cosmic rays would be overwhelming even at $1000\text{\,}\mathrm{m}$ below
ground level with a data-taking gate of $3\text{\,}\mathrm{ms}$, whereas this
background becomes negligible with a $1.2\text{\,}\mathrm{\SIUnitSymbolMicro
s}$ gate. Another is that it is not possible to maintain a flat top longer
than a few microseconds of the $350\text{\,}\mathrm{kA}$ pulse that is fed to
the neutrino horns 14 times a second because of the very large Joule heating
caused by the high current.

The underground accumulator ring, which has a circumference of
$384\text{\,}\mathrm{m}$, will receive the four $0.79\text{\,}\mathrm{ms}$
long sub-pulses separated by $100\text{\,}\mathrm{\SIUnitSymbolMicro s}$,
which is the time needed to prepare the injection kicker magnets for the
injection of the next sub-pulse. Each sub-pulse will be injected during ca 600
turns and then extracted in one turn, thus producing four ca
$1.2\text{\,}\mathrm{\SIUnitSymbolMicro s}$ long proton pulses separated by
almost 0.9 ms that will each be sent to one of the four separate targets. The
H- pulse, which will be injected into the accumulator ring using so-called
phase-space painting, will be stripped at the entrance of the accumulator ring
using thin carbon foils. The temperature to which these foils are heated must
be kept below $2000\text{\,}\mathrm{K}$ above which the foil sublimation rate
will be too high. To achieve this, the phase-space painting procedure is
optimized so that the number of foil crossings from already stripped particles
is minimized. This also reduces detrimental effects from space charge in the
ring. As a round beam cross-section is desirable when the beam hits the
target, anti-correlated painting of the beam has been opted for. The peak
temperature in the stripper foil is further reduced by injecting a mismatched
beam, to dilute the thermal load from the injected beam, and, by using
multiple thin foils instead of a single thicker foil, in order to increase the
effective foil surface area. It is planned to investigate, as an alternative
to foil stripping, the use of laser-assisted stripping of the incoming H-
ions. This method is currently being developed at the SNS in the US [628].

The performance of the accumulator ring design has been verified through
multi-particle simulations including direct and indirect space charge. The
simulations show that a geometric 100$\%$ emittance as low as 60 $\pi$ mm mrad
is achievable. The total tune spread expected is around 0.05, which implies
that space charge is not a limiting factor for the accumulator ring design, in
the operating scheme that we envision. We chose an accumulator layout that has
four rather short arcs connected by relatively long straight sections, see
Figure 34. The arcs contain four Focusing-Defocusing (FODO) cells, each with
two dipole magnets, with the dipole magnet centered between two quadrupole
magnets. The number and length of the dipole magnets have been chosen to reach
the desired bending radius using a moderate magnetic field strength of
$1.3\text{\,}\mathrm{T}$. The main challenges of the design are to control the
beam loss and to find a H- stripping scheme that is reliable over time. The
design of a two-stage collimation system has been made to meet these
challenges. A barrier RF cavity will be used to contain the beam pulses
longitudinally and preserve the $100\text{\,}\mathrm{ns}$ particle-free gap
required for extraction. The beam will be extracted from the ring using a set
of vertical kicker magnets and a horizontal septum and the four sub-pulses
will be guided by a $72\text{\,}\mathrm{m}$ transfer line up to the beam
switchyard.

Figure 34: The accumulator ring layout.

The beam switchyard directs each compressed sub-pulse to one of the four
targets by fast switching of dipole magnets. Figure 35 shows a 3D CAD drawing
of the $45\text{\,}\mathrm{m}$ long switchyard, where the first switching
occurs in the horizontal plan and the second level switching is in the
vertical plane. Switching during less than $0.9\text{\,}\mathrm{ms}$ between
the sub-pulses requires dipole magnets with low inductance. As an alternative,
a kicker in combination with a septum dipole will be considered. Four
collimators are included at the end of the line to perform a final beam
cleaning before it hits the target. Both the transfer line and the switchyard
have been designed so as to produce a round beam suitable for the target and
for minimal beam loss.

Figure 35: A 3D isometric view of the beam switchyard.

####  9.1.3 Short pulses for neutron production

Unlike ESS, the SNS is a short-pulse spallation facility where an accumulator
ring is used to produce proton pulses of $1\text{\,}\mathrm{\SIUnitSymbolMicro
s}$ duration, which, in turn, are used for generating short pulses containing
a large number of spallation neutrons in a liquid mercury target. Such a short
proton pulse would induce very high thermomechanical stress on a solid target.
In Sweden, where a mercury target is not allowed, a liquid lead target could
be considered for a similar scheme. On the other hand, the neutron moderation
process will later stretch the initially short pulse to about
$100\text{\,}\mathrm{\SIUnitSymbolMicro s}$. Therefore, as an alternative, the
ESSnuSB accumulator could be used in a resonant slow-extraction mode [629],
where the compressed sub-pulse is extracted over approximately 75 turns. This
would produce a $100\text{\,}\mathrm{\SIUnitSymbolMicro s}$ proton pulse,
which is then matched to the neutron moderation time, thus substantially
reducing the thermomechanical stress on the target. It may be possible to find
a solid-target design that can withstand such a pulse. However, resonant slow
extraction is an inherently lossy process where high irradiation of the
extraction zone is inevitable. The accumulator ring design would have to be
carefully studied if single and multi-turn extraction were to be used
simultaneously.

####  9.1.4 Target Station

Four identical separate targets will be operated in parallel in order to
reduce the beam power that a single target will have to sustain, i.e., from
$5\text{\,}\mathrm{MW}$/target to $1.25\text{\,}\mathrm{MW}$/target. The
target design is based on a tube-shaped canister, of ca
$3\text{\,}\mathrm{cm}$ diameter and ca $78\text{\,}\mathrm{cm}$ length,
filled with $3\text{\,}\mathrm{mm}$ diameter titanium spheres, and cooled
using a forced transverse flow of helium gas, pressurised at 10 bar. The
primary advantage of such design, in comparison to the monolithic targets,
lies in the possibility of making the cooling medium flow directly through the
target and by doing so to allow for a better heat removal from the target
areas of highest power deposition. Each target is surrounded by a pulsed
magnetic horn (mini-Boone type [630]) providing a strong toroidal field, with
a value of the magnetic field strength of $B_{max}=$1.97\text{\,}\mathrm{T}$$
at peak current. This is required for the focusing of the charged pion beam,
produced from the interaction between the impinging protons on the titanium
target in the forward direction into a $50\text{\,}\mathrm{m}$ long decay
tunnel filled with He gas to reduce interactions. The charge sign of the pions
being focused will be changed by reverting the direction of the current in the
horn. Each horn will have a separate power supply-unit capable of providing a
$350\text{\,}\mathrm{kA}$ semi-sinusodial current pulse of order
$100\text{\,}\mathrm{\SIUnitSymbolMicro s}$ length, which at a peak current
provides a sufficiently constant current within
$1.3\text{\,}\mathrm{\SIUnitSymbolMicro s}$. These current pulses will be sent
to the horn through strip lines. Several horn designs were investigated in
this study, of which the Van der Meer horn structure [631] showed the best
performance. Figure 36 shows a 3D CAD drawing of the target station complex
with a zoom-in on the 4-horn system. The geometry of the horn has been
designed and optimised using the so-called genetic algorithm to provide an
optimal signal efficiency in the Far Detector. Figure 37 (right) left shows
the (anti) neutrino flux distribution at a $100\text{\,}\mathrm{km}$ distance
from the neutrino source, resulting from the horn and decay tunnel geometry
optimisations.

Figure 36: Overview of the target station complex with a zoomed view of the
4-horn system.

Figure 37: ESS$\nu$SB neutrino (left) and antineutrino (right) energy spectrum
at $100\text{\,}\mathrm{km}$ from the neutrino source.

The magnetic field in each horn is produced by a Power Supply Unit (PSU),
which delivers the current pulses to the four horns, synchronised with the
proton beam pulses coming from the switchyard. The PSU unit consists of 16
modules connected in parallel and capable of delivering
$350\text{\,}\mathrm{kA}$ with $100\text{\,}\mathrm{\SIUnitSymbolMicro s}$
time width pulse at $14\text{\,}\mathrm{Hz}$ to each horn. Each proton pulse
will deliver $2.23\times 10^{14}$ protons per target and will have a total
energy of $89\text{\,}\mathrm{kJ}$. Due to the high power and short pulse
duration of the proton beam, the ESS$\nu$SB target will be operating under
severe conditions. The energy deposition and the resulting displacement per
atom (DPA) in the target have been studied using Fluka. The simulations show a
total energy deposition of $0.276\text{\,}\mathrm{GeV}$/pot/pulse,
corresponding to $138\text{\,}\mathrm{kW}$, in the target body. The results of
the DPA analysis show that ca 8 DPA/yr are produced along the target. If we
consider 1 DPA as a reference value, to estimate the lifetime of the target,
the previous value of the DPA corresponds to $3.024\times 10^{7}$ pulses.

At the end of the decay tunnel there will be a water-cooled beam-dump (BD)
that will absorb the non-interacted primary proton beam and the undecayed
muons. The BD core structure will consists of four independent graphite
blocks, each block facing one of the four horns. The four segments are
supported on a cross-like structure, made of a Copper-Chromium-Zirconium
(CuCr1Zr-UNS C18150 [632]) alloy, similar to that used for the new PSB [633]
and ESS beam dumps. Each segment is in turn constructed from two zigzag blocks
with $1\text{\,}\mathrm{cm}$ spacing (play) between them, to allow for the
thermal expansion of the individual blocks. The $30\text{\,}\mathrm{cm}$
support plates are used as heat sinks with water channels drilled inside the
plate body.

####  9.1.5 Detectors

Near Detector

The purpose of the near detector is to monitor the neutrino beam intensity and
to measure the muon- and electron-neutrino cross sections, in particular their
ratio, which is important for minimizing the systematic uncertainties in the
experiment. The near detector will be located underground within the ESS site
ca $250\text{\,}\mathrm{m}$ from the target station. It will be composed of
three coupled detectors: A kiloton mass Water Cherenkov detector (WatCh),
which will be used for event rate measurement, flux normalisation and for
event reconstruction comparison with the far detector, a magnetised super
Fine-Grained Detector (sFGD) [634], located inside a $1\text{\,}\mathrm{T}$
dipole for measurements of the poorly known neutrino cross sections in the
energy region below $600\text{\,}\mathrm{MeV}$, and placed upstream of, and
adjacent to the water volume, and an emulsion detector of similar type as in
the NINJA experiment [635]. Figure 38 (right) shows the layout of the near
detector complex.

The WatCh water-tank will be a horizontal cylinder of $\sim$
$11\text{\,}\mathrm{m}$ length and $4.72\text{\,}\mathrm{m}$ radius (total
volume $767m^{3}$) with the inner walls having a 30% coverage of 3.5 inch
Hamamatsu R14689 photomultiplier tubes (PMTs). The WatCh detector consists of
modules, each of them housing 16 PMTs. There are in total 1258 modules
altogether containing 20128 PMTs. The 1.4 $\times$ 1.4 $\times$ 0.5 $m^{3}$
sFGD, located in front of the WatCh detector, will be composed of $10^{6}$
$1\text{\,}\mathrm{cm}$3 plastic scintillator cubes read out by three-
dimensional pattern of wave-length-shifting optical fibres (Figure 39 (left)).
The thickness of $0.5\text{\,}\mathrm{m}$ along the beam axis is chosen in
order to have a sufficient number of charged leptons that continue into the
WatCh and thus to allow the combination of the information from the two
detectors. A magnetic field of up to $1\text{\,}\mathrm{T}$ and perpendicular
to the beam is applied in the tracker by a dipole magnet. In front of the
tracker, a NINJA type emulsion detector is situated that will be used for
cross section measurements. The NINJA detector is an emulsion-based detector
with a water target, currently under operation at J-PARC with the T2K near
detectors. Its primary purpose is to measure precisely the neutrino
interaction topology, double differential cross sections, and search for
sterile neutrino [635, 636, 637]. Members of the NINJA Collaboration are
prepared to add a similar detector to the ESS$\nu$SB suite of the near
detector.

Figure 38: The ESS$\nu$SB near detector layout. (Left) An artistic view of the
detector, with an event in the sFGD. The trajectory of a positive muon (red)
in the sFGD (bended by the magnetic field) and the two neutrinos (blue) from
its decay in the WatCh. Emitted Cherenkov photons in the WatCh are shown in
orange. (Right), an engineering design of the detector and the cavern.

Figure 39: (Left) design of the Super Fine-Grained Detector with three-
dimensional read-out. (Right) An $\nu_{\mu}$ interaction event in the SFGD
cube with a secondary muon producing a Cherenkov light in the near water
Cherenkov detector.

sFGD and WatCh combined analysis

Figure 39 (right) shows an example of what is here called a cross-over event
in which a muon neutrino interaction in the sFGD and the secondary muon
continues into the WatCh and produces Cherenkov light. Around 12% (20%) of
positive (negative) muons produced in the sFGD will continue into the WatCh
and be detected there. For electron neutrino interactions such events
represent about 6% of the sample. For the crossover events we aim at a good
purity of the electron neutrino event sample by efficiently rejecting events
originated in the sFGD that have muons continue into the WatCh by exploiting
the sFGD and WatCh ID capabilities together, which will be used for electron
neutrino cross section measurement.

Figure 40: Left: “Measured” $\nu_{\mu}$ cross section (blue) compared to the
cross section used by GENIE (red). Right: “Measured” $\nu_{e}$ cross section
(blue) compared to the cross section used by GENIE (red).

Neutrino cross section measurements at near detector

As pointed out above, one of the tasks of the sFGD is to measure neutrino
cross sections. In Figure 40, “measured” $\nu_{\mu}$ and $\nu_{e}$ cross
sections are compared with the ones used for simulation of neutrino events.
Good agreement up to $E_{\nu}\sim 500$ MeV is observed in both cases. Above
that, the discrepancy is big, especially in the muon case. The reason is
related to the limited statistics due to the limited number of neutrinos above
this momentum in our low-energy neutrino beam. The number of expected
(anti)neutrino interactions in the sFGD, obtained by using GENIE neutrino
event generator [638, 639, 640], is given in the tables in Figure 41 (bottom)
top.

The Far Detector

The water Cherenkov Far Detector, which will detect the rate and energy
distributions of the muon- and electron-neutrinos, respectively, will be
composed of two vertical cylinders of ca $74\text{\,}\mathrm{m}$ in height and
ca $74\text{\,}\mathrm{m}$ in diameter, installed in caverns ca
$1000\text{\,}\mathrm{m}$ under the ground level to protect them from the
cosmic radiation background. Two locations for the far detector have been
under consideration in the design study, both near the position of the second
$\nu_{\mu}-\nu_{e}$ oscillation maximum, thereby resulting in a majority of
the events being collected at the second oscillation maximum. One location is
in the Zinkgruvan mine, $360\text{\,}\mathrm{km}$ from the ESS, and the other
is in the Garpenberg mine, $540\text{\,}\mathrm{km}$ from the ESS. Both mines
are active, presenting the advantage of local services like access shafts and
declines, ventilation, drainage and other services that are in operation. The
locations of the detector caverns are planned to be outside the region of
exploitable ore, but still accessible from the mine drifts and at a sufficient
distance (a few hundred meters) from the mining activity areas to avoid any
kind of mutual disturbance. After careful investigation of the physics
performance of the two Far Detector positions, Zinkgruvan has be selected as
having the preferred position as discussed in Section 9.2. The detailed design
of the cavern locations in the mine must be preceded by core drilling to
enable measurements of the rock strength and pressure in the planned
underground regions.The photomultiplier tubes coverage of the ca
$25\,000\text{\,}\mathrm{m}$2 inner detector walls will be 40% (requiring,
e.g., ca 50,000 PMTs of 20 inch diameter). The water in the detector tanks
will be purified using an industrial-sized water-cleaning plant in order to
achieve about $100\text{\,}\mathrm{m}$ absorption length for the light
wavelength that the PMTs are sensitive to. The ability to dissolve gadolinium
salt for increased neutron detection efficiency, and thereby of electron-
antineutrinos, will be included.

Figure 41: Number of expected interactions in the sFGD: (top) positive, i.e.
$\nu$, horn polarity. (Bottom) negative, $\overline{\nu}$, horn polarity.

###  9.2 Optimizing the neutrino baseline

The preliminary optimisation studies presented in Ref. [4], as well as the
follow-up studies [641, 241, 242, 243, 244, 642], of the physics reach of the
ESS$\nu$SB facility for leptonic CP-violation, demonstrate that the best
baseline at which to study the neutrino beam would be between
$350\text{\,}\mathrm{km}$ and $550\text{\,}\mathrm{km}$. This makes the
ESS$\nu$SB design unique, as the neutrino flux observed by the detector mainly
corresponds to the second maximum of the $\nu_{\mu}\to\nu_{e}$ oscillation
probability, with a more marginal contribution of events at the first
oscillation peak. However, as discussed before, there is a price to pay in
order to observe the oscillation probability at its second maximum. Even
though it is the optimal choice to maximise the dependence of the oscillation
probability on the $\delta_{CP}$, the ratio of the oscillation baseline to the
neutrino energy ($L/E$) needs to be a factor 3 larger compared to the first
maximum. This means that the statistics will be about an order of magnitude
smaller than if the detector had been located at the first oscillation peak.
Furthermore, the neutrino cross section decreases and beam spread increases
for smaller neutrino energies. The $360\text{\,}\mathrm{km}$ baseline option,
corresponding to a point between the first and the second oscillation maxima
as seen in Figure. 31, represents a compromise between the two choices. The
neutrino flux would be 2.25 times larger than that at the
$540\text{\,}\mathrm{km}$ option and roughly the same number of events
belonging to the second oscillation peak would be observed at either site. At
the higher energy end of the spectrum, events from the first oscillation
maximum would also be observed for the shorter baseline. This can be seen in
the event rates expected at each of the two detector locations depicted in
Figure 42. In any case, for the ESS$\nu$SB the choice close to the second
oscillation maximum was shown to be optimal for its increased dependence on
$\delta_{CP}$ and despite the reduced event rate.

Figure 42: Event rates for the different signal and background components for
the e-like sample with positive (left panels) and negative focusing (right
panels) and for the Zinkgruvan $360\text{\,}\mathrm{km}$ (upper panels) and
Garpenberg $540\text{\,}\mathrm{km}$ baselines.

###  9.3 Physics reach of the ESS$\nu$SB experiment

Figure 43 shows the CP discovery potential obtained for the two baselines for
different assumptions about the size of the systematic uncertainties.
Generally, we find that the performance of both baselines is very similar,
with only slightly different areas covered above the 5 $\sigma$ mark,
depending on the systematic uncertainties considered. In the upper panels, the
impact of an overall normalization uncertainty, uncorrelated among the
different signal and background samples of $1\%$, $5\%$, $10\%$ and $25\%$
uncertainties, is shown.

It is remarkable that, even for an extremely large uncertainty value of
$25\%$, a significant portion of the values of $\delta_{CP}$ would still allow
a discovery of CP violation above the 5 $\sigma$ level. In the simulation,
this uncertainty is uncorrelated between the neutrino and antineutrino samples
and therefore is able to mimic the effect of CP violation. Nevertheless, a
discovery would be possible even in this scenario. This can be understood from
Figure 31 where, close to the second oscillation peak, changes in
$\delta_{CP}$ can lead to changes in the probability, even above the $25\%$.
The dependence of the shape of the oscillation probability on the value of
$\delta_{CP}$ may also contribute to the sensitivity. In the middle and lower
panels of Figure 43, we also explore how robust the results obtained are
against other systematic uncertainties that might affect the shape of the
measured spectrum. In particular, in the middle panels, the impact of a $1\%$,
$5\%$, $10\%$ and $25\%$ uncertainty in the energy calibration is shown. In
the lower panels, a more general bin-to-bin uncorrelated set of nuisance
parameters has been considered. In both cases, a $5\%$ normalization
uncertainty has been added to allow the possible interplay between the
different sets of systematic uncertainties that may be relevant. We find that
the energy calibration uncertainty has a rather minor impact in the CP
discovery potential for both baselines under study. Conversely, the more
general implementation of uncorrelated uncertainties in each bin can have a
more significant impact, but still a smaller one than the overall
normalization considered in the upper panels. The results demonstrate that the
ESS$\nu$SB setup has remarkable CP discovery potential even for very
conservative assumptions on the systematic uncertainties that could affect the
far detector. Indeed, the measurements of the near detector will keep these
uncertainties at the few $\%$ level, for the present generation of neutrino
oscillation experiments. In particular, assuming a $5\%$ normalization
uncertainty in line with assumptions made for similar facilities, we find that
CP violation could be established for a $71\%$ ($73\%$) of the values of
$\delta_{CP}$ for the $360\text{\,}\mathrm{km}$ ($540\text{\,}\mathrm{km}$)
baseline.

In Figure 44, we estimate the precision with which the ESS$\nu$SB will be able
to measure the CP-violating phase $\delta_{CP}$. For each given possible value
of $\delta_{CP}$, Figure 44 shows the standard error with which $\delta_{CP}$
is determined marginalizing over all nuisance parameters and oscillation
parameters other than $\delta_{CP}$. We again observe a similar behaviour to
that of Figure 43. In particular, we find that the energy calibration
uncertainty has a very minor impact, while the other two studied sources of
uncertainties have a more important effect. Interestingly, the uncertainty on
the overall normalisation is most important for values of $\delta_{CP}\sim 0$.
Conversely, the bin-to-bin uncorrelated systematics that can also affect the
shape of the recovered spectrum are more relevant close to maximally CP
violating values, that is $\delta_{CP}\sim\pm\pi/2$.

Finally, in the left panel of Figure 45 the dependence of the precision with
which $\delta_{CP}$ would be measured is studied as a function of the
splitting of the total running time between positive focusing (neutrino mode)
and negative focusing (antineutrino mode). As an example, the Zinkgruvan (the
$360\text{\,}\mathrm{km}$) option is shown, but the behaviour is very similar
for Garpenberg (the $540\text{\,}\mathrm{km}$). As can be seen, the optimal
splitting depends in the actual value of $\delta_{CP}$. Given the larger
fluxes and cross sections, it is easier to accumulate statistics in neutrino
mode and thus the best precision would be obtained by devoting longer periods
of data taking to positive focusing. Conversely, around $\delta_{CP}=0$ or
$\pi$ the complementary between the neutrino and antineutrino samples pays off
and more even splits of the running time provide better sensitivity. The
measurement strategy of the ESS$\nu$SB can profit from previous hints by
preceding oscillation experiments and adapt the splitting between neutrino and
antineutrino modes according to the left panel of Figure 45, depending on the
value of $\delta_{CP}$ that the data point to. Following such a strategy, if
the best splitting between neutrino and antineutrino modes is adopted for each
value of $\delta_{CP}$, the precision that could be obtained is presented in
the right panel of Figure 45. While around CP conserving values the precision
achievable in the measurement of $\delta_{CP}$ is around $5^{\circ}$ for both
the Garpenberg and Zinkgruvan options, Zinkgruvan outperforms Garpenberg
around $\delta_{CP}=\pm\pi/2$, with the former providing a sensitivity better
than $7^{\circ}$ for any possible value of $\delta_{CP}$. The conclusion of
this study is thus that the ESS$\nu$SB experiment with its far detector
located at $360\text{\,}\mathrm{km}$, in the Zinkgruvan site, can provide
unprecedented precision on the measurement of $\delta_{CP}$ ranging between
$5^{\circ}$ and $7^{\circ}$ depending on its value. The same setup could
deliver a $5\sigma$ discovery of CP violation for a $71\%$ of all possible
values of $\delta_{CP}$.

Figure 43: CP discovery potential of the ESS$\nu$SB. Significance in number of
standard deviations on the vertical axis and value in degrees of the CP phase
angle on the horizontal axis. Left (right) panels for the Zinkgruvan
$360\text{\,}\mathrm{km}$ (Garpenberg $540\text{\,}\mathrm{km}$) baseline.

###  9.4 ESS$\nu$SB Synergies with Future Projects

####  9.4.1 Low Energy nuSTORM

The basic idea of nuSTORM is to store muons, generated from pion decays, in a
racetrack storage ring and use the muon- and electron-neutrinos that are
created, from the muon decays, in one of the two straight sections to form a
beam that can be used to measure neutrino cross sections as well as search for
sterile neutrinos. Contrary to a neutrino beam generated from pion decay,
which contains nearly muon neutrinos only, like that of the ESS$\nu$SB, the
nuSTORM neutrino beam will contain equal amounts of muon- and electron-
neutrinos, thus making high statistics measurements of both electron- and
muon-neutrino cross sections possible. In particular, precise electron-
neutrino nuclear cross sections are needed for the interpretation of the
electron-neutrino spectrum detected by the ESS$\nu$SB far detector.

Figure 44: ESS$\nu$SB precision measurement of $\delta_{CP}$. Standard error
in degrees in the CP phase angle on the vertical axis and value in degrees of
the CP phase angle on the horizontal axis. Left (right) panels for the
Zinkgruvan $360\text{\,}\mathrm{km}$ (Garpenberg $540\text{\,}\mathrm{km}$)
baseline.

So far, nuSTORM design studies have been made for the Fermilab and CERN
accelerators with proton energies in the order of $100\text{\,}\mathrm{GeV}$
[643, 644]. Pions produced from protons of such energies have an average
energy of ca $5\text{\,}\mathrm{GeV}$ and will decay to muons with an average
ca $4\text{\,}\mathrm{GeV}$ energy, which will in turn decay to neutrinos of
average ca $3\text{\,}\mathrm{GeV}$ energy. The length of the racetrack
straight sections was chosen to be about $180\text{\,}\mathrm{m}$. Even if the
neutrino momentum distribution so produced is broad, it will hardly cover the
low neutrino momentum region of ESS$\nu$SB project, which has a neutrino beam
of ca $0.4\text{\,}\mathrm{GeV}$ average energy, nor that of the Hyper-K
project, which will use a water Cherenkov detector located at the first
neutrino oscillation maximum and for which the neutrino beam average energy is
ca $0.6\text{\,}\mathrm{GeV}$.

Figure 45: Left, precision on the ESS$\nu$SB measurement of $\delta_{CP}$ for
different splittings of the running time between neutrino and antineutrino
modes at the Zinkgruvan baseline. Standard error in degrees in the CP phase
angle on the vertical axis and value in degrees of the CP phase angle on the
horizontal axis. The lines span from 9 (1) years to 1 (9) in (anti)neutrino,
the total running time is always 10 years. Right, the precision on the
measurement of $\delta_{CP}$ when the running time is optimised as in the left
panel comparing the Zinkgruvan and Garpenberg options.

The ESS-based Low Energy nuSTORM (LEnuSTORM) would use the pulses of protons
of $2.5\text{\,}\mathrm{GeV}$ extracted from the ESS$\nu$SB accumulator ring
from which a neutrino average energy of ca $0.4\text{\,}\mathrm{GeV}$ will be
obtained. It would be difficult to generate a sufficiently powerful beam from
the CERN PS, $1.4\text{\,}\mathrm{GeV}$, Booster or the CERN,
$26\text{\,}\mathrm{GeV}$, PS to cover the low neutrino energies of ESS$\nu$SB
and Hyper-K with sufficient statistics. In view of this, it is proposed to
carry out a design study of an LEnuSTORM using the ESS$\nu$SB-upgraded ESS
LINAC. The target to produce the muons could be either the already designed
targets used for producing the neutrino Super Beam with the
$1.3\text{\,}\mathrm{\SIUnitSymbolMicro s}$ proton pulses or a new dedicated
target. The length of the racetrack straight sections will be much shorter
than in the Fermilab and CERN designs and the required strength of the large
aperture magnets in the racetrack arcs will be much lower. The lattice design
could be of the Fixed-Field Alternating-Gradient accelerator or FODO type or a
mixture of both. Figure 46 shows a lay-out of ESS$\nu$SB on the ESS site with
proposed positions of the LEnuSTORM racetrack ring and, in this case, a
dedicated target station. The LEnuSTORM straight section is directed such that
the neutrino beam produced will first hit a LEnuSTORM near detector and then
the ESS$\nu$SB near detector, which is not visible in this figure but located
to the right and just above the figure, that would be used as the far detector
for the LEnuSTORM beam.

####  9.4.2 A Proton Complex Test Facility for a Muon Collider at ESS

It is proposed to make, as part of the International Muon Collider design
study project [645], a design study of a Muon Collider Proton Complex Test
Facility which will be based on the use of the ESS LINAC, on the already
designed ESS$\nu$SB accumulator ring and on a new compressor/buncher ring. If
CERN should decide around 2030 to go forward with the construction of a high
energy Muon Collider with a collision energy of 3, 10 or
$14\text{\,}\mathrm{TeV}$, the construction of such a Proton Complex Test
Facility at ESS could be started around the same time for the purpose of
demonstrating that $2\text{\,}\mathrm{ns}$ proton pulses of 1014-1015 protons
at a rate of $14\text{\,}\mathrm{Hz}$ can actually be produced in practice.
Such a test facility at ESS would require substantial funding but even more
funding would be required to start the construction at CERN of such a test
facility, as the build-up of a $5\text{\,}\mathrm{MW}$ proton accelerator
would have to be initiated and this well before 2030 to be in time. Moreover,
with such a Proton Complex in operation at ESS and with muon cooling at low
intensity being demonstrated in practice in a test facility at CERN, this
would open the way - in a longer perspective - for the construction at ESS of
a $125\text{\,}\mathrm{GeV}$ Higgs Factory Muon Collider with a unique
potential for measurements of the Higgs self-coupling, extremely rare decays
and the width of the Higgs boson [646] and a 3, 10 or
$15\text{\,}\mathrm{TeV}$ Muon Collider at CERN for Energy Frontier
experiments.

The design study of a Muon Collider Proton Complex at ESS would be based on,
inter alia, a faster chopping scheme for the LINAC, a new operation scheme for
the accumulator ring, a new design of a compressor/bunch rotation ring and, in
a second phase, a separate target station with a target and capture system
(horn or solenoid) that could withstand the $2\text{\,}\mathrm{ns}$ short
bunches of 1015 protons. The basic principle for the generation of the
$2\text{\,}\mathrm{ns}$ long pulses from the $2.86\text{\,}\mathrm{ms}$ 1015
proton LINAC pulses is illustrated in Figure 47. The LINAC H- pulse is chopped
into many short pulses that are injected into the accumulator ring from which
the proton pulses are extracted into the compressor/buncher ring where they
are phase-rotated to ca $2\text{\,}\mathrm{ns}$ length
($1.5\text{\,}\mathrm{ns}$ in the Figure). This calls for the development of a
high frequency chopper acting at the level of the LINAC H- source and an
adaptation of the accumulator ring acceptance, RF system, timing and optics.
As to the design of the accumulator and the compressor/buncher rings, there
has been a design based on the use of the $5\text{\,}\mathrm{GeV}$
$4\text{\,}\mathrm{MW}$ SPL proton LINAC, that was planned for construction at
CERN [647] as well as a design based on the use of the
$8\text{\,}\mathrm{GeV}$ high power Project-X proton LINAC, that was planned
at Fermilab [648]. These designs will be used as starting points for the
design and simulation of a compressor/buncher ring based on the use of the ESS
LINAC.

Figure 46: Layout of the ESS$\nu$SB with the proposed LEnuSTORM elongated
racetrack ring (in red) and a dedicated target station (in yellow).

In Figure 46, there is an indication of the direction of the ejected
$2\text{\,}\mathrm{ns}$ pulsed muon beam towards an area at ESS, where there
is free space for a second phase project to use the beam so-produced to build
and test a target station and cooling front-end set-up there. The compressor
ring is tentatively assumed to be located in the same tunnel as the
accumulator (the red ring in Figure 46).

Figure 47: The proposed accumulator ring layout dedicated for the Muon
Collider Complex at ESS. The transport of the four 1.5 ns pulses will be done
through lines of different lengths, such that the four pulses reach the target
at the same time

###  9.5 Proposed Project Time Line

The proposed time line of the ESS$\nu$SB experiment is the following:

  * 1.

2022: End of ESS$\nu$SB Conceptual Design Study, CDR, and preliminary costing

  * 2.

2023-2026: Civil engineering, technical build-up schedule and LEnuSTORM
Conceptual Design Study

  * 3.

2026-2027: TDR, Preparatory Phase

  * 4.

2027-2030: Preconstruction Phase, International Agreement

  * 5.

2030-2037: Construction of the neutrino beam facility and the detectors,
including commissioning

  * 6.

2037- : Start of data taking

The details of the construction schedule 2027-2037 will be studied in
2023-2026 period.

##  10 Conclusion

The ESS will open up new intensity frontiers for particle physics. At design
performance, it will be the world’s brightest neutron source and provide
intense neutrino pulses. The flexible design of the target area allows for the
installation of an intensity-optimised moderator and the extraction of the
world’s most intense neutron beams. Its world’s most powerful proton
accelerator offers the possibility to be upgraded and complemented by a
compressor ring to produce the world’s most intense microsecond-pulsed
neutrino beams.

These world-leading capabilities enable an ambitious programme of particle
physics experiments at the neutron and neutrino intensity frontiers. Among the
projects presented in this paper are precision measurements of neutron decay,
neutrino-nucleus scattering, the neutron electric dipole moment and neutrino
flavour oscillations at the second oscillation maximum, and searches for and
measurements of neutron-antineutron oscillations, leptonic CP violation,
sterile neutrons and sterile neutrinos. These measurements and searches tackle
several outstanding questions in our understanding of nature, such as the
structure of fundamental interactions, the origin of the matter-antimatter
asymmetry in the Universe, or the nature of dark matter or dark energy.

This paper presents concepts and expected performances of possible
experiments. Some of the proposed experiments can be realised within the
mission of the ESS as a user facility and require the installation of state-
of-the-art instrumentation in line with the usual investment at such
facilities, as for example a neutron beam line for particle physics. Some
neutrino-nucleus scattering experiments are already under construction to be
ready for early ESS operation. Other projects require additional design
studies and further investment in the ESS and experiment infrastructure. Such
investment includes both the provision of a high-intensity neutron moderator
as well as funding for large scale experiments.

The proposed experimental program of particle physics illustrates the unique
scientific potential of the ESS. The realisation of this programme would place
the ESS at the forefront of particle physics with neutrons and neutrinos.

## Acknowledgements

J.B. acknowledges support from the Swedish research council grants 2016-05996
and 2019-03779. L.B. and F.G. acknowledge support from from the U.S.
Department of Energy (DOE), Office of Science, Office of Nuclear Physics.
Grant No. DE-AC05-00OR22725. The work of Z.B. was supported in part by the
MIUR research grant "The Dark Universe: A Synergic Multimessenger Approach"
PRIN 2017 No. 2017X7X85K, and in part by the SRNSF. J.I.C. acknowledges
support by the European Research Council under Grant Agreement
No.101055120-ESSCEvNS ERC-2021-ADG. V.C. acknowledges support from the U.S.
Department of Energy Grant No. DE-FG02-00ER41132. M.G.-A. acknowledges support
from Generalitat Valenciana (Spain) through the plan GenT program
(CIDEGENT/2018/014), and MCIN/AEI/10.13039/501100011033 Grant No.
PID2020-114473GB-I00. L.L. is supported by the predoctoral training program of
non-doctoral research personnel of the Department of Education of the Basque
Government. L.L. and F.M. are also supported by the European Research Council
(ERC) under Grant Agreement No. 101039048-GanESS and the Severo Ochoa Program
grant CEX2018-000867-S. V.N. acknowledges support from L’Agence nationale de
la recherche, France, ANR-20-CE08-0034. D. M. gratefully acknowledges support
from the Swedish Research Council and the Swedish Research Council’s Council
for Research infrastructure. T.O. acknowledges support from the Swedish
Research Council (Vetenskapsrådet), Contract No. 2017-03934. A.S.P.
acknowledges support from the Marie Skłodowska-Curie grant agreement No.
101026628. V.S. acknowledges support from the HighNESS project at the European
Spallation Source. HighNESS is funded by the European Framework for Research
and Innovation Horizon 2020, under grant agreement 951782.

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