated according to Equation 4, at temperatures from 4 K to 20 K and a porosity of 85% to 95%.

Table 12

Heat conductivity λeff[Wm−1K−1] in different porosities Φ for pure aluminum (99.994%)

Φ	0.85	0.93	0.95
λeff(4K)	85.97	41.02	29.78
λeff(10K)	200.24	101.90	77.35
λeff(20K)	213.12	99.59	71.2

A uniformly distributed volumetric heat source induced by the spallation reaction was considered over the moderator volume. Only steady-state simulations have been performed (no pulsed heat). Two cases where studied, one corresponding to full-load operation (5 MW proton beam power Q = 60 kW) and one to partial-load operation (2 MW proton beam power Q = 24 kW). The heat is removed by a surface cooling only. Helium is the cooling medium, having an average temperature of 3.75 K. The heat transfer coefficient of the He-wall is considered to be infinite. The thermal contact of the foam to the aluminum vessel wall is also assumed as optimal. All of the approximations listed need to be checked performing detailed simulations.

Table 13

Intensity gain factors in the SD₂ lower moderator at different volume percentages of aluminum (Al), beryllium (Be), and graphite (C) approximating embedded foam densities. Counts are measured at the Beam Port Tally and gains are reported as ratios over the baseline with 4% aluminum added. In the non-uniform cases (second rows), the boundary is a higher-density 10-cm-radius sphere encompassing the SD₂ core; only such non-uniform trials are reported for graphite

λ range	Al %	2.5 Å to 4 Å	4 Å to 10 Å	10 Å to 40 Å	>40 Å
WP7	15%	0.57	0.68	0.95	2.5
	15/7 %	0.68	0.94	1.52	5.73
NNBAR	15%	0.48	0.71	0.95	1.9
	15/7 %	0.56	0.96	1.50	4.15

λ range	Be %	2.5 Å to 4 Å	4 Å to 10 Å	10 Å to 40 Å	>40 Å
WP7	15%	0.64	1.10	2.12	10.0
	15/7 %	0.77	1.27	2.47	18.3
NNBAR	15%	0.56	1.10	1.93	10.1
	15/7 %	0.63	1.26	2.33	13.8

λ range	C %	2.5 Å to 4 Å	4 Å to 10 Å	10 Å to 40 Å	>40 Å
WP7	15/7 %	0.79	1.28	2.57	22.0
NNBAR	15/7 %	0.64	1.25	2.42	16.1

Fig. 93.

Lower-moderator cell heat deposition for metallic (Al and Be) and graphite (C) foam configurations, divided by the proton current in mA impinging on the target (for a 5 MW beam). The green triangles show results accounting for additional heating due to ²⁷Al activation.

Neutronics simulations aimed at investigating the effect of metallic foam on the VCN production are summarized in Table 13. The system of crystal and foam was first approximated in MCNP by a uniform mixture of 85% volume fraction of SD₂ and 15% foam inlay. The gains are reported as count ratios at 2 m (Beam Port Tally) over the baseline LD₂ moderator with 4% aluminum added, which approximates the LD₂ cooling-flow channels, allowing for fairer comparison. The possibility of reducing the amount of foam material by having an inlay with different densities between the core region and the outer corners, where it is less important, was also explored. In these calculations, the boundary between these two regions is a sphere of 10 cm radius, and the volume percentage of the outer foam is reduced from 15% to 7%. This last configuration has a significant advantage over the uniform case in terms of neutron yield, while keeping the required cooling power almost unchanged. We also studied the increase of heat deposition in the moderator cell as a function of the foam volume percentage (Fig. 93).

According to the results presented, graphite and beryllium outperform aluminum regarding neutronic, self-heating, and thermal conductivity. In terms of performance, beryllium is a promising candidate but manufacturing a beryllium foam would be challenging due to the higher melting point and non-standard safety measures in handling this material. Graphite then appears as an appealing candidate material in general terms.

However, at roughly 3200 W m⁻¹ K⁻¹ [126] near the melting point of SD₂, the thermal conductivity of high-quality bulk beryllium at the relevant temperature range of 5–20 K is particularly high with an effective thermal conductivity value of roughly 200 W m⁻¹ K⁻¹ for a porosity of approximately 85%; the thermal conductivity of graphite foam is likely to be lower by at least a factor of two [109,228]. Depending on the purity of the material, it should also be mentioned that the thermal conductivity for aluminum and beryllium can vary by orders of magnitude [198,211], for example, the thermal conductivity of ultra-high-purity aluminum is 35,000 Wm⁻¹ K⁻¹ at 10 K [194].

A foam with open pores (I) or a 3D printed grid structure (II) would be two interesting options worth investigating regarding the manufacturability of the inlay [92,151]. In the case of option (I), a melting of the optimized alloy can be frothed through the addition of a foaming agent. The density and porosity can be tuned homogeneously for the inlay in this process. The second option (II) would consist of a grid structure manufactured using the selective-laser-sintering (SLS) 3D printing technique; a thin layer of metal powder is locally sintered by a laser beam. A defined three-dimensional geometry can be created by repeating the operation layer-by-layer. The advantage of this method in comparison with option (I) is the capability to adapt the geometry to the need of an optimal thermal conduction while minimizing the reduction of SD₂ volume. This is overcoming the limitations due to the homogeneous properties of option (I).It should be noted that this heatsink inlay is not intended to act as a structural support, its only goal is to improve the thermal conductivity. When incorporating such an inlay into the moderator design, a critical aspect is its thermal coupling with the surrounding moderator vessel walls and the liquid helium channel. This coupling could be realized by a defined press fit or a soldering process with a matched plumb alloy. Inlay-type (II) would allow for the printing of a thin-wall structure in the geometry to enlarge the connecting interface surface. This would increase the thermal coupling compared with the press fit and soldering option. Further experimental investigations will be necessary to investigate more in details this point.

4.7.2.Hydrogen and Para-D₂ impurities

Thanks to its small nuclear mass and absorption cross section, deuterium is one of the best neutron moderator materials. The importance of having high-purity ortho-D₂ crystals for UCN production through the use of SD₂ have been highlighted in the literature [120,134]. Hydrogen and para-deuterium are the elements usually considered as impurities due to their respectively higher absorption and upscattering cross sections [120]. However, in view of the similarities between the two spin isomers in the VCN energy range and the achievable ortho-D₂ purity, the impact of these impurities on the VCN yield are expected to be small, as discussed in the following.

The effect of hydrogen impurities was simulated by adding increasing percentages of solid para-H₂ at 5 K in the SD₂. Hydrogen impurities have typically been found in the form of HD and not para-H₂. However, since this was the only library available and impurity concentrations in D₂ are usually around 0.2% [134], those data were considered to give a reasonable approximation of the absorption problem. The impact of the impurities was assessed at the exit of the twister where statistical uncertainties were lower. The results are plotted in Fig. 94. For concentrations ranging up to 1%, an average drop in neutron counts of roughly 0.35% was highlighted for λ>40Å for every 0.01% increase of the hydrogen content. For the scattering instruments opening, this linear approximation is less accurate, showing a relatively larger loss, especially for hydrogen concentrations higher than 0.5%. An impurity level of 0.2% is achievable in D₂. Considering more pure D₂ reaching 0.05%, these effects would hardly downgrade the gains observed considering the ideal crystal.

Fig. 94.

Effects of introducing small vol% of solid para-H₂ in the ortho-D₂ crystal for neutrons with λ>40Å.

Similarly, the addition of 1% para-D₂ to the material mix did not lead to significant effects exceeding the statistical uncertainty at the exit of the twister. However, due to recombination following the radiolysis induced by fast neutrons and gammas, it could be expected that the para-D₂ concentration will increase as a function of the operation time. After the radiolysis of an ortho-D₂ molecule, according to the natural proportion of the two spin isomeric forms, the recombination will produce a para-D₂ molecule 33% of the time [96]. Preliminary calculations performed using a solid para-D₂ thermal scattering library at 5 K showed small losses (less than 5%) for neutrons with λ>40Å when adding 30% para-D₂. As the two spin isomers’ cross sections are similar in the VCN energy range, this last result is not surprising. Even though the neutronic performance at 5 K is reassuring, a high content of para-D₂ would drastically decrease the thermal conductivity of the crystal, leading to difficulties to keep it at 5 K. The neutronic effects of para-D₂ at higher temperatures should then be further investigated in a dedicated study.

4.8.Combined option

Fig. 95.

Original concept of the SD₂ converter as presented in [141].

The idea of a VCN source combining an SD₂-based VCN converter with an existing CN source was proposed at the first HighNESS workshop on UCN and VCN Sources at ESS [141]. The rationale behind the concept is to maximize the VCN flux to the NNBAR experiment. A dedicated VCN source could overcome the well-known low phase-space density (the neutron flux decreases as the square of longitudinal neutron velocity in a cold source), while retaining the sensitivity increase as the square of the free flight time (≈λ2). The net gain factor would then be simply proportional to the increase in the phase-space density over the cold source. The original concept is shown in Fig. 95 and it can be described as follows:

Contrary to UCN extraction with SD₂, VCNs penetrate through the inhomogeneities in the SD₂ bulk, and are thus more easily extracted with minimal losses.

The source flexibility and the ease of implementation within the current LD₂ cold source make this an interesting design for a general-purpose VCN beamline. Therefore, the performance of a possible converter on the WP7 has also been studied.

4.8.1.NNBAR side

As a starting point, the simplest study one can imagine is to measure the effect of a thin converter on the VCN flux at the beam port, which is located 2 m from the center of the moderator. For this test, we put 5 cm of SD₂ in a 170-cm-long ND-filled channel with 2-cm reflector thickness on the sides and 1 cm in the direction of the cold neutron beam. The reason for having a thick ND layer is to increase the diffusive transport of VCNs. The very cold energy range is far from the quasi-specular regime; thus, the intense albedo from the powder is exploited instead. The first tests did not have any structure around the converter and for the inner walls. This is clearly an oversimplification, since in reality both the D₂ (gas) and the NDs (powder) must be stored in a container, but it allows for a verification of the predicted enhancing effect, neglecting the engineering complications. The model used is shown in detail in Fig. 96.

Fig. 96.

Table 14. (Left) MCNP model of the preliminary test run to check the separate and combined effect of ND and the SD₂ block. (Right) parameter table for this model.

The performance of the converter is measured with a current tally (F1) through a fixed surface placed at the beam port with several energy-grouped resolutions and coarse angle bins. The effect on the neutron counts was studied separately for each component of the system. The Table 15 summarizes these preliminary results at all angles.

Table 15

Preliminary results at all angles of the SD₂ converter design on the NNBAR side. The tally is measuring the counts at all angles through a fixed surface placed at the beam port. Gains are measured over the third optimized baseline (see Section 2.3.6)

Gains	Al casing	SD2 only	NDs only	SD2 + NDs
4Å<λ<10Å	0.98	0.54	1.71	0.87
20Å<λ<40Å	0.95	0.71	0.84	1.76
λ>40Å	0.86	0.93	0.44	16.9

First, the Al case was added in the opening, which produced overall small losses in the energy ranges studied. Then, only the SD₂ crystal was inserted, without the surrounding NDs. As a result, cold neutron (4 Å to 10 Å) and VCNs from 20 Å to 40 Å are less, while an increase in the coldest neutron counts (λ>40Å) is the first sign of enhanced VCN production over the LD₂ baseline.

Similarly, results for ND reflector but no SD₂ are shown. In this third case, it is possible to observe an increase in the cold counts for the ND guide only, which is due to the quasi-specular reflection. On the other hand, huge losses are observed in the VCN energy region. The difference with the previous model, and cause of the losses, is in the additional layer at the emission surface, which is back-scattering and diffusing the VCNs coming from the LD₂ moderator.

Finally, the two pieces are coupled, SD₂ and NDs in the Al case, and the VCN counts at the beam port almost double from 20 Å to 40 Å and increase by a factor 17 above 40 Å. In the next section, this tentative simple case is improved by an optimization of the parameters.

4.8.2.Optimization of the ideal case

For a robust and methodical approach to the optimization task, Dakota [2] and the EGO algorithm were used. The optimization parameters were the thickness of the SD₂ block and the thickness of the ND layer both on the sides of the guide-like system and behind the SD₂ (in front of the emission source) designated as side and back thicknesses, respectively. The FOM chosen to drive the algorithm is the VCN counts at the beam port between 20 and 40 Å and at all angles. In fact, it is more convenient to use this tally since it converges faster while following approximately the same behavior as the VCNs above 40 Å. The results of this multi-dimensional optimization are shown in Fig. 97.

Fig. 97.

Results of the multi-dimensional optimization. Each run of the optimization is represented by three vertically aligned points, one for each energy-group of interest and each one with its own scale for the gains over the LD₂ baseline. Trend lines are shown with the sole purpose of guiding the reader’s eye.

Before discussing the results, the content of the plots in Fig. 97 should be clarified:

• - Each run of the optimization is represented by three vertically aligned points, one for each energy-group of interest and each one with its own scale for the gains over the LD₂ baseline.

• - Since we are showing one parameter at a time, the presence of different counts values for the same parameter value is to be interpreted as a run where one (or both) of the other parameters was changed.

• - The lines shown are mere trend lines with the sole purpose of guiding the reader’s eye and not fitted models.

• - The EGO algorithm does not sample uniformly the parameter space, hence the larger clusters of points visible in the plots are formed to better sample the region around the maximum of the FOM. This is also why this approach can be much faster than a simpler evaluation of a parameter grid.

The first important result of the optimization is that large blocks of SD₂ produce the highest VCN yields. Here 20 cm was the upper boundary given to Dakota for the thickness, but it is reasonable to assume that there would be higher gains for larger crystals. However, with approximately 14 L of SD₂, this moderator has already unprecedented dimensions for a crystal at 5 K, with non-negligible issues pertaining to cooling and engineering (the estimated heat deposition from prompt neutron and gammas is 2.5 kW). The cost for the high gains in the VCN energy range are considerable losses in the cold range around 4 Å. A possible explanation for these losses is in the large SD₂ elastic cross section (see Fig. 91) that decreases the mean free path, effectively making the cold source appear further away from the beam port and increasing the chances of absorption or leakage.

Additionally, the thickness of the crystal seems to be the most important parameter by looking at the range of the results, while the thickness of the back ND layer is the least crucial for an optimal design. The latter is due to the relatively high transmission fraction of cold neutron through thick ND layers. Meanwhile, once the neutrons are moderated to VCN energy, that layer, even when few millimeters thin, suddenly becomes opaque, reducing the chances of leakage.

Conversely, the thickness of the ND layer on the sides seems to have a more important role. In particular, both too-thick and too-thin values are penalizing for VCNs. In the first case because there is not enough reflecting material, while in the second case, too much moderating material is lost to accommodate NDs. Also, the emission surface is considerably shaded by the reflector layer, inevitably reducing the neutron counts at the beam port. The optimized model is shown in Fig. 98. Compared to the LD₂ baseline, this model is able to deliver 47 times more neutrons above 40 Å and 3 times more neutrons in the range from 20 Å to 40 Å, while retaining only 40% of the cold neutrons between 4 and 10 Å.

Fig. 98.

Table 16. (Left) MCNP model of the optimized converter. (Right) parameter table for this model. The optimized parameter are in bold.

4.8.3.Engineering details

In order to make the model more realistic, we added an aluminum vessel 2 mm thick at 5 K around the SD₂ crystal. An additional 5 mm vacuum gap separates the converter vessel from the ND reflector surrounding it. Finally, we add 1 mm of aluminum as internal cladding for the reflector. We have already mentioned that the model without inner Al structure was a simplified test to study the validity of the idea. For a ND guide, this is quite a critical feature, especially in the VCN range. This model is shown in Fig. 99.

Fig. 99.

Table 17. (Left) MCNP model of the optimized converter with engineering details. (Right) parameter table for this model.

Compared to the ideal case, this model performs much worse. We estimated that, in terms of gain over the baseline, it yields only 2.6 times more neutrons above 40 Å and 10% more neutrons in the range from 20 Å to 40 Å. While 1 mm is already a reasonable thickness, one way to improve the model is to use thinner Al cladding for the extraction. Another way to improve performance would be using other metal foils, like magnesium [42]. Preliminary calculations with 1 mm of pure Mg showed gains over the baseline as high as a factor of 12 for neutrons above 40 Å and a factor of 2 in the range from 20 Å to 40 Å. Here, it is probably most noteworthy that the flexibility of the design could be used to improve the performances, keeping in mind that reducing the thickness of the inner walls or changing the material tends to be beneficial.

4.8.4.Improvements to the design

The first change we can make to the model that will predictably improve the performance is removing the cold beryllium filter from the LD₂ vessel. The reason for this is that the beryllium at 20 K reflects any neutrons with wavelengths below 4 Å back to the moderator; whereas for longer wavelength neutrons, the crystal is almost transparent. Although this is beneficial for NNBAR, whose FOM is proportional to λ2, it is detrimental for a VCN converter, given that neutrons in the range from 2 Å to 4 Å contribute significantly to the VCN production in SD₂. The model without the Be filter is shown in Fig. 100. Removing the filter to add more moderating LD₂ has the effect of increasing the gains by ≈20% over the case with the filter (Fig. 99). Another important result is in the increase to 3 kW of the heat deposition in the moderator volume due to the higher neutron and gamma flux.

Fig. 100.

Table 18. (Left) MCNP model of the optimized converter with engineering details and without Be filter in the cold source. (Right) parameter table for this model.

Since the thermal and cold neutron flux have an important role in VCN production when with SD₂, a further improvement to the design should be obtained by moving the converter closer to the source. In other words, it is worth studying the effect of embedding the converter inside the LD₂ vessel, regardless of its feasibility. To this end, we inserted the converter 11 cm deep inside the cold source. Due to the major shift in the design, we chose to optimize this model separately. The parameters are, within the statistical uncertainty, identical to the previous optimization, except for the thickness of the back ND layer which is 1.2 cm (still a low-sensitivity parameter).

The model implementing this idea is shown in Fig. 101. In terms of performances, this solution provides an average factor of two improvement for all energies over the case with the Be filter (Fig. 99). If we compare the neutron counts over the baseline without a VCN converter, this model is able to deliver 5.7 times more neutrons above 40 Å and 2.5 times more neutrons in the range from 20 Å to 40 Å, while retaining 60% of the cold neutrons between 4 and 10 Å. However, once again, the price to pay for the increased flux is a significant increase in heat-load. We estimate that just moving the converter 11 cm inside the moderator nearly doubles the heat deposition to a value of 5.8 kW.

Fig. 101.

Table 19. (Left) MCNP model of the optimized converter embedded in the LD₂ cold source. (Right) parameter table for this model. The optimized parameters are in bold.

4.8.5.Converter for neutron scattering instruments

Similarly to the tests on the NNBAR side, the effects on VCN flux were studied for a thin converter on the WP7 side. The F1 tally measures the current at a fixed surface placed at the beam port, 2 m from the center of the moderator, with the same energy-angle resolution. For this test, the opening is 10 cm × 10 cm and the SD₂ crystal is 5 cm thick. The ND guide is 190 cm long with 2-cm-thick walls on the sides and 1 cm in the direction of the cold neutron beam. No structure is present around the converter and for the inner walls. The model used is shown in detail in Fig. 102.

Fig. 102.

Table 20. (Left) MCNP model of the converter embedded on the WP7 side for the preliminary test run to check the separate and combined effect of NDs and the SD₂ block. (Right) parameter table for this model.

The preliminary test with this tentative setup did not show, compared to the baseline, any gain in using the converter independently from the energy-group considered. To be sure that the bad performances observed are not strictly bound to a particular configuration, the most important parameters of the geometry were optimized with Dakota. Namely, the EGO algorithm found the best values for the SD₂ thickness, the ND layer thickness on both the sides and the back. Similarly to the NNBAR case, the figure of merit of the optimization was the VCN counts between 20 Å and 40 Å and the minimum value set as boundary for the ND layers is 0.1 cm. Despite the precision being lower than the NNBAR case, especially at very long wavelength, the results suggest with a good degree of convergence that the most favorable configuration has only 1 mm of NDs on the sides (Fig. 103).

The fact that gains are observed over the baseline in the VCN range suggests that inserting a block of SD₂ has the intended effect of further moderating the cold spectrum coming from the LD₂. Also, as expected, the system is not very sensitive, within few centimeters, to the thickness of the NDs in the back due to the high neutron transmission in the cold range.

Fig. 103.

Results of the multi-dimensional Dakota optimization of the 10 cm × 10 cm opening for WP7. Each run of the optimization is represented by a point. Only gains for the VCN energy-group from 20 Å to 40 Å are shown. The gains are calculated over the baseline with the same opening. (A) SD₂ thickness vs ND layer side thickness (b) SD₂ thickness vs ND layer back thickness.

However, the configuration that maximizes the gains between 20 Å and 40 Å is found at the minimum of the ND thickness on the sides. The different behavior observed between WP7 and NNBAR in the optimization of the ND side layer thickness is explained by a poor parameterization of the model. As already mentioned, the increase of the reflector thickness on the side has the effect of reducing the amount of SD₂ and occluding the emission surface. Despite being present also on the NNBAR side, this effect seems to be crippling only on the WP7 side.

One way to fix this is to move the SD₂ block out of the reentrant hole and by changing the thickness of the ND layer outward at the cost of the reflector, not the emission surface. In this setup, the SD₂ block has the same lateral dimensions as the opening and it is decoupled from the NDs. This allows for an unrestricted increase to the ND layers on the sides to reduce the leakage, without occluding the opening. Finally, the thickness of the reflector layer outside the twister (i.e. the guide-like part) is also decoupled and optimized separately. The cost in terms of performance for this setup is a lower cold flux due to the longer distance from the center of the cold source. The optimized model for a 15 cm × 15 cm opening is shown in Fig. 104, while in Fig. 105 an overview of the results of the optimization is presented.

Fig. 104.

Table 21. (Left) MCNP model of the converter for the WP7 side with improved parameterization. (Right) parameter table for this model. The optimized parameters are in bold.

Fig. 105.

Results of the multi-dimensional Dakota optimization of the 15 cm × 15 cm opening for WP7. The gains are calculated at all angles over the baseline with the same opening. (A) each run of the optimization is represented by three vertically aligned points, one for each energy-group of interest and each one with its own scale for the gains. Trend lines are shown with the sole purpose of guiding the readers’ eye. (B) each run of the optimization is represented by a point. Only gains for the VCN energy-group from 20 Å to 40 Å are shown. The two parameters plotted are: SD₂ thickness vs ND layer side thickness. (C) SD₂ thickness vs. ND layer thickness in the extraction.

From the analysis of the parameter space, the behavior of the improved model is more similar to what was expected by such system. In Fig. 105a, the different trends of the gains for different energy groups as a function of the SD₂ thickness are highlighted. It is clear that, for small amounts of SD₂ in the opening, the overall effect of the setup is to increase the CN transport by exploiting the quasi-specular reflection on the ND layers on the sides. Notably, the factor 2 increase in the flux is compatible with the results in Section 4.9 at all angles. As the thickness of the converter increases, the shift at longer wavelengths becomes more and more pronounced. Around 15–20 cm, the converter yields an average gain factor of more than 3 for VCNs between 20 Å and 40 Å and 30 for VCNs at longer wavelengths and at all angles. In Fig. 105b and Fig. 105c the gains from 20 Å to 40 Å are plotted as function of the SD₂ thickness and ND layer on the sides and in the extraction, respectively. In both cases, a thicker reflector is correlated with higher gains. In the case of the NDs on the sides, the removal of standard reflector does not seem to produce a significant loss.

It should be noted at this point that each step of the optimization is computationally more expensive and tally precision is lower than for the NNBAR opening. This limits the exploration of the parameter space and the extraction of key insights about the system. Despite the lower cold flux on the converter caused by the longer distance from the center of the moderator, the system is able to deliver order-of-magnitudes gains in the lower VCN range, with potentially smaller impact on the cold flux at the beam port and a smaller heat load to remove (cfr. Figure 104). Finally, in Section 4.8.3 the losses caused by adding the engineering details were discussed for the setup in the NNBAR opening. Similar observations are reasonably valid for the WP7 opening.

4.8.6.Gains at small angles

The results discussed so far are for neutrons reaching the beam port at any angle. The presence of a ND channel allows neutrons with a large divergence to reach the recording surface. However, for most conventional neutron scattering instruments, neutrons with large divergence are collimated along the way and do not contribute to the flux at the sample. The gains for the neutrons with vertical divergence between 0° and 2° are shown in Fig. 106a for the NNBAR opening, and Fig. 106b for the WP7 opening.

Fig. 106.

Results of the multi-dimensional Dakota optimization of the (a) NNBAR opening and (b) the 15 cm × 15 cm opening for WP7. The gains are calculated at small angle over the baseline with the same opening. Each run of the optimization is represented by three vertically aligned points, one for each energy-group of interest and each one with its own scale for the gains. Only the SD₂ thickness is reported. Trend lines are shown with the sole purpose of guiding the readers’ eye.

The gains are reported solely as a function of the SD₂ thickness, as the strongest predictor. While the trends are similar to the all-angles cases, the scale of the VCN gains is smaller. Up to 20 Å, there is no advantage in using the converter. The initial VCNs produced inside the LD₂ cannot reach the beam port due to the thin ND layer between the main source and the converter. Since ND channels have proven to be effective in improving the neutron flux at small divergence, the reason for the lower gains can be attributed only to a lesser production in the SD₂. The neutron flux out of the SD₂ at small divergence does not compensate for the initial VCN flux, yielding an overall loss between 20–30%. Above 40 Å, the neutron production by the SD₂ crystal over the LD₂ baseline is enough to achieve a net gain. Due to the wide applications of low-divergence neutrons, this effect should be studied in detail, in order to tailor the source to the specific needs of the instruments placed at the end of the extraction system.

4.9.Beam extraction with nanodiamonds

An additional option for improving VCN yield regardless of the source configuration is to use a dedicated guide-like system to more efficiently extract the VCN tail from the LD₂ spectrum. In a dedicated study, since the quasi-specular reflection on thin ND powder samples has been experimentally observed [5,47,143,144], a straight ND guide with walls thickness of 5 mm was considered adequate to observe the improvement of extracting CNs and VCNs. Preliminary simulations were conducted on both sides of the LD₂. The ND powder had an effective density of 0.6 g/cm³, so it was compressed inside the hollow space created by two Al walls. The inner wall was a 0.1 mm thick Al foil, and the outer Al wall had a thickness of 2 mm. The geometry is shown in Fig. 107.

Fig. 107.

MCNP model of the LD₂ baseline with ND extraction system (a) vertical cross section, perpendicular to the proton beam direction. (B) cross section parallel to the target plane with the proton beam impinging from the left.

Fig. 108.

Gains with ND guide 2 m away from the center of the moderator (beam port position) as a function of neutron wavelength groups for NNBAR (left) and WP7 (right) openings.

Fig. 109.

Divergence of cold neutrons at the beam port (λ>4Å) for the baseline without (blue) and with (orange) ND guide. Left for the NNBAR opening, right for the WP7 opening. The vertical axis is neutron counts/nps.

The result of the study are summarized in Figs 108 and 109. As expected, the ND guide can transport cold neutrons and can provide on average a factor of 2 gain at 2 m over the baseline. However, most of these gains are obtained for neutrons reaching the beam port with vertical divergence greater than 2°, that is, the more pronounced effect is observed in the region of the phase space where fewer neutrons (or none at all) would be allowed to reach the beam port without the guide. The gain provided by the ND guide reached the maximum at around 10 Å on the WP7 side, and then decrease in the VCN energy range. Here, due to the multiple large-angle interactions, the reflections on the ND layer very quickly produce an isotropic distribution. The large NNBAR beam port is more likely to accept those large divergence neutrons, while in the smaller guide on the neutron scattering side, they are easily lost (absorbed, back-scattered, and so on) after multiple interactions with the ND and the Al walls. The idea of a ND guide between the emission surface and the beam port as a VCN-enhancing system is further investigated in the following section.

4.10.Comparison of the different options

Fig. 110.

MCNP models of the VCN sources compared in this work: (a) standard LD₂ with advanced ND extraction system (b) dedicated SD₂ with advanced ND extraction system (c) combined LD₂ and SD₂ source with ND extraction (ideal case) (d) combined LD₂ and SD₂ source with ND extraction (Al vessel and void gap).

In this section, we compare the performance of the VCN options presented thus far, except for the clathrates option because it is still at a conceptual level. The models compared here are shown in Fig. 110. In order for the comparison to be meaningful, it is important to account for the differences that are not at the core of the design (e.g. the size of the recording surface, or the thickness of the Al walls). Here, we focus only on the NNBAR opening since its size is very similar between the cases, and it is more reliable in terms of statistical convergence. Below is a description of each model that is part of the comparison:

Table 23

Neutron current and brightness gains over baseline in wavelength groups calculated from Table 22. Propagated statistical error is also reported

For each of these cases, we calculated the current in n/s and the brightness in n/s/cm²/sr/Å. The calculation of the absolute brightness for this comparison is similar to what has been done in Section 4.7. First, we recorded the raw counts per spallation proton through the surface at 2 m from the center of the moderator. Then, we divided the counts at ±2° from the surface normal, by the emission surface, by the solid angle in the 2° cone, and by the wavelength range of the group, then we multiplied the result by the expected proton current on the ESS target at 5 MW, as in Equation (3). All the results in the appropriate units are presented in Table 22. To facilitate the comparison, in Table 23 we calculated the gains over the baseline for each option, while in Fig. 111 the current spectra at all angles highlights the effect of ND, SD₂, and the combination of the two in two wavelength regions.

Fig. 111.

Current at all angles [n/s/Å] at 2 m from the moderator center for all the VCN options studied in this section. (A) Bragg peaks from Be filter, ND and D₂ crystal are visible in the range between 2 and 10 Å. (b) VCN tails are highlighted in the range between 10 and 50 Å.

The best option for both the figure of merits studied is undoubtedly the dedicated full SD₂ moderator at 5 K. From the neutronic point of view, order-of-magnitude VCN gains are complemented by a high CN yield. This makes such a moderator an ideal candidate to replace the LD₂ cold source. However, as already highlighted in Section 4.7, this solution comes with great challenges from the engineering point of view.

On the other hand, the easiest solution is using the LD₂ moderator as it is would be to place a guide-like system made of a thick layer of ND and enhance the VCN tail of the cold spectrum. The simulations show that the longer the wavelength, the higher the gain factor for the current; but when it comes to brightness (low angles) the gains are more limited. The interactions with dedicated VCN instruments need to be investigated for a complete overview of the impact of such device. There is, nevertheless, room for further improvement in the design both in terms of materials (e.g. metal walls, packing of the powder etc.) and configuration (e.g. position of the guide) that should be further investigated in a new project.

The option of combining SD₂ and LD₂ is a midpoint between the previous two cases. Even though the possibility of cooling a 5-K D₂ block so close to the spallation target is yet to be determined, this case promises to be much easier to handle if compared to the full SD₂. At the same time, other challenges would arise in terms of the engineering development (e.g. finding room for the cooling infrastructure in the limited space of the opening, replacing components etc.) that do not need to be faced in the case of a simpler ND guide. In terms of neutronic performance, this option can potentially provide order-of-magnitude gains in the VCN current, without structural changes to the CN baseline. As with the other cases, the optimization of the materials used for the extraction and the containment of the D₂ is crucial to preserve the ideal gains. Lastly, this option takes a significant toll on the CNs, which are drastically reduced at 2 m with the insertion of the SD₂ block. A possible explanation for this effect is the decrease of the neutron mean free path due to the elastic scattering inside the D₂ crystal, which increases the effective distance between the moderator surface and the recording surface.

5.1.Experimental characterization of clathrate hydrates

A necessary characteristic to assess the suitability of a material for moderation purposes is the dynamic structure factor S(q,ω), which accounts for its structure and excitation spectrum and enters the cross section for VCN production. To determine this quantity in absolute units for the THF-d clathrate hydrate, inelastic scattering experiments using thermal- and cold-neutron time-of-flight instruments at ILL have recently been performed in addition to diffraction experiments for sample characterization. Results of these measurements have been published in [48], the key findings are summarized below. Additional experiments on VCN transmission can provide important complementary information, which determines the maximum depth from which VCNs can be extracted from a moderator to a beam.

5.1.1.Manufacturing of THF-hydrates

A starting point of this experimental campaign is establishing a reliable and scalable technique, that allows production of relatively large quantities of hydrates with minimal amounts of residual ice. This technique is described in detail in [48] for THF-hydrates having different protonated and deuterated components. The obtained structures were studied by neutron diffraction at the high-intensity two-axis diffractometer D20.

THF (molecular formula C₄H₈O) is an organic compound which has a ring structure. A great advantage of THF-hydrates, compared to most other clathrate hydrate compounds, is that they form at ambient pressure from a stoichiometric mixture of its two liquid components, water (H2O) and THF (C4H8O), in a ratio of 17 to 1 [102] at 280 K and below. After carefully weighing and mixing the two liquids with a teflon-coated magnetic stirrer, a cool-down of the solution results in solidification in the CS-II structure (see Table 24). The diffractogram that verifies this structure is shown in Fig. 112. Depending on the sample, a clathrate weight percentage of 95.1±1.5% to 98.4±1.6% was reached for the samples investigated, with the uncertainty being dominated by the quality of the fit. The details of the refinement are given in Table 25. The fit is significantly affected by the crystallite size, attributed to the texture arising during in situ formation. Despite this it provides evidence that the clathrate structure is reliably produced with high purity from the stoichiometric liquid mixture.

Table 24

Characteristics of the CS-II hydrate crystal cell structure. In the case of THF-hydrates the unit cell formula reduces to 8THF: 136H₂O, with the small cages remaining empty. Table adapted from [187, p. 60]

Crystal system	Cubic
Space group	Fd3m (N°227)
Lattice description	Face centered
F Lattice parameters	a = 17.1 Å–17.33 Å
	α=β=γ=90∘
Number of cages	8 large (51264), 16 small (512)
Ideal unit cell formula	8(51264)·16(512)·136H2O

Fig. 112.

Diffraction pattern of fully deuterated THF-hydrates (THF-d·D2O) formed in situ taken on D20 with λ= 1.546 Å at a temperature of 230 K (red) and the corresponding multi-phase rietveld-refinement (black). The blue line depicts the difference between the data and the fit. The calculated peak positions (green ticks) correspond to phases considered for the refinement, which are, besides the THF-d-hydrate, the aluminum sample environment and residual hexagonal ice. The upper right corner shows 1 of the 8 large cages (51264) within the unit cell hosting a THF-d molecule, as well as 1 of the 16 empty small cages (512). The experimental conditions are described in detail in [48]. The data is available under  [233].

Table 25

Refinement details of the diffraction pattern depicted in Fig. 112. The Bragg R-factor (RB) and the weighted profile R-factor (Rwp) indicate an acceptable fit

Phase	THF-d·D2O	Ice Ih
Crystal system	Cubic	Hexagonal
Space group	Fd-3 m	P 63/m m c
Cell parameters	a = 17.22(7)	a = b = 4.50(7)
		c = 7.35(4)
RB	10.49	27.92
Rwp	4.89	4.89

5.2.Low-energy excitations of THF-hydrates

After verifying the formation of the CS-II structure in the samples subjected to both solidification through quenching and slower cooldown, we undertook an investigation of their low-energy excitations. For this purpose, experiments were carried out using the ILL time-of-flight (TOF) spectrometers, specifically IN5 [147] and Panther [62]. These experiments aimed to measure the dynamic structure function S(q,ω) across a substantial portion of the (q,ω)-space. Details can again be found in [48]. The data obtained from these measurements play a crucial role in benchmarking density functional theory (DFT) and molecular dynamics (MD) simulations, as elaborated in [215] and in this report. The four samples with different combinations of protonated and deuterated components as described in Table 26 were measured at a temperature of 1.5 K. Data reduction, analysis and visualization were carried out using the Mantid software package [10,125].

Figures 113a and 113b show two spectra for different THF hydrate samples measured at Panther and IN5, respectively. These spectra are obtained by integration over a given q-range, providing an average of the coherent signal in this range.

Fig. 113.

(A) constant q-slice at q=(4±1)Å−1 through S(q,ω) for different deuterations and protonations of the THF-hydrate measured at Panther with an incident energy Ei=19meV at a temperature of T=1.5K. The characteristic peaks at 7 meV and 10.5 meV of CS-II can be well discerned. Preliminary results, data is available under [234]. (B) constant q-slice at q=(3.5±0.75)Å−1 through S(q,ω) at IN5 with an incident energy Ei=9meV at a temperature of T=1.5K. The observed peaks are due to localized excitations of the THF molecules (see text). The shoulder of the elastic peak is not a feature of the sample but back scattering of the sample environment. The experimental conditions are described in detail in [48]. The data is available under [233].

In the investigated energy range, the dynamics of the host structure are primarily determined by the translational modes of the H2O or D2O molecule. This results in two distinct peaks at approximately 7 meV and 10.5 meV for each CS-II hydrate structure (see, e.g. [27,35,39,46,179]). This can also be observed in Fig. 113a for both the protonated and the deuterated host lattice. The most pronounced peaks can be observed in the THF−d·H2O sample (orange), as the influence of the deuterated guest molecule is reduced in the scattering signal. The vibrations of the guest molecule occur at lower energy levels and exhibit clear peaks around 2.9 meV and 4.7 meV, as highlighted in the THF·D2O sample (depicted in green) in Fig. 113b. These localized excitations hold significant potential for moderation into the VCN range. Substituting hydrogen with deuterium results in an enhanced mass and consequently a greater moment of inertia. This applies to both the translational modes of the host lattice and the excitations of the THF molecule, resulting to a shift towards lower energies. This observation aligns with the phonon density of states (PDOS) computed within the collaboration [215].

5.3.Simulation of a clathrate hydrate moderator

To study the use of clathrate hydrate as a VCN moderator, neutron flux in a simple spherical model was initially calculated in OpenMC [168]. In this model, a sphere with radius of 22 cm was filled with the clathrate hydrate at 2 K (see Fig. 114a) with a thermal (1 eV) isotropic point source of neutrons located in the center of sphere. The radius of the sphere was chosen so that it has a similar volume as the baseline LD₂ cold moderator. The sphere was subsequently filled with LD₂ and SD₂ for comparison with clathrate.

The neutron energy spectrum for each case can be seen in Fig. 115a, and the neutron wavelength spectrum for each case can be seen in Fig. 116a and Fig. 116b. Here, the SD₂ outperforms the clathrate for both the CN (2Å<λ<10Å) and VCN range (λ>10Å), while the clathrate was only competitive with LD₂ in the VCN range above 14Å. The reason for the sudden increase in the neutron flux at 14Å for the clathrate-filled moderator is that the cross section for the magnetic down-scattering is maximal at that wavelength (see Fig. 117). The wavelength spectrum in Fig. 116a shows a peak for SD₂ at about 5Å, which appears due to a sharp peak in the elastic cross section for SD₂ at this wavelength. These results from an OpenMC simulation are consistent with those from an identical simulation in MCNP (see Fig. 118a).

Fig. 114.

An initial model of the clathrate VCN source. (A) initial model with sphere of radius 22 cm filled with clathrate hydrate. (B) second model with additional 5 cm thick layer of MgH₂ cold neutron reflector.

Fig. 115.

Calculated neutron flux inside a sphere filled by O₂-clathrate, LD₂ or SD₂. (A) model without the cold neutron reflector. (B) comparison of the model with and without the cold neutron reflector, which was is MgH₂ at 20 K.

Fig. 116.

Neutron spectrum computed in the sphere filled by O₂-clathrate, LD₂ or SD₂. (A) spectrum between 1 and 15 Å. (B) spectrum between 10 and 20 Å.

Fig. 117.

Cross-section for the magnetic scattering in O₂-clathrate hydrate with 136 D₂O and 24 O₂ in each unit cell. Generated using the tool ncplugin-MagScat presented in ref. [214].

A limiting factor of the selected clathrate at 2 K is the large mean free path of cold neutrons, about 30 cm, for magnetic down scattering that can be deduced from Fig. 117. The cross sections are computed using the tool ncplugin-MagScat in which the physics of inelastic neutron magnetic scattering [230] is implemented [214]. To mitigate this deficiency, a 5 cm thick shell of material to reflect cold neutrons was designed around the sphere to allow for more interactions between cold neutrons and the clathrate (see Fig. 114b). This shell was filled with MgH₂ because of its promising properties as a cold neutron reflector, as reported by Granada et al. [83] and based on a study of several neutron reflector materials. This study was conducted using the model in Fig. 114b where the 5 cm thick outer shell was filled with several possible cold neutron reflectors (results shown in Figs 119a and 119b). In this case, the presence of MgH₂ at 20 K maximized the neutron flux for the cold and very cold regions.

The resulting neutron energy and wavelength spectra for the spherical moderator surrounded by the cold neutron reflector is shown in Figs 115b, 120a and 120b. It is clear that the presence of the MgH₂ reflector improves the efficiency of the clathrate as a VCN moderator much more than for the case of SD₂ and LD₂. The performance of clathrate with an MgH₂ reflector nearly reached that of SD₂ with a MgH₂ reflector in this scenario. The peak for the SD₂ spectrum at about 5 Å appears in the case with the MgH₂ reflector as well. This result from OpenMC is again consistent with the results from MCNP (see Fig. 118b).

Fig. 118.

Comparison of the neutron wavelength spectra for the spherical moderator filled with SD₂ calculated in MCNP and OpenMC. (A) spectra without the MgH₂ reflector at 20 K. (B) spectra with the MgH₂ reflector at 20 K.

Fig. 119.

Neutron spectra computed in the sphere filled by O₂-clathrate and different neutron reflector materials around the moderator. (A) spectrum in energy. (B) spectrum in wavelength.

Fig. 120.

Neutron spectrum computed in a sphere filled by O₂-clathrate, LD₂, or SD₂; with or without the MgH₂ reflector at 20 K. (A) spectrum between 1 and 15 Å. (B) spectrum between 10 and 22 Å.

Fig. 121.

Drawing of the OpenMC toy model of a clathrate moderator, with size of moderator box of 40 × 40 × 40 cm³.

Fig. 122.

Neutron energy spectrum computed 50 cm away from the emission surface with size of moderator box of 40 × 40 × 40 cm³.

Fig. 123.

Neutron wavelength spectra computed 50 cm away from the emission surface for the model with moderator volume of 40 × 40 × 40 cm³. (A) spectra from 1 to 15 Å. (B) spectra from 10 to 20 Å.

A toy model was designed after finishing the initial study to simulate more realistic conditions for a source made of clathrate hydrate inserted below the spallation target at the ESS. This model contains a cell with a beryllium thermal reflector, a 2-cm thick thermal premoderator filled with H₂O, and a cubic-shaped moderator filled either with the clathrate hydrate, LD₂, or SD₂ surrounded by a 5-cm thick MgH₂ cold reflector filled. The emission surface has an area of 20 × 20 cm², designed together with a 50-cm vacuum pipe for neutron extraction. A surface source with area of 40 × 40 cm² was located at the top of the H₂O premoderator. The volume of the moderator cell was fixed at 40 × 40 × 40 cm³ (see Fig. 121).

The neutron energy spectrum was calculated (see Fig. 122) 50 cm away from the emission surface in the extraction pipe. The neutron wavelength spectra in Figs 123a and 123b show that the clathrate hydrate becomes a competitive moderator material with LD₂ above about 14Å. This result is consistent with the results from the spherical moderator and MgH₂ reflector model.

6.1.UCN scientific case and general overview of the field

The extremely low energies of ultracold neutrons, in the order of several hundred neV and below, enable them to exhibit unique properties. Neutrons are massive, neutral, nuclear particles and are affected by the gravitational, magnetic, week and strong interaction. Usually, the UCN’s energy is defined as being smaller than the effective strong interaction potential VF (Fermi potential) of Beryllium, which is 252 neV. The reflecting properties, together with gravity and magnetic fields led to the idea of building traps for UCNs [205,225], in which they can be stored for a long time limited by neutron β-decay. This characteristic makes them highly responsive to subtle phenomena. In many cases, despite their significantly lower fluxes, UCNs prove to be more sensitive probes compared to thermal and cold neutrons.

It was F.L. Shapiro, who pointed out the possibility of precession measurements with UCN [183], followed by the first reported observations of UCNs [122,189]. This led to rapid developments in the field during the 1970s, resulting in substantial enhancements in precision in measuring the neutron lifetime [153]. They also played a crucial role in setting constraints on the electric dipole moment (EDM) of the neutron [76], and later in the discovery of gravitational eigenstates of UCN above a flat mirror [142].

Increasing the quantity of ultracold neutrons introduced into experiments remains a valuable approach for improving experimental precision. In cases where the free neutron lifetime is not the main limiting factor for losses, as observed in neutron EDM measurements, significant enhancements can also be achieved by extending the storage duration.1111 However, it is important to highlight that regardless of the scenario, existing experiments with ultracold neutrons are primarily restricted by counting statistics. For a comprehensive overview of the scientific capabilities of UCNs and the specific needs of respective experiments the reader can refer to [1].

Currently, there are only a handful of operational UCN sources worldwide, including those at ILL, PSI, TRIGA-Mainz, and LANL. PNPI in Russia has operated several UCN sources in the past, and a new one is currently under construction. Additionally, various UCN sources are either in the construction phase or have been proposed at prominent facilities like FRM-II in Germany, TRIUMF in Canada, LANL and SNS in the USA. For a comprehensive overview of the global UCN landscape, refer to [180].

The first UCN source developed for user applications is PF2 at the ILL. It is based on the vertical extraction of VCNs from the tail of the Maxwellian distribution of a cold source, followed by final slowdown to UCNs using the Steyerl-turbine [190]. All the other sources, operating, under design or under construction, are based on neutron conversion, using either SD₂ at about 5 K, or superfluid ⁴He (He-II) at about 1 K or less. While other materials have been considered and are still studied (see [235] and references therein), these two materials have been identified as particularly suitable for UCN production. The transition from a cold neutron to an ultracold neutron occurs in both of these materials through a single scattering event. Consequently, the UCN do not reach thermal equilibrium with the medium, leading to the classification of such sources as “superthermal”. It is imperative to maintain the medium at extremely low temperatures to minimize the loss of UCN due to up-scattering.

One of the primary objectives of HighNESS is to design a UCN source at ESS. Extensive studies have been conducted, drawing from the two materials mentioned above. This exploration includes various concepts for UCN sources, ranging from those positioned in close proximity to the neutron-production target (referred to as “in-pile” options) to sources located further away and supplied with a cold neutron beam (referred to as “in-beam” options). You can find a comprehensive list of concepts and potential locations for possible UCN sources at ESS in [221]. The findings presented herein are based on the assumption of ESS operating with a proton beam power of 5 MW, equivalent to a beam energy of 2 GeV and an average current of 2.5 mA. As discussed in Section 1.2.3, ESS will start its operation with the reduced power of 2 MW corresponding to an 800 MeV beam energy and maintaining an average current of 2.5 mA. Given the linear increase of the neutron spallation yield, the calculated UCN performance and heat loads can be directly scaled to the 2 MW operational scenario.

6.2.In-pile and in-beam UCN sources

We have divided the possible implementations of UCN sources at ESS into two groups: in-beam and in-pile UCN sources.

An in-pile source is placed near the primary source of neutrons, i.e., a reactor core, or the target in a spallation source. Thus, an in-pile source has the advantage of receiving a high neutron flux, with the possibility of delivering high UCN yields. This comes however with the challenges related to positioning such a source near the target, and in particular to keep the source at the desired low temperature (about 5 K for an SD₂ source, and below 2 K for a He-II source). Conversely, an in-beam source is placed at some distance (typically several tens of meters) from the primary cold source. Such an in-beam source, fed by a cold neutron beam, will have lower UCN production rate than for an in-pile source, but there are several advantages, such as: easier engineering (for example, more freedom about the placement of the source, more available space); much easier cooling of the source to sub-K temperature; easier access for maintenance.

Fig. 124.

A horizontal cut through the target region, at the height of the LD₂ moderator (shown in green) situated below the spallation target (not visible). The cylindrical region of radius 5.5 m around the center represents the shielding monolith (shown in red). The right figure is a zoom of the central part of the left figure. About half of its 42 standard beamports are visible in the cut plane. The possible locations of UCN sources, as studied within the HighNESS project are: (1) inside the “twister”; (2) inside the moderator cooling block; (3) in a standard beamport; (4) in the large beamport (shown as a white segment in the monolith); (5) outside the “bunker”, a heavy concrete shielding structure (shown in orange) placed around the monolith; the minimum distance of this location from the moderator is 15 m. See [221] for details and explanation of options for the various source positions. Reprinted from [221].

The list of the identified in-pile and in-beam options is given in [221] and shown in Fig. 124. We have adopted the convention to label a source located inside the ESS monolith, i.e., within 5.5 m from the center of the monolith (corresponding to the center of the main moderator) as in-pile. A source located at larger distance is considered in-beam (cf. Fig. 4 in [221]). In HighNESS, we have intestigated only one in-beam concept, which has been published in [235]. This in-beam concept exploits the larger field of view offered by the large beamport, and adopts novel nested mirror optics [231]. Alternatively, a regular beamline, i.e. from one of the available beamports of ESS, could be used for an in-beam source similar to the ILL SuperSUN [37]. Performance estimates are given in [52].

An alternative approach for UCN studies is to perform the intended experiment in-situ [52]. Such experiments have previously been realized and are proposed for ESS and other facilities. In this approach, the measurements are performed inside the source, which is based on He-II. The proposed experiments are EDM searches, thus requiring polarized neutrons. The detector is also placed inside the source and can be based on ³He. The major advantage of in-situ measurements is the fact that transport losses are avoided altogether. There are some challenges, in particular related to the guiding of cold neutrons in the source, in-situ detection of UCN, and balancing UCN accumulation time with measurement time. In-situ measurement might be possible for the in-beam option [235] that we propose which uses a He-II source placed at a distance from the ESS cold source, and nested mirror optics to transport the neutrons from the LBP to the UCN source. Additionally, an in-situ configuration could also be possible for a He-II source placed directly in the LBP at about 2 m from the cold source.

Concerning the possible converter materials for in-beam and in-pile UCN sources, we have adopted the following: in the case of in-pile sources, both SD₂ and He-II are possible candidates; therefore both materials have been studied. For an in-beam source, we considered only the option of He-II. The reason for this choice is that we expect higher total UCN production in a large He-II converter placed in a cold neutron beam than in a SD₂ converter. The latter, even when placed in beam, would have to be of relatively small volume, to overcome the issue of poor UCN extraction from the bulk of the SD₂ converter. Because of that, SD₂ is considered a valid candidate for a UCN source only in the in-pile option. In fact, all the UCN sources in operation (LANL, PSI) or under construction (FRM-II), based on SD₂, are in-pile designs.

In summary, the list of possible UCN sources which have been analyzed within the HighNESS project is the following:

Regarding the last case, He-II in-beam, we have only studied the source’s performance using the LBP where thanks to the large available solid angle, special optics can be employed. Performance of a generic in-beam He-II source at the ESS using a regular beamport, can be estimated rescaling the results obtained from this case.

6.3.UCN production

There are several quantities that can be used to characterize the performance of a UCN source:

Given the multitude of quantities involved, it becomes evident that there is no single, unambiguous figure of merit for optimizing a UCN source. In our studies, our primary focus was on achieving high N˙ and P, with our analysis primarily centered on the source itself. Assessments of UCN experiment performance connected to a source should be conducted in a subsequent stage, during the design of the UCN experiments.

For the same reason, the performance of SD₂-based and He-II based sources are not directly comparable: the UCN lifetimes in the two materials are very different, of the order of 40 μs for SD₂, and of the order of hundreds of seconds for He-II below 1 K. The scopes of these two source types are thus different as well. SD₂ close to a primary cold source can produce a large UCN flux which is suitable for experiments in flow-through mode or if large vessels need to be filled, whereas He-II enables UCN accumulation to high saturated UCN densities, which can be advantageous for small storage vessel with a long storage time constant. Finally a prerequisite for in-pile source variants, where the UCN converter medium is installed close to a primary cold source, is the capability to transport UCNs with low losses over large distances of several tens of meters.

6.4.Methods for calculating the UCN production rate density PUCN

6.4.1.Calculating PUCN in SD₂

PUCN cannot be estimated directly in an MCNP simulation by the conventional method of measuring a neutron flux tally, since MCNP does not transport neutrons in the energy range of UCNs. For converters made of SD₂, PUCN was therefore estimated by calculating the cold neutron flux and multiplying it by the UCN production cross-section. The accuracy of such calculation depends on the accuracy of the thermal scattering libraries used in the MCNP calculation, as well as on the accuracy of the UCN production cross-section in SD₂. Several SD₂ UCN cross-sections have been published. We adopted the cross section calculated by Frei et al. [66] at the Technical University of Munich. This cross-section was calculated from a dynamical scattering function extracted from the IN4 experiment conducted at ILL with the SD₂ sample kept at 4 K and an incident neutron energy of 67 meV (see Fig. 125). This cross-section differs slightly from the one measured in an experiment at the FUNSPIN beamline at PSI with a sample kept at 8 K (see Fig. 125). The observed discrepancies between these two cross sections can be, for example, explained by a different crystal orientation, sample temperature, sample purity and crystal quality.

Fig. 125.

The comparison of UCN production cross sections in SD₂. Adapted from Liu et al. [121]. The red squares depict the cross section measured at PSI [11], whereas the blue circles depict the cross section calculated at TUM in Munich [66]. The calculation of cross section at TUM was based on experimental data from neutron time-of-flight experiment at IN4 (ILL).

Fig. 126.

The scattering function, s(λ), for UCN production in He-II. The curve from Schmidt-Wellenburg et al. [177] has been determined experimentally. The ESS model 1 curve was used for this work and is based on an early version of the scattering library [85], while ESS model 2 is an improved version, which can be used for future work [84]. The single-phonon peak for ESS model 2 has been multiplied by a factor of 0.065 for visualization purposes.