The European Spallation Source, currently under construction in Lund, Sweden, is a multidisciplinary international laboratory. Once completed to full specifications, it will operate the world's most powerful pulsed neutron source. Supported by a 3 million Euro Research and Innovation Action within the EU Horizon 2020 program, a design study (HighNESS) has been completed to develop a second neutron source located below the spallation target. Compared to the first source, designed for high cold and thermal brightness, the new source has been optimized to deliver higher intensity, and a shift to longer wavelengths in the spectral regions of cold (CN, 2–20 Å), very cold (VCN, 10–120 Å), and ultracold (UCN, ${>}\,{500}$ Å) neutrons. The second source comprises a large liquid deuterium moderator designed to produce CN and support secondary VCN and UCN sources. Various options have been explored in the proposed designs, aiming for world-leading performance in neutronics. These designs will enable the development of several new instrument concepts and facilitate the implementation of a high-sensitivity neutron-antineutron oscillation experiment (NNBAR). This document serves as the Conceptual Design Report for the HighNESS project, representing its final deliverable.

§ LIST OF ACRONYMS

Acronym/term     Meaning

BNV     Baryon number violation

BZ     Brillouin zone

BNC     Budapest Neutron Center

CAD     Computer Aided Design

COMSOL     A finite element analysis and simulation software package

CDR     conceptual design report

CEF    Current ENDF Format

CMTF     Cold Moderator Test Facility

CN     cold neutron

CNS     Cold neutron source

COSY     COoler SYnchrotron

DF-DND     Deagglomerated F-DND

DFPT     Density Functional Perturbation Theory

DFT     Density Functional Theory

DFTB     Density Functional Tight Binding

DOS     Density of States

DND     Detonation Nanodiamond

EDM     electric dipole moment

EGO     efficient global optimization

ESS     European Spallation Source

F-DND    Fluorinated DND

FOM     figure of merit

FRM-II     Forschungsreaktor München II

FZH      Forschungszentrum Jülic

GEANT4     A Monte Carlo simulation program for GEometry ANd Tracking

HDPE      high-density polyethylene

HiCANS     High Current Accelerator-driven Neutron Source

HighNESS     High intensity Neutron Source at the European Spallation Source

IKP     Institute of Nuclear Physics

ILL     Institut Laue Langevin

JCNS     Jülich Centre for Neutron Science

JULIC     JUelich Light Ion Cyclotron

LANSCE     Los Alamos Neutron Science Center

LANL     Los Alamos National Laboratory

LBP     large beamport

LD$_2$     liquid deuterium

LH$_2$     liquid hydrogen

MCB     moderator cooling block

MCNP     Monte Carlo N Particle

MCPL     Monte Carlo Particle Lists

ML     Machine Learning

MSD     mean squared displacement

MEF     Mixed Elastic Format

ND     Nanodiamond

NMO     Nested Mirror Optics

NW     North-west

MP     Monoplanar reflector

NNBAR     An experiment to search for neutrons converting to anti-neutrons at the ESS

ND     Nanodiamond

§ LIST OF ACRONYMS (CONT.)

Acronym/term     Meaning

PBE     Perdew-Burke-Ernzerhof

PHITS     Particle and Heavy Ion Transport code System

PMT     Photo-Multiplier Tube

PSI     Paul Scherrer Institut

R&D     research and development

SiPM     Silicon photomultiplier

SANS    Small Angle Neutron Scattering

SD$_2$     solid deuterium

SNR      Signal-to-Noise ratio

SW     South-west

TEM     Transmission electron microscopy

TMR     Target-Moderator-Reflector

SNS     Spallation Neutron Source

TSL     Thermal Scattering Library

UCN     ultra cold neutron

VCN     very cold neutron

VDOS     Vibrational density of states

WP     work package

§ INTRODUCTION AND SCIENTIFIC MOTIVATIONS

§.§ 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 <cit.>. 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 <cit.>.

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 <ref>), 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 <ref> and shown in <ref>.

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

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

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 <ref>) 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 <ref>.

Beyond the ESS monolith, the beamlines reside in the bunker, as referenced in <cit.>. 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 <ref>) constructed from heavy magnetite concrete, complemented by a roof of variable thickness, also composed of heavy concrete.

<ref> shows the completed bunker in the instrument hall. After the bunker, the neutron instruments reach the instrument halls, as shown in <ref>. The instruments hall areas are located in the D01, D03, and E01 buildings. <ref> shows the complete layout of the facility.

The ESS bunker.

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

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

ESS layout and building description.

§.§.§ 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  <ref>, 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 two moderator-reflector systems positioned both above and below the spallation target, as shown at the center of <ref>. 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.

<ref> 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 <ref> 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.

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.

§.§.§ The ESS upgrade area

The HighNESS project will also make use of the availability of extra beam ports. <ref> shows the available sectors of experimental zones, the distribution of the 15 instruments of the initial suite, and the additional beam ports and areas still available for additional future instruments that can be fed by a second moderator system. These areas, highlighted in green in <ref>, serve as the primary locations for designing instruments and experiments that will utilize the moderators developed in the HighNESS project.

In addition to the extra beam ports, ESS is also equipped with a large beam port in the shielding of 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 <ref>. This infrastructure has been installed in anticipation of the Neutron-to-Antineutron Oscillation Experiment, NNBAR <cit.>, in order for the experiment to achieve its design goals (see <ref>). 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 Ultra-Cold Neutron (UCN) sources, as detailed in <ref>.

The ESS facility. The location of the instruments of the initial suite, plus some additional instruments beyond the initial 15, are shown. In green the upgrade areas, where the HighNESS instruments and experiments could be placed, are highlighted.

<ref> 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 as shown in <ref> (see <ref> for more information)  .

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.

(a) Side view of opening in correspondence of NNBAR. (b) Top view of the large beam-port opening for NNBAR.

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

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

§.§.§ ESS timeline and beam power projections

Owing to delays from the covid-19 pandemic and other technical challenges, the ESS in 2021 conducted a rebaseline exercise to revise its construction and commissioning schedule [<https://europeanspallationsource.se/article/2021/12/10/ess-revises-project-plan-and-budget>]
. The revised baseline plan introduces a two-year delay with respect to the previous schedule and will enable the ESS to start full operations and be open for scientific users working with up to fifteen instruments in late 2027. The maximum accelerator power and proton beam energies will be 2 MW and 800 MeV, respectively. The possibility of operating the accelerator at its nominal design power of 5 MW is taken as part of an ESS upgrade project.

The installation of the ESS second moderator would occur after 2030. 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.

§.§ HighNESS scientific motivations

As described in the previous section, the flexible design of ESS, with only one moderator located above the target, leaves a great opportunity to implement a second source with complementary characteristics going well beyond the initial goals of the facility development. This new infrastructure has been designed with the purpose of delivering the highest possible total intensity (as opposed to brightness which was the main design criterion for the first source) of cold neutrons with wavelengths above 4 Å (see <ref>), including neutrons in the long-wavelength part of the spectrum, referred to as Very Cold Neutrons (VCN) and Ultra Cold Neutrons (UCN).

With these new source capabilities, various condensed matter instrument concepts have been considered, as detailed in <ref>.
Furthermore, the presence of a high-intensity neutron source is of paramount importance for the NNBAR experiment and for the development of UCN and VCN sources.

§.§ HighNESS objectives

The HighNESS project, <cit.>, 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:

- Increase in Source Intensity: this entails boosting the total number of neutrons emitted from the source. Achieving a more intense source necessitates larger moderators and emission surfaces to enhance the count rate for instruments or experiments that require high flux.

- Shift toward colder neutrons: this shift has manifested in the development of a very-cold neutron source and an ultra-cold neutron source, in addition to the second cold neutron source. To create a highly intense VCN source as part of the project, we have invested significant effort in extensively characterizing promising candidate materials. This comprehensive characterization is essential for fully developing the capabilities required to design a source utilizing these materials. The HighNESS project has placed specific emphasis on some distinct materials:
solid deuterium and deuterated clathrate hydrates, that can be used as dedicated VCN moderator materials;
nanodiamonds, graphite intercalation compounds, magnesium hydride, and clathrate hydrates
as advanced reflectors to increase the VCN flux.

The second source was designed as a liquid-deuterium (LD$_{2}$) moderator based on proven technology. One of the main results of this work is a complete engineering design of the LD$_{2}$ 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 designs possibilities are described in <ref>, and <ref> respectively. Furthermore, the project has successfully developed a set of neutron scattering instruments (see <ref>) and conducted a conceptual design study for the NNBAR experiment in <ref>.

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:

-	A high brightness bi-spectral (thermal–cold) moderator, based on water and liquid para-hydrogen, placed above the spallation target and able to serve all the 42 beam ports of the ESS grid with a thermal and cold brightness spectrum higher than anywhere other facility worldwide.

-	A high-intensity LD$_{2}$ moderator, placed below the target station, capable of directly serving instruments demanding a cold-neutron flux of unprecedented intensity or acting as a primary source for secondary VCN and UCN sources for experiments requiring sub-cold neutrons. In particular, the ESS would provide the first high-intensity VCN source in the world.

Thus, in this scenario of separate moderators optimized for separate neutron characteristics, ESS would offer a versatile neutron source of outstanding performance, spanning a large neutron wavelength range and without compromising performance (which is inevitable for a single-moderator case). 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.

§.§ The HighNESS project in the neutron landscape

HighNESS aims at serving instruments and experiments with high intensity beams of neutrons, and preferably of lower energy than what is typically available at existing neutron sources. Some examples are already given in this introduction, but more are outlined in <ref>, <ref>, and <ref>. It is crucial to emphasize that 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. These are 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 5MW. For the majority of applications targeted by the HighNESS project, a high time-average intensity is essential. This requirement implies that even with the upgrades, such facilities would not be able to compete with ESS. Furthermore, it's 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 significantly outperform these planned upgrades in the long-wavelength regime by more than an order of magnitude.

The installation of a long-wavelength facility at the ESS is uniquely favorable due to the high proton power and long-pulse time structure. In other words, no existing facilities can be upgraded in this way.  Furthermore, 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.

§.§ HighNESS project structure

HighNESS project Work Package structure.

The HighNESS project is organized into ten distinct Work Packages (WPs), as illustrated in <ref>. 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 sources, and ultra-cold sources. These two work packages require input and specifications from the scientific-oriented WPs, WP7 (“Condensed Matter Science") and WP8 (“Fundamental Physics"). These scientific WPs efforts ensure that the source designs deliver the necessary neutron fluxes and spectra, enabling groundbreaking scientific experiments at ESS that are beyond the capabilities of high-brightness moderators. WP5 (“Engineering") is responsible for handling all 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.

§ DESIGN OF THE COLD SOURCE

The design of the LD_2 moderator is one of the main objective of the  HighNESS project. This moderator has been designed to outperform the low-dimensional moderator located above the spallation target in terms of intensity, thus delivering a wold-leading flux of cold neutrons to beamlines serving condensed matter research and fundamental physics.

The design of the LD_2 moderator has been carried out using the MCNP6 <cit.> code. The work has been performed incrementally, considering initial, simple figures of merit (FOMs), and later in the project using those developed and reported in Deliverable 4.1 of the HighNESS project  <cit.>. Likewise, the work started considering a single opening (channel for neutron extraction), and then moved to a configuration closer to the one needed for ESS, with openings for both fundamental physics and condensed matter experiments.
The results from the study with a single opening are detailed in <cit.> and will not be described in this document where the focus will be on the design with two openings.

§.§ General Description of the ESS Moderator Area

The neutron production core at ESS comprises two moderator-reflector systems, one positioned above the spallation target (referred to as the "upper moderator") and the other located below the target (referred to as the "lower moderator"). In <ref>, one can see a cross-sectional view of the target system, highlighting the locations of these two moderators.

<ref> shows the openings available below the target for the neutron extraction. Overall, they cover two areas of 120$^\circ$ each. Neutrons are emitted towards four sectors which are conventionally labelled with their cardinal directions (see <ref>).

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. In the picture is also shown  one of several candidate UCN source locations is indicated with the red dotted circle. For more details see <ref>

The lower moderator system will be installed within the twister structure.
The coordinate system used to described 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 center of the upper moderator.
We have the following constraints for the liquid deuterium moderator and reflector: 400 mm in height, and 720 cm in diameter.
This corresponds to between -78 mm and -478 mm along the Z-TCS. The twister starts at -610 mm with respect to Z-TCS, hence we have 132 mm 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 (as shown in <ref>) is essentially a block of shielding material that is water-cooled and positioned adjacent to the twister. Its location has been considered  for the placement of a secondary source, such as a UCN source see  <ref> for more information. The placement of a source in that location would require a modification of the MCB. This possibility has been discussed with the ESS Target management and is considered feasible. It has therefore been explored, along with a variety of other UCN-source candidate locations, as part of the HighNESS project (see  <ref>). <ref> and <ref> show the twister and the MCB next to each other. Such a source embedded in the MCB could serve more easily beamlines placed in the North sector.

Twister and moderator cooling block (MCB). The twister consists of two steel structures containing the upper and lower moderator-reflectors assemblies, and its name is derived from the fact that it rotates around its shaft during the periodic exchange procedures. Drawing courtesy of C. Jones, ESS. See explanation in the text.

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

§.§ Figures of merit

It is important to define the wavelength ranges for the three groups of neutrons of interest in HighNESS (<ref>). Cold neutrons are defined in the range from about 2 Å to about 20 Å, (i.e. the typical range for the instruments using the cold neutrons from the upper moderator <cit.>).  Then, VCNs as defined in <cit.>, 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 CN production, in order to establish a high-intensity baseline in order to complement the high-brightness upper moderator; the design for this moderator was produced with the Monte Carlo code MCNP versions 6.2 <cit.>. The refinements of this lower moderator and/or addition source placements for producing VCNs and UCNs are discussed in <ref> and <ref> .

The wavelength range that defines cold, very cold, and ultra cold neutrons.

cold     2-20 Å

very cold     $\sim$ 10–120 Å

ultracold     $>$ 500 Å

To design the best possible neutron source, one must consider the whole process from neutron moderation to the transport to the experimental area: the performance of an experiment is determined by the count rate of the desired neutrons (in terms of wavelength and divergence) at the experimental position.
The transport to the experimental station is therefore essential to the design of the experiment or instrument, and is linked to the performance of the source (the moderator) and its simulation with MCNP. In other words, the design of the source must be done taking into account both the MCNP for initial CN flux calculation as well as the neutron transport using ray-tracing Monte Carlo simulations using the McStas code <cit.>.

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 <ref>
), 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 <cit.>), which is then read by McStas. The latter is the preferred option within HighNESS.

There is an additional parameter that complicates the work of the source designers in HighNESS, this 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 <ref>).

To optimized the moderator design it is necessary to define a metric, or FOM.  Several FOMs are needed, to accommodate the needs of the various instruments.

§.§.§ Figures of Merit for condensed matter

For the neutron scattering instrument designs developed by HighNESS, what is essential for the instrument optimization is the number of neutrons reaching the sample, within the desired wavelength range and divergence.

As far as the FOM is concerned, this is not always as straightforward as for instance in the case of NNBAR (see below). The reasons are as follows: first, there are three classes of instruments under study: SANS, imaging, and spin-echo. Second, for a given class of instruments, different solutions for the optics can be considered, which might work best for competing features of a moderator.

In general, however, a few guidelines have been established, that can be used to define the way of working and a useful FOM. Since the neutron divergence at the sample can only be studied with McStas, and it is not a parameter controlled with MCNP it has been  omitted from the FOM. The FOM to be used in designing the source should rather concentrate on the intensity and spectrum:

- Different emissions surfaces from the moderator are of interest a priori for the relevant instruments. The reference emission surfaces are:
5$\times $5 cm$^2$, 10$\times $10 cm$^2$, 15$\times $15 cm$^2$, 20$\times $20 cm$^2$.

- For each of these surfaces, an optimization of the moderator can be done, using as FOM the integrated intensity for wavelengths up to 2.5 Å.

- For some instruments, in particular spin-echo – and potentially future SANS instruments – the instrument design team (WP7) is also interested in a colder spectrum. That is, an increase in the spectrum for wavelengths greater than 10 Å. For this purpose, the combined efforts of WP4 and the advanced reflector team, WP6, were needed (i.e., using advanced reflectors to enhance the coldest part of the spectrum from the cold moderator). It is likely that the greatest increase will be achieved using a smaller viewing surface than the reference ones under study by WP7. This could be obtained with a smaller extraction surface, such as 3$\times $3 cm$^2$, surrounded by a layer of advanced reflectors such as nanodiamonds. This option has also been investigated, and in this case smaller openings will also be considered, in addition to the larger openings mentioned above.

§.§.§ Figures of Merit for fundamental physics

§.§.§ NNBAR

The NNBAR experiment will search for baryon number violation (BNV) via neutron ($n$) antineutron ($\bar{n}$) oscillation. The full experiment and its scientific motivation are described in <ref>.
In <ref> a schematic overview of the planned NNBAR experiment  <cit.> 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 from perturbation to the detector region at the end of the instrument. The moderator-to-detector distance is 200 m.

Schematics of the NNBAR Experiment (not to scale).

The probability of an oscillation is proportional to the (uninterrupted) flight time squared $t^2$ of the neutrons. The FOM of the NNBAR experiment is then defined as $\sum_{i} N_i t_i^2$ with $N_i$ being the number of neutrons with a specific flight time $t_i$. Thus, slower neutrons are favored and a trade-off between intensity and wavelength will be established.

In the lower plot of <ref>, 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 LD_2 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 and weighted with $ \lambda^2$. We note that there will be a natural cutoff at $\lambda$ 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 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 $\lambda^2$, for two ranges of neutrons: above 2.5 Å and above 5 Å, with an upper cut of about 15 Å.

Wavelength spectrum of the LD_2 source (upper plot) and the distribution of wavelength contribution to FOM for NNBAR (lower plot).

§.§.§ Figure of merit for UCN

A further goal of the HighNESS project is to design and simulate a source of ultra cold neutrons. This UCN source can be located in-pile or in-beam. For example, the moderator cooling block discussed previously (see <ref>) has been investigated as possible location for the in-pile option. These designs are described in detail in <ref>, but we discuss a FOM also here for completeness.

Such a moderator can be a large volume of superfluid helium as converter material, fed by the beam of cold neutrons emanating from the liquid deuterium moderator, as proposed in <cit.>.

The two most relevant parameters for UCN production with liquid He4 sources are:

- 9 Å flux in the UCN source area that contains superfluid helium <cit.>.

- stability of the cooling temperature of the converter material liquid.

For the former, in <cit.> it is reported that a flux of $\Phi_{9\AA} = 10^9cm^{-2}s^{-1}\mathrm{\AA}^{-1}$ at 9 Å leads to a UCN density of $\rho_{UCN} = 1.3 \times 10^3 cm^{-3}$ in the source volume. The FOM for UCN production has to take this into account and will consist of the $\Phi_{9\AA}$ inside the designated volume of the UCN moderator. This has been used as the initial FOM, with later refinements adding slightly larger wavelength range (roughly 8–10Å).

For the later engineering design stages, the stability of the cooling temperature was also considered. Designs that minimize the heat impact on the UCN converter module will be preferred.

Other possible converter materials than liquid He have also been investigated, particularly solid deuterium (SD_2) which produces UCNs primarily from 2.5–7 Å neutrons, and has a superior UCN production rate per volume compared to He-II. However, the lifetime of UCNs within the bulk of the SD_2 is dramatically reduced compared with He-II
, thus allowing only thin segments to be used effectively for extraction (see <ref>).

§.§.§ Figure of merit for VCN

The emphasis on colder neutron spectra is one of the key aspects of HighNESS, and consequently a great effort has been devoted to the design of a source delivering high intensity of neutrons above 10 Å.

Concerning the FOM,
for fundamental physics applications using VCNs, we are mostly interested in neutrons in the range 40-120 Å.

For condensed matter applications, the range of 10–40 Å is in general more useful (see <ref>), as neutron scattering experiments are interested in extending existing techniques such as SANS and spin-echo to the use of neutrons of longer wavelengths than traditionally used.

§.§.§ Summary of FOMs

In <ref> the FOMs to be used for the designs of the moderators in WP4 are summarized. In the intensity calculations with MCNP, a point detector tally is placed at a distance $r$ large compared to the moderator, and an artificial collimator limits the view to the emission surface from the moderator. For the option of the VCN source where advanced reflectors are used to increase the transport of VCNs, the viewed surface must also include the reflectors.

List of FOMs.  $I_P$ is the proton beam intensity (for 2.5 mA is 1.56 10$^{16}$ protons/s). $\Delta \Omega$ is the solid angle defined by the emission  surface and the distance at which the  tally is calculated. The integral in $dA$ is over the emission surface of the moderator; as per definition of f5 tally, the integral in $d \Omega$ is over 4$\pi$ sr and the integral in $dt$ is over all times; the integral in $d\lambda$ over the two values of wavelength is performed in MCNP by specifying the corresponding values of neutron kinetic energy in the tally energy bin. Collimators are used in the calculations to limit integration to the desired $\Delta \Omega$.

COLD SOURCE

NNBAR     $\frac {I_P}{ \Delta \Omega} \int dA \int d \Omega \int dt  \int_{\lambda=2.5 \AA}^{ 15 \AA} d\lambda \phi(\lambda,\Omega,\boldsymbol{r},t) \lambda^2  $

$\frac {I_P}{ \Delta \Omega} \int dA \int d \Omega \int dt  \int_{\lambda=5 \AA}^{ 15 \AA} d\lambda \phi(\lambda,\Omega,\boldsymbol{r},t) \lambda^2  $

condensed matter
$\frac {I_P}{ \Delta \Omega} \int dA \int d \Omega \int dt  \int_{\lambda=2.5 \AA}^{ 40 \AA} d\lambda \phi(\lambda,\Omega,\boldsymbol{r},t)   $

VERY COLD SOURCE

fundamental physics
$\frac {I_P}{ \Delta \Omega} \int dA \int d \Omega \int dt  \int_{\lambda=40 \AA}^{ 120 \AA} d\lambda \phi(\lambda,\Omega,\boldsymbol{r},t)   $

condensed matter
$\frac {I_P}{ \Delta \Omega} \int dA \int d \Omega \int dt  \int_{\lambda=10 \AA}^{ 40 \AA} d\lambda \phi(\lambda,\Omega,\boldsymbol{r},t)   $

ULTRA COLD SOURCE

He-II     Flux of 9 Å neutrons inside the helium converter

SD_2     Flux of 2.5–7 Å neutrons inside the SD_2 volume

§.§ 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 both fundamental physics experiments and the NNBAR experiment, while the opening for one or more neutron scattering instruments is referred to as the "WP7 opening".

§.§.§ Iterative design process

The design of the cold moderator has followed several iterations, which are summarized in the following Sections. The following design steps were performed:

- Preliminary neutronic studies using a cylindrical moderator shape and one opening for beam extraction (Ref. <cit.> and <ref>).

- First neutronic optimization (<cit.> and <ref>). In this step, a box shape of the moderator was selected, and the design was performed with two openings. The FOM used for the optimization was the intensity of cold neutrons above 4 Å.

- Second neutronic optimization (Ref.<cit.> and <ref>). The optimization from the previous step was repeated using the FOM from <ref>.

- Engineering study based on the model from second neutronic optimization resulting in new engineering requirement for adding aluminum into LD$_2$.

- Third neutronic optimization, see <ref>, motivated by updated constraint on adding aluminum into LD$_2$ and the effort to minimize heatload by reducing the volume of the moderator.

- Engineering design based on the model from third neutronic optimization, see <ref>.

- Evaluation of the impact of the engineering design on neutronic performance, <ref>.

- Additional neutronic model with separated LD$_2$ box and Be filter, U-shaped reentrant hole and rounded walls of the LD$_2$ box based on new engineering study which is in preliminary stage, see <ref>

§.§.§ Summary of the results with a single opening cylindrical moderator

The first part of the neutronic design of the LD_2 moderator
explored the
sensitivity of the performance to a large set of parameters. It used a reference cylindrical geometry of the moderator, and a single opening for neutron extraction <cit.>.

Here we summarize the most important results, which provide important recommendations for the design, before reporting on results for the two-openings model, and with the study of different shapes of the moderator vessel.

- Ortho-para deuterium fraction. A 100% orthodeuterium composition gives 7 % higher CN intensity than the natural composition (67 % ortho - 33% para). It may therefore be beneficial to use a catalyzer to increase the fraction of orthodeuterium.

- Temperature effect. A comparison of intensities was performed with scattering kernels at different temperatures, ranging from 19 K to 23 K, for a composition of (67% ortho - 33% para). The results indicate that the lower the temperature, the higher the intensity. A temperature of 20 K gives an intensity 7 % higher than at 23 K. It is therefore recommended to run at a temperature closer to 20 K.

- Top premoderator thickness. The top premoderator (i.e. the water layer between moderator and target) was found to have an ideal thickness of approximately 3 cm.

- Bottom premoderator thickness. The bottom premoderator (i.e. the water layer below the moderator, between moderator and reflector) has an ideal thickness of approximately 1 cm.

- Radial premoderator thickness. The radial premoderator should be 1 cm thick. An interesting effect was observed, that there is a large (28%) difference between having 1 cm water layer, and having no layer at all. The reason for this effect may require further investigation.

- Size of emission window. For a given, fixed moderator size, the intensity increases linearly with the height of the emission window opening, as expected.

- MgH$_2$ as side and bottom premoderator. In the cylindical configuration considered, there is no gain in using a MgH$_2$ side and bottom layer instead of the water layer.

- Use of HD. With the tests performed so far, little (if any) gain in intensity is observed using a small amount of hydrogen in the liquid deuterium.

- Intensity vs moderator size for a fixed 24$\times$24 cm$^2$  opening. The general trend observed is that the intensity is increased with the moderator size.

- Reentrant hole. A preliminary study of the effect of a reentrant hole on the intensity of a 10$\times$10 cm$^2$ emission window indicated strong increases, at the level of 30 % in the intensity. A box-shaped reentrant hole was found a preferable option over the wedge-shaped reentrant hole after assessing the neutronic performance of both options.

- Be filter/reflector. A first study of the effect of a Be filter/reflector on the intensity was performed. The study was done also with two openings. The first results, later investigated in more detail, indicate very promising gains, especially for the NNBAR experiment.

§.§.§ Design optimization

The design of the cold source is extremely important, as two objectives must be achieved: first, to provide high-intensity cold beams to the experiments; second, to serve as primary source for a secondary VCN or UCN source. Therefore, the following design study of the cold source was performed throughout the whole duration of the HighNESS project.

§.§.§ First iteration

For the first baseline model to be sent to the engineering team (WP5), it was selected the box-shaped geometry, which was found to have better neutronic performance than the cylindrical-shaped moderator.
An alternative box-shaped geometry was analyzed in <cit.>, and, while the performance was comparable to the selected geometry, the heat load was significantly higher, and therefore it was discarded.

For the selection of the dimensions, among the three optimization criteria chosen for input into the optimization code Dakota <cit.> (sum of intensities, sum of brightness, and NNBAR intensity), it was selected the sum of brightness. 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, when the size of the window is fixed.
However, among the many results provided by Dakota, with the criteria of maximization of the sum of brightness, it was selected the one that gives more intensity to NNBAR, while still having a high intensity to WP7. Such geometry has the following parameters:

The Be filter was introduced into this 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 <ref>).

The dimensions of the moderator are 45x47x24cm for width (parallel to the proton beam), length (perpendicular to the proton beam) and height, and two 11cm thick Be filters on both the NNBAR and WP7 sides.

For this configuration, the NNBAR intensity for neutrons above $>$ 4 is 6.89e+15 and for WP7 intensity for the same energy range is 2.50e+15, with heat load of 56.4 kW. This model is illustrated in <ref>.

Graphical representation of baseline design for the LD_2 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.

Below is the description of this “1st iteration” model of the LD_2 moderator.

The LD_2 moderator is represented by a rectangular vessel made of aluminum.
Its inner dimensions are:

- 450 mm long in the proton beam direction (“width”),

- 470 mm long in the direction transverse to proton beam direction (“length”),

-  240 mm long in the vertical direction (“height”).

In neutronics calculations, the thickness of the vessel Al walls was set to 3 mm 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.

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

- NNBAR opening serving the North-west (NW) sector (see <ref>);

- WP7 opening serving the defined South-east (SW) sector (see <ref>).

The NNBAR opening has an emission surface of 400 mm width by 240 mm height, while the WP7 opening has an emission surface of 150 mm width by 150 mm height.
The geometric centers of both emission surfaces and of the LD_2 moderator are situated at the same level, -237 mm  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.

The LD_2 moderator is placed inside a  “standard” moderator plug, thus, surrounded by the following layers:

- 3 mm thick Al vessel around LD_2 and Be filter;

- 5 mm vacuum gap around the Al vessel (engineering constraint);

- 3 mm thick Al walls surrounding the H$_2$O premoderator and Be reflector (engineering constraint);

- 10 mm thick layer of H$_2$O below and on the sides to serve as a premoderator, as a result of the neutronic optimization,

- 25 mm H$_2$O layer above (between the moderator and the target), as a result of the neutronic optimization

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

The materials in the list above (Al, H$_2$O, Be) are at ambient temperature.

Heat load on cryogenic parts of the MR plug:

The summary of the expected performances, integrated over various wavelength ranges, is shown in <ref>.

Neutronic performance and characteristics of the model from first 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 Ref <cit.>. To calculate the intensity we considered the following size of emission windows: NNBAR: 960 cm$^2$; WP7: 225 cm$^2$; upper moderator: 42 cm$^2$. The heatload on Be filter accounts for both the contribution at NNBAR and WP7 openings. The moderator volume is the sum of volume of the LD$_2$ box and Be filter.

3cBRIGTHNESS [n/cm/s/sr]

$>$ 2     $>$ 4     $>$ 10

NNBAR     9.11e+12     7.04e+12     5.51e+11

WP7     1.45e+13     1.08e+13     8.13e+11

upper moderator     5.3e13     1.7e13     9.9e11

3cINTENSITY [n/s/sr]

$>$ 2     $>$ 4     $>$ 10

NNBAR     8.74e+15     6.76e+15     5.29e+14

WP7     3.26e+15     2.42e+15     1.83e+14

upper moderator     2.2e15     7.0e14     4.2e13

NNBAR FOM     3.00e+17 [n/s/sr $\times$ $\lambda^2$]

WP7 FOM     2.96e+15 [n/s/sr]

Heatload on LD$_2$ 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]

§.§.§ Second iteration

In the first iteration, all the optimizations and calculations were done where the FOM was the intensity for neutrons above 4. This was a FOM meant to generally target cold neutrons in the early optimization steps. The second round of optimization was performed using the more elaborate FOMs, cf. <ref>. Moreover, a reentrant hole (REH) was introduced at the emission surface of the WP7 opening replacing the Be filter, providing a considerable gain in cold neutron intensity and brightness (see <ref>)).

The optimization is described in detail in <cit.>.

The design of this moderator optimized according to the procedure outlined above gives the intensity of the source at the NNBAR side, integrated above 4 of 6.7e15n/s/sr.
This is the intensity of the emission window of 24$\times$40 cm$^2$, for 5 MW of beam power (i.e. 2 GeV for 2.5 mA average proton current). The intensity at the WP7 side is lower, because of the smaller size of the opening, although it has a greater brigtness.
For a beam power of 2 MW (800 MeV for 2.5 mA average proton beam current) the intensity is simply a factor of 2.5 lower, because as shown in <ref>, the difference in emitted spectra from the moderator between 800 MeV and 2 GeV proton beam is negligible. Therefore, at 2 MW the intensity of the moderator is 2.7e15n/s/sr.

To have an idea of what these numbers mean in terms of performance of the experiments intended to use this moderator, we can compare with the original calculations done for the NNBAR experiment in <cit.>: at 5 MW beam power, the intensity was predicted to be 2.9e15n/s/sr. That calculation was the basis for the original estimate of the performance increase of NNBAR compared to the ILL measurement <cit.>. It would therefore mean that the NNBAR performance estimate of this second iteration of the moderator at 2 MW is equivalent to the previous estimate for 5 MW. However, a large part of this gain is due to the increase in the size of the emission window (nearly a factor 2 increase).

A summary of the expected performances for this iteration, integrated in different wavelength ranges, is shown in <ref>.

Neutronic performance and characteristics of the model from second 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 Ref <cit.>. To calculate the intensity we considered the following size of emission windows: NNBAR: 960 cm$^2$; WP7: 225 cm$^2$; upper moderator: 42 cm$^2$. The moderator volume is the sum of volume of the LD$_2$ box and Be filter.

3cBRIGTHNESS [n/cm/s/sr]

$>$ 2     $>$ 4     $>$ 10

NNBAR     8.87e+12     6.95e+12     5.77e+11

WP7     1.79e+13     1.07e+13     9.16e+11

upper moderator     5.3e13     1.7e13     9.9e11

3cINTENSITY [n/s/sr]

$>$ 2     $>$ 4     $>$ 10

NNBAR     8.52e+15     6.67e+15     5.54e+14

WP7     4.03e+15     2.42e+15     2.06e+14

upper moderator     2.2e15     7.0e14     4.2e13

NNBAR FOM     3.03e+17 [n/s/sr $\times$ $\lambda^2$]

WP7 FOM     3.68e+15 [n/s/sr]

Heatload on LD$_2$ moderator     29.8 [kW]

Heatload on Be filter     15.1 [kW]

Heatload on Al vessel     7.2 [kW]

Total heatload     52.1 [kW]

Moderator volume      49.6 [liters]

§.§.§ Third iteration

A third optimization was performed using Dakota with the model from the second iteration updated by the engineering constraint of requiring a 2.5% volume of aluminum in LD$_2$ 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 LD$_2$ in the moderator vessel was increased from 20 K to 22 K.

For the purpose of third iteration of optimisation, 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 <ref>) were optimised with respect to NNBAR and WP7 FOMs. A multi-objective genetic algorithm (MOGA) <cit.> was implemented resulting in the set of solutions over a wide range of NNBAR and WP7 FOMs (see <ref>). In the subsequent analysis of possible solutions, NNBAR and WP7 FOMs vs moderator length (see <ref>), moderator width (see <ref>), Be filter thickness (see <ref>) and the depth of reentrant hole (see <ref>) were plotted. A subsequent analysis of these figures resulted in setting the following limits on variable parameters used in the optimisation to maximize NNBAR and WP7 FOMs:

-  45 cm $\leq$ moderator length $\leq$ 50 cm;

- 40 cm $\leq$ moderator width $\leq$ 45 cm;

- 11 cm $\leq$ Be filter thickness $\leq$ 15 cm;

- 9 cm $\leq$ depth of reentrant hole $\leq$ 15 cm;

- Gain wrt baseline $\geq$ 1.

A smaller subset of solutions was then filtered out based on these limits (see <ref>). The goal was to select a solution that is close to the utopia point (idealized point with highest recorded performance for both NNBAR and WP7 FOMs), and which also minimizes the moderator volume in order to reduce heatload. In the end, this combination of parameters, was selected for the LD_2 moderator:

- Moderator length = 48 cm;

- Moderator width = 41 cm;

- Be filter thickness = 13 cm;

- Reentrant hole depth = 10 cm;

- Volume of LD$_2$ in moderator = 32.2 l.

For reference, we can also compare the intensity of the lower cold moderator from this neutronic optimization with the model of upper moderator. The upper moderator has a higher brightness, however, because of the smaller size, its intensity is lower. This can be seen in <ref>(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 cm$^2$ would be available, and this give an intensity of the upper moderator above 4 of 7e14n/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 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 <ref>. There is a decrease in NNBAR and WP7 FOMs in comparison to the model from second iteration of neutronic optimisation (see <ref>) due to increase in temperature of LD$_2$ from 20 K to 22 K and the presence of 2.5 vol% Al in LD$_2$.

Neutronic performance and characteristics of the model from third iteration of cold moderator. Brightness and intensity integrated over different wavelength ranges, for the third iteration of lower moderator (NNBAR and WP7 openings) and compared with the upper moderator. The values for the upper moderator are from <cit.>. To calculate the intensity we considered the following emission window sizes: NNBAR: 960 cm$^2$; WP7: 225 cm$^2$; upper moderator: 42 cm$^2$. The moderator volume is the sum of volume of the LD$_2$ box and Be filter.

3cBRIGTHNESS [n/cm/s/sr]

$>$ 2     $>$ 4     $>$ 10

NNBAR     7.89e+12     6.07e+12     4.46e+11

WP7     1.60e+13     8.76e+12     6.89e+11

upper moderator     5.3e13     1.7e13     9.9e11

3cINTENSITY [n/s/sr]

$>$ 2     $>$ 4     $>$ 10

NNBAR     7.57e+15     5.83e+15     4.28e+14

WP7     3.60e+15     1.97e+15     1.55e+14

upper moderator     2.2e15     7.0e14     4.2e13

NNBAR FOM     2.51e+17 [n/s/sr $\times$ $\lambda^2$]

WP7 FOM     3.22e+15 [n/s/sr]

Heatload on LD$_2$ 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]

Graphical representation of  design for LD_2 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.

§.§.§ Effect of Be filter and reentrant hole

A quantification of the effect of the Be filter and reentrant hole on the neutronic performance was done in the third iteration of optimisation. <ref> clearly shows that the NNBAR side benefits from the presence of the Be filter. The gain in the NNBAR FOM observed when comparing the case with no Be filter (Be filter thickness = 0 cm) and the cases with Be filters having thicknesses between about 10 and 15 cm was about 30%. Similarly, the WP7 side benefits from the presence of reentrant hole (see <ref>). In this case, the WP7 FOM increases by about 20% for reentrant holes with depths between about 10 and 15 cm.

§.§.§ 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 <ref>). Subsequently, the neutronic performance on the WP7 side was estimated with this shape of reentrant hole for the
beamport adjacent to S11
(S" stands for South Sector, and "11" refers to the number of the beamport. In this case, it is the beamport perpendicular to both the incoming proton beam and the emission surface of the moderator at the WP7 side.), namely the S9 beamport with  an offset of 6$^{\circ}$ with respect to S11 (see <ref>
for a depiction of the beamport positions). The calculated values of the WP7 FOM at various reentrant hole depths are shown in <ref>. The maximal gain with respect to the baseline 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
also for this round of optimization.

Third iteration optimization: each point represents the gain with respect to NNBAR and WP7 figures of merit of the model from second neutronic iteration for a given set of parameters. The Pareto front was fitted through points closest to Utopia point, idealized point with highest possible NNBAR and WP7 gains. The aim is to select a model with parameters that lies as close as possible to Utopia point. The moderator volume is the sum of volume of LD$_2$ box and Be filter.

Selected models (yellow circles) from the optimisation according after applying the limits on moderator parameters.

Performance of models with respect to moderator length. (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.

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.

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.

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.

Comparison of neutron spectra for the lower and upper moderators for the third iteration of optimisation. (a) Time-averaged intensity. (b) Time-averaged brightness.

Model of the wedge-shaped reentrant hole. (a) Horizontal view of the wedge-shaped reentrant hole. (b) Vertical view of the wedge-shaped reentrant hole.

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

Performance of wedge-shaped reentrant hole at different depths.

§.§.§ Moderator characterization

The model of the cold moderator from the second neutronic iteration was used to perform a comprehensive moderator characterization. Its characteristics in this context are comparable to the performance of cold moderator from the third iteration.

The energy distribution binned in wavelength for the MOGA optimization is shown in <ref> (this was the best-performing optimization approach for a variety of algorithms, for a comparison of these methods see <cit.>.) The baseline case has protons impinging on the target at 2GeV, and the additional case shows protons at 800MeV. Both cases are normalized to the accelerator power in MW, respectively 5 and 2MW. The fact that spectra match for the two openings suggests that lowering the power of the accelerator will not affect the energy distribution besides the obvious drop in absolute intensity.

Spectra comparison for NNBAR the WP7 neutron-scattering instruments (NSI) sides of the LD_2 using MOGA optimization for protons impinging on the target at 2GeV (baseline for the design) and 800MeV, per unit power, respectively.

The main feature of the wavelength distribution on the NNBAR side is the very sharp cut-off at 4 due to the Be filter. The peak between 12 is not likely due to a thermal peak, but rather a feature introduced by the filter. The thermal and cold peaks are instead clearly visible on the neutron scattering instruments (WP7) opening.

The neutrons spatial distribution coming out of the surface of the moderator was studied with a pinhole-camera tally integrated in MCNP. The pinholes are placed 2m away from the center of the moderator along the central axis for both openings, while the detectors are 2m away from the pinholes on the same axis and have dimensions of 50x50cm and 30x30cm for the NNBAR and WP7 sides, respectively. The results are shown in <ref> (NNBAR on the left and WP7 on the right) for three wavelength ranges: $\lambda < \SI{4}{\angstrom}$, $\lambda > \SI{4}{\angstrom}$, and $\lambda > \SI{9}{\angstrom}$.

Pinhole images of the 24x40cm NNBAR opening (left) and the 15x15cm WP7 opening (right) with filters for neutron at different energies. The pinholes are placed 2m away from the center of the moderator along the central axis, while the detectors are 2m away from the pinholes on the same axis and with the dimensions 50x50cm and 30x30cm 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 and shallower NNBAR opening has a nonuniform 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 and deeper opening for the neutron scattering instruments, instead, 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 <cit.>. 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 <ref> the pulse shape of the neutrons coming out of the moderator at 2, 4, and 9 is presented. The curves were obtained by recording the neutrons crossing outward the moderator surface on the NNBAR side through a SSW card <cit.> . The neutrons were then filtered in energy using the Monte Carlo Particle Lists (MCPL) interface <cit.> 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 (2.86ms). This is due to the slow LD_2 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 interesting quantity is the time-averaged flux.

Pulse shape of the neutrons coming out of the moderator at 2, 4, and 9. The proton beam impinging on the target lasts 2.86ms, indicated by the shaded region on the left. The neutrons are binned in elapsed time in milliseconds and the respective histograms are normalized to probability density functions (a.u.) for comparison. The smoothed curves are obtained with Gaussian kernel density estimation.

§.§.§ Effects of engineering design on neutronic performance

An engineering design was made based on the optimized neutronic model (see <ref>). 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 (8 mm) 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, a recommendation came from the engineering designers, that it would be
better to place the beryllium outside the LD$_2$ moderator, for the following reasons: 1) there is a significant reduction of the heat load which has to be handled by the LD$_2$ stream inside the moderator when the beryllium is not inside. 2)  There was an issue with film boiling in the slit in between the beryllium blocks in the thermomechanical simulations when the blocks are inside the LD$_2$. That issue is solved by placing them outside the LD$_2$ vessel.

Finally, the engineering team suggested a simplification of the flow structure, that would reduce the amount of Al inside the vessel. This implied a change of the shape of the reentrant hole from the square  shape, designed by the neutronic team, to a U-shape 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 modifications of the models:

* LD_2 with Al flow guides modeled explicitly, and wall thickness increased from 3 mm to 8 mm (<ref>).

* Be filter separated from LD_2 moderator (<ref>).

* Reentrant hole with U-shape and a few parameters slightly changed to streamline the model (<ref>).

* LD_2 with  Al flow guides modeled explicitly, and wall thickness increased from 3 mm to 4 mm (<ref>).

* rectangular REH is tapered (<ref>).

The conclusions from this analysis are that a thickness of 8 mm 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-shape reentrant hole, does not give a large penalty.

Impact of engineering refinements on neutronic performance, normalized to the optimized LD_2 baseline.

NNBAR     WP7

<ref>     100     100

<ref>     75     77

<ref>     92     98

<ref>     91     93

<ref>     94     93

<ref>     94     94

Original optimized design for the LD_2 source.

As in <ref>, but  Al flow guides modeled explicitly, and wall thickness increased from 3 mm to 8 mm.

As in <ref>, but Be filter separated from LD_2 moderator.

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

As in <ref>, but  Al flow guides modeled explicitly, and wall thickness increased from 3 mm to 4 mm.

As in <ref>, but rectangular REH is tapered and the geometry is slightly changed to increase the overall performance.

The solution to reduce the thickness of Al vessel to 4 mm proposed by WP5 was to round the walls of moderator and to model the U-shaped reentrant hole on the WP7 side to simplify the flow. The WP5 team also provided a detailed CAD model of the LD_2 moderator with Al vessel. It was additionally required to separate LD_2 and Be vessels with a gap of thickness of 5 mm. An MCNP model was designed according to this CAD model (see <ref> and <ref>). This last step of the design is described in <ref>.

§.§ Rounded shape model

As a final step of the design of the liquid deuterium moderator, we investigated a model updated following a preliminary engineering study based on the model from third neutronic optimisation of cold moderator (<ref>). This study revealed that 8 mm thick Al vessel and additional Al flow guides would be required given the engineering constraints (see model on <ref>) leading to a significant drop in NNBAR FOM of about 25 % (see <ref>). To reduce this negative impact on the neutronic performance of the cold moderator, it was proposed to round the walls of LD$_2$ box and Al vessel around it. Moreover, the Be filter and LD$_2$ box was separated and the shape of reentrant hole was simplified to U-shaped reentrant hole. This allowed reducing the thickness of Al vessel to 4 mm.

Design of LD_2 moderator with rounded shape, developed by the engineering team.

LD_2 moderator with rounded shape shown with horizontal cut, developed by the engineering team.

We note that there was no time available in the project to perform a full engineering study of this option, and the neutronic design of this model was not optimized. Nevertheless, we report these results in this document since it should be further investigated in future projects.

The MCNP model is shown in <ref>. The summary of the expected performances, integrated in different wavelength ranges, is shown in <ref>.

Neutronic performance and characteristics of the most recent model of cold moderator updated based on the preliminary engineering study. Brightness and intensity integrated over different wavelength ranges, for the last iteration of lower moderator (NNBAR and WP7 openings) and compared with the upper moderator. The values for the upper moderator are from Ref <cit.>. To calculate the intensity we considered the following size of emission windows: NNBAR: 960 cm$^2$; WP7: 225 cm$^2$; upper moderator: 42 cm$^2$.

3cBRIGTHNESS [n/cm/s/sr]

$>$ 2     $>$ 4     $>$ 10

NNBAR     7.05e+12     5.40e+12     3.92e+11

WP7     1.47e+13     7.77e+12     6.22e+11

upper moderator     5.3e13     1.7e13     9.9e11

3cINTENSITY [n/s/sr]

$>$ 2     $>$ 4     $>$ 10

NNBAR     6.77e+15     5.18e+15     3.76e+14

WP7     3.30e+15     1.75e+15     1.40e+14

upper moderator     2.2e15     7.0e14     4.2e13

NNBAR FOM     2.24e+17 [n/s/sr $\times$ $\lambda^2$]

WP7 FOM     2.91e+15 [n/s/sr]

Heatload on LD$_2$ moderator     25.8 [kW]

Heatload on Be filter     16.3 [kW]

Heatload on Al vessel     10.5 [kW]

Total heatload     52.6 [kW]

Graphical representation of the final design for LD_2 moderator with U-shaped reentrant hole, separated Be filter and LD_2 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.

MCNP model of the cold moderator vessel with rounded shapes, according to the technical drawing from the engineering team.

§.§ Summary of the cold moderator design

We have successfully designed a cold 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 [<https://www.psi.ch/en/sinq>].
The design of the cold moderator has been refined throughout the whole duration of the project, with several iterations with the engineering teams. Details on the engineering design are provided in the next section. Although an engineering design of the latest model with the rounded shapes has not been performed, due to time constraints, there are strong indications that this approach could be the best one for the cold source and should be further investigated.

§ ENGINEERING DESIGN OF THE LIQUID DEUTERIUM MODERATOR

The first moderator and reflector system (so called twister I) will have two liquid parahydrogen moderators above the target wheel only. However, there is available space below the target wheel (lower moderator plug), which has been reserved for future moderator upgrades that could be used for a LD$_\text{2}$ volume moderator.
In the HighNESS project, Work Package 5 (WP5) is in charge of   the engineering implementation of new cold moderator concepts.
This includes the definition of fluid parameters; cooling process concept design; structural materials choice; detailed CAD design of the advanced moderator concepts for the lower moderator plug including manufacturability verification; weldability analysis; structural-mechanics and fluid-dynamics simulations; and integrability into the ESS facility <cit.>.

From an engineering point of view, the cooling and integration into the existing facility of such a large cryogenic pressure vessel in the high-power spallation source ESS is critical and must be analyzed in combination with the mechanical design <cit.>.

§.§ Moderator Engineering - 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. <ref> shows the isometric view of the ESS Target Monolith. The colored components are subjects of the planned upgrades of the ESS Target station <cit.>.

ESS Target Monolith, isometric cutaway view.

The major engineering challenge here is to handle the enormous heat load into the LD$_\text{2}$ moderator of around 60kW resulting from the spallation process of a 5MW accelerator-driven neutron source. Following the several iterations discussed in the previous section, the following preliminary engineering design of the LD$_\text{2}$ moderator was developed. The moderator vessel consists of high-strength Aluminum alloy EN AW-6061 T6, which allows local stresses up to 87MPa and will be filled with approximately 30L 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 ($\leq$ 80K) is installed inside the cold moderator vessel on the NNBAR side serving the large beam port  (see <ref> blue block) <cit.>.

Pre-design of the LD$_\text{2}$ moderator

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 LD$_\text{2}$ 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. <ref> shows the twister with the upper moderator on the left-hand side and on the right-hand side the integrated volume LD$_\text{2}$ moderator in the lower moderator plug. <cit.>

Integration of LD$_\text{2}$ moderator: 1. Upper moderator plug; 2. upper moderator plug in the moderator support structure; 3. moderator plug with LD$_\text{2}$ moderator; 4. and 5. moderator plug in the moderator support structure near the outer reflector <cit.>.

§.§ Definition of fluid parameters & 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. <ref> shows a simplified representation of LD_2 (blue line) at the chosen operation pressure of 5bar. It can be seen that the deuterium solidifies at a temperature of $\approx$19K and vaporizes at $\approx$30K, 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 20K. In addition, it is assumed that additional heat load from the circulation pumps and insulation losses will increase the deuterium temperature by 1K before it arrives at the moderator inlet. The average temperature increases in the moderator due to particle heating of 59.8kW will be up to 3K, which means that the average outlet temperature will be around 24K. As a result, there is still a contingency factor for local temperature peaks of approximately 6K before the deuterium evaporates.

Definition of fluid parameters for the moderator LD_2 volume.

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 liquid deuterium is needed to remove the enormous particle heat and to keep the average temperature increase below $\leq$ 3K. Assuming a flow velocity of up to $\leq$ 5, an inlet\outlet pipe diameter of 70mm would be required, which has to fit into the existing twister structure.

Critical design parameters.

Liquid ortho-Deuterium volume     V$_{Mo} \approx$ 30L

Heat load into oLD$_\text{2}$-moderator     $\Sigma$Q$_{Mo}$ = 59.8kW (@ 5MW)

Total heat load     $\Sigma$Q$_{To} \approx$ 70kW (60kW + 10kW)

Average pressure (Moderator)     p = 5bar

Average density     $\rho$ = 173.8

Flow velocity     w $\leq$ 5

Average mass flow     ṁ $\geq$ 3400

Average temperature increase (mo.)     dT $\leq$ 3K

Average temperature     T$_{Av}$ = 22.5K

Average inlet temperature     T$_{AVI}$ = 21K

Average outlet temperature     T$_{AVO}$ = 24K

With the defined fluid parameters, a first piping and instrumentation diagram (P& ID, see <ref>) 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 <ref> is a simplified system flow diagram of the cryogenic deuterium moderator system (CDMS), consisting of the helium refrigeration system (TMCP II) with 75kW cryo-power at 20K, 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 cryostate 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.

Piping and instrumentation diagram for the LD_2 moderator system.

§.§ Costs estimation of LD$_\text{2}$ infrastructure

The rough cost estimation shown in <ref> 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. 75kW) compared to the hydrogen moderator system (ca. 30kW). 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.

Cost estimation of the LD$_\text{2}$ moderator system.

Item     Cost [M€]     Comments

Helium refrigeration system     35     Ca. 75kW @ 20K

Helium transfer lines     1.93     Assumed: 2x100m

D$_{2}$ cryostat     14

LD$_\text{2}$ transfer lines     2.75     Assumed: 2x40m

LD$_\text{2}$ moderator plug     5.5     Complete new twister

D$_{2}$ storage system     2.5

New building for He-refrigaration system
room preparation for LD$_\text{2}$ cryostat, ATEX, ...     5     No room selected so far

Total:     66.68

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.

§.§ Selection of materials and overall design

For the newly designed moderator, the moderating medium of LD_2 is kept at 20K. 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 LD$_\text{2}$.

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 LD$_\text{2}$ moderator. Therefore, heat treatable aluminum alloys (6000 series) or non-heat treatable (5000 series) are the preferred choice <cit.>.

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 <cit.>.
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.

§.§ 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 <ref>. All details about the integration of the LD$_\text{2}$ moderator assembly into the already existing ESS twister can be found in <ref>.
The lower moderator plug consists of the inner LD$_\text{2}$ 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 <ref>).

3D cross section illustration of the lower moderator plug.

<ref> 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 LD$_\text{2}$ moderator sits within the surrounding vacuum vessel with a 5mm 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.

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 <ref>.

3D cross-section of the neutron windows.

§.§ Assembly and welding of the moderator

A cold beryllium filter is embdedded within the LD_2 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 8mm are shown in <ref>.

Detailed view of the LD$_\text{2}$ moderator structure within the moderator plug.

The assembly sequence of the LD$_\text{2}$ moderator is shown in <ref> and <ref>. 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.

Assembly of the LD$_\text{2}$ moderator vessel – parts overview.

Assembly of the LD$_\text{2}$ moderator vessel – assembly sequence.

One challenge when manufacturing the inner LD$_\text{2}$ 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 5bar and the unusual box shape for a pressurized vessel.
<ref> 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.

EB-welding of the LD$_\text{2}$ moderator vessel.

§.§ Structural mechanical calculations

Structural strength simulations with a design pressure of 7bar (operation pressure 5bar) following the design rules of RCC-MRx 2012 code were performed to analyze the static behavior of the LD$_\text{2}$ moderator, which basically behaves as a pressure vessel. <ref> 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 $1.5 \cdot S_{m}$ for EN AW-6061 T6, with $S_{m}$ = 87MPa and $1.5 \cdot S_{m}$ = 130.5MPa.

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 $\overline{P_{L}+P_{b}}$ on the fillet at the boundary of the rear wall still slightly exceeded the limit of $1.5 \cdot S_{m}$.

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 <ref>, shown with a 10$\times$ 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 10mm.

Shape of membrane under pressure, magnified 10$\times$ for visualization purpose

<ref> shows the updated equivalent primary stresses at a design pressure of 7bar. Here, it is indicated that the stress only exceeds the maximum of 130.5MPa by 0.92MPa at a single spot in a rounded corner. However, the linearized stresses at surfaces with $\sigma_{eqv}\geq S_{m}$ shown in <ref> demonstrate that the local primary membrane stress (left) and the primary membrane plus bending stress (right) completely satisfy the allowed strength criteria of $\overline{P_{m}}\leq\overline{P_{L}}\leq S_{m}(\Theta_{m})$ = 87MPa and $\overline{P_{L}+P_{b}}\leq 1.5\cdot S_{m}(\Theta_{m})$ = 130.5MPa.

Updated equivalent primary stress at design pressure.

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

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 10mm. The sum of local membrane and bending stress $\overline{P_{L}+P_{b}}$ on the fillet at the boundary of the rear wall is below the limit of $1.5 \cdot S_{m}$. With this design modification the strength criteria are met.

§.§ 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 $>$ 0.1mm 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 15mm 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 LD$_\text{2}$ moderator is given in <ref>.

Heat affected zones of the LD$_\text{2}$ moderator.

The structural strength simulations with a static design pressure of 7bar 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 $\overline{P_{m}}\leq \overline{P_{L}}\leq S_{m}(\Theta_{m})$ = 47MPa at all locations, but the criteria of $\overline{P_{L}+P_{b}}\leq 1.5 \cdot S_{m}(\Theta_{m})$ = 70.5MPa was not satisfied for one weld of one cover plate. These results are visualized in <ref>.

Linearized stresses at the weld seams of cover plates.

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. <ref> shows that the criteria of $\overline{P_{m}}\leq\overline{P_{L}}\leq S_{m} (\Theta_{m})$ = 47MPa as well as the criteria of $\overline{P_{L}+P_{b}}\leq 1.5 \cdot S_{m} (\Theta_{m})$ = 70.5MPa are satisfied for the welds of all cover plates.

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 <ref> shows that the nominal stresses at the weld seams of the stiffening rods all satisfy the strength criteria of $\overline{P_{m}}\leq S_{m}$ = 27.5MPa and $\overline{P_{L}+P_{b}}\leq 1.5\cdot S_{m}$ = 41.3MPa.

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.

§.§ 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 LD_2 with an average inlet temperature of approximately 21K. The heat input by neutrons is pulsed, with a 14Hz pulse frequency and 2.86ms 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 5MW load case with the given design and requirements. Further details on this issue and remedial measures are discussed in <ref>. The simulations were thus carried out using the design shown at reduced beam power 2MW, since ESS will run at this power in the initial operations phase. A corresponding total heat deposition of 28.4kW 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 LD$_\text{2}$ 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 <ref>).

Flow pattern of LD$_\text{2}$ through the moderator vessel, below and above the reentrant hole on window A.

<ref> shows the velocity streamlines of the liquid deuterium inside the moderator vessel that result from the CFX analysis <cit.>. Time-averaged results confirm a pressure drop of 0.15bar in the moderator and a maximum fluid velocity of 7.26 at an inlet velocity of 5.16.

Velocity streamlines of LD$_\text{2}$ inside the moderator vessel

The temperature difference from the inlet to the outlet is 1.4K with an outlet temperature of 22.4K (time averaged). The boiling temperature of deuterium at a pressure of 5bar is 30.6K. 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 <ref>, but the main flow is still sufficiently subcooled. Therefore, there is no risk of film boiling.

Time-averaged fluid temperatures for the LD_2 moderator.

In summary, it can be said that the fluid mechanical requirements for the 2MW 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.

§.§ Design solution of the vacuum vessel

Assembly of outer vessel for the lower moderator.

The outer vessel shown in <ref> 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 LD$_\text{2}$ moderator there is an insulation vacuum gap of 5mm to minimize the heat transfer between the cold and warm parts.

<ref> shows the different parts of the assembly, that consists of the center LD$_\text{2}$ moderator, the warm beryllium reflector parts, and the outer aluminum vessel.

Assembly of the lower moderator plug – parts overview.

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

Flow pattern of water through the premoderator.

It is assembled as shown in <ref>. 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.

Assembly and EB-welding detail of the premoderator.

<ref> to <ref> 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.

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

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

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

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

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

When the smaller neutron window A opening is reached in <ref> and <ref>, the water flows downwards again.

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

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

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

Flow pattern of water through the warm beryllium reflector parts

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

Flow pattern of water through the warm beryllium reflector parts

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

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

The vessel is then flipped upside down and the LD$_\text{2}$ moderator in inserted. After this is complete, the inner bottom plate of the vacuum vessel is welded on via electron-beam welding (<ref>).

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

<ref> 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.

Positioning of the LD$_\text{2}$ 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 (<ref>).

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

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

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

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 <ref>.

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.

§.§ 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 LH$_\text{2}$ 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 <ref>.

Media interfaces on the lower moderator plug.

Twister integration and interface description.

The attachment and integration of the lower moderator plug into the twister, underneath the target wheel, is illustrated in <ref>. 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.

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.

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

In summary, it can be stated that the integration of the new LD$_\text{2}$ moderator system into the existing twister is a very complex process, but feasible.

§.§ Summary and outlook: engineering implementation of deuterium moderator

In general, it can be concluded that a LD_2 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 5MW. Without further optimization, the proton beam power is currently limited to 2MW. 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:

§.§.§ Recommended further engineering investigations

- Building a full-scale prototype is recommended, because of the stringent requirements on the manufacturing process and specifically because of the welding process. Electron-beam welding of the aluminum alloy EN AW-6061 T6 can be critical, because of the weld-in depth of the needed filler material. Therefore, thorough welding tests should be performed to determine the final design.

- Thermo-hydraulic analysis needs further investigations, especially for 5MW beam power.

- Separation of the beryllium filter from the LD$_\text{2}$ moderator, to reduce the heat load.

- Reducing aluminum content by changing the shape of the moderator to reduce the heat load and to improve the neutronic performance.

- Better understanding of local nuclear boiling on the wall with subcooled main flow.

- Thermo-hydraulic analysis, considering boiling on the wall (by experiment).

- Possibly relaxing ESS requirements regarding local boiling and measurement of critical heat flux.

- Analysis of the risk of cavitation due to wall boiling in-pulse (by experiment).

§ DESIGN OF A VERY COLD NEUTRON SOURCE

§.§ 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 <cit.> was held in 2005 to discuss ideas for sources and applications. While several ideas on possible materials for VCN were raised (cf. <ref>), 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. This included 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.

§.§ VCN neutrons: a brief introduction

Very cold neutrons cover a wide spectral range within the long-wavelength tail of cold neutron sources[The standard cold moderator materials for both spallation and fission sources are liquid or solid deuterium ($\mathrm{S_2}$), liquid hydrogen ($\mathrm{H_2}$) and liquid or solid hydrocarbons (e.g. methane($\mathrm{CH_4}$)).], with energies ranging from below 1 meV (9) to few hundreds of neV ($>$ several  100), the domain of UCN.
A VCN source offers new possibilities in neutron scattering applications <cit.> and fundamental physics research. Extended neutron wavelengths ($\lambda$) inherently enhance the capabilities of diverse instrument categories.

This impact can be observed in the $\lambda$ dependencies of the gains in instrumental resolution at fixed geometry and in intensity at fixed resolution. For example,
gains in resolutions  proportional to
$\lambda^{-1}$, $\lambda^{-3}$  and $\lambda^{-3}$ 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  $\lambda^{2}$, $\lambda^{2}$  and
$\lambda^{3}$ for these three classes of instruments <cit.>.

Particle physics experiments can benefit from enhanced VCN fluxes, including the search for neutron-antineutron oscillations (described in <ref>), beam experiments looking for  a non-zero neutron electric dipole moment and search for novel fundamental forces (discussed in <ref>).

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.

§.§ 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.

§.§.§ Beam Experiments

Recently suggested particle physics experiments using beams of slow neutrons include:[Note that this list is not exhaustive.]

- In-beam searches for a permanent neutron electric dipole moment (nEDM) <cit.>, and searches for new fundamental forces <cit.>. These kind of experiments profit linearly from the interaction time $t$ of the neutron in the apparatus. Therefore, their figure of merit can be considered proportional to $\lambda$.

- Measuring the neutron lifetime $\tau_n$ by means of the beam method. Typically these experiments contain a trapping region of some length $L$ that intercepts a neutron beam. The neutron decay is observed by detecting decay protons within the volume of these region. In an experiment similar to <cit.>, the mean number of neutrons in the decay region at any time is given by,

\begin{equation} \label{eq_beam_lifetime}
N_n = L \int_A \int da I(v) \frac{1}{v} dv \;,
\end{equation}

where $A$ is the cross-sectional area of the trap and $I(v)$ is the velocity-dependent fluence rate <cit.>.
By increasing the VCN flux through such an experiment, the neutron density and hence the observed neutron decay rate increases, which in turn improves the statistical accuracy of the result. Similarly to the nEDM experiments, there is an expected $\mathrm{FOM} \propto \lambda$. It should be noted that these experiments still suffer from a systematic uncertainty, associated with the determination of the absolute neutron flux. Further progress towards the reduction of this uncertainty, as pointed out in <cit.>, could increase the precision of VCN beam lifetime experiments significantly and  shed light on the neutron lifetime puzzle <cit.>.

- Experiments searching for neutron anti-neutron oscillations <cit.>. Here it is not the interaction time, but quasi-free flight time of VCN that allow to significantly increase the sensitivity of the experiment. Under these conditions the probability for a transition can be expressed by:

\begin{equation}
P_{n \rightarrow \Bar{n}} = \left( \frac{t}{\tau_{n \rightarrow \Bar{n}}}\right)^2 \; ,
\end{equation}

with the free oscillation time $\tau_{n \rightarrow \Bar{n}}$ <cit.>. This results in a $\mathrm{FOM} = N_n t^2$, with $N_n$ being the total number of neutrons observed.
Due to the proportionality of the ($\mathrm{FOM}$) to $\lambda^2$, VCN exhibit specific potential for neutron oscillation experiments.

One should note, that, under the assumption of equivalent phase-space density, in most experiments the long interaction time or the longer free flight time of VCN is in competition with their lower flux. It is therefore crucial, in order to truly increase the sensitivity of the experiments described above, to increase the phase space density of VCN in the source. This has been discussed in <cit.> and <cit.>.

§.§.§ Wave‐Optical Experiments

Another class of experiments that could potentially benefit from VCN's exploit the wave-optical properties of the neutron, in terms of diffraction and interferometry. The potential of low wavelength neutrons for wave optics experiment was already pointed out in the 80s and early 90s in the works of A.G. Klein, A. Zeilinger et. al. <cit.>.
An extensive list of fundamental physics experiments utilizing neutron interferometry techniques is provided in <cit.>. Some of these experiments can benefit from lower energy neutrons. While certain proposed experiments may have become less relevant due to advancements in other fields, wave-optical experiments involving VCN remain an exciting avenue for fundamental physics research.

A dedicated VCN source could for example be used for:

- Further investigation of gravitationally induced quantum interference as measured in the famous COW[Acronym for R. Colella, A. W. Overhauser, and S. A. Werner.] experiment <cit.>. While this effect was already measured with VCN <cit.>, the experiment could be significantly improved with higher fluxes, brightness and modern VCN optics.[It should be noted that VCN might not be competitive with the accuracy of atom interferometers, as pointed out in <cit.>.] With regard to the latter, especially the field of holographic gratings, as described in <cit.>, made significant progress.

- Improve the current limit on the neutron charge <cit.> with a Talbot-Lau interferometer <cit.>.

- Measurement of the gravitational constant G by means of an active gravitational mass other then the Earth itself, in a Cavendish experiment, as described in <cit.>.

§.§ 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 therefore are 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 $\lambda^{-5}$.

High-resolution techniques such as small-angle neutron scattering SANS, time-of-flight spectroscopy, and neutron spin-echo (NSE) are mostly seen as standing to gain from longer-wavelength neutrons <cit.>. Moreover, other methods such as neutron imaging, which is a real-space technique, might benefit in some cases from improved flux conditions down to the VCN regime.

Small angle scattering is an elastic neutron scattering technique, where the resolution of small angles enables studying large-scale structures on the nanometer scale (i.e. from a few to a few thousand nanometers). Flux limitations typically prohibit probing larger structures up to the micrometer scale with 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. Thus, it is desirable to increase the resolution of conventional SANS instruments.

An elementary analysis shows that a $\lambda^{-5}$ slope of the long wavelength tail of a moderator spectrum marks the break-even for gaining either efficiency or resolution at longer wavelengths with SANS <cit.>. This is due to the momentum transfer being $q=2\pi/\lambda\sin\theta$, and thus larger wavelengths enable lower collimation and larger sample sizes in both dimensions across the beam for achieving the same angular resolution. Together with the increased $d\lambda$ for constant $d\lambda/\lambda$, the gain equals $\lambda^5$. Hence, a long-wavelength tail that decays at a rate less than $\lambda^{-5}$ will have corresponding performance gains (either in data rate or resolution, or a balanced gain in both).

However, these simplified considerations do not yet take into account some additional aspects, in particular the downsides, of utilizing very long wavelength neutrons – namely their increased absorption

probability and the significant impact of gravity on their trajectories. Increased absorption heightens 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 along with an increased scattering probability will favor thin samples to avoid absorption losses due to the former effect and multiple scattering from the latter. Effects from gravity can in principle be countered by means of instrumentation but might contribute to complexity and additional absorption issues.

When turning to experimental methods probing energy transfers and thus dynamics, the same break-even principle is found for time-of-flight spectroscopy probing inelastic scattering. Here, basic estimates can take into account that the energy change $dE\propto dt/\lambda^3$, where $dt$ is the time resolution. The estimated gains, taking into account a lower repetition rate, and thus scaling with $\lambda^5$ again, imply wavelength-independent performance at constant resolution for a long wavelength tail of an Maxwellian spectrum decaying with $\lambda^{-5}$ <cit.> (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 $\lambda^4$. Only the required momentum-transfer range limits such gains, where for example, for quasi-elastic measurements the wavelength must be limited to $\lambda < 4\pi/k_{max}$, where $k_{max}$ denotes the maximum momentum transfer.

In NSE, longer wavelengths are utilized to improve the energy resolution based on the relation $dE\propto dt/\lambda^3$, but without being able to profit from relaxing the requirements on incoming wavelength resolution, divergence, or increased beamsize, like in the cases outlined above. However, results from high-resolution NSE instruments such as IN15 at ILL imply that the current technology of magnetic field configurations does not allow for further gains beyond about 25 <cit.>.

For neutron imaging, different considerations have to be taken into account. Currently, neutron imaging reaches resolutions of a few micrometers, enabled by progress in detector technology. 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. Here, a colder spectrum is beneficial, since absorption tends to increase with longer wavelengths, thereby 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 $\lambda^{-5}$ prevents the effective use of very cold neutrons for high-resolution imaging.

On the other hand, novel lens systems for neutrons promise gains of the order of e4 <cit.> and long wavelengths are advantageous for lenses due to the refractive index increasing with $\lambda^2$ , the focal length with $\lambda^{-2}$, and the critical angle with $\lambda$.
The concern regarding increased absorption makes reflective focusing optics, like Wolter optics <cit.>, an attractive choice. 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 <cit.>.
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 <cit.> the possible advantages of using VCNs in reflectometry techniques are discussed in several configurations. Gains are expected if there is a shift of the neutron spectrum towards colder energies, provided that the brightness is preserved. The use of VCNs for reflectometry is considered particularly promising for compact sources, due to their intrinsically limited performance and to the fact that new compact sources could be designed for optimal use of VCNs.

§.§ VCN design options

In the original proposal of the HighNESS project, two approaches were considered for the design of such a 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
at the ILL, extracts VCNs directly
from  the cold source. At the dedicated workshop in 2022 <cit.>, an additional concept was suggested, that can be considered a merger of  the two approaches <cit.>.

§.§.§ Dedicated VCN moderator