1 Executive summary

An EU-supported Design Study has been carried out during the years 2018–2022 of how the \(5\,{{\text {MW}}}\) proton linear accelerator (linac) of the European Spallation Source under construction in Lund, Sweden, can be used to produce the world’s most intense long-baseline neutrino beam for CP violation discovery in the leptonic sector and, in particular, precision measurement of the CP violating phase \(\delta _{{\mathrm{CP}}}\). The project is called the European Spallation Source neutrino Super Beam (\({\text {ESS}}\nu {\text {SB}}\)). This Conceptual Design Report describes the design of:

  • the required upgrade of the ESS linac,

  • the accumulator ring used to compress the linac pulses from \(2.86\,{\text {ms}}\) to \(1.2\,\upmu {\text {s}}\),

  • the target station where the \(5\,{\text {MW}}\) proton beam is used to produce the intense neutrino beam,

  • the near detector which is used to monitor the neutrino beam as well as measure neutrino cross-sections, and

  • the large underground far detector where the magnitude of the oscillation appearance of \(\nu _{e}\) from \(\nu _{\mu }\) is measured.

The report also provides the results of the physics performance study of the neutrino research facility that is proposed.

About a decade ago, results were published of the measurement of the neutrino mass-state mixing angle \(\theta _{13}\) which was found to be \(8.6^{\circ }\), a value that was much higher than that which had until then been presumed. This result made the discovery of leptonic CP violation significantly more viable in practice than previously foreseen, as well as shifting the optimal place for such a measurement from the first neutrino oscillation maximum to the second oscillation maximum where, given the relatively high \(\theta _{13}\) value, the CP violation signal is close to three times larger than at the first. As the second maximum is located further away from the neutrino source, a higher intensity is required when measuring at the second maximum as compared to the first maximum, to obtain the same event statistics.

At about the same time as the results of the measurement of the high \(\theta _{13}\) value became known, the decision was taken to build the European Spallation Source ESS at Lund in southern Sweden. With its \(5\,{\text {MW}}\) proton linear accelerator, ESS will produce the world’s highest flux of slow neutrons for materials science studies, generated by the spallation process. The neutrons will be produced in \(2.86\,{\text {ms}}\) pulses at \(14\,{\text {Hz}}\). The \({\text {ESS}}\nu {\text {SB}}\) conceptual design study has demonstrated that, given the high power and inherent upgrade capacity of the ESS linear accelerator, the linac can be used to produce, in addition to the high-intensity spallation-neutron flux, and concurrently with it, a neutrino beam sufficiently intense to provide a statistically significant number of events at the second oscillation maximum. Thanks to these factors, the evaluated performance of the proposed \({\text {ESS}}\nu {\text {SB}}\) research facility is considerably higher than that of the other proposed neutrino super-beam facilities, which are constrained to make measurements at the first oscillation maximum.

To reach large enough event statistics, an additional requirement is that the far water Cherenkov detector should have an appropriately large mass. For \({\text {ESS}}\nu {\text {SB}}\), the designed mass is 540 kton. To ensure a negligibly small background of neutrinos from cosmic rays, this detector will be installed in a mine \(1000\,{\text {m}}\) underground and the data-collection time-gate for each of the 14 neutrino pulses per second generated by ESS will only be \(1.2\,\upmu {\text {s}}\). The use of this short time-gate will require that the pulses from the ESS linac be compressed from \(2.86\,{\text {ms}}\) to \(1.2\,\upmu {\text {s}}\). To accomplish such a compression, each \(2.86\,{\text {ms}}\) linac pulse will be fed into a \(380\,{\text {m}}\) circumference accumulator ring, located underground on the ESS site, and be extracted in just one turn. This pulse compression is also necessary to be able to operate the target magnetic horns with sufficiently short current pulses. The current required for an efficient focussing of the pions emitted from the target in the forward direction into the decay tunnel is \(350\,{\text {kA}}\). To keep the heating of the horns to a manageable level, the current must be delivered in very short pulses with a flat top that still need to be at least as long as the proton pulses from the accumulator, i.e., \(1.2\,\upmu {\text {s}}\).

The design of the \({\text {ESS}}\nu {\text {SB}}\) research facility is largely conditioned by the above considerations. The doubling of the power of the linac from 5 to \(10\,{\text {MW}}\) is facilitated by the fact that adequate space has already been foreseen in the ESS modulators feeding the accelerating cavities, that can be used to install twice the amount of charging capacitors. To be able to feed the very high charge of \(2.2\times 10^{14}\) protons per pulse into the accumulator, \({\text {H}}^{-}\) ions will be accelerated in the linac and stripped of their two electrons at the injection point into the accumulator. For this, an \({\text {H}}^{-}\) source has to be furnished at the side of the ESS linac proton source. There are several mechanisms that will result in a fraction of the \({\text {H}}^{-}\) ions being stripped of their electrons and therefore lost in the accelerator or the transfer line to the accumulator, causing activation of the accelerator and transfer line components. In order for this activation to be kept at an acceptable level, the beam losses must not exceed \(1\,{\text {W/m}}\). The simulations of the operation of the linac and the transfer line with the selected design have demonstrated that all of these requirements can be fulfilled and that the required \(5\,{\text {MW}}\) \({\text {H}}^{-}\) beam for neutrino production can therefore be produced, concurrently with the \(5\,{\text {MW}}\) proton beam for spallation neutron generation.

The design of the underground accumulator ring and its beam optics must satisfy a number of different conditions. Among these are that the emittance must not exceed \(60\pi\) mm mrad, that the temperature of the carbon electron-stripping foils must not exceed \(2000\,{{\text {K}}}\), and that the beam losses in the accumulator must be kept sufficiently low by sequential collimation to keep the irradiation of the beam line components below \(1\,{\text {W/m}}\). Furthermore, the edges of the \(100\,{\text {ns}}\) gap in the circulating beam, needed for the extraction of the circulating beam and generated by chopping in the low energy part of the accelerator, must be kept sufficiently sharp using radiofrequency cavities to limit the irradiation of the extraction-region components in the ESS linac. The rise time of the current in the extraction magnets must not be longer than \(100\,{\text {ns}}\) in order for the beam extraction to fit within the time gap made available, which is achieved by having the inductance of these magnets sufficiently low. The design of the accumulator ring has been optimised through many iterations and the results of the simulation of the final design show that it will be feasible to deliver the required short and intense proton pulses to the target station.

The underground target station design is conditioned by the requirement that the target must stand the formidable shocks, heat dissipation, and radiation damage of a \(5\,{\text {MW}}\) proton beam delivered in \(1.2\,\upmu {\text {s}}\) short pulses 14 times a second. To manage these severe conditions, the design adopted foresees the chopping of the \(2.86\,{\text {ms}}\) pulse into four sub-pulses in the low energy part of the linac, the compression in sequence of these four sub-pulses in the accumulator ring, and their extraction into a magnet switchyard, which will direct each of the four sub-pulses to one of four separate targets, each of which will thus receive a \(1.25\,{\text {MW}}\) beam. Each of the four targets is designed as a \(78\,{{\text {cm}}}\) long tube, \(3\,{{\text {cm}}}\) in diameter and filled with \(3\,{\text {mm}}\) titanium balls that are cooled by a high-pressure transverse helium-gas flow. The extreme heating, high irradiation and radiation damage of these targets, the surrounding focusing magnetic horns, the walls of the \(50\,{\text {m}}\) long pion decay tunnel, and the water-cooled beam stop at the end of the tunnel have been simulated and found to be within tolerable limits.

The neutrino beam resulting from the decay of the pions produced in the four targets will be directed towards the 1 kton underground near detector located on the ESS site \(250\,{\text {m}}\) from the target station and the 540 kton underground far detector, located at a distance of \(360\,{\text {km}}\) from ESS. The two detectors are based on the water Cherenkov technique. The near detector is in addition equipped with a tracking detector mounted inside a dipole magnet and consisting of 1 million \(1\,{\text {cm}}^{3}\) scintillator cubes read out with wavelength-shifting fibres, and with an emulsion stack detector immersed in water. The excavation of the two cylindrical far detector caverns, each \(78\,{\text {m}}\) high and \(78\,{\text {m}}\) in diameter, at a depth of \(1000\,{\text {m}}\) in the Zinkgruvan mine, represents a unique geotechnical design-challenge, requiring the rock strength and rock pressure to be measured using core drillings before the final design can be certified. About 92,000 \(20''\) single-photon sensitive photomultipliers will be mounted on the walls of these caverns, providing a 30% photocathode coverage.

The physics performance of the \({\text {ESS}}\nu {\text {SB}}\) research facility has been evaluated considering two baselines corresponding to the positions of two active mines, Zinkgruvan at \(360\,{\text {km}}\) and Garpenberg at \({540}\,{\text {km}}\) from ESS in Lund. The result of the evaluation is that, although the CP violation discovery capability is comparable for the two baselines, the accuracy with which \(\delta _{{\mathrm{CP}}}\) can be measured is higher with the far detector being installed at Zinkgruvan. After 10 years of data-taking with the detector located in Zinkgruvan, leptonic CP violation can be detected with more than 5 standard deviation significance over 70% of the range of values that the CP violation phase angle \(\delta _{{\mathrm{CP}}}\) can take, and \(\delta _{{\mathrm{CP}}}\) can be measured with a standard error less than \(8^{\circ }\) irrespective of the measured value of \(\delta _{{\mathrm{CP}}}\). These results demonstrate the uniquely high physics performance of the proposed \({\text {ESS}}\nu {\text {SB}}\) research facility.

The geological conditions of the ESS site allow for that all installations needed for the operation of \({\text {ESS}}\nu {\text {SB}}\) will be located underground at a depth between 10 and 30 m, thereby eliminating all risk for radiation hazard above ground level. It has also been possible to locate the \({\text {ESS}}\nu {\text {SB}}\) installations in such a way that there will be no interference with the existing ESS installations.

The CDR has resulted in a preliminary estimate of the construction cost of \({\text {ESS}}\nu {\text {SB}}\) which is on the level of \(1.4\,{\text {B}}\)€. For more details concerning the costing, see Ref. [1]. The current estimate does not include the cost of the associated civil engineering work on the ESS site, which has not yet been evaluated in detail. The plan is to achieve, after another period of design work, a Technical Design Report, including a more accurate cost estimate, and to seek the necessary support for approval and financing of the \({\text {ESS}}\nu {\text {SB}}\) construction project. The plan for the following period of build-up and commissioning of the facility is such that \({\text {ESS}}\nu {\text {SB}}\) will be ready for start of data-taking operation around year 2035. The operation of the facility is foreseen to continue for several decades, possibly including intermediate upgrades.

Throughout, the Design Study leading up to the present CDR has had the strong support of the ESS management. The international nature of the \({\text {ESS}}\nu {\text {SB}}\) project is demonstrated by the list of the authors’ institutions of the present CDR, which all have, together with the EU Horizon 2020 Frameworks Programme and the European Cooperation in Science and Technology Programme COST, provided the personnel, technical and financial resources for the 4 years of Design Study.

Significant effort has been spent on different outreach activities with the aim of informing the scientific and general public of the goals and achievement of the \({\text {ESS}}\nu {\text {SB}}\) Design Study. One part of this has been the production of two video films, each ca \(6\,{\text {min}}\) long, one intended for the scientifically literate public and the other for the general public and both of which are available at the \({\text {ESS}}\nu {\text {SB}}\) home page https://essnusb.eu/.

2 Introduction

This report gives an account of the results of a 4 year design study of a European neutrino Super Beam facility \({\text {ESS}}\nu {\text {SB}}\) to be based on the use of the ESS linear accelerator (linac), currently under construction in Lund, Sweden. When this linac will have reached its full design performance, it will be the world’s most powerful accelerator, delivering a proton beam of 5 MW average power. The original purpose of creating such a powerful proton beam is to provide the world’s most brilliant neutron spallation source. The linac will deliver the 5 MW by accelerating ca 1015 protons in each of 14 pulses/s of length 2.86 ms, to 2 GeV energy, implying a duty cycle of just 4%. By accelerating additional 14 pulses, interleaved with these 14 pulses, the duty cycle can be raised to 8% and the extra 5 MW used to produce a neutrino Super Beam of world-unique intensity.

The motivation for proposing the European Spallation Source neutrino Super Beam (\({\text {ESS}}\nu {\text {SB}}\)) as a next-generation long-baseline neutrino experiment and the results of the work made on the design of the main components of the \({\text {ESS}}\nu {\text {SB}}\) facility, which are the ESS linac upgraded to produce a 10 MW and 2.5 GeV proton beam, the pulse accumulator ring, the target station, and the near and far neutrino detectors, are described in the following sections of this report. The general layout of the proposed facility is shown in Fig. 1. The results of the evaluation of the physics performance for leptonic CP violation discovery and, in particular, the precision with which it will be possible to measure the CP violation phase \(\delta_{\text {CP}}\) are also included in this report.

Fig. 1
figure 1

The layout of the \({\text {ESS}}\nu {\text {SB}}\) components on the ESS and the far detector sites

3 The motivation for \({\text {ESS}}\nu {\text {SB}}\) as a next-generation long-baseline neutrino experiment

Charge-Parity (CP) symmetry violation in the quark sector was discovered and measured already in the 1960s. The discovery of neutrino oscillations in the 1990s opened the possibility to seek for CP violation in the leptonic sector. To describe how the initial creation of exactly equal amounts of matter and antimatter in the Big Bang did not subsequently lead to a complete annihilation of all matter and antimatter, which would have resulted in a Universe containing only radiation and no matter, CP violation is required. In our Universe, there is on average about a billion photons for each matter particle, the latter constituting the galaxies, stars, planets, and ourselves, that remain from the matter–antimatter annihilation process. Notwithstanding that the relative amount of matter is very small, its presence can be shown to require that there be a sufficient effect of CP violation for which the effect provided by the CP violation measured in the quark sector and described by the Standard model is very far from enough.

There are several different beyond-the-Standard-Model theories proposed, based on flavour symmetries, which include leptonic CP violation and which each predicts a different value of the CP complex phase-angle \(\delta _{{\mathrm{CP}}}\) from the observed matter density in the Universe. Discovering leptonic CP violation will check the validity of this type of theories and the measured value of \(\delta _{{\mathrm{CP}}}\) will be used to discriminate between them. This currently makes the precise measurement of value of the leptonic \(\delta _{{\mathrm{CP}}}\) one of the most urgent research tasks in elementary particle physics and cosmology.

The Neutrino Factory was first proposed in the 1990s as an accelerator-based infrastructure for producing a neutrino beam of sufficiently high intensity for leptonic CP-violation discovery and measurement. In a Neutrino Factory, a very high-power proton accelerator is used to produce a high-intensity pion flux from which, by the decay of the pions, a high-intensity muon beam is derived. This muon beam is subsequently cooled, accelerated, and led into a racetrack storage ring, where the muons decay and produce a beam composed of equal amounts of \(\nu _\mu\) and \(\nu _{\mathrm{e}}\). Building a Neutrino Factory will be a very challenging task, in particular because of the required cooling and acceleration of the very short-lived muons.

The interest and possibility of discovering and measuring leptonic CP violation in the leptonic sector increased even further in 2012 when the first measurements of the till then unknown value of the \(\theta _{13}\) neutrino mixing angle were published. The measured value of ca \(8.3^\circ\) of \(\theta _{13}\) was nearly an order of magnitude higher than what had earlier been expected from general but, as it turned out, incorrect assumptions. This implied that, instead of using the Neutrino Factory technique, it would be possible to measure the effect of CV violation using a beam of the \(\nu _\mu\) created in the classical way, i.e., from the decays of the pions that are produced from the high energy protons delivered by a high-power accelerator, provided that the power of the accelerator is sufficiently high.

The high value found in 2012 for \(\theta _{13}\) furthermore implied that the sensitivity to CP violation is close to three times higher at the second \(\nu _\mu\)-to-\(\nu _{\mathrm{e}}\) oscillation maximum as compared to the first oscillation maximum. For a low value of \(\theta _{13}\), the sensitivity at first maximum would have been higher than that at the second maximum. Several long baseline experiments with the neutrino detector placed at the first oscillation maximum were already in operation around 2012, likeT2K in Japan with which data taking was started in 2011, and NOvA in the US that started in 2014. The next-generation long-baseline experiments, T2HK in Japan and DUNE in the US, were already in the planning stage at that time and are also designed to collect the large majority of the data at the first oscillation maximum.

A difficulty with measuring at the second oscillation maximum is that the neutrino detector will be located 3 times further away from the neutrino source and that, since the neutrino beam is divergent, the neutrino flux-density therefore will be 9 times smaller at the second maximum as compared to the first. This implies that a very high-power proton driver is required for realising an experiment measuring at the second oscillation maximum and thereby profit from the higher sensitivity to \(\delta _{{\mathrm{CP}}}\) there.

In 2009, it was decided to build the European Spallation Source in Lund, Sweden, with a proton driver producing a 5 MW beam, which was close to an order of magnitude higher power than for any accelerator in the world at that time. The purpose was to use the 5 MW proton beam to produce spallation neutrons. It was, however, soon realised that, with a further comparatively limited investment, it would be possible to raise the power of the ESS accelerator to 10 MW by doubling the number of accelerated pulses per second from 14 to 28 with the purpose of using the additional 14 pulses to generate a world-uniquely intense neutrino beam. The ESS neutrino Super Beam project that is described in the present report is designed to perform high-precision neutrino-oscillation measurements using a 540 Mton water Cherenkov detector and this world-uniquely intense ESS neutrino beam, which will allow the detector to be placed at the second maximum and thus to take advantage of the close to 3 times higher \(\delta _{{\mathrm{CP}}}\) signal there.

4 Proton driver

4.1 Introduction

The \({\text {ESS}}\nu {\text {SB}}\) linac upgrade consists of the modifications of the ESS proton linac needed to be able to produce and accelerate interleaved pulses of \({\text {H}}^-\) for the generation of the proposed neutrino super beam, while the acceleration of protons for the production of spallation neutrons continues uninterrupted. This section presents the upgrade requirements for the linac, its auxiliary systems, as well as design considerations for the linac-to-ring (L2R) transfer line. The schematic in Fig. 2 details each of the portions of the linac which must be reviewed for the present upgrade study. The low-energy beam transport (LEBT) and medium-energy beam transport (MEBT) lines have been modelled and simulated in terms of the necessary modifications for transporting both proton and \({\text {H}}^-\) bunches.

Fig. 2
figure 2

Proton driver layout indicating the different sections and the beam energy at different points along the LINAC. The portions of the LINAC that have been reviewed in this upgrade study are also indicated

Fig. 3
figure 3

Pulse structure alternatives. Option A+ is the baseline design, with minimal powering requirements for the superconducting RF cavities

Table 1 Nominal ESS design parameters versus \({\text {ESS}}\nu {\text {SB}}\) upgrade\(^*\)

A comprehensive study of \({\text {H}}^-\) beam stripping was performed, with simulations of the beam transport and evaluation of the loss magnitude for the baseline beam parameters; this included end-to-end simulations of the upgraded linac and trajectory analysis of ionisation energy deposited from stripped particles (see Sect. 4.10). The upgrade requirements for the superconducting (SC) linac sectors and the linac-to-ring (L2R) transfer line have also been studied both in terms of beam dynamics and stripping.

A detailed study of the modifications needed on the modulators was also performed, showing the possible upgrade paths for the modulators, with an evaluation of the energy efficiency of each option, their cost, and their added footprint on the klystron gallery. This analysis is summarised in Sect. 4.11.

4.2 Pulse structure

Different pulsing schemes of the \({\text {H}}^-\) beam have been considered; see Fig. 3. To accommodate the rise and fall times of the extraction magnet in the accumulator ring, and also owing to space charge and beam instabilities, the full 2.86 ms beam pulses cannot be injected in one filling of the ring. Each beam pulse must instead be split into several sub-pulses or batches. The batch length is limited by the storage time in the accumulator ring—about 1000 turns, corresponding to 1.3 ms—before instabilities are likely to develop [2].

Fig. 4
figure 4

Detailed schematic of the nominal \({\text {ESS}}\nu {\text {SB}}\) pulsing scheme, Option A+ from Fig. 3

A pulsing scheme with an overall 28 Hz macro-pulse structure has been selected as the baseline design, corresponding to Option A+ in Fig. 3. The pulse length in this case is limited by the flat-top length of the present RF modulators (3.35 ms). Since the filling time of the superconducting cavities is about 0.3 ms, and the time to stabilise the radio frequency (RF) regulation is about 0.1 ms, the effective pulse length is limited to about 2.9 ms. If the pulse length from the modulators could be extended, this would decrease the demand of the current. Other pulsing schemes have also been reviewed (Options B and C) where the \({\text {H}}^-\) beam is pulsed at 70 Hz, (4 out of 5 pulses are \({\text {H}}^-\)). Compared with Option A+, these alternatives relax the performance demands on the accumulator ring (in particular, the stripping foil) and the target focusing system, but come with substantial costs due primarily to RF system upgrades and annual electrical running costs.

The total number of particles delivered to the accumulator ring will be \(8.9\times 10^{14}\) per pulse cycle (macro-pulse), divided into four batches of \(2.3\times 10^{14}\), as shown in Fig. 4. Further beam parameters are summarised in Table 1. Each batch is stacked in the accumulator ring, compressing the pulses to \(1.2\,\upmu {\text {s}}\), which are subsequently extracted to the target. By splitting the macro-pulse into four batches, the power on each target is limited to 1.25 MW, and the space charge tune shift [3] in the accumulator ring is limited to an acceptable level [2, 4].

As mentioned above, the disadvantage to a 70 Hz pulsing is a higher total load on the RF system (along with uncertainty on the duty-cycle rating for the nominal ESS superconducting cavity couplers, see Sect. 4.11); this is due to the filling time of the superconducting (SC) cavities of 0.3 ms. Option B, with a pulse length of up to 1.3 ms, has the advantage of allowing for a lower beam current of about 30 mA, relaxing the demands on the ion source requirements and reducing beam stripping losses, particularly intra-beam stripping (IBSt). The impact on the RF modulator systems of the different pulsing options is also discussed in Sect. 4.11, with a detailed analysis available in [5].

4.3 Front-end baseline and overview

The upgrade of the ESS linac for \({\text {ESS}}\nu {\text {SB}}\) requires an additional ion source for delivering \({\text {H}}^-\) ions at the correct energy, and a low energy beam transport (LEBT) to merge this beam and the nominal proton beam into the radiofrequency quadrupole (RFQ) for the first stage of acceleration. Alternatively, the two beams could be merged in the medium-energy beam transport (MEBT), see Fig. 5. This option with separate RFQ units and merging MEBT sections could more straightforward to realise in terms of beam dynamics, since the transport of the two beams is independent.

However, the option with shared RFQ and MEBT would be less expensive and require less downtime for nominal ESS operation. Extensive beam dynamics simulations with this option have shown no prohibitive drawbacks, making it the favoured baseline design. A few key considerations for this design are as follows:

  • The MEBT chopper will need to be redesigned to deflect along both transverse axes due to the opposite charges of the accelerating ion species. Otherwise, the entire linac design is charge-agnostic in terms of transverse dynamics, despite having vertical and horizontal envelope profiles reversed for protons and \({\text {H}}^-\). The chopper will also need to be redesigned to accommodate the fast beam-chopping requirements for creating extraction gaps in the beam.

  • The use of switching magnets (changing sign/magnitude between proton and \({\text {H}}^-\) pulses) is optional, though it may be beneficial in the MEBT for better matching with the drift-tube linac (DTL). Without switching magnets, compromising the matching of both ion species at the MEBT/DTL interface incurs a small overall emittance growth downstream.

  • The RFQ is designed for compatibility with the nominal ESS proton source, and \({\text {H}}^-\) transmission is poorer (especially for the case of injection at 60\(^\circ\), see Fig. 6, right-hand side). This means requiring a substantially greater current from the \({\text {H}}^-\) source. However, as the presently installed RFQ is designed for a maximum 5% duty cycle and the upgraded RF duty cycle would be 10–15%, a redesign of the RFQ would be necessary regardless, and may be more forgiving in terms of H\(^-\) losses. The maximum 5% duty cycle of the present RFQ is imposed by the cooling needed for resistive losses. Thus, the main design issue is allowing for a greater heat load.

Fig. 5
figure 5

Two front-end layouts for a merged proton/\({\text {H}}^-\) beamline. The left-hand layout uses a common LEBT and RFQ, while the right-hand layout merges the two species in the MEBT

Fig. 6
figure 6

Two layouts for merging the proton/\({\text {H}}^-\) sources. The left-hand layout requires moving the current proton source and bending both beams at \(30^\circ\); the right-hand side layout leaves the proton source unchanged and bends the \({\text {H}}^{-}\) beam by \({60}^\circ\)

For this baseline design with beams merged in the LEBT, two layouts have been studied in terms of source position: a symmetric layout (the \({\pm }\,30^\circ\)) and an asymmetric one (\(+\,60^\circ\) layout), as shown in Fig. 6. In other words, merging the sources requires moving the current proton source and bending both beams at \(30^\circ\), or leaving the proton source and bending the \({\text {H}}^{-}\) beam by \(60^\circ\). This second layout is less costly in terms of equipment and may require less downtime for nominal ESS operation, but increases dispersion dramatically (thus reducing RFQ transmission). Space limitations in the tunnel may also be unavoidable and prohibitive for the second layout, especially in terms of structural requirements, personnel access issues, or wiring and grounding. Specifically, the right-hand solution’s \({\text {H}}^-\) source position makes it difficult to pass and that the drop hatch area has to be used for logistics and included in each search of the tunnel. Meanwhile, left-hand solution means that a realignment of the beam is also required for the proton beam by adjusting the steering magnets.

Both layouts have been simulated in terms of losses and RFQ–DTL transmission. At present, the symmetric layout is taken as the baseline and has been used for end-to-end simulations.

As mentioned above, the total RF duty cycle with both proton and \({\text {H}}^-\) beams will be between 10% and 16%. The maximum 5% duty cycle of the present RFQ is imposed by the cooling needed for resistive losses. Thus, for the nominal case of merging the beams into a single redesigned RFQ, the main design issue is allowing for a greater heat load.

For a more in-depth discussion of the options for the LEBT and MEBT design, see Sects. 4.5 and 4.6.

4.4 Ion source design

The requirements of the \({\text {H}}^-\) source are closely related to the pulsing structure of the beam shown in Fig. 3. For the baseline solution (Option A+), which pulses the \({\text {H}}^-\) source at 14 Hz, a long pulse of 3 ms is needed. For the alternative schemes with 70 Hz, a pulse length of around 1 ms is needed.

There will inevitably be losses along the linac and the cumulative radiative activation from power loss along the linac for the proton and \({\text {H}}^-\) beams must not exceed 1 W/m for safe, hands-on maintenance (or 0.1 W/dm, in terms of machine protection limits [6]). In the high-energy sections of the linac, stripping losses due to intrabeam collisions, which has been identified as a major loss mechanism at the Spallation Neutron Source (SNS), are expected to dominate, along with stripping due to Lorentz-shifted electromagnetic forces [7, 8]. Although though these losses are of great concern in terms of activation, they only involve a small fraction of the accelerated beam.

However, losses in the low-energy sectors can involve significant fractions of the beam being lost; with, for example, the residual gas stripping, intrabeam stripping, and other losses in the LEBT and RFQ estimated to comprise about 25% of the initial bunch population exiting the source.

A large fraction of beam losses are expected to occur in the LEBT and the transmission through the RFQ, where the beam is bunched. Simulations show that roughly 10–15% losses are expected in transport through the LEBT and RFQ, depending on ion source emittance. For the \({\text {H}}^-\) beam, there are also losses expected due to stripping, since the extra electron has a binding energy of only 0.75 eV. The stripping loss mechanisms have been summarised in [8], and will be discussed in detail in Sect. 4.10.

Assuming 25% losses in total, for a 60 mA beam to reach the accumulator ring, a 80 mA beam current is needed from the ion source (required for Option A+ in Fig. 3). The limiting factor for the current is the pulse length of the flat-top of the RF modulators being 3.35 ms in the present design. With a superconducting cavity filling time of about 0.3 ms and the time to stabilise the regulation at 0.1 ms, the effective supported pulse duration is about 2.9 ms. For Options B and C, the beam current requirements from the ion source are more relaxed, since the overall beam current requirements are lower.

The beam from the ion source has to match the acceptance of the RFQ, and therefore, the emittance should ideally be less than 0.25 \(\pi\) mm mrad; higher emittance will lead to higher loss and downstream emittance growth. However, since a new RFQ design will needed, and since the 80 mA required current is at the upper end of conventional \({\text {H}}^-\) source design [9, 10], it can be expected that this emittance requirement will relax. Simulations completed for this report using the present RFQ design show that for source emittances of up to \({\sim }\,0.38\) \(\pi\) mm mrad, the required current can be accelerated through the upgraded 2.5 GeV linac, with emittance growth limited to \({<}\,5\%\) of the ideal case.

The pulse-to-pulse variations in beam current, and the flat-top stability, are also important parameters. These must be managed to avoid field and phase variation in the cavities, which would increase losses in the linac. The variations of the beam current are assumed to be acceptable within \(\pm \, 3\%\). The requirements for the \({\text {H}}^-\) ion source are summarised in Table 2.

Table 2 Required \({\text {H}}^-\) source parameters for the \({\text {ESS}}\nu {\text {SB}}\) upgrade

4.4.1 Ion source baseline

A variety of \({\text {H}}^-\) ion sources have been studied to meet the linac requirements and there is expertise at leading facilities with ion sources having similar performance as that needed for \({\text {ESS}}\nu {\text {SB}}\). The strongest limitation here is that the \({\text {ESS}}\nu {\text {SB}}\) ion source will require an output current, emittance, and repetition rate roughly matching the limits of technological performance of those currently in operation. For selection of the \({\text {H}}^-\) ion source, recent reviews of various ion source types can be found in [11,12,13]; further reviews are also available [14,15,16]. Additionally, a workshop on the subject was held in 1994, which focused on surveying possible ion sources for SNS  [17].

At present, the favoured source design is that of SNS at Oak Ridge National Lab in Tennessee, USA. It is an RF-antenna multicusp (i.e., multipole magnet) volume and surface source; this source operates via inductive excitation of the plasma using a porcelain-coated copper antenna. Caesium is added for enhancing the surface ionisation rate [11, 18] and the beam is injected at an angle to improve electron extraction [19].

Recent experience at SNS shows that such an ion source can be operated routinely, delivering 50–60 mA \({\text {H}}^-\) beams into the RFQ at a 6% duty cycle, with availability of \({\sim }\,99.5\)% [18]. Additional labs in the US have adopted this design for its performance and ease of installation [20]; SNS is also now testing the performance of an external-antenna type source (not pictured) with improvements in efficiency (output current vs. input power) and a smoother beam pulse profile.

The lifetime remains limited for these ion sources before their caesium supply must be replenished, despite improvements in the last few years; it is now on the order of 10 weeks. At Japan’s Particle Accelerator Research Complex (J-PARC) in Tokai, Japan, there has recently been a development of a similar source with \({\sim }\,0.25\) \(\pi\) mm mrad emittance and \({\sim }\,65\) mA beam current [21].

The characterisation of multicusp magnets for plasma confinement may also be a worthy avenue of study, with the influence of pole count [22] and the use of virtual cusps [23] strongly affecting plasma characteristics. The use of pulsed, switching multicusp magnets (e.g., from virtual-cusp to non-virtual-cusp modes) may also be worth investigating, with the goal of leveraging the benefits of various modes. Such technology may be more feasible from an engineering standpoint thanks to recent developments with compact switching multipole magnets [24].

In the following section, more details are provided on this favoured ion-source type, along with other available technologies.

4.4.2 Available ion-source technologies

The production of \({\text {H}}^-\) ion beams is more complex than providing proton beams; and an \({\text {H}}^-\) ion, once formed, can easily be stripped to neutral hydrogen atom, \({\text {H}}^0\), since the binding energy (also termed electron affinity) of the outer electron is only 0.75 eV. This can be compared with, for example, the electron-binding energy of neutral hydrogen at 13.6 eV.

There are essentially two types of ion sources in use at accelerator facilities, one is the surface production type—Penning or magnetron sources—where the plasma discharge is generated by an applied DC voltage. The other main type is the RF volume source, where the plasma discharge is driven by an applied electromagnetic field with a high frequency (MHz range).

In a volume source, the production of ions takes place by first creating highly excited ro-vibrational hydrogen molecules, \({\text {H}}^2\)*, by collision with fast electrons. In a second step, a slow electron (\({\sim }\,1\) eV) is attached to the \({\text {H}}^2\)* which dissociates into \({\text {H}}^-\) and \({\text {H}}^0\). In order for this process to be successful, the fast and slow electrons need to be separated. This is done by a magnetic filter field which separates the plasma into two distinct regions: one with fast electrons and one with slow electrons, where the \({\text {H}}^-\) can be produced [11, 25].

In high-current \({\text {H}}^-\) sources, caesium (Cs) is commonly used for increasing the production rate of \({\text {H}}^-\) in the surface process, since Cs has the lowest work function of all elements at 2.1 eV (and by surface adsorption, it can also reduce the work function of other metals). Molybdenum is also commonly used in ion sources, owing to its low sputtering rate, but has a relatively high work function of 4.2 eV.

Moreover, a variety of metals can be coated with a sub-monolayer of Cs, to reduce the work function further than possible with solid Cs; this yields a theoretical optimum coverage of around 0.6 monolayers, having a work function of about 1.5 eV [26]. The low work function is important for an electron to be easily transferred from the cathode surface toward a hydrogen molecule to form an \({\text {H}}^-\) ion. Maintaining an optimal coverage of Cs throughout the discharge is thus very important.

The most promising ion sources to meet the requirements of the future \({\text {ESS}}\nu {\text {SB}}\) ion source have been identified as follows: the Penning ion source (surface) in use at ISIS, Rutherford Appleton Laboratory (RAL), UK; and the RF volume sources in use at SNS and J-PARC. From this point, the text remains focused on these ion sources and the on-going development at RAL and SNS, with a few comments on other source types. Penning ion sources

The ion source in use at ISIS, RAL, is a surface plasma ion source of Penning type, see Fig. 7 [11]. The Penning source was first developed by Dudnikov [13] and has also been used at Los Alamos National Laboratory (LANL) [27]. The Penning ion source can produce high currents, up to 100 mA, provide high-emission current densities > 1 \({\text {A/cm}}^{2}\) and have a fairly low energy spread of \({<}\,1\) eV. In routine operation, the Penning 1X source at ISIS produces 55 mA in 0.25 ms pulses at 50 Hz (1.5% duty cycle).

Studies pursuing longer pulse lengths are ongoing at RAL. With the Penning 1X source, \({\text {H}}^-\) ion pulses of 6 mA at 1 ms and 50 Hz can be reached with a stable flat-top current. However, for longer pulse-lengths at a pulse frequency of 50 Hz, there is a droop in the beam current [28]. To reach a more stable flat-top current for longer pulses, a research program is underway at the Vessel for Extraction and Source Plasma Analyses (VESPA) test stand [29] and at the Front End Test Stand (FETS). One mitigation that is explored is to have a controlled power supply that can counteract the droop by increasing power in the discharge. Additionally, by improving the stability in the beginning of the discharge, more of the pulse can be used in the extracted beam. Today, about 0.3 ms is required for the discharge to stabilise and noise to reduce before beam is extracted.

Another area of study is to scale up the dimensions of the ion source, which is done in a Penning 2X source [30]. The flat-top droop is believed to be related to thermal variations during the discharge, which causes the Cs coverage of the electrode surfaces to deviate from ideal conditions for \({\text {H}}^-\) production (\(\sim 0.6\) monolayers). By scaling the size of the electrode surfaces, and thereby the plasma volume, the thermal variation of the components is reduced, which will increase the pulse stability and the potential ion current [31, 32]. The aim of the Penning 2X source is to deliver a 60 mA beam at 2 ms and 50 Hz (10% duty cycle).

One disadvantage with the Penning source is its relatively short lifetime of about 4 weeks, limited by sputtering of the anode and cathode. The refurbishing process is also tedious, including mounting new parts to high mechanical precision. The sources routinely in use at ISIS are exchanged every 2 weeks as a preventive maintenance.

Using Cs is an effective way of enhancing \({\text {H}}^-\) ion production, and also reduces co-extracted electrons. However, one needs to ensure that Cs is not transported further through the LEBT to reach the RFQ, or other accelerating structures, where it may cause unwanted electron emission. In the Penning 1X type source, this is done by a cold trap, operated at roughly \(-5\,{^{\circ }}\)C, along with a 90\({^{\circ }}\) bending magnet placed directly after the ion source. In the Penning 2X type source, initial focusing is provided by an Einzel lens, and the Cs is trapped by a carbon gettering system [33, 34]. The extraction voltage used is 18 kV, which is lower than the requirements for the \({\text {ESS}}\nu {\text {SB}}\) ion source. However, the energy can be increased with a post-acceleration gap, which is used at FETS to accelerate the beam to 65 keV [28]. The performance of the Penning ion source comes close to meeting the requirements of the \({\text {ESS}}\nu {\text {SB}}\) ion source (see Table 3). With the development program taking place at RAL, the Penning ion source could potentially reach the long pulse requirements of 3 ms at 14 Hz and 80 mA.

Fig. 7
figure 7

Schematic cross section of a Penning ion source, from [11] RF volume and surface \({\text {H}}^-\) sources

The SNS ion source has an internal RF porcelain-coated copper antenna for inductive excitation of the plasma, and permanent cusp magnets surrounding the plasma chamber to create a magnetic field which confines the plasma, see Fig. 8 [19]. The SNS ion source is based on a design from Lawrence Berkley National Laboratory LBNL [35], with a filter magnetic field separating the fast- and slow-electron regions. This ion source is of volume type; however, it has an additional Cs collar near the outlet, which enhances the ionization rate. This source therefore combines the phenomena of volume and surface ion production. The plasma is excited using 55–65 kW of 2 mHz RF, and the plasma is sustained using a low power 13.56 mHz RF at 200 W. In this way, the plasma is quickly ignited when the high power RF is turned on.

The SNS ion source is operated routinely with 50–60 mA \({\text {H}}^-\) beams directed into the RFQ at a 6% duty cycle (1 mA, 50 Hz). Caesium is added using caesium-chromate cartridges at the outlet collar; the Cs release is adjusted by controlling the temperature. The amount of Cs used is in the order of 10 mg, for one operation cycle, without the need for continuous Cs injection [36]. An updated design places the RF antenna external to the plasma chamber (not pictured); although this technology is much less mature than the internal-antenna design, early results show improvements in efficiency [37].

The LEBT used at SNS is a short electrostatic type, of about 12 cm, without any diagnostic capability (on the test stand, sources are fitted to a false RFQ aperture, beam-current toroid, and Faraday cup for RFQ input-current estimates). The extraction voltage is 65 kV and could potentially be increased to 75 kV to meet the requirements of the \({\text {ESS}}\nu {\text {SB}}\) ion source [38]. Recently, the development of a magnetic LEBT has been studied, which would allow for diagnostics and prevent problems with electric discharges [39].

Fig. 8
figure 8

General schematic of an internal RF negative-ion source (left) and a cross section of the SNS RF ion source (right), both from [11]

At SNS, there has been success in addressing issues limiting the source lifetime and availability. Problems with the insulation of the porcelain-coated antenna were solved by improving the coating procedure and careful selection of the antennas. More recent improvements include increasing the electron dump efficiency and minimizing electrical discharge problems in the electrostatic LEBT. These developments have led to a high power, high duty-cycle RF \({\text {H}}^-\) ion source with a long lifetimes of up to 14 weeks, and availabilities of \({\sim }\,99.5\)% [18, 36].

The performance of the SNS ion source is summarised in Table 3. Its regular operation is with 1 ms pulse length and 60 Hz. It should also be possible to extend the pulse length to 3 ms at 14 Hz to reach \({\text {ESS}}\nu {\text {SB}}\) requirements [38]. Assuming tests with longer pulses prove successful, the SNS RF ion source will stand as the most feasible alternative for the \({\text {ESS}}\nu {\text {SB}}\) ion source. At J-PARC, there has recently been a development of a similar source, with reports of 66 mA ion beam currents [21].

Table 3 Summary of parameters for the RAL penning source and the SNS RF source [11, 38, 40] Other ion sources

A few other available sources are mentioned here, with some commentary on their performance:

The magnetron surface-plasma ion sources used at Fermi National Laboratory (FNAL) [41] and Brookhaven National Laboratory (BNL) [42] are similar to the Penning source, but use a different geometry. Such ion sources can produce high currents, on the order of 100 mA, with a long lifetime of > 9 months but have a higher noise level, about 10%, and higher energy spread than Penning sources; and have typically been used at relatively low beam duty cycle of about 0.5% [11]. However, recent improvements to the BNL source and its LEBT transport line have resulted in a 120–130 mA current at a 7 Hz repetition rate and 600–1000 \(\upmu {\text {s}}\) pulse length, with an 80 mA beam transmitted through the RFQ [43].

In addition to SNS, RF sources using external antennas have been used at the Deutsches Elektronen-Synchrotron (DESY), reaching 80 mA at a duty cycle of 0.8% [14] and the ion source for Linac 4 at the European Council for Nuclear Research (CERN) is of a similar design, producing 45 mA at a low duty cycle of 0.04% [11].

There is also a development at RAL of a Cs-free RF source. This ion source will have a 30 mA current at a 5% duty cycle. This source is designed to meet the demands of the regular user beam at ISIS, which will be sufficient if the transmission is increased by introducing an MEBT into the linac [44]. Summary

Studies have been performed by the authors of this report on the Penning source at RAL and the RF source at SNS closer, since these were identified as being the most promising ion sources to meet the requirements for \({\text {ESS}}\nu {\text {SB}}\). For the pulsing Option A+, with long pulses of 3 ms, the closest to match is the Penning source at RAL. However, this source type is quite service-demanding and requires relatively high amount of Cs. The RF source at SNS has a higher lifetime and uses less Cs. For both ion sources, it remains to be seen whether they can deliver long pulses which can maintain a stable flat-top current of roughly 80 mA over 3 ms at 14 Hz.

For the pulsing Options B and C, with 50–80 mA, \(\sim\)1 ms at 70 Hz, both types of source are feasible. The RF source seems the most promising from the lifetime point of view, and the requirements are nearly met by the state-of-the-art ion sources at SNS and J-PARC.

There are ongoing discussions between \({\text {ESS}}\nu {\text {SB}}\) and both RAL and SNS, to follow their developments and determine if there are any areas of research needing attention to meet the upgrade requirements for \({\text {ESS}}\nu {\text {SB}}\) (since neither of these sources do so as of today). However, steady improvements in performance of the ion sources lead to the expectation that they will meet the requirements within the schedule of the \({\text {ESS}}\nu {\text {SB}}\) project. Moreover, it is worth recalling from the introductory remarks to this section that preliminary simulations with a relaxed emittance limit from the source of 0.38 \(\pi\) mm mrad showed acceptable transmission through the RFQ as well as through the DTL, with total emittance growth at the end of the linac less than 10% versus the nominal 0.25 \(\pi\) mm mrad source emittance.

4.5 Low-energy beam transport (LEBT) design

In studies of the front end, the primary focus has been on finding solutions where a common LEBT, RFQ, and MEBT are used for the proton and \({\text {H}}^-\) beams, as in the left panel in Fig. 5. The alternative, which uses separate front ends, would be more straightforward, but more expensive.

One challenge with the LEBT is that the beam is highly space-charge dominated; this implies the beam tends to “blow up” spatially, has increased emittance, and that the beam transport generally should be kept as short as possible. Space-charge compensation is therefore critical; this involves an injected inert gas or mixture of gases [45]. The process for the space charge compensation is different for protons and \({\text {H}}^-\). For protons, space-charge compensation is largely imparted by electrons, while for \({\text {H}}^-\), it is induced by positively charged ions, which are heavier and alter the underlying dynamics. With an excessive gas pressure, there is also a risk of introducing stripping losses with the \({\text {H}}^-\) ions (see Sect. 4.10), although the required gas concentration is likely to be at least an order of magnitude below the point of problematic stripping, it can cause a non-negligible portion of total losses, and should be simulated carefully in the design stages [45,46,47].

As discussed above, there are two options for how to integrate the ion source with the LEBT, with one option keeping the proton ion source and the beam aligned, and installing the \({\text {H}}^-\) ion source at an angle of 60\({^{\circ }}\), Fig. 6 (left) or with both ion sources displaced by an angle of \({\pm }30^{\circ }\), Fig. 6 (right). It should be noted that the first option requires a switching dipole to be introduced; the second option can use a fixed-field dipole magnet, since the proton and \({\text {H}}^-\) beams have different charge.

Moreover, when merging the beam in the LEBT and using the same RFQ, the energy of the different species should be equal. The platform of the proton ion source is + 75 kV, and so the platform voltage of the \({\text {H}}^-\) source will be − 75 kV relative to ground. The ion sources must therefore lie on two different platforms, with a grounded cage between for shielding. The shortest distance in air at the present proton ion source is about 185 mm, without any discharge problems, so both options in Fig. 6 seem feasible from a high-voltage perspective.

There are physical limitations in the linac tunnel and how accelerator equipment can be added in different directions. From a building design perspective, it is easier to add components in the area to the left of the beam line (eastward, facing the direction of the beam). In the front-end building, the wall to the right in the tunnel is solid and several components are installed in the intervening space, which makes it easier to install equipment on the left-hand side. This makes the 60\({^{\circ }}\) option easier to accommodate.

4.5.1 Simulations of beam transport

Simulations of the beam transport through the LEBT and RFQ have been carried out utilising the TraceWin software [48]. This effort began with 60\({^{\circ }}\) layout, since in this case, the proton beam line would be more or less unchanged. The bending magnet has a bending radius of 0.4 m and edge angles of 20.5\({^{\circ }}\), which balances the focusing effects in horizontal and vertical directions. The first solenoid is kept as close as possible to the ion source.

The dipole bend introduces dispersion, and in principle, the bend could be made achromatic. However, this would require a longer beam line with greater decoherence from space charge forces; this has therefore been avoided. The dispersion introduced is relatively small, about 0.5 m. and considering the limited momentum spread of the beam, in the order of 0.1% determined mostly by the ripple of the power supply for the extraction voltage, this dispersion will not affect the beam significantly.

Simulations with the 60\({^{\circ }}\) layout, assuming a beam from the ion source of emittance 0.14 \(\pi\) mm mrad, and assuming a space charge compensation of 95%, give a transmission of about 93% from the ion source to the end of the RFQ. However, simulations with emittance from the ion source of 0.2 \(\pi\) mm mrad and assuming 85% space charge give a transmission of only 60% from the ion source to the end of the RFQ. This is because the beam envelopes in this case become large and particles at large amplitudes are affected by non-linear fields in the solenoids and fringe fields of the dipole. This result indicates that the beam transport in a LEBT with a 60\({^{\circ }}\) bend is sensitive to both space charge and initial beam distribution from the ion source.

Simulations with a 30\({^{\circ }}\) magnet show that the beam transport becomes much less sensitive to input emittance and space charge compensation (since the envelopes are smaller) and is not influenced by aberration and fringe fields to the same degree. Simulations with a distribution of 0.2 \(\pi\) mm mrad and space charge compensation of 95% show a transmission of about 95%. Using the same input emittance, but space charge compensation of 85%, also gives a transmission of about 95%. A distribution of 0.25 \(\pi\) mm mrad, which is the nominal requirement for the ion source, and space charge compensation of 85%, which is a reasonable assumption for the LEBT [40] gives a transmission of 84%. The beam distribution after the RFQ for this case is shown in Fig. 9, tracking 200 k macroparticles. The output emittance from the RFQ is about 0.25 \(\pi\) mm mrad. A beam density plot in the LEBT is shown in Fig. 10 for this case.

As mentioned in Sect. 4.4.2, further simulations at an upper limit emittance of 0.38 \(\pi\) mm mrad were also carried out for the 30\({^{\circ }}\) case assuming a source capable of delivering \({\sim }\,85\) mA. Here, the transmission through the RFQ is limited to \({\sim }\,70\%\), but the beam is delivered to the end of the linac with a modest emittance growth of \({<}\,10\%\) versus the nominal case.

These simulations demonstrate that the case with a source placement of \({\pm }\,30{^{\circ }}\) is much less sensitive to the initial ion source distribution and the degree of space charge compensation than the 60\({^{\circ }}\) design. However, the impact on ESS operations due to installation is also a significant factor; this is covered in depth in Sect. 4.13. Although both options have serious merits and drawbacks, considering all these aspects discussed here and those discussed in Sect. 4.3, the present baseline is the 30\({^{\circ }}\) option.

4.6 Medium-energy beam transport (MEBT) design

The function of the MEBT is to match the RFQ output beam to the DTL; to characterise the beam with different diagnostics; to clean the head of pulse using a fast chopper (2.86 ms long for the proton beam); and to clean the transverse halo using scrapers, see Fig. 10. The chopper is also part of the machine protection system, which shuts down the linac on detection of any serious faults. Details of the ESS MEBT design and matching can be found in [49, 50].

For the \({\text {H}}^-\) beam, the MEBT will also be used to chop the beam to create extraction gaps for the accumulator ring. The beam envelopes from the RFQ are similar for the proton and \({\text {H}}^-\) beams, but since the DTL has permanent quadrupole magnets, the orientations of the beam envelopes are opposite for \({\text {H}}^-\) and proton beams, see Fig. 9.

Fig. 9
figure 9

Beam envelopes for different ion species at different stages in the linac

Fig. 10
figure 10

Schematic MEBT drawing with different functions indicated

As a starting point for the MEBT design, the proton MEBT is used (see Fig. 10). The ESS MEBT contains 11 quadrupoles for transverse focusing and 3 buncher cavities for longitudinal focusing, opposing the space charge forces in the beam. Figure 11 shows the beam envelopes and expected emittance development taken from simulations.

The MEBT must be redesigned to meet the requirements of the \({\text {H}}^-\) beam. The chopper for the standard ESS MEBT is designed to remove the head and tail of the 2.86 ms pulse. It consists of electrostatic plates, and a dump in one plane, with a quadrupole that is used to deflect the beam. This does not work, however, for a beam with the opposite charge (without switching the polarity of the quadrupole). Alternative methods for chopping will be discussed shortly.

Fig. 11
figure 11

Standard proton MEBT, simulations of envelopes (top) and emittance growth for both the MEBT and first DTL tank (bottom), from [50]

The first elements in the MEBT are used to form a beam which is circular at the chopper, both for the proton and \({\text {H}}^-\) beams. The focusing elements after the dump will be used to match the beam to the DTL. Some elements may have to be pulsed between the proton and \({\text {H}}^-\) beams, 28 Hz in the baseline design, but it is desirable to find an MEBT design that switches as few elements as possible. Simulations performed in TraceWin show an emittance growth of \({\,3\%}\) for the case having no switching magnets versus having both beams matched to optimal Twiss parameters at the MEBT-to-DTL interface via switching. The exact design of the quadrupoles will need to be studied further, especially the choice of iron or ferrite-based design.

The critical design criteria for the MEBT are summarised here:

  • Use as few switching magnets and/or focusing elements as possible; these switch the value between p and \({\text {H}}^-\).

  • The longitudinal phase spread should be limited to less than \({\pm }\,25{^{\circ }}\) (rms) to avoid non-linear fields in the buncher cavities, which would lead to halo and/or emittance growth longitudinally.

  • In case one or more cavities fail in the superconducting (SC) section of the linac, parts of the SC linac need to be returned to the order of 10 MeV. This means that no dispersion can be allowed downstream of the MEBT, and that an achromatic solution should be sought as a translation stage.

  • For the option of merging beams in the MEBT, the new RFQ and ion source need to be displaced from the proton RFQ by about 3 m to allow access, and space for installations. It also requires further investigation on whether it is feasible to install a second \({\text {H}}^-\) front end, considering the required waveguides and other auxiliary equipment.

4.6.1 Option for a separate \({\text {H}}^-\) MEBT with a 45\({^{\circ }}\) translation stage

In an alternative design for the \({\text {H}}^-\) MEBT, the standard MEBT design was used, and then split after the diagnostics unit and before the last four quadrupoles, where the translation stage with two 45\({^{\circ }}\) magnets is introduced, see Figs. 12 and 13. The translation section includes three buncher cavities to focus the bunch longitudinally. The quadrupoles and the buncher cavities are matched to create an achromatic section, so that the dispersion and its gradient remains zero at the MEBT exit. As mentioned above, the new RFQ and ion source must be displaced from the proton RFQ by about 3 m to allow access and space for installations; the length of the 45\({^{\circ }}\) translation stage thus becomes 4.2 m.

The proton and \({\text {H}}^-\) beams merge at a second dipole magnet. Thus, for optimal beam conditions, the last four quads and the last buncher cavity need to act in a switching mode, since they require different settings for each of the two beams to provide matching to the DTL. In the DTL, permanent quadrupoles are used for focusing, so no switching can be done between the two beams.

The first section of the MEBT is essentially identical to the nominal proton MEBT, and includes the beam chopper and diagnostics. The chopper cavity is rotated 90\({^{\circ }}\) compared to the proton one, to deflect the beam in x instead of y, and the fifth quadrupole from the MEBT entrance acts as a kick-magnifying element. The quadrupoles in the first section have approximately the same values those in the nominal MEBT.

Table 4 lists the major drawbacks and benefits of this scheme. One additional advantage with merging the beams in the MEBT is that the proton MEBT can be kept more or less intact except for the last section of the MEBT, consisting of four quads and one buncher cavity.

However, the space restrictions, emittance growth, and other listed drawbacks have left this option as a backup, with the design of merging further upstream into a common RFQ being favoured as a baseline, as discussed in Sects. 4.3 and 4.5. Further details on this study can found in [51].

Fig. 12
figure 12

Detailed schematic for the 45\({^{\circ }}\) merge-in-MEBT option

Fig. 13
figure 13

MEBT lattice including the translation stage, indicating the quadrupoles and buncher cavities

Table 4 Pros and cons of merging the beams in the MEBT

4.6.2 Matching the MEBT to the DTL

Tracking calculations were performed in TraceWin, which does multi-particle tracking with the PICNIC 3D space-charge routine. The beam was tracked in the MEBT and DTL with the input beam distribution provided by tracking an \({\text {H}}^-\) beam through the LEBT and RFQ.

A precision matching of the MEBT was performed using the four final quadrupoles, along with its second and fifth buncher cavities, using multi-particle tracking, to a precision of 2.4e-4 by TraceWin’s optimisation routine. Some oscillations (beat) in the emittances in the DTL can be seen due to imperfect matching; this can probably be improved with further refinement.

Fig. 14
figure 14

Emittance in the MEBT and the first DTL tank for a nominal \({\text {H}}^-\) beam

It is worth noting in Fig. 14 that there is a noticeable emittance growth. This can be compared to the standard proton MEBT where the emittance growth is about 10% transverse, see Fig. 11. The emittance growth is, to a large extent, taking place in the dipoles, where there is a coupling between x, z and dp/p. In an achromat with two dipoles, this emittance growth will cancel after the second dipole, but this does not take place in this lattice which has a \(3\pi\) phase advance. This issue is discussed further below.

Additional matching studies were performed using the technique described in [49], with a modified solver to accommodate the interleaved pulses of \({\text {H}}^-\) and protons without the use of switching magnets. This results in a modest emittance growth versus the single-species simulations, reaching the end of the linac at roughly 3–10% above the nominal case for both \({\text {H}}^-\) and protons (depending on emittance and current parameters of the ion source). Further optimisation of the matching should be performed to finalise the MEBT chopper design.

4.6.3 Chopping

The chopper in the standard proton MEBT is used for removing the head and tail of the macropulse of 2.86 ms. For the \({\text {H}}^-\) beam, the chopper will also be used to create extraction gaps for the accumulator ring [52].

This means chopping off about \(0.13\,\upmu {\text {s}}\) every \(1.35\,\upmu {\text {s}}\), or 670 kHz, about 2000 times for every macropulse of 3 ms. This is a considerably higher frequency than the standard chopper. It also means that about 10% of the \({\text {H}}^-\) beam will be dumped in the chopper beam dump. With a beam current of 62 mA, this corresponds to a power of 22 kW at 3.62 meV, and with a beam duty cycle of 5%, an average power of 1.1 kW. The chopper and chopper dump will thus have to be redesigned to meet these requirements.

Assuming the same design of the RFQ as for the standard proton MEBT, envelopes are exchanged in x and y between proton and \({\text {H}}^-\) if using the same gradient strengths for the quadrupoles. The chopper must be designed to deflect the beam in x, with the fourth quadrupole used to amplify the kick in x. (For protons, the chopper cavity deflects in the y direction.) The chopping is efficient with a full voltage applied of \({\pm }\,2.5\) kV (the total voltage difference is 5 kV), see Fig. 15.

Fig. 15
figure 15

Chopper at full deflection; \({\text {H}}^-\) beam deflected to the intended beam dump

One of the challenges with 5 kV chopper is to achieve a rise time as fast as the bunch spacing (2.84 ns). The present requirements for the chopper are 4 kV and 10 ns for the ESS MEBT. There will thus be partially chopped bunches that are deflected, but do not feel the full chopper voltage, and thus will be lost in the MEBT or the DTL. For the standard MEBT, such losses are on an acceptable level [49]; but these losses will be roughly 2000 times greater for the \({\text {H}}^-\) case. For the merge-in-MEBT option, these lost particles can probably be handled within the MEBT and not reach higher energies, since the translation stage is situated after the chopper. However, for the baseline option of merging in the front end, this may be more difficult and should be studied further.

4.7 Superconducting linac

The medium-to-high-beta acceleration process is also being studied with the TraceWin program. It is of primary interest that the beam exiting the linac is matched to the accumulator ring to have efficient injection and to avoid losses. The simulations presented in the above sections focused on the first part of the accelerator, from the ion source to the DTL. Simulations of the beam acceleration and transport from the entrance of the DTL to the injection point to the accumulator ring—with and without errors—were performed as well for the \({\text {H}}^-\) beam. The summary of the losses from the machine errors and different \({\text {H}}^-\) stripping sources are reported in [53], with results of a supplementary study also available in [47]; this issue is also discussed in detail in Sect. 4.10.

From the DTL onwards, the settings of the quadrupoles can be identical for the \({\text {H}}^-\) and proton beams, although the trajectory correction for the two species will most likely need to be different. This requires that the steerer magnets operate in pulsed mode, which will mean modifying their corresponding power converters.

The RF power needed for the combined \({\text {ESS}}\nu {\text {SB}}\) and ESS beams is nearly double the current design (although there most subsystems, as well as overall grid power requirements have significant percentages of overhead reserved for contingency and upgrade). This issue has been studied in detail and is reported in [5] and [54]. Such modifications to the RF system were evaluated for different pulsing schemes of the linac; these are discussed further in Sect. 4.11.

In the superconducting cavities, it is a concern that the RF couplers feeding from the waveguides may experience electrical breakdown due to the increased duty cycle. Based on conditioning data, these couplers are rated to handle the required 10% duty cycle for accelerating both the proton and \({\text {H}}^-\) beams. Thus, the risk of their needing to be retrofitted or replaced is considered very low. However, since the scenario of their needing replacement presents a significant disruption risk to ESS operations, a detailed replacement plan is presented in Sect. 4.13.

4.8 Linac-to-ring (L2R) transfer line

The L2R transfer line has been designed to transport the fully accelerated 2.5 GeV \({\text {H}}^-\) beam from the upgraded high-\(\beta\) line (HBL) at the end of the linac to the accumulator ring (AR) [55]. The L2R line bends the beam both horizontally away from the linac and vertically down towards the underground AR as shown in the L2R tunnel engineering drawing in Fig. 16. The beam is horizontal both entering and leaving the L2R line, but at a height difference of 7.864 m.

The transfer line lattice is based on a quadrupole-doublet cell structure, taken from the ESS high-energy beam transport (HEBT) line design. The cell length is 8.52 m long, each quadrupole is 0.35 m long, and the separation of the mid-points of the quadrupoles in each doublet is 1.08 m. The remaining part of a cell constitutes a drift space which is 7.09 m long. It is in these long drifts where the dipole magnets are placed for the transfer line.

In designing the lattice, it is important to stay below the ESS beam-loss limit of 1 W/m [56] which restricts the radioactive activation of the accelerator elements. To this end, the dipole strengths are set to 0.15 T, which limits \({\text {H}}^-\) losses from Lorentz stripping (see Sect. 4.10) to a fractional loss of \(5.7 \times 10^{-8}/{\text {m}}\) [57], corresponding to a stripping loss in the dipole magnets of 0.3 W/m for a 5 MW beam. The 0.15 T field corresponds to a dipole bending radius of 73.5 m, which is used for all horizontal and vertical dipole magnets in the transfer line. All dipole magnets in the L2R line have been taken to be sector dipoles.

Following the tunnel engineering design [58] in Fig. 16, the beam is bent horizontally by \(\theta = 68.75^\circ\), starting from the ESS linac tunnel (point A). For the L2R lattice design, the horizontal bending is performed over 16 lattice cells each of 8.52 m. Each cell therefore bends the beam horizontally by \(4.3^\circ\), and this can be achieved using a single 0.15 T horizontally bending dipole of length 5.512 m per lattice cell.

Fig. 16
figure 16

Layout of the L2R transfer line [58]. Sections are colour-coded according to the presence of horizontal and/or vertical bending

Regarding the vertical bending, the tunnel engineering design calls for a maximum vertical tunnel incline of \(3.38^\circ\). The tunnel incline is progressively increased in section B–C in Fig. 16, from horizontal to \(3.38^\circ\) [58]. After the section of maximum incline (section C–E), the tunnel incline is progressively decreased (section E–F) to return to fully horizontal upon reaching the AR (section F–G). Injection into the AR occurs at, or immediately after, point G in Fig. 16.

Such a design can be achieved by assigning 8 lattice cells in section B–C and 4 lattice cells in section E–F, with an incline change of \(0.42^\circ\) per cell and \(0.84^\circ\) per cell, respectively. This calls for single 0.15 T vertically bending dipole magnets per cell of length 0.542 m and 1.084 m, respectively. It is noted that the longer magnets are not problematic in section E–F as these magnets do not need to share the drift space with horizontally bending magnets.

The dipole and quadrupole distributions within the different 8.52 m lattice cells are shown in Fig. 17. In the section with both horizontal and vertical bending (section B–C in Fig. 16), both the horizontally and vertically bending magnets are distributed to maintain an equal separation of 0.345 m between adjacent dipoles—and between the dipoles and adjacent quadrupoles. In this way, the magnet separations are maximised to minimise cross-talk between magnetic field edge effects.

In the sections with horizontal bending only (sections A–B and C–D in Fig. 16), the location of the horizontally bending dipole magnet is preserved within the lattice cell (see Fig. 17b); this ensures that the beam optics in the horizontal plane is identical throughout sections A–D. For section E–F with vertical bending only, given the freedom of the vertical dipole magnet location, it is placed in the centre of the long drift between quadrupoles, as shown in Fig. 17c.

Fig. 17
figure 17

Quadrupole (Q), horizontally bending dipole (H) and vertically bending dipole (V) distributions within 8.52 m lattice cells for (a)–(c) sections listed in the legend of Fig. 16

Using 16 horizontally bending, 8 vertically down-bending and 4 vertically up-bending dipole magnets, an AR depth of 7.864 m can be achieved. The assignment of the 32 lattice cells is shown in Table 5, and the locations at which the sections of horizontal and vertical bending start and endFootnote 1 are shown in Table 6.

Table 5 Assignment of lattice cells according to the presence of horizontal and/or vertical bending; the colour key follows the legend in Fig. 16
Table 6 Section start and end locations, as defined in Fig. 16, for the proposed lattice, measured from the start of the L2R line

4.8.1 Beam dynamics

Beam dynamics simulations have been performed in TraceWin from the start of the DTL to the end of the L2R transfer line [59]. The L2R quadrupole strengths are optimised to make the L2R line achromatic (that is, with no output horizontal and vertical dispersion) and to limit intra-beam stripping by avoiding beam sizes that are too small (see also Sect. 4.10). A matched beam is also ensured between accelerator sectors by matching the Twiss parameters sector-to-sector.

The optimised choice of phase advance is shown in Fig. 18. The phase advance up to and including the HBL matches closely that used for protons, to allow concurrent operation of protons and \({\text {H}}^-\) ions. There is no step in the transverse phase advance on entering the L2R line to ensure efficient matching; beam matching is performed in TraceWin using the last 2 cells in the HBL section and the phase advance adjustment is minimal, as shown in Fig. 18.

Fig. 18
figure 18

Transverse x (red) and y (blue) phase advance per cell along the linac and L2R line. Positions are given relative to the start of the DTL. The lattice sections are indicated along the top of the plot

To make the L2R line achromatic, the total phase advance is set to a multiple of \(180^{\circ }\) [60]. A relatively low transverse phase advance of \(22.5^{\circ }/{\text {cell}}\) is used at the beginning of the L2R line, providing relatively weak transverse beam focusing [61] and a large transverse beam size of up to \(\pm \, 4\) mm (root mean square) in the dispersive section. Critically, this large beam size limits the intra-beam stripping losses [62] to under 0.4 W/m, at or below the level observed in the linac (Fig. 19).

The magnitude of intra-beam stripping losses decreases along the L2R line as the longitudinal bunch length increases in the absence of accelerating cavities for longitudinal focusing. Therefore, one can take the opportunity to ramp up the phase advance from \(22.5^{\circ }/{\text {cell}}\) to \(45^{\circ }/{\text {cell}}\) (Fig. 18), increasing the transverse focusing and reducing the transverse beam size to below \(\pm 2\) mm (root mean square). This is beneficial in that the number of cells with vertically up-bending dipole magnets (section E–F in Fig. 16) can be reduced from 8 to 4; thus reducing the number of magnets required for the project, while maintaining the \(180^{\circ }\) requirement for keeping the line achromatic.

Fig. 19
figure 19

Intra-beam stripping power loss along the linac and L2R line. Positions are given relative to the start of the DTL. The lattice sections are indicated along the top of the plot

In the absence of accelerating cavities in the L2R line, the energy spread grows due to space-charge forces. Figure 20 shows how the energy spread increases from \(\pm \, 0.4\) meV to \(\pm \, 2.3\) meV (1 sigma) along the L2R line. Introducing accelerating cavities towards the end of the L2R line, operated at the zero-crossing (i.e., at an RF phase of \(-\,90^\circ\) from the RF peak), allows bunches to be rotated in the longitudinal phase space to significantly reduce the outgoing energy spread. Figure 20 shows how using four such pi-mode structures (PIMS) with 4 MV/m [63] towards the end of the L2R line brings the energy spread down from \(\pm \, 2.3\) meV to \(\pm \, 0.6\) meV.

Fig. 20
figure 20

Energy spread (1 \(\sigma\)) along the linac and L2R line, with four cavities operated at the zero-crossing near the end of the L2R line. Positions are given relative to the start of the DTL. The lattice sections are indicated along the top of the plot

4.8.2 Energy collimation

Given the strong horizontal dispersion in the L2R line, its energy acceptance is \(\pm 20\) meV. When the energy error exceeds this limit, the beam is lost in the beam pipe, whose aperture is \(\pm 50\) mm. Therefore, beam energy collimation is necessary for the protection of beam line equipment.

For the results presented here, a multiparticle beam was tracked through an error-free lattice from the start of the DTL to the end of HBL line. This provided the Twiss parameters at the input to the L2R line. To test the energy acceptance of the L2R line, the longitudinal emittance was blown up from 0.446 \(\pi\) mm mrad to 1000 \(\pi\) mm mrad, and a beam distribution with a random longitudinal phase-plane ellipse was adopted in TraceWin.

The most effective beam-energy collimation locations were found to fall after the second and third horizontal dipole magnets in the L2R line, at 16.4 m and 24.9 m from the start of the L2R line, respectively. Given the strong correlation of particle offset on energy in the dispersive section of the L2R line, the phase advance between the collimators was found to be non-critical for the collimation efficiency. To distribute the energy deposition further, each collimator can be split into a triplet of closely spaced collimators. For example, three successive collimators with apertures of \(\pm \, 12\), \(\pm \, 10\) and \(\pm \, 8\) mm after the second dipole magnet have been tested; along with a further three successive collimators with apertures of \(\pm \, 13\), \(\pm \, 10.5\) and \(\pm \, 8\) mm located 24.9 m downstream from the third dipole magnet. The collimators within each triplet are separated by 250 mm.

The results are shown in Fig. 21. The energy collimation keeps the full energy spread within the allowed \(\pm \, 20\) meV (Fig. 21a), therefore maintaining the beam within the \(\pm \, 50\) mm beam pipe aperture (Fig. 21b). Figure 21c shows how the energy deposition is shared amongst the collimators for this particular incoming energy distribution.

Fig. 21
figure 21

a Energy and b transverse x particle densities, and c integrated particle losses, for the L2R line with triplets of x-collimators after both the second and the third L2R dipoles

The simulation does not include collimation for incoming–transverse position or angle errors. An additional collimation system to address these incoming transverse errors would most likely call for pairs of collimators separated by a phase advance of \(90^\circ\) for both position and angle collimation [64].

4.9 Proton driver beam dynamics summary

Simulations of the \({\text {H}}^-\) beam have been completed along the entirety of the linac both to the line-of-sight beam dump (not illustrated) and through the L2R transfer line (Fig. 22).

Fig. 22
figure 22

Average transverse beam sizes (left) and emittances (right) for the \({\text {H}}^-\) beam through the length of the linac and L2R transfer line

This set of simulations was completed in TraceWin. Here, it is worth noting that normalized emittance levels throughout the linac are comparable with the nominal ESS proton linac at an average of \(\epsilon {\sim }\,0.35\,\pi \,{\text {mm mrad}}\). These simulations demonstrate that beam transport is viable without the use of switching magnets throughout the linac. The blow-up seen for both size and emittance in the transfer line (beyond the 400-m point) is intentional: this reduces intra-beam stripping (see Sects. 4.10 and 4.8). The results here are strongly dependent on the \({\text {H}}^-\) source meeting design current and emittance requirements (roughly 80 mA and 0.25 \(\pi\) mm mrad, respectively). The optics for this beam line were optimised for both protons and \({\text {H}}^-\), such that an each species shared an emittance growth beyond nominal of approximately 2–5% from the MEBT to the end of the linac.

4.10 Beam losses

4.10.1 Introduction

The use of \({\text {H}}^-\) is essential in the design of the accumulator ring, where charge-exchange injection strips both electrons and puts them in orbit adiabatically with already-inserted protons—a process which effectively circumvents Liouville’s theorem by allowing the beam’s phase-space density to be increased. However, at any point between the ion source and injection point, \({\text {H}}^-\) can be easily stripped of its outer electron a owing to the electron’s low-binding energy (0.75 eV [65]). This makes \({\text {H}}^-\) a particularly difficult species in terms of beamline transport.

Stripping leads to the production of electrons, which have negligible energy; and neutral \({\text {H}}^0\) atoms. Because of the low energy of the stripped electron, the \({\text {H}}^0\) carries nearly all the energy of the original \({\text {H}}^-\). Because it is uncharged, the \({\text {H}}^0\) follows a drift trajectory, eventually striking a machine-element wall or a line-of-sight beam dump.

There are four main types of \({\text {H}}^-\) stripping: residual gas, blackbody radiation, Lorentz-force or field-induced, and intrabeam stripping (IBSt).

For the linac, IBSt and Lorentz stripping are of primary concern in terms of component activation, as these are prevalent at high energies, where deposited ionising radiation scales with power loss from the beam and can reach conventional limits. For the linac-to-ring (L2R) transfer line, all four types of stripping must be evaluated.

At beam energies greater than \({\sim }\,100\) meV, activation of machine components could become a concern if the loss values exceed acceptable limits. The beam-loss limit at ESS has been set to 1  W/m, from a commonly accepted standard [6]. This ensures a maximum 1 mSv/h ambient dose rate due to activation at 30 cm from a surface of any given accelerator component, after 100 days of irradiation and 4 h of cool-down [56].

Since the addition of the \({\text {H}}^-\) beam will increase the total duty cycle of the linac to about 8% (depending on the pulsing schemes), and with the loss for both beams in total kept below 1 W/m, the beam loss in the linac for \({\text {H}}^-\) is limited to 0.5 W/m. In the L2R, where only \({\text {H}}^-\) is present, this limit can be relaxed to 1 W/m.

Simulations predict the loss from the proton beam to be well below 1 W/m (estimated at roughly 0.1 W/m). If this is confirmed during beam commissioning and operation of the proton beam, the loss limit for the \({\text {H}}^-\) beam may be relaxed provisionally.

4.10.2 Residual gas stripping

This type of stripping occurs when an \({\text {H}}^-\) ion collides with a neutral gas molecule in the beam pipe. It can be modelled in terms of fractional beam loss of total particle count N per unit length L [65,66,67,68]:

$$\begin{aligned}&\tau = \sum _i \frac{1}{\rho _i \sigma _i \beta c} \\&\frac{\Delta N}{L} = \frac{1}{\tau \beta c}. \end{aligned}$$

In this formula, \(\tau\) is the \({\text {H}}^-\) lifetime, i is the residual gas species with a molecular density \(\rho _i\) and a scattering cross section of \(\sigma _i\), and \(\beta c\) is the particle velocity.

This type of stripping is suppressed for high energies and high vacuum levels. For \({\text {ESS}}\nu {\text {SB}}\), it is then only a major concern as the beam leaves the ion source into the LEBT and neutral gas is injected as a space-charge compensation measure for avoiding emittance blow-up. Depending on the gas species used and the degree of space-charge compensation needed, the gas pressure required for well-saturated space charge compensation can be roughly an order of magnitude below where stripping causes substantial beam loss [69], or high enough to cause serious beam loss [68]. It should be stressed, however, that the energies here are so low that activation and prompt radiation are not significant.

In the L2R transfer line, ultra-high vacuum levels are no longer required. A high vacuum is still required to prevent ordinary gas scattering. TraceWin has built-in capability for estimating both gas scattering and gas stripping, and predicts power loss from stripping to be below 0.05 W/m at nominal ESS vacuum levels [70]. Double stripping in residual gas

A secondary effect that must be considered here is that a proportion of the ions may also be fully stripped to protons; this is often referred to as double stripping. Such protons can ultimately cause activation or structural damage, particularly if they are inadvertently accelerated to higher energies.

Some success has been reported in J-PARC in Tokai, Japan using a chicane after the chopper in the MEBT to divert protons produced by double stripping. Nevertheless, their recommendation is to use a quadrupole FODO lattice instead of solenoid focusing in the LEBT to avoid proton capture at the outset [71].

If allowed to reach higher energies, double-stripped protons can even survive a frequency jump from the normal to superconducting sections of the linac: they do not survive the doubled frequency at SNS, but they do survive tripled frequency at JPARC [72,73,74,75]. Thus, double stripping is not likely to lead to the production of high-energy protons at \({\text {ESS}}\nu {\text {SB}}\), where the frequency is doubled between normal and superconducting linac sections. However, long-term cumulative damage from undetected double stripping “hot spots” as reported in [76] may still be a risk, and should be prevented.

A general preventative measure to reduce the risk of such damages could be collimation of either double-stripped protons or H0 particles (using stripping foils in the latter case).

4.10.3 Blackbody radiation stripping

The infrared photons emitted by the beam pipe or other machine parts, when Lorentz-shifted into reference frame of the beam, can cause significant \({\text {H}}^-\) stripping.

Fig. 23
figure 23

Temperature dependence of blackbody-radiation stripping for 60 mA beams at a 4% duty cycle for the \({\text {ESS}}nu{\text {SB}}\) beam energy of 2.5 GeV, with curves for a more restrictive 8 GeV case shown as reference. Left- and right-hand markers in the legend correspond to fractional loss rate and beam power loss scaled by the left and right-hand y axes, respectively. Reproduced from [47]

Here, the fractional loss per unit length is used as a figure of merit, which can be taken as [67, 77,78,79]

$$\begin{aligned}&\frac{\Delta N}{N}\frac{1}{L} =\int _{0}^\infty {\text {d}}\epsilon \int _0^\pi {\text {d}}\alpha \frac{{\text {d}}^3 r}{{\text {d}}\Omega {\text {d}}\nu {\text {d}} l} \\&\frac{{\text {d}}^3 r}{{\text {d}}\Omega {\text {d}}\nu {\text {d}} l} =\frac{\left( 1+\beta cos\alpha \right) n(\nu ,r)\sigma (v')}{4\pi \beta }, \end{aligned}$$

where h is Planck’s constant; \(n(\nu ,r)\) is the spectral density of thermal photons (a function of frequency \(\nu\), and radius r); \(\alpha\) is the angle between the incoming photons and the beam; and the factor \(\epsilon\) is defined as \(\epsilon =h\nu /E_0\), with \(E_{0}=0.7543\,{\mathrm {eV}}\) being the electron-binding energy for \(H^-\). The stripping cross section in the beam frame is represented by \(\sigma (\nu ')\). This integral can be broken into factors which can be evaluated analytically and numerically, for further detail, see [65, 78, 80, 81].

In the linac, the low temperature of the superconducting cryomodules suppresses blackbody stripping. However, the L2R transfer lines have no such nominal cooling needs, and as shown in Fig. 23, beam power loss from blackbody stripping is roughly 0.4 W/m for a 2.5 GeV beam at room temperature.

Cooling the L2R to 100–200 K would limit blackbody stripping, and is expected to be a cost-effective solution, given the existing cooling infrastructure serving the nominal ESS linac.

However, low-emissivity beam-pipe coatings may a viable alternative; Eq. (4.2) and the results in Fig. 23 assume a 100% emissivity, which is expected to scale linearly with blackbody stripping. Emissivity is dependent on surface characteristics including roughness and susceptibility to oxidation. For stainless steel, an emissivity of up to 0.4 can be observed, whereas copper, nickel, or gold can have values as low as 0.03 [82,83,84].

A coating of TiN is often used in accelerators to reduce secondary electron yield and may be a strong candidate for blackbody stripping reduction, owing to its mechanical and thermal properties [85,86,87]. Similarly, the non-evaporable getter (NEG) TiZrV coating is also effective in reducing secondary-electron emission, which, depending on surface roughness, may also indicate a low infrared emissivity [88, 89].

It should be noted that such metal-based coatings have emissivities in the 0.2 range, but similar carbon-based coatings should be avoided, with emissivities closer to 0.8 [90]. A variety of alternatives may also be worth further study, as discussed in [91, 92].

4.10.4 Lorentz stripping

A transverse external magnetic field either from focusing quadrupoles or from dipoles is Lorentz transformed into an electrical field as [47, 93]

$$\begin{aligned} |E_\perp | = \beta \gamma c |B_\perp |, \end{aligned}$$

where \(|B_\perp |\) and \(|E_\perp |\) are the originating magnetic field and beam-frame electric field, respectively, and where \(\beta\) and \(\gamma\) are the relativistic Lorentz factors while c is light speed in vacuum. This relation indicates that H\(^-\) beams at GeV energies can have problematic stripping from the field gradients needed for focusing and steering.

For the simpler case of dipole magnets (approximated as a uniform field near the beam axis), the Lorentz stripping probability per unit length can be modelled as [93, 94]

$$\begin{aligned} \frac{\Delta N}{N}&\frac{1}{L} = \frac{|B_{\perp }|}{A_1}{\text {exp}}\left( {-\frac{A_2}{\beta \gamma c \left| B_{\perp }\right| }}\right) \\ A_1&= 3.073 \times 10^{-6}\,{\text {sV/m}} \\ A_2&= 4.414 \times 10^9\,{\text{V/m}}, \end{aligned}$$

where \(A_1\) and \(A_2\) are empirical-fit parameters. With this equation, calculating Lorentz stripping for bunches traversing dipole magnet fields is straightforward. Quadrupoles, however, have a transverse field-strength dependence which makes particles in the outer halo or misaligned beams more likely to undergo stripping. This probability of Lorentz stripping through a quadrupole can be thus calculated as

$$\begin{aligned} P = \int ^{2\pi }_{0}\int ^r_0 f(r',\sigma )\frac{\Delta N}{N} \frac{1}{L} r' {\text {d}}r {\text {d}}\theta , \end{aligned}$$

where L is the magnet length and \(f(r',\sigma )\) is a radially symmetric particle density distribution [95]. The general result is that a small RMS transverse beam size \(\sigma _{\perp }\) advantageous. However, the opposite is true for IBSt. This converse dependence on beam size will be analysed shortly.

4.10.5 Intra-beam stripping (IBSt)

The phenomenon of IBSt arises from the collisions of \({\text {H}}^-\) ions within a bunch, and can be the predominant form of stripping in high-intensity \({\text {H}}^-\) linacs [96]. The fractional loss rate per length, in the laboratory frame, is given as

$$\begin{aligned} \frac{\Delta N}{N}\frac{1}{L} = \frac{N\sigma _{{\mathrm{max}}_{{\mathrm{IB}}}} \sqrt{\gamma ^2\theta _x^2+\gamma ^2\theta _y^2+\theta _z^2} }{8\pi ^2\gamma ^2\sigma _x\sigma _y\sigma _z}F\left( {\gamma \theta _x,\gamma \theta _y,\theta _z}\right) , \end{aligned}$$

where \(F\left( {\gamma \theta _x,\gamma \theta _y,\theta _z}\right)\) is the shape function for momentum spreads with a weak dependence on its parameters from 1 to 1.15. (For more detail, see [47, 97, 98]). The factor \(\sigma _{{\mathrm{max}}_{{\mathrm{IB}}}}\) is the maximum stripping cross-section; this is approximately

$$\begin{aligned} \sigma _{{\mathrm{max}}_{{\mathrm{IB}}}} \approx \frac{240 a_{0}^{2} \alpha _{f}^{2} \ln {\left( 1.97\frac{\alpha _{f} + \beta }{\alpha _{f}} \right) }}{\left( \alpha _{f} + \beta \right) ^{2} }\,\,\le \,\,4\times 10^{-15}/{\mathrm {cm}}^{2}, \end{aligned}$$

where \(\alpha _f\) is the fine-structure constant, \(a_0\) is the Bohr radius, and \(\beta =v / c\) is the velocity between ions. The bunch sizes and angular momentum spreads (RMS) are then, respectively, defined as

$$\begin{aligned} \sigma _{x,y} = \sqrt{\epsilon _{x,y}\beta _{x,y}} \quad \quad \theta _{x,y} = \sqrt{\frac{\epsilon _{x,y}}{\beta _{x,y}}}, \end{aligned}$$

where the factors \(\epsilon _{x,y}\) and \(\beta _{x,y}\) are the transverse Twiss parameters.

Fig. 24
figure 24

Intra-beam stripping (IBSt) power losses for a nominal trajectory and a corresponding error study for the \({\text {ESS}}\nu {\text {SB}}\) linac (\({\text {H}}^-\) only). Static and dynamic machine errors are incorporated along with beam misalignment. Standard deviations are from the cumulative trajectories of 100 trials

Since Eq. (4.6) has an inverse dependence on bunch length \(\sigma _z\), IBSt can be limited by maximising length—minimising momentum spread has a similar effect. One can also infer dependencies on accelerating phase and RF frequency: both can be reduced to mitigate stripping.

Relaxed transverse focusing also limits IBSt, and has been shown to be highly effective [96]. In doing so, one may use accelerating cavity defocusing strength as a limiting parameter for a minimally focused beam [97].

Figure 24 shows the power loss rate per meter derived from Eq. (4.6) and corresponding power loss for a 5 MW, 2.5 GeV \({\text {H}}^-\) linac. These calculations were done as a post-processing step, with trajectories outputted from TraceWin. This post-processing approach is feasible, since the loss rates from IBSt are orders of magnitude below that of a bunch population and do not affect the overall dynamics of the bunch (i.e., beyond the LEBT, it is activation from stripping losses that is critical, not whether such losses affect the delivery of a desired beam current).

Figure 24 also shows error study trajectories, which account for static and dynamic dipole, quadrupole, and cavity errors, as well as beam misalignments. (Specifically: 0.1 mm and 10 mrad static errors for the beam position and momentum, respectively; 0.1 mm for displacement, \(1^\circ\) rotation, and 0.5% gradient errors for quadrupoles; and 1% field and 0.5% phase error for cavities.)

4.10.6 \({\text {H}}^0\) traversal and power deposition

For the simulation underlying Fig. 25, the neutral \({\text {H}}^0\) created by IBSt are tracked from the instant they are stripped to when they collide with the beam pipe or other machine element. As these particles are not affected by external fields, this calculation could be performed using an elementary trajectory integrator.

Error studies were also done for this set of power losses using the same error parameter set as above. Comparing these results with Fig. 24, one can see a significant improvement in power deposited versus instantaneous power lost.

Fig. 25
figure 25

Power deposition of \({\text {H}}^0\) into beam-pipe and machine element walls for a 62.5 mA \({\text {H}}^-\) beam accelerating to 2.5 GeV for the \({\text {ESS}}\nu {\text {SB}}\) linac. Only IBSt is accounted for

Figure 26 further illustrates this notion, showing the distances travelled by the stripped \({\text {H}}^0\) particles before reaching a collision point (with a remaining \(\sim 50\) W deposited into the beam dump at the end of the linac). However, this advantage does not come in to play for the L2R transfer line: in this case, the \({\text {H}}^0\) particles will collide shortly after passing the nearest bending dipole.

Fig. 26
figure 26

Traversal of \({\text {H}}^0\) particles from the point of IBSt to collision with the nearest machine-element wall or aperture for the \({\text {ESS}}\nu {\text {SB}}\) linac. Inset shows the depositions occurring within 2 m of stripping Optics, emittance, and optimization

For quadrupoles, as mentioned above, relaxed quadrupole focusing can improve the IBSt rate while being detrimental for Lorentz stripping, as particles furthest from the beam axis are closer to the magnet pole tips (specifically, the Hamiltonian describing a quadrupole’s magnetic vector potential has quadratic dependence on position, extending radially outward from the magnets’ transverse centre).

Figure 27 shows the inter-dependence for these two types of \({\text {H}}^-\) stripping, along with blackbody stripping, for a dummy FODO lattice of 20 cells with buncher cavities. Figure 28 extrapolates this result to quadrupole strength. An energy of 2.5 GeV and current of 62.5 mA was used for all test points.

This analysis follows Eq. (4.6) for IBSt, and Eq. (4.5) adapted to a Gaussian distribution for Lorentz stripping; this is integrated numerically over a radius r as

$$\begin{aligned} \frac{\Delta N}{N}\frac{1}{L} &= \int _{0}^{3 \sigma } \frac{ \sqrt{2} G r^{\prime }}{2 \sqrt{\pi } A_{1} \sigma } {{\mathrm{exp}}}\left[ -\frac{\left( -\mu +r^{\prime }\right) ^{2}}{2\sigma ^{2}}\right] \\ & \quad \times {\mathrm{exp}}\left[ -\frac{A_{2}}{G \beta \gamma c}\right] d r. \end{aligned}$$

A misalignment of \(\mu = 1.5\) mm is used in Fig. 27 for the upper error limit; and the factor G is quadrupole field gradient in T/m. The blackbody-stripping results are based on Eq. (4.2) convolved to a Gaussian beam.

For this test, different trials were performed with varied quadrupole strengths and gap voltages over a phase-advance range of 1–\(90^{\circ }\). Beam parameters for each run were matched to the increasing phase advance, with longitudinal-to-transverse emittance ratios also varied from 0.5 to 2 at each phase-advance step, giving a variety of bunch sizes for each test lattice.

This result is not specific to the \({\text {ESS}}\nu {\text {SB}}\) lattice as-is, since the present baseline keeps all optics identical for protons and \({\text {H}}^-\) where possible, and thus favours a smaller beam size. However, these results provide a benchmark for optimisation, should relaxed quadrupole strengths become necessary to reduce IBSt in the linac. Thus, at present, Lorentz stripping is expected to be negligible along the ESS linac, which has an average transverse beam size of 2.5 mm for both particle species. For \({\text {H}}^-\) in the L2R transfer line, this size is increased to 4.0 mm to further reduce IBSt as illustrated in Sect. 4.8; here, Lorentz stripping in quadrupoles remains low, effectively nearing the optimised crossing point for the IBSt and Lorentz stripping curves shown in Fig. 27.

Fig. 27
figure 27

Dependence of blackbody, IBSt, and Lorentz stripping (quadrupoles only) on average transverse beam size \(\sigma _\perp\) for a 2.5 GeV, 62.5 mA beam traversing toy FODO lattices (\(6\,{\text {m}}\) \(\times\) 20 cells) of one quadrupole pair and one bunching gap per cell. Beam parameters are determined by setting phase advance and solving for optimum inputs. A range of 1–\(90^\circ\) phase advance runs gives the shown range of beam sizes. Blackbody stripping is simulated separately, assuming a constant \(\sigma _\perp\) for each point

Fig. 28
figure 28

Dependence of IBSt and Lorentz stripping (quadrupoles only) on field gradient for the same lattice and optimisation scheme as Fig. 27

For emittance, the situation is simpler: transverse emittance growth implies a larger \(\sigma _{\perp }\), which means greater Lorentz stripping; it also means increased intra-bunch velocities, causing more IBSt. Thus, a linac design with limited emittance growth is particularly important for \({\text {H}}^-\) beams. This trait was confirmed by comparing preliminary lattice designs with high emittance growth to the a finalised, well-matched baseline design; a reduction of IBSt rates by a factor of 1.5–2 was observed.

4.10.7 Linac-to-ring transfer line losses

In the linac, the proportion of \({\text {H}}^0\) power deposited into the line-of-sight beam dump affords some relief in terms of component activation. This is not the case, however, for the L2R transfer line. As mentioned earlier, since L2R is curved, the stripped \({\text {H}}^0\) collide with the nearest bend after passing a dipole magnet.

Activation from residual gas stripping should also be mentioned: at 2.5 GeV, a higher vacuum level is needed to prevent problematic stripping losses than that needed to prevent losses due to scattering. However, the nominal ESS vacuum pressure required for ideal longevity of the ion pumps [70] is such that gas stripping levels may be taken as negligible.

Lorentz stripping is also compounded in transfer lines. Although it is below problematic levels in the quadrupoles, in the bending dipoles, it makes a significant contribution. (The Lorentz stripping scales with the bending radius, e.g., \(\rho =73\) m for a field strength limited to \(|B|=0.15\) T in a 5 MW, 2.5 GeV beam [95].)

Additionally, blackbody-radiation stripping can become problematic, as discussed earlier. Without remediation, this leads to a problematic power loss of roughly 0.4 W/m, as shown in Fig. 23.

The L2R stripping levels can then be summarised as follows:

  • Blackbody radiation \(\, \sim 0.4\) W/m (room temperature, 100% emmissivity)

  • IBSt \(\sim 0.3\) W/m

  • Lorentz \(\sim 0.29\) W/m (dipoles)

  • Residual gas \(< 0.05\) W/m.

This puts the activation level of L2R transfer line near the 1 W/m limit. Since the IBSt and Lorentz stripping levels are not likely to be improved further beyond minor refinements, it is imperative that measures be taken to reduce blackbody stripping (either by cooling the beam pipe to at least approximately 200 K or reducing emissivity of the beam-pipe surface by at least a factor of two). However, as mentioned earlier, some well-polished metals have emissivities less than 0.1, and stainless steel can have emissivity as low as 0.4. Thus, blackbody radiation may be more likely to fall roughly a factor of two below the simulated 100% emissivity, leaving the total stripping loss rate at an adequate level of 0.8 W/m.

An additional design measure is advisable: placing local beam dumps after each dipole bend. The trajectories of stripped particles should be calculable to a scale comparable to the transverse beam size, so the placement of such dumps may be fairly simple.

4.11 RF systems

In this section, a description of the RF systems used for the proton driver of the neutrino facility is described and the upgrade on the RF power sources and stations is outlined.

4.11.1 RF modulator upgrade

The RF modulators designed for the current ESS linac are based on the stacked multi-level (SML) topology and are each rated for peak power 11.5 MW and average power 650 kVA [99]. This modulator topology permits control of output pulse amplitude as well as offering variable pulse length on a pulse-to-pulse basis, thus allowing output of any one of the proposed pulsing schemes for \({\text {ESS}}\nu {\text {SB}}\).

For the ESS linac baseline design at 2.0 GeV, a total of 33 modulators are needed. For upgrading to 2.5 GeV, additional 32 high-beta cavities are needed, requiring 8 additional modulators. In total, 36 modulators must be upgraded to meet the increased power demands of \({\text {ESS}}\nu {\text {SB}}\), and 8 new ones must be constructed, for a total of 41 modulators.

Upgrading the SML modulators will require no additional footprint in the accelerator gallery, but will extend the height of the modulators by 0.5 m. The estimated time of work to perform the upgrade is approximately 2 weeks per modulator, provided that the necessary components can be prepared and pre-cabled in advance.

Additional insulated-gate bipolar transistors will be necessary in the upgrade [54], allowing for increased cooling capacity without altering the nominal heatsink design.

It should be noted that the peak pulse power, and therefore also output pulse voltage and current amplitudes, are in the proposed pulsing schemes not greater than that specified for the baseline ESS RF modulators. This means that all components are already appropriately scaled for peak pulse power conditions, and that the upgrade will largely concern the capability of the modulators for handling increased average power.

The oil-tank assembly, including the high-voltage components contained within, is designed conservatively with respect to necessary isolation distance, using mineral oil as insulating medium. Since the oil is continuously circulated for a high heat-transfer capacity (and since the high-voltage components are relatively large with respect to the power they convert), it has been determined that the oil tank assembly will require no upgrades to handle the increased average power represented by the proposed scenarios.

To study the performance of the present SML modulators for the new pulsing conditions of the proposed scenarios, a simulation model was developed using MATLAB Simulink [100]. First, to maintain flicker-free operation, charging power was proportionally increased with the idea of recovering the lost energy of all pulses (1 proton pulse plus 1–4 \({\text {H}}^-\) pulses) in time for the next proton pulse. Consequently, in scenarios B and C, reduced capacitor-bank voltage is available for each of the four \({\text {H}}^-\) pulses. SML modulator pulse generation control systems were, in these cases, adjusted to compensate. The following text details the simulation results for each scenario with particular focus on (1) rise time, used in deriving modulator beam efficiency, (2) pulse flat top ripple, and (3) the dynamics of the capacitor charger waveforms.

Figure 29 shows simulation results for the upgraded SML modulator with the baseline 28 Hz pulsing scheme from Fig. 3. In this scenario, pulse repetition rate is doubled from the nominal ESS value. Consequently, with doubled charging power, the following \({\text {H}}^-\) pulse is identical to the first pulse. Flat top ripple is seen to be within specification, and pulse rise time is verified to be just over \(120\,\upmu {\text {s}}\). This pulse rise time corresponds to a modulator-beam efficiency of 82%, and to an annual electricity cost of M€14.6 for all 41 modulators (this is the lowest-cost option, representing is a 100% increase from the nominal ESS).

Simulations for the alternative pulsing schemes using the existing modulator design with additional capacitor banks, or with pulse-transformer technology, were performed and reported in [5]. The 28 Hz scheme was found to outperform the 70 Hz options considerably in terms of efficiency and annual electricity cost, which leaves it as a strongly favoured baseline.

Fig. 29
figure 29

Simulation results for pulsing Option A+ from Fig. 3; Top: modulator output voltage and capacitor bank charging waveforms; Bottom: flat top ripple, confirmed to be within acceptable limits

4.11.2 Grid-to-modulator transformers

For the nominal ESS design, there are 11 transformers feeding grid power to three modulators each. These are rated for 2000 kVA, with each modulator requiring 650 kVA. Taking a conservative estimate of a 100% increase in power for the \({\text {ESS}}\nu {\text {SB}}\) upgrade, these transformers can be reused—but only supplying one modulator each instead of three each.

Beyond this, 15 new transformers would be needed, each delivering power to two modulators (for the remaining 22 upgraded and 8 newly installed modulators). These new transformers would need ratings of 2600 kVA, 600 V, and 50 Hz, with an estimated total cost for the 15 new units at M€5.6.

4.11.3 Klystron upgrades

Only Pulsing Scheme A from Fig. 3 is considered here, as it is presently a strongly favoured baseline. (For details on the klystron power requirements for other pulsing schemes, see [5].) Given the timeframe of the \({\text {ESS}}\nu {\text {SB}}\) project, it can be assumed that the klystrons in operation on the ESS linac will be nearing the end of their lifetime. The requirement for klystrons in operation in the linac (352 MHz, 3 MW klystrons and 704 MHz, 1.5 MW klystrons) was for a lifetime exceeding 60,000 h (about 10 years). Hence, it is reasonable to consider that they will have to be replaced once \({\text {ESS}}\nu {\text {SB}}\) is operational.

There are several options for the replacement:

  1. 1.

    In the first option, the klystrons are replaced with similar devices. The klystron beam voltage, current, and the RF circuit design are left unchanged. The only modifications required would be related to the increased average power dissipation (with collector size and cooling redesigned for operation at 28 Hz), and possibly shielding. Klystron manufacturers have been involved to understand the implication of the possible modifications and the cost and some details will be discussed shortly.

  2. 2.

    In the second option, the klystrons can be replaced with tubes that have been redesigned and optimised for the new operating conditions and increased efficiency. Again, two alternatives can be evaluated:

    1. (a)

      In this case, a complete tube re-design can be studied, including optimisation of:

      • Micro-perveance

      • Electron gun

      • Cavity circuit

      • Cooling

      • Collector.

      Increasing the beam voltage to about 140 kV could have a positive effect on the klystron efficiency, as demonstrated by several studies. An 800 mHz klystron has been designed for the Future Circular Collider (FCC) at CERN (134 kV, 12.5 A, 1.3 MW), showing an efficiency of about 80% in 3D simulations [101, 102]. This klystron has specifications similar to the ESS requirements, and it makes use of the new bunching methods for high efficiency, with no major technological changes. Another innovative design with two HV stages has shown an efficiency of 82% in 3D simulations [103], but this technology is quite new and might be not mature enough by the time procurement must be negotiated.

      At the same time, increasing the klystron beam voltage has important implications from the modulator design point of view, with several components needing replacement and possibly requiring major design changes. This option should thus be evaluated with the help of the power converter experts. A recent report [104] demonstrates by particle-in-cell (PIC) simulations an efficiency for this option of 73% (about 9% higher than the one achieved by the klystrons currently installed on the ESS linac). For the 352 mHz klystrons (RFQ-DTL), such work has not been carried out yet. As there will be only six of these klystrons, it should be evaluated whether the efficiency gain would justify the investment in a new design. The cost of the different scenarios has to be evaluated against their advantages. Klystron manufacturers have to be involved in all cases, to assess the feasibility. Scenarios 1 and 2b will be discussed in the following paragraphs.

Scenario 2a will not be considered further at this time, as it would require major changes on the modulator design and collaboration with the power converter group to assess the feasibility of such a design. Modifications required on ESS klystrons for the \({\text {ESS}}\nu {\text {SB}}\) upgrade

This section will focus on the modifications required to operate the current klystrons at 28 Hz repetition rate (Scenario 1). The klystrons presently used for the ESS linac have been provided by three different manufacturers: Thales and CPI for the normal-conducting linac (352.21 mHz) and Thales, CPI, and Canon for the medium and high beta part of the linac (704.42 mHz). A first enquiry regarding the modifications required to operate the klystrons at 28 Hz has been carried out, with the following outcome [105,106,107]:

352.21 MHz Klystrons

  • Thales TH2179D klystrons (352.21 MHz, 3 MW peak)

    • Some modifications in the oil tank cooling circuit are required to dissipate the heat caused by the current in the limiting resistors.

    • The flow rate of the body should be slightly increased (16 to \(25\,{\text {l/min}}\)).

    • The lead shielding will need to be locally adjusted.

    • The presently installed collector can dissipate about \(560\, {\mathrm {kW}}\) (average). The margin should be enough to ensure safe operation at \(28 \,{\mathrm {Hz}}\), but additional thermomechanical simulations are needed. The temperature of inlet water at \(50\,^{\circ } {\mathrm {C}}\) should also be considered.

    • The collector flow rate should also be increased from 300 to \(600\,{\text{l/min}}\).

  • CPI VKP-8352A (352.21 MHz, 2.9 MW peak).

    • CPI provided a detailed report including simulations of the thermomechanical behaviour of the collector at \(28\,{\mathrm {Hz}}\), and of the klystron output cavity and output window.

    • For the collector, CPI found a limited margin, and recommends a collector upgrade. CPI is currently under contract with ESS Bilbao to repair a VKP-8352A klystron and upgrade it with a larger collector (from the VKP-8352C klystron). This collector will be capable of operating at the double duty requirement of \(28\,{\mathrm {Hz}}\). The klystron will have a new model number.

    • The output window and output cavity are capable of higher duty.

    • Increased coolant flow rate would be required at \(28\,{\mathrm {Hz}}\) for the collector and body circuits. The electromagnet flow rate would not change.

    • The X-ray shielding should be adequate for the higher duty, but there may be some areas that need upgrading. It is difficult to estimate the impact on life of operating the existing tubes at \(28\,{\mathrm {Hz}}\). The only vulnerable component is the collector. CPI will review the current design for projected cycling fatigue.

704.42 mHz Klystrons

  • Thales TH2180 klystrons (704.42 mHz, 1.5 MW peak)

    • The oil tank cooling seems sufficient, but this will need to be confirmed by further testing.

    • The flow rate of the body should be slightly increased (from 14 to \(16\,{\text{l/min}}\) ).

    • The lead shielding will need to be locally adjusted.

    • A water-cooling circuit will have to be added for the output waveguide transformer and RF window.

    • The collector should be able to dissipate the increased power, but this has to be confirmed by further simulations. However, the margin is higher in this case (compared to the \(352\, {\mathrm {MHz}}\) klystrons). Collector flow rate must be increased to \(275\,{\text {l/min}}\).

  • Canon E37504 (704.42 MHz, 1.5 MW peak).

    • The collector cooling will need an increased flow rate \((365 \,{\text {l/min}})\), which will bring the pressure drop just below the upper limit of 3 barg. An alternative is to decrease the inlet temperature of the collector cooling water to \(43\,^{\circ }{\mathrm {C}}\) instead of the \(50\,^{\circ }{\mathrm {C}}\) currently allotted. Otherwise, no other issues are foreseen with the collector design: the average power density on the collector inner wall will increase from \(122\,{\text {W/cm}}^{2}\) at \(14\,{\mathrm {Hz}}\) to \(243\,{\text {W/cm}}^{2}\) at \(28\,{\mathrm {Hz}}\). This is within the range of performance experience of other \({\mathrm {CETD}}\) products.

    • No issues for the body and window design. The power dissipation will double but will still be well within the absolute rating for this klystron. The temperature of the outlet water will increase about 6\({^{\circ }}\) with the present flow rate.

    • \({\mathrm {X}}\)-ray shielding is expected to be sufficient with the new repetition rate, but this should be confirmed with testing, and it might need to be locally adjusted.

    • It is difficult to estimate the impact of the higher duty cycle on the klystron lifetime. It is reasonable to expect a shorter lifetime, and if the warranty is to be kept as it is for the present klystrons, the cost will increase accordingly.

  • CPI VKP-8292A (704.42 MHz, 1.5 MW peak).

    • CPI provided a detailed report including simulations of the thermomechanical behavior of the collector at \(28\,{ \mathrm {Hz}}\), and of the klystron output cavity and output window.

    • Thermomechanical simulations of the collector show an instantaneous power density distribution for the existing design of about 3800 W/cm\(^{2}\), which is considered too high. A modified geometry has been studied and it is able to reduce the maximum value from 3800 to \(2575\,{\text {W/cm}}^{2}\). The reduced power density for the proposed VKP8292A collector design results in predicted mechanical performance within guidelines for reliable performance at the specified pulse parameters. Therefore, \({\mathrm {CPI}}\) recommends a collector upgrade for the \(28\,{\mathrm {Hz}}\) duty cycle.

    • According to thermomechanical simulations carried out by CPI, the output window and output cavity are capable of higher duty cycles.

    • The X-ray shielding should be adequate for the higher duty cycle, but there may be some areas that need upgrade.

    • Increased coolant flow rate would be required at \(28\,{\mathrm {Hz}}\) for the collector and body circuits. The electromagnet flow rate would not change. Efficiency and electricity consumption for the upgraded medium and high beta klystrons

Scenario 1

As already mentioned, three different types of klystrons are being used for the ESS linac. They have been procured from three different manufacturers, Thales, Canon, and CPI. The klystrons have similar specifications, with efficiencies between 63 and 66%, in worst and best cases. These data have not been fully confirmed in site acceptance tests yet, but have been provided by the manufacturers. The calculations below are based on the data provided by Canon [108], as Canon klystrons are used in both the medium and high beta linac. Similar performance values are expected from the other klystrons.

It is possible to increase the klystron efficiency in operation at beam voltages lower than the nominal by introducing a mismatch on the output of the klystron. This has been demonstrated and could present advantages, especially for the first medium-beta klystrons (which will operate at lower output power). However, this improvement will not be considered in the calculations to follow, since it is assumed that the same technique could also be adopted for the second Scenario (a–b), bringing the same advantage to the three different cases.

The power required by the cavities in the medium and high beta linac is shown in Fig. 30. To estimate the efficiency of the klystrons at the operating point, some considerations must be taken into account:

  • The output power required from the klystron (Table 7) will have to include the losses in the RF distribution system (RFDS), which are estimated to be about 5%.

  • In order for the low-level RF (LLRF) systems to be able to regulate the power, the amplifiers have to operate in the linear regime. This means that the klystrons cannot be operated at saturation, but at a power level which is about 25% below saturation.

  • To increase the overall efficiency, the first klystrons of the normal-conducting linac can be operated at beam voltages lower than nominal (nominal here is defined as the beam voltage required to reach 1.5 MW output power), since they will have to provide lower power to the first cavities (the power required from the first medium beta cavities is lower than 400 kW). However, four klystrons share the same modulator, so the chosen voltage has to accommodate four klystrons at the time.

  • The klystron saturated efficiency when operating at lower beam voltages is lower than the one at nominal voltage. This is shown in the following figures for the Canon E37504 klystrons (no mismatch assumed).

  • The modulator efficiency is estimated to be around 82% [5].

Fig. 30
figure 30

Power curves for SN18K010 Canon klystron. Curve 4 and 5 have been obtained by introducing a mismatch at the klystron output. This case will not be considered in the following calculations, so the klystron output power is considered at these voltage levels is slightly lower

Table 7 Output power for different klystron settings

Due to the limited efficiency of the systems in the chain from the input to modulators to the beam, the power goes up as the distance to the beam increases; this is illustrated in Fig. 31.

Fig. 31
figure 31

Peak power profiles for the superconducting linac at different stages in the RF chain. Blue—power to cavity; magenta—klystron output power; orange—klystron saturated power; grey—power provided from the modulator to klystrons; cyan—modulator input power

Assuming that each klystron will operate for about 5500 h/year (with a duty cycle of 9.8%), and a cost of electricity of about 0.11 € kW/h; this means, for the cost of electricity:

  • Medium Beta: 3.35 M€/year

  • High Beta: 12.26 M€/year

  • Total: 15.6 M€/year.

Scenario 2b

In this case, the maximum modulator beam voltage is not modified, while the perveance can still be changed by reducing the electron beam current.

CPI is currently studying a new high-efficiency klystron design for the medium and high beta sections of the linac. Here, the tube micro-perveance is kept unchanged at 0.6; they then attempt to increase the efficiency using the new core-stabilisation method (CSM) bunching technique. The first simulation results show a very limited improvement (about 2% with respect to the current design, leading to a maximum of 68% efficiency), but more studies and optimisations are ongoing, and the company believes that there is high margin for improvement.

For the medium–high beta klystrons, a high efficiency design study has also already been carried out at ESS (HEK-ESS-8) [104], demonstrating an efficiency of almost 74% in simulations using the KlyC 1.5 D code [109], and about 73% in MAGIC 2D PIC simulations [110]. Some results from Magic 2D and KlyC simulations are shown in Fig. 32.

Fig. 32
figure 32

Clockwise from top left: electron beam trajectory simulation in a klystrons, efficiency vs. input power, klystron bandwidth, operation on a mismatched load, efficiency and output power vs. cathode voltage, and efficiency vs. input power at different cathode voltages

In the following calculations, results from KlyC simulations are used. The HEK-ESS-8 klystron has a slightly lower micro-perveance compared with the klystrons currently in use at ESS (0.46 versus 0.6). The klystron efficiency at nominal high voltage (115 kV) and output power (1.53 MW) is 73.8% (see Fig. 33). This efficiency is lower when the klystron is operated at lower beam voltages, but it could be improved by adding a mismatch at the klystron output as discussed above (and already demonstrated for the present ESS klystrons).

Fig. 33
figure 33

Saturated output power (top) and efficiency at saturation (bottom) of the HEK-ESS-8 klystrons

The power profile along the superconducting linac at different stages of the RF chain is shown in Fig. 34.

Fig. 34
figure 34

Blue—power to cavity; magenta—klystron output power; orange—klystron saturated power; grey—power provided from the modulator to klystrons; cyan—modulator input power

Assuming that each klystron will operate for about 5500 h/year (with a duty cycle of 9.8%), and a cost of electricity of about 0.11 €/kWh one finds, for the cost of electricity:

  • Medium Beta: 3.1 M€/year

  • High Beta: 11.08 M€/year

  • Total: 14.17 M€/year.

A comparison of the peak power provided by the modulator to the klystron in the case standard klystrons is used (blue) or HEK-ESS-8 klystrons are used is shown in Figs. 35 and 36.

Fig. 35
figure 35

Peak power from modulator to klystrons in the elliptical part of the linac. Blue—ESS baseline linac; red—HEK ESS-8 klystrons

Fig. 36
figure 36

Klystron efficiency along the elliptical linac. Blue—ESS baseline linac; red—HEK ESS-8 klystrons

It can be seen from the analysis presented herein that several options are available for the klystron upgrade in terms of cost, efficiency, and power consumption. Making the most appropriate choice may depend heavily on the end-of-lifetime plan for the existing ESS klystrons.

4.11.4 RF distribution system

The standard waveguide and coaxial components are expected to be capable of operation at 28 Hz without any critical issues. However, the thermal impact of the higher average power on some “special” components (magic tee, switches, phase shifter, etc.) should be evaluated. Also, the present cooling solution for the stubs connecting the klystron gallery to the accelerator tunnel should be re-evaluated.

4.11.5 Circulators and loads

The high-power loads and circulators currently installed in the ESS linac are supplied by AFT Microwave. For the high-power loads, it is likely that it will be possible to upgrade the current devices by modifying the cooling circuit and possibly by introducing an additional attenuating section in a modular way [111].

Regarding the circulators, these would require more detailed studies (according to AFT).

4.11.6 Low-level RF (LLRF) subsystems

The real-time operation of LLRF is controlled by events from the timing system and can be run at higher repetition rates. What becomes critical at higher rates is the shorter computation time available for the data processing required between pulses. However, this can be mitigated by updating only some of the algorithms at every second pulse at the highest repetition rates without sacrificing performance significantly [112]. Therefore, no major issue is expected.

4.11.7 Existing solid-state power amplifiers (SSPAs) for buncher cavities

From a first enquiry, according to the supplier [113]:

  • The current design of the SSPA could withstand the new conditions but:

    • A new power supply (PS) drawer would need to be added to maintain the desired redundancy.

    • One load of the 5-way combiner would be replaced by a bigger one (1600 W instead of 1250 W) to keep a similar safety margin. The combiner heatsink is already prepared to host the new load. Thus, no mechanical modifications would be needed on the heatsink.

  • The new PS drawer could be implemented in two different ways:

    • With a bigger rack: 44 rectifier units (RUs) instead of 41 RUs, if possible. This option has less of an impact in terms of mechanical redesign.

    • Using the same 41 RU rack but trying to accommodate the new PS drawer. This option has a bigger redesign impact.

4.11.8 Tetrode amplification for spoke cavities

The spoke cavities of the ESS linac each use a pair of tetrodes as an RF power source, and an upgrade of the anode power supplies will be needed (consisting of increased capacitor chargers). Considering the lifetime of the tetrodes powering the linac’s spoke section, another solution could be to use a solid-state amplifier, or a klystron-based solution, at the time when \({\text {ESS}}\nu {\text {SB}}\) is built. In summation, there are 26 spoke cavities which are powered using 52 tetrodes; each pair of tetrodes is fed by an anode power supply, making a total of 26 anode power supplies in this part of the linac.

Research is ongoing at the FREIA laboratory in Uppsala, Sweden, on the reliability and feasibility of tetrode solutions for both ESS and \({\text {ESS}}\nu {\text {SB}}\). At this laboratory, two 400 kW RF stations at 352.21 mHz have been installed. One manufactured by Itelco-Electrosys [114] was commissioned in 2015; the other was manufactured by DB Science and commissioned in 2016 [115]. These stations were used for testing spoke cryomodule prototypes for ESS.

Unfortunately, multiple issues with both RF stations delayed or inhibited normal operations. The tetrodes have shown certain reliability issues and the new version of the vacuum tube, i.e., the TH595A (in replacement of the TH595) has yet to prove its reliability. However, the most worrying issue for the future operations of ESS is that there is only a single manufacturer worldwide supplying such vacuum tubes, which may pose serious supply issues. Recently, prices are up by 40%, with a 6-month lead-time for orders. The future of these tubes is not guaranteed, as the market is shifting towards solid-state technology. Spoke cavity solid-state power amplifiers (SSPAs)

A pioneering work using SSPAs for high-power applications began in 2014 at the SOLEIL synchrotron in Saint-Aubin, France, with a high-power amplifier at 352.21 mHz, combining several 330 W MOSFET modules for the first time: 40 kW for the booster, then \(2 {\times } 180\,{\mathrm {kW}}\) for the storage ring; these demonstrated extremely high reliability [116]. Seven high-power amplifiers (150 kW) were also constructed at ESRF [117] in Grenoble, France. The technology is now proposed commercially by an increasing number of industrial suppliers (e.g., Thales at 200 mHz for CERN, and IBA at 176 mHz for MYRRHA).

A major leap forward comes from CERN, where 200 mHz tetrodes have been replaced by SSPAs for the upgrade of the acceleration system of the Super Proton Synchrotron (SPS). The transistors are assembled in sets of 4 per module, for a total of 2 kW. A sum of 2560 modules, i.e., 10,240 transistors, will then be spread across 32 towers. The full system will be able to provide two times \(2{\times }21.6\,{\mathrm {MW}}\).

Power combination is crucial for enabling the economic competitiveness of a system of this size, and relies on a cavity combiner. A prototype was realised at ESRF with a 144:1 cavity combiner [118]. Since the power is distributed across hundreds of transistors, if a few transistors stop working, the RF system will not stop completely, which would be the case for a vacuum tube-based station.

The cavity combiner is designed with the magnetic field independent of the azimuthal and vertical positions, such that 100 input ports are homogeneously coupled using inductive coupling via loops. Then, feeding these ports with efficient SSPA modules allows for high RF power combination with high efficiency, within one stage of combination. Another advantage is that a variable number of inputs are allowed. Not requiring a set number at the design stage allows for redundant implementation [119]. Research and development at FREIA on SSPAs

Work is also ongoing at FREIA laboratory on the development of SSPA technology for ESS, MAX IV (a neighbouring fourth-generation synchrotron light source in Lund), and \({\text {ESS}}\nu {\text {SB}}\). Specifically, upgrading the ESS accelerator power from 5 to 10 MV to serve the neutrino beam \({\text {ESS}}\nu {\text {SB}}\) experiment is required due to the accelerator’s pulse frequency increasing from 14 to 28 Hz (5 to 10% duty cycle); this will put even more stringent requirements on the RF amplifiers.

A 10 kW prototype SSPA has been built at FREIA [120] and will be used as a starting point to design, construct, and test a 400 kW SSPA station. This development may be of decisive importance for as a replacement of the current vacuum-tube-based RF power amplifiers to guarantee a long-term stable and more energy-efficient operation of the accelerators.

The ongoing research resulted in several publications on a compact, 10 kW, solid-state RF power amplifier operating at 352 mHz. During tests, a total output peak power of 10.5 kW has been measured. The amplifier combines SSPA modules at 1.25 kW each, built around a commercially available LDMOS transistor in a single-ended architecture with 71% efficiency in pulsed operation [121]. A feedback-controlled RF power flatness compensation was also demonstrated at a 10 kW level [122].

The forthcoming work on project will involve producing a 400 kW prototype power station based on combining \(4{\times }100\) kW units, each unit composed of \(70{\times }1.5\) kW SSPA modules. A current budget of approximately 3.5 m Swedish Krona is available at FREIA from a Vetenskapsrådet (VR) grant to purchase transistors, manufacture a cavity combiner procured by Swedish industry and assemble a 100 kW prototype. Commissioning of the prototype is planned for late 2022. Replacement of the spoke power amplifiers with solid-state power amplifiers is estimated to cost about 1.2 m€ per unit, for a total of 31.2 m€ to power the 26 Spoke cavities sections.

4.11.9 Superconducting cryomodule couplers

Given that the average current during the pulse decreases in the \({\text {ESS}}\nu {\text {SB}}\) operation mode (for the \({\text {H}}^-\) beam) due to the high-frequency chopping of the \({\text {ESS}}\nu {\text {SB}}\) (extraction gap generation), the coupler design envelope of maximum delivered power is not affected (\({\sim }\,1.1\) MW) [123].

Therefore, the only remaining issue is accommodating the increased duty cycle. The present coupler was designed to accommodate the 10% duty cycle of the SPL [124], which is not a hard limit. The 28 Hz option is thus well within its operating envelope. Increasing the duty cycle and repetition rate for the 70 Hz scheme (\(5{\times }\) the nominal ESS value of 14 Hz), the duty cycle increases further; whether or not this can be accommodated needs to be verified.

The conditioning of the couplers is done at CEA for repetition rates of up to 48 Hz (limitations of the power source did not permit going to higher repetition rates), but at shorter pulse lengths due to the absence of beam which creates standing waves (reflection) at the coupler [125, 126].

The hard limit here is the electrical breakdown on peak power, and these coupler have a wide margin for average-power dissipation capabilities. The external conductor is gas cooled and the internal antenna is water cooled. There is also the possibility to cool the ceramic window, but at the ESS duty cycle, this is not necessary, and the circuit is not connected to the water manifolds. However, for the higher duty cycles, it may be necessary to bring the water cooling to the ceramic window.

4.12 Cryogenic systems

The total cryogenic load for nominal operation is two-thirds static load and one-third dynamic load. If the dynamic load is doubled (from \({\text {ESS}}\nu {\text {SB}}\)’s \({\text {H}}^-\) beam), then the total load increases by one-third. The nominal ESS cryogenic plant has capacity to cover the needs of additional cryomodules in the linac’s contingency space; these are the cryomodules needed to bring both the proton and \({\text {H}}^-\) beams to 2.5 GeV. A 30% overhead margin is also included in the design to account for unforeseen cryogenic losses (e.g., badly performing RF cavities)

In total, the ESS cryogenics design already includes an extra capacity of 63% (including the contingency space and overhead margin) which is expected to adequately accommodate the extra 33% heat load generated by doubling the dynamic load.

Dynamic heat comes largely from heat that must be collected from the accelerating cavities and is directly related to the quality factor of those elements. If the quality factor does not degrade beyond nominal when the cavities are assembled into cryomodules—a fact that is considered unlikely—then the present cryogenic plant should be able to meet the cooling needs of the upgraded ESS linac.

In terms of impact on operations: the installation of new cryogenic distribution lines in the high-energy part of the linac can only be done when the machine is stopped. The primary cost for this upgrade, then, is the new cryogenic distribution lines for the high-energy area in the accelerator tunnel.

Despite the estimate that existing cryogenic plant can accommodate the linac upgrade, the cooling needs of the of newly constructed \({\text {ESS}}\nu {\text {SB}}\) facilities (the L2R, accumulator, horns, and target) may also deplete a considerable percentage of the cooling capacity overhead. This may result in relatively tight margins, which can impact overall availability of the facility.

4.12.1 Diagnostics Beam current monitors (BCM)

The beam current monotor (BCM) sensors—that is, the AC current-transformers (ACCTs)—including their analogue front-end/back-end electronics—work equally well with positively and negatively charged particles. The existing BCM system has already successfully measured sub-mA proton beams with pulse lengths as short as \(1\,\upmu {\text {s}}\). However, with such short pulses, the ACCT bandwidth limitation (i.e., 1 mHz) becomes visible in the rise–fall times of the measured beam pulse.

The linac upgrade will put new requirements on the BCM, primarily due to the combined proton and \({\text {H}}^-\) pulses, with the \({\text {H}}^-\) pulses being as short as \(1\,\upmu {\text {s}}\) and their separation being as small as 0.75 ms. The effect of the BCM bandwidth limitation and droop rate on measuring a combined proton/\({\text {H}}^-\) beam and new timing requirements will require more detailed study. Considering the new linac layout, this may even require customised ACCT sensors with a better compromise between the bandwidth and droop rate, particularly on the sections that simultaneously accelerate proton and \({\text {H}}^-\) pulses. Similarly, the existing BCM firmware/software, including the machine protection functions, will need to be modified and tested and verified. This is where most of the required effort is likely to be necessary. Further scopes

The following topics must also be re-evaluated for the \({\text {ESS}}\nu {\text {SB}}\) linac upgrade:

  • Additional systems for the new \({\text {H}}^-\) ion source and LEBT sections, including new LEBT chopper and upgraded MEBT chopper.

  • Laser-based instrumentation, transverse and longitudinal (mode-locked). Laser-wires typically measure a 1D beam profile and/or 2D transverse emittance from the products of photo-detached ions as a laser beam is scanned across the \({\text {H}}^-\) beam [127].

  • Addition of beam-in-gap measurement if needed. This could be a function of the laser-based instrumentation.

  • Additional collimation and associated instrumentation as needed.

  • Additional instrumentation to support the new cryo-modules, particularly BLMs

  • Replacement of analogue front ends for systems that must resolve the extraction gap

  • Upgrade of data acquisition and protection functions consistent with the increases of the repetition rate, data rate, and beam power. Two classes of upgrades: firmware/software alone and replacement/modification of electronics.

  • Power deposition assessment and signal estimation for beam-intercepting devices, particularly in cases where atomic electrons or \({\text {H}}^0\) are stopped. Modification to these devices as required, such as different beam-intercepting materials.

  • Upgraded instrumentation to accommodate any special studies/tuning beam modes. Ring injection and accumulation may benefit from unusual chopping configurations.

4.13 Operations and installation

4.13.1 Upgraded LEBT

For the \({\text {H}}^-\) beam, all new components will be needed upstream of the second solenoid. All LEBT components upstream of this point will have to be either newly installed and commissioned or reinstalled or recommissioned. To minimise the risk of impact on nominal ESS neutron production, the elements required for accelerating protons along the nominal linac towards the neutron source must be prioritised.

4.13.2 RFQ upgrade

As discussed previously, an upgraded RFQ must be designed and procured, since the duty cycle to deliver the two beams will increase by at least a factor of two (up to a minimum of 8%)—the maximum duty cycle (due to cooling) is currently at 5%. This new RFQ will have to be installed, conditioned, and commissioned. To mitigate the risks of affecting nominal ESS neutron production, the main conditioning could be done inside a test-stand bunker before the swap of the RFQs.

4.13.3 MEBT upgrade

The current MEBT may need replacement of bunchers and new pulsing quadrupoles; and it will certainly require a higher frequency chopper. Simulations and tests are required to prove that the rest of the components in this section will withstand the increased duty cycle. The worst-case scenario would be that a more substantial number of the MEBT components have to be replaced.

4.13.4 Upgraded DTL tanks

The DTL tanks are rated for a maximum duty cycle of 10%, which indicates that they will withstand the increased duty cycle. However, simulations and testing will have to be done to demonstrate this, and there are concerns that the considerable increase in deposited heat may be exceed the present cooling capacity. In the worst-case scenario, tests and simulations results would show that the DTL tanks could not withstand the increased duty cycle and that replacements are needed for all 5 tanks.

4.13.5 Upgraded modulator capacitors

As detailed previously, the modulator capacitors for the nominal ESS linac are each rated for a peak power of 11.5 MW and average power 660 kVA. Since the peak power does not increase, only the capacitor chargers of the modulators need to be upgraded to deliver power at an increased repetition rate.

4.13.6 Upgraded cooling systems

The cryogenic distribution system is expected to be able to handle the additional cooling to the upgraded couplers and the additional 8 HBL cryomodules. However, these expansion activities result in some risks of affecting the neutron production program, since warm-ups and cooldowns take time, potential leaks may have to be fixed, along with other minor concerns.

The doubling in average power requires modifications of the skids (as discussed in Deliverable 2.1 [52]), which is thus also included in the suggested timeline.

4.13.7 Upgraded superconducting Linac

The cryomodule (CM) couplers may have to be upgraded due to insufficient cooling. Replacing the couplers at ESS would require the establishing of a clean room (preferably near Test Stand \(\#\)2, where site acceptance tests are currently performed on procured cryomodules). Furthermore, simulations and tests are required to prove that the spoke, medium-beta (MB), and high-beta (HB) cryomodules will withstand the increased duty cycle after the coupler upgrades. The steerer magnets also have to be upgraded to pulsed steerer magnets, and within the High Energy Beam Transport (HEBT) section, eight new HB cryomodules must be installed for the energy upgrade from 2.0 to 2.5 GeV.

4.13.8 Installation windows

As presented in [128], a possible \({\text {ESS}}\nu {\text {SB}}\) schedule is as follows:

  • 2021: End of \({\text {ESS}}\nu {\text {SB}}\) Conceptual Design Study, CDR, and preliminary costing

  • 2022–2024: Preparatory Phase, TDR

  • 2025–2026: Preconstruction Phase, International Agreement

  • 2027–2034: Construction of the facility and detectors, including commissioning.

The operational challenges would begin with the construction and installations of the linac upgrade. In the report [129], for 2028 and onwards, the schedule for normal operations of the neutron source includes two long shutdowns per year:

  • Winter (ca 8.9 weeks)

  • Summer (ca 8.1 weeks).

This amounts to a total of 17 weeks of shutdowns per year. This condition is projected to apply for the year 2027; for the present planning study, these windows are extended through the entire construction phase.

To mitigate the risks with swapping the RFQ, it is highly beneficial to properly condition it within a test-stand bunker beforehand. Due to the limited time constraints, and since eight new HB cryomodules are to be ordered and installed, this (or another) test-stand bunker can and is assumed to be used for conditioning the CMs before installations in the tunnel. Following such a procedure should allow for a smoother integration into the linac.

Schedule prototype

To address the contingency of having to upgrade all CM couplers, a procedure is considered, such that 3–5 CMs are swapped during multiple shutdown periods (winters and summers, [129]). The estimated time has been determined by constructing a prototype procedure for the CM swaps, as shown in Fig. 37.

Fig. 37
figure 37

A swap procedure considered for each cryomodule during an ESS neutron program shutdown period (8–9 weeks each)

For this schedule prototype, the colour-coding of the different activities is defined in terms of risk for affecting the neutron-production program:

  • Red = High (or very high) risk of a serious negative impact

  • Yellow = Medium risk of a moderate negative impact

  • Green = Low risk.

By these definitions, attempting to swap 5 CMs during a single shutdown period is a high-risk activity, while a 3–4 CM swap is a medium-risk activity. To mitigate the potential negative impact on neutron production, fewer high-risk activities are preferred over fast completion of the linac upgrade. An attempt at solving this planning challenge can be seen in Fig. 38.

Fig. 38
figure 38

A visual outline for scheduling the CM coupler upgrades during the ESS neutron production program and its shutdown periods. This plan takes as few high-risk activities as possible, but remains within the \({\text {ESS}}\nu {\text {SB}}\) upgrade timeline

As can be seen in Fig. 38, the CM coupler upgrade plan shows a possible solution and is used in the initial schedule prototype, attached in Fig. 39. Note that activities in the NCL/SCL areas during Autumn and Spring may also be planned during any downtime of the machine which may occur (e.g., for machine studies, or maintenance).

It becomes evident that, during the \({\text {ESS}}\nu {\text {SB}}\) upgrade of the ESS linac, seven shutdown periods involve a high risk of impacting nominal neutron production.

4.13.9 Analysis of the timeline prototype

From further assessment, it can be concluded that the tasks with the highest risk—and the most challenging from an operations point of view—are those involving a vital system or component which has to be reinstalled, reconditioned, and/or recommissioned.

One such system is the RFQ. The current RFQ has to be disconnected from all electrical wiring, network cables, water cooling, etc., and the new RFQ must then be integrated into the linac (including installations, re-conditioning, and commissioning with beam); this must all be accomplished during a time window of less than 9 weeks, as per Fig. 38. It is assumed, as mentioned above, that the main conditioning of the RFQ has taken place inside a test-stand bunker, and is completed prior to its installation and integration into the linac.

The nominal RFQ conditioning was conducted in June 2021, reaching nominal conditions in roughly 5 weeks. Hence, as this section is a vital part of the ESS linac to obtain neutron production, this activity can be considered as having the highest risk of affecting the ESS neutron production program negatively.

Fig. 39
figure 39

The first suggested timeline for the installations, aimed at mitigating the operational challenges arising from the required linac upgrade

Another section vital for neutron production is the LEBT, of which all components upstream of the second solenoid must be replaced, along with the installation of a new switch dipole magnet for merging the proton and \({\text {H}}^-\) beams from the two ion sources. This will require a new support platform. As can be seen in Fig. 39, its suggested installation period is during the winter shutdown 2029–2030. This activity carries a high risk, since this section is required by the linac for neutron production.

Using the left-hand layout of Fig. 6, the proton ion source must be moved and realigned from the downstream beam axis at a 30\({^{\circ }}\) angle. For this approach, the realignment has to be done during the LEBT upgrade, which includes the installation of the switch dipole. This installation has a very high risk of causing a negative impact on the neutron production, as the LEBT section’s systems are partially replaced with new systems needing to be properly integrated and recommissioned. As a mitigation effort, scheduling this high-risk action at the same time as the installation of the first 2 HEBT cryomodules can reduce the total number of high-risk periods.

4.14 Safety

The ESS is a complex facility where several hazards might occur. These hazards include radioactive hazards as well as non-radioactive hazards. Although ESS is not defined as a nuclear facility according to Swedish regulations, ESS emphasises the objective of setting radiation shielding and safety as a main priority for all phases of the project: from design, through construction and operation, to decommissioning. This should be no different with the \({\text {ESS}}\nu {\text {SB}}\) project.

When starting the operation of ESS, there will be no significant radioactive inventory. During operation, penetrating fast neutrons are generated in the target and by proton beam losses in the accelerator. The main inventory of nuclides will be in the target, and thus, it is in the target station where most radioactivity will be generated. This means that the main hazards arise from radioactive sources. However, other hazards, here termed non-radiation hazards, must be addressed as well. Examples are hazards originating from cryogenics, high-voltage, electromagnetic fields, heavy equipment, working at high elevation, transports, etc. Thus, to protect the ESS staff, the public, and the environment, it is necessary that ESS states and defines specific General Safety Objectives (GSO). The GSO will serve as a guiding document at ESS, giving necessary input of how to design the ESS facility. Many of the work already done for the ESS proton linac in developing the GSO will have to be revisited or done for part of the \({\text {ESS}}\nu {\text {SB}}\) upgrade.

At the time when the linac upgrade for the \({\text {ESS}}\nu {\text {SB}}\) project starts, many of the procedures and internal safety regulations at ESS will be well established. However, the power upgrade in the linac, which will be doubled from 5 to 10 MW, will have to re-addressed. Radiation regarding neutrons generated from losses (coming from \({\text {H}}^-\) losses and stripping) must be evaluated to guarantee staff and public safety, but also non-radiation hazards will have to be studied. It import to stress that all cavities will operate at a doubled duty cycle (for the baseline \({\text {ESS}}\nu {\text {SB}}\) \({\text {H}}^-\) pulsing scheme) and thus the effects from X-rays coming from the electromagnetic fields have to be reviewed. The same in-depth analysis will have to be performed for the transport lines and accumulator as well.

With extensive competence developed in this area, given the experience with the spallation source, ESS should have sufficient expertise on hand to aid the \({\text {ESS}}\nu {\text {SB}}\) project to address such safety issues in due time [130].

4.15 Summary

The unprecedented power of the ESS linac set the impetus to investigate the feasibility of increasing its duty cycle to be the driver for a neutrino oscillation experiment. The target and horn requirements put a limit on the final pulse length, which is obtainable only by adding an accumulator between the linac and the target. For improved injection to such an accumulator, the \({\text {H}}^-\) beam is accelerated in the linac and through a charge-exchange system—in the subsequent injection stage, the ring already contains circulating ions. This process entails the addition of an \({\text {H}}^-\) ion source to the facility; the specifics have been presented on how and where the beam from this additional ion source is merged with the proton beam of the ESS linac. The acceleration of negatively charged ions in the same lattice that is used for the acceleration and transport of positively charged protons was simulated and no prohibitive issues were found. The losses specific to \({\text {H}}^-\) were studied in detail; it was found that these losses are within acceptable limits (additional mitigating actions to further reduce the losses were also proposed).

The baseline pulse structure was established to be 14 \(\times\) 4 batches of 650 \(\upmu\)s with a gap of 100 \(\upmu\)s between batches, leaving the 2.86 ms proton pulses for the nominal ESS neutron production interleaved with 2.9  ms \({\text {H}}^-\) pulses of 62.5 mA peak current. Increasing the pulse length to 3.5 ms would even allow for a reduction to the peak current to 50 mA, reducing the \({\text {H}}^-\) specific losses even further. This depends on the possibility of increasing the RF pulses to 4 ms. Generating the RF at 28 Hz requires modifications in the power chain from the grid to the cavity, the major components in this chain were studied and solutions were presented whenever a change was needed, and the capability of the components which could operate at increased duty cycle were also discussed. Finally, the preliminary schedule for the installation and modification of components, compatible with the ESS’s neutron programme, were presented.

5 Accumulator ring

The purpose of the \({\text {ESS}}\nu {\text {SB}}\) accumulator is to transform long pulses of \({\text {H}}^-\) ions, delivered by the ESS linac, into very short and intense pulses of protons through multi-turn injection and single-turn extraction. A long transfer line brings the \({\text {H}}^-\) ions from the end of the linac to the injection point of the ring. This transfer line is described in the previous section. A second transfer line brings the compressed pulses from the ring extraction point to the beam switchyard where they are distributed over the four targets. The ring and transfer lines together constitute 900 m of new beam line which has been designed with strict requirements on beam loss control [131]. In addition, this section includes a short discussion on the possibilities of using ESSnuSB accelerator complex to produce short neutron pulses for material science.

5.1 Accumulator ring lattice and optics

The lattice for the \({\text {ESS}}\nu {\text {SB}}\) accumulator ring has been developed based on the following main requirements:

  1. 1.

    The circumference of the ring must be such that the duration of the extracted beam pulse is less than \(1.5\,\upmu {\text {s}}\), to comply with the requirements of the neutrino horns that determine the final shape of the neutrino super-beam. For a proton beam with a kinetic energy of 2.5 GeV, this means a ring circumference of less than 433 m.

  2. 2.

    The ring, the associated transfer lines, and the beam switchyard must fit physically within the perimeter of the ESS site.

  3. 3.

    The ring must be able to store 2.23\(\times 10^{14}\) particles per filling at a beam energy of 2.5 GeV, with an uncontrolled beam loss below 1 W/m to minimise activation of the accelerator equipment.

The ring has similarities in terms of size and beam parameters to existing machines in operation, namely, the Proton Synchrotron Booster (PSB) at CERN [132, 133], the Rapid Cycling Synchrotron (RCS) at the China Spallation Neutron Source (CSNS) [134], the SNS accumulator ring [135], and the RCS at the J-PARC which provides beam to the Material and Life Science Experimental Facility (MLF) [136]. Table 8 lists selected parameters of comparable rings as a comparison to the \({\text {ESS}}\nu {\text {SB}}\) accumulator ring.

Table 8 A comparison with other machines of ring and beam parameters

The SNS accumulator has the most similarities, because it serves as an accumulator only, whereas the other rings are synchrotrons which increase the beam energy before extraction. The number of particles stored in each fill is slightly reduced for present SNS operation, but with the planned proton power upgrade [137], the bunch intensity will be similar to that of \({\text {ESS}}\nu {\text {SB}}\). Nevertheless, the target average beam power for \({\text {ESS}}\nu {\text {SB}}\) is much higher; this is possible, because each linac pulse is split into four batches, as illustrated in Fig. 4. In addition, the \({\text {ESS}}\nu {\text {SB}}\) beam energy is higher, which results in fewer issues from space-charge forces.

Fig. 40
figure 40

The layout of the accumulator ring used to adjust the pulse length of the proton beam. The legend indicates the different beam optical elements used in the design. Two opposing positions of the ring are used for the injection and extraction of the beam, while the remaining two sides are used for collimation and RF (see text for more information)

The overall layout of the accumulator is designed with four relatively short arcs connected by longer straight sections, taking the SNS accumulator as a basis (see Fig. 40). This layout offers ample space in the straight sections for all necessary equipment, such as the injection and extraction system, RF systems for longitudinal beam control, and a collimation system for managing controlled beam loss. The fourfold symmetry makes it possible to suppress systematic resonances, but not as efficiently as with the 16-fold symmetry of the PSB, where the beam is stored for a much longer duration.

The arcs contain four focusing-defocusing (FODO) cells, each with two dipole magnets and with the dipole magnet centred between two quadrupole magnets. The number and length of the dipole magnets have been chosen to reach the desired bending radius with a moderate magnetic field strength of 1.3 T.

The advantage of an FODO structure versus, for example, a quadrupole triplet structure, or a double-bend achromat, is that it provides a smoothly varying optical \(\beta\)-function both in the horizontal plane and the vertical plane. In addition, a FODO structure allows all the quadrupole magnets to be manufactured with identical configuration, and be driven by a limited number of power supply units, which makes construction and operation less costly.

Fig. 41
figure 41

Optical \(\beta\)-functions and the horizontal dispersion \(D_x\) in one FODO cell

Fig. 42
figure 42

Optical \(\beta\)-functions throughout the ring

The focusing strength of the FODO quadrupoles is chosen to provide a \(2\pi\) phase advance in the horizontal plane and a vertical phase advance near \(2\pi\). This closes the dispersion generated in the horizontal plane by the dipole magnets, which means that the straight sections connecting the arcs are dispersion free. Figure 41 shows the optical \(\beta\)-function in the horizontal and vertical planes, together with the horizontal dispersion function \(D_x\), in one of the FODO cells. See Table 9 for a selection of lattice parameters in the ring.

Table 9 Overall parameters of the accumulator ring lattice and beam

Figure 42 shows the beta functions for both transverse planes in the full ring. The optical functions exhibit a fourfold symmetry, with only small variations from sector to sector. This symmetry is crucial for suppressing structural resonances.

Additional “trim” coils on the quadrupole magnets can be used to restore the designed super-periodicity, in the case of manufacturing and alignment errors, etc. This scheme is implemented at SNS [138] and will be considered also for \({\text {ESS}}\nu {\text {SB}}\).

By adding five short sextupole magnets to each arc section, the natural chromaticity can be fully corrected using limited sextupole strength (\({\sim }\,2\,{\text {T/m}}^{2}\)). Correcting the chromaticity may turn out to be important if the beam energy spread is large, since an uncorrected chromaticity would yield a chromatic tune spread proportional to the chromaticity and the momentum spread. Considering the limited sextupole magnet strength, the dynamic aperture is not expected to be reduced dramatically. In the SNS accumulator, sextupole magnets are never used during normal operation despite the significantly larger beam energy spread [139]. So far, the study has not revealed a need for using the sextupole magnets in the \({\text {ESS}}\nu {\text {SB}}\) accumulator, but they are included in the final design nonetheless, to be adaptable to future changes of the conditions.

5.2 Injection

Also the lattice in the injection region is inspired by the SNS accumulator ring [135], which has had success in their high-power beam accumulation with charge-exchange injection and \({\text {H}}^-\) stripping using a foil. Furthermore, there are advanced experimental activities on using laser-assisted stripping currently performed at the SNS [140,141,142]. If the efforts are successful, it would be beneficial if also the laser stripping setup can be relatively easily adapted to the \({\text {ESS}}\nu {\text {SB}}\) accumulator ring.

In the injection region, there are four dipole magnets, two on each side of the centre, which are used to create a permanent orbit bump. This bump brings the ideal orbit of the circulating beam closer to the point where the incoming beam is injected. This layout facilitates the merging of the two beams. Inside the orbit bump, the dispersion is non-zero (as opposed to elsewhere in any of the straight sections). The configuration of the permanent orbit bump is illustrated in Fig. 43, as seen from the top of the accumulator. The red rectangles in the centre of the bottom figure mark the position and length of the dipoles forming the permanent orbit bump depicted in the top graph. The stripping of the \({\text {H}}^-\) ions will take place near the peak of the permanent orbit bump.

Fig. 43
figure 43

The permanent orbit bump (upper), to facilitate injection, formed by four dipole magnets marked as red boxes in the lower frame. Four fast kicker magnets in each plane are used to generate a varying orbit bump additional to the permanent one

The injection region contains four fast kicker dipole magnets that generate an orbit bump in addition to the permanent orbit bump. These kickers are represented by the pink and blue rectangles before and after the constant field dipoles in Fig. 43. The amplitude of this additional bump will vary during the injection, so that the injected beam, which has a very small emittance, fills the larger phase space in the ring, through so-called phase-space painting.

The phase-space painting has been optimised with two main goals:

  • To form a beam distribution which minimises the effects of space charge.

  • To minimise the number of times that an already circulating particle traverses the stripper foil. Ideally, each particle only crosses the foil at injection and never after it has already been stripped, due to the fact that each foil crossing leads to a heat deposition, and to scattering, in the foil. Since this is not feasible in practice, it becomes important to minimise the foil hits by varying how the bump changes with time.

An extensive study of different painting procedures was made as part of the ring design. There are two classes of phase-space painting: correlated painting and anti-correlated painting. In correlated painting, the circulating beam is moved with respect to the injection point in the same direction in the horizontal plane as in the vertical plane. Normally, this means starting close to the injection point and gradually moving away, both horizontally and vertically, as the injection proceeds. This produces a beam which resembles a square in real space.

In anti-correlated painting, the beam is moved in opposite directions. In the \({\text {ESS}}\nu {\text {SB}}\) case, the closed orbit and therefore the circulating beam starts close to the injection point in the horizontal plane and gradually moves away, while the beam approaches the injection point in the vertical plane. This process yields a round beam. Since a round beam is desirable when the beam hits the target, anti-correlated painting was selected for the \({\text {ESS}}\nu {\text {SB}}\) injection. The disadvantage is that this scheme, as a general rule, results in twice as many stray foil hits as correlated pointing; this occurs, since there are more circulating particles when the beam approaches the foil in the vertical plane.

The way the injection bump amplitude varies with time during injection will affect the final beam distribution, as well as the space charge forces during the injection. The aim has been to generate a final distribution that is as flat as possible, both because it leads to fewer space charge issues at the end of injection, but also because a flat distribution has advantages in terms of the thermal response of the target. However, since a beam will not circulate in the ring for more than a few turns after a filling, it would be interesting to, in the future, investigate the effect of having a painting procedure that instead minimises space charge effects during injection.

5.2.1 Numerical simulations

Fig. 44
figure 44

Example of a 10 mm orbit bump generated by the injection kicker magnets illustrated in Fig. 43

Multi-particle simulations have been performed with the Particle-In-Cell (PIC) code PyORBIT [143] and external PTC libraries [144] to evaluate the injection procedure. In this simulation framework, the magnetic lattice is represented by a so-called flat file in which all elements are split into a given number of slices. The slices are associated with computation nodes where mathematical operations are applied. The beam is represented by macro-particles, and these macro-particles are transported through the lattice slice by slice. Space charge effects are computed at every node with a sliced 2D (two-dimensional) model, also referred to as 2.5D model, in which the beam is sliced in the longitudinal direction. For each slice, the projected transverse distribution is placed over a grid to calculate the space charge forces using the Fast Fourier Transform (FFT). These forces are then scaled according to the longitudinal line density of the slice. Finally, the force is translated to a kick given to each grid unit, before the beam is propagated to the next node. An overall aperture 200 mm is applied to the ring to handle lost particles. This aperture is also used in the calculation of indirect space charge, i.e., space charge induced by mirror charges in the vacuum chamber.

The number of lattice nodes, macro-particles, and space charge grid bins are optimised in a contingency study, to find the optimum level where the accuracy as well as the simulation CPU time are satisfactory.

The simulation of the whole injection is made by setting the strength of a given set of magnets on a turn-by-turn basis. In this way, the amplitude of the closed-orbit bump can be controlled with respect to the injection point. The location and dimensions of a stripper foil is defined and every particle crossing through the foil is registered. Particle scattering from the interaction with the foil is included through a model including multi-Coulomb scattering, elastic and inelastic nuclear scattering. No significant halo formation has been observed due to foil scattering.

Figure 44 shows the displacement of the orbit trajectory in the injection region when the fast kicker magnets are powered. In this example, the amplitude of the orbit bump is set to +10 mm at the middle point, although an amplitude of at least \(\pm 50\) mm can be reached with the present design. The horizontal and vertical amplitudes can be set independently of each other, which provides excellent flexibility. The fast orbit bump is local, which implies that the beam trajectory outside of the injection region remains unaffected when the bump is activated.

Both correlated and anti-correlated painting have been successfully tested. Figure 45 shows six examples of how the amplitude of the fast orbit bump changes along the injection in both transverse planes. Both correlated and anti-correlated painting are shown. These orbit-bump functions, ranging from a slow, linear function to a more rapid exponential dependence, have been used to optimise the final beam distribution, which are depicted in Fig. 46.

Fig. 45
figure 45

The closed-orbit bump amplitude as a function of time during the injection. Six different functions are shown, ranging from a linear slope to a more dramatic exponential slope

Fig. 46
figure 46

The particle density distribution in horizontal (top row) and vertical (bottom row) phase space resulting from anti-correlated painting with three selected cases of the orbit bump functions, shown in Fig. 45. The distribution goes from under-painted (case #1, left), where the particle density is very high in the centre, to over-painted (right, case #6), with a underpopulated core. The best case (middle, case #4) gives the most uniform beam distributions

An example of the rectangular beam shape resulting from correlated painting is shown in Fig. 47. This particular distribution has been produced using the orbit bump function in Case #4. The difference in particle density when space charge is activated or ignored in the simulations is very small, which indicates that the painting process fulfils its purpose.

Fig. 47
figure 47

The particle distribution (left) and the particle density distribution (right) when correlated painting is used

Since a round beam is optimal for the target, anti-correlated painting is the preferred option. Figure 48 shows the transverse distribution in horizontal and vertical phase space as well as in real space, when the orbit bump function denoted Case #4 is used in the anti-correlated configuration. This is the procedure that best meets the requirements targeted in the optimisation of the injection process: a uniform transverse beam distribution, an elliptical beam shape, and minimised number of stray foil hits.

Fig. 48
figure 48

The particle density distribution in horizontal phase space (left), vertical phase space (middle), and real space (right) resulting from anti-correlated painting with the orbit bump function in case #4, see Fig. 45

The resulting transverse beam emittance is illustrated in Fig. 49, together with the corresponding tune diagram. In this case, 100% of the simulated particles are contained in a geometrical emittance of about \(70\pi\) mm mrad, and with a tune spread well below 0.05. These results assume an incoming beam energy spread of the order of 0.02% which is the same as at the end of the linac.

Fig. 49
figure 49

Transverse beam emittance \(\epsilon _{\mathrm{T}}\) with and without space charge (left) and the corresponding tune diagram (right). The plot to the left shows the fraction of the beam that is contained within a specific beam emittance. When space charge is considered, the 100% beam emittance is roughly \(70\pi\) mm mrad and the tune spread is less than 0.05

5.2.2 \({\text {H}}^-\) stripping

The painting process has been optimised for injection with foil stripping. Limiting the thermal load on the stripper foil is a focus—and one of the main challenges—of the accumulator ring design and operation [145]. The painting is strongly affected by this challenge, in the sense that the thermal load on the stripper foil sets a limit for how small the transverse emittance can be. Painting to a small emittance implies that the circulating beam travels closer to the injected beam, which results in more unwanted foil crossings and a higher peak temperature in the foil.

The thermal load on the stripper foil has been estimated by (1) registering all the foil hits in the numerical simulation of the injection; (2) translating each foil hit to an energy deposition; (3) calculating the temperature in the foil as a function of time with a temperature model which includes blackbody radiation as only cooling mechanism. The model has been bench marked with a similar model used at SNS, a model which in turn has been compared with measurements [146, 147]. A carbon foil with emissivity 0.8 has been assumed in the study.

Figure 50 shows the energy density in a carbon foil of density \(500\,\upmu {\text {g/cm}}^{2}\), corresponding to 99% stripping efficiency [148, 149], after the injection of one batch. In the left plot, the injected beam has the same beta function \(\beta _i\) as the circulating beam, \(\beta _m\), at the point of injection. In this case, the peak temperature is at the centre of the stripper foil, which implies that the peak temperature cannot be reduced by further optimising the painting. In the plot to the right, the beam size of the injected beam has been increased, so that \(\beta _i=2\beta _m\) which results in an energy density which is spread over a larger part of the foil. Note that also the foil size has been slightly increased to make sure that all injected \(H^-\) ions are stripped. Through this measure, the peak energy density per batch is decreased by about 30%.

Fig. 50
figure 50

Particle density distribution in the stripper foil using matched injection (left) and mismatched injection (right)

The peak temperature can be further reduced by increasing the effective foil surface area. A preliminary investigation indicates that by replacing the single foil of density \(500\,\upmu {\text {g/cm}}^{2}\) with four foils of density \(125\,\,\upmu {\text {g/cm}}^{2}\) the peak temperature in the steady-state mode can be reduced by almost 800\({^{\circ }}\). This assumes a comparable total stripping efficiency for \(500\,\upmu {\text {g/cm}}^{2}\) and \(4\times 125\,\,\upmu {\text {g/cm}}^{2}\), which must be confirmed, in particular, since accurate models of \(H^0\) stripping have not been identified in this study. In addition, a detailed study of the placing of these sequential stripper foils, so that the blackbody radiation and/or the convoy electron emitted by the first one is not absorbed by the second, etc, will be required.

Figure 51 shows the full result of the injection optimisation, from a careful choice of painting scheme, to mismatched injection and having several thin foils placed after each other. The steady-state peak temperature is reached within a couple of pulses and stays around 1900 K, almost 100 K below the target value of 2000 K at which temperature the sublimation rate of carbon becomes unreasonably high [145].

Fig. 51
figure 51

Peak foil temperature as a function of time following several injected pulses. With mismatched injection and four sequential stripper foils, the peak temperature stays below 2000 K

The conclusion of the painting optimisation study is that \(60\pi\) mm mrad is the minimum emittance that can be tolerated with foil stripping. By carefully setting up the injection painting, choosing the adequate mismatch parameter, and using sequential thin stripper foils instead of a single thicker foil, the steady-state peak temperature in the foil can be kept below 2000 K.

If, at a later stage, laser stripping can be employed in the \({\text {ESS}}\nu {\text {SB}}\) accumulator ring, the situation changes. Laser stripping requires a different optical setup, where the \({\text {H}}^-\) beam is squeezed in one dimension to create sufficient overlap with the laser beam [140]. In this case, the circulating proton beam is not a threat to the stripping procedure, and a smaller emittance is desirable, since it directly affects the required aperture, and, in turn, the cost of vacuum chambers and magnets.

To this end, the painting process was further modified to generate a beam with successively smaller emittance. At \(40\pi\) mm mrad in both planes, the tune shift is of the order of 0.1, and negligible halo formation is observed. Even if the beam is painted to an even smaller phase-space area, the final vertical emittance does not decrease further; it instead remains near \(40\pi\) mm mrad, while the horizontal emittance can reach \(25\pi\) mm mrad. Halo formation is observed in this case. Although the painting process can be further optimised for smaller emittance, it may be the case that space charge forces set a lower limit on the achievable emittance to \(40\pi\) mm mrad.

5.3 Longitudinal dynamics and radiofrequency cavities

Single-turn extraction requires a beam-free gap of at least 100 ns. Injecting a coasting beam and adiabatically forming such an extraction gap within the ring has proven unfeasible, due to the fact that both the momentum spread and the phase slip factor are small, which makes the beam quite stiff. Such a process would then take thousands of turns [150] rendering it incompatible with the \(100\,\upmu {\text {s}}\) batch-to-batch distance. Instead, a 10% beam gap (i.e., 133 ns) is formed by chopping in the early stages of the linac (see Sect. 4.2) at a frequency corresponding to the revolution frequency in the ring. While the beam is accumulated in the ring, this gap must not shrink below 100 ns—something that can only be guaranteed by the use of RF cavities. These RF cavities will be accommodated in the last straight section in the ring, see Fig. 40.

Conventionally, dual-harmonic cavities are used for this kind of application [135], since they offer a large energy acceptance and effective beam-gap preservation. The cavity voltage is specified to guarantee a clean extraction gap while limiting the induced energy spread.

As an alternative, barrier RF systems [151] have become increasingly popular for bunch manipulations in rings and synchrotrons. The barrier RF system utilises a waveform which leaves the centre of the beam unaffected. Only the head and the tail of the bunch are forced back towards the core as the beam traverses the cavity. Figure 52 shows an example of the RF voltage waveforms in the two cases.

Fig. 52
figure 52

RF waveforms of a dual-harmonic cavity and a barrier RF cavity with a single sinusoidal pulse with a frequency 9 times the first harmonic, i.e., the revolution frequency

Fig. 53
figure 53

The beam energy distribution before accumulation

Three cavities of 1 m length each have been included in the ring lattice for simulation purposes, and the two different types of RF cavities described above have been studied through multi-particle simulations using PyORBIT [143] and external PTC libraries [144]. Two separate initial conditions have been considered. The first is when the beam energy spread is controlled in the linac-to-ring transfer line, so that the energy spread of the incoming beam is similar to that at the end of the linac. This option requires additional RF cavities at the end of the transfer line, as described in Sect. 4.8. The second situation is when the energy spread is allowed to grow along the transfer line, due to space charge. The beam energy profile at the end of the transfer line is shown in Fig. 53 for these two cases, together with the energy profile at the end of the linac.

The longitudinal particle distribution at the end of injection is shown in Fig. 54. When the incoming energy spread is large (i.e., when there are no cavities in the transfer line), a voltage of at least 20 kV is needed to maintain the gap with a barrier RF system. When the incoming energy spread is controlled through PIMS cavities in the transfer line, 10 kV is enough to preserve the gap. Note that only the head and tail of the bunch are affected by the cavity, so that the induced energy spread is small.

Fig. 54
figure 54

The longitudinal particle distribution at the end of injection. If the incoming energy spread is large, i.e., the case of having no cavities in the transfer line (see Fig. 53), it takes a barrier RF cavity with a voltage of 20 kV to preserve the extraction gap, the border of which is marked with the vertical dotted lines. With a reduced incoming spread, 5–10 kV are enough

Having a low spread in beam energy gives the advantage of a small chromatic tune spread, since the chromatic tune shift is directly proportional to the energy deviation of a particle. If the chromatic tune spread is small enough, correcting the natural chromaticity in the ring with the use of sextupole magnets may be unnecessary. This, in turn, means that the dynamic aperture, which is generally reduced by the use of sextupole magnets, remains unaffected.

Conversely, having a low energy spread may prove problematic because of the risk of longitudinal microwave instabilities. A way of estimating this risk is through the Keil–Schnell stability criterion [152] with which it is possible to calculate the longitudinal impedance threshold for a set of given parameters. It reads [153, 154]

$$\begin{aligned} \left| \frac{Z_{||}}{n}\right| \le F\frac{\beta ^2E|\eta |}{q\bar{I}}\left( \frac{\Delta p}{p}\right) ^2, \end{aligned}$$

where F is the form factor, determined by the longitudinal energy distribution, E is the total beam energy, \(\eta\) is the phase slip factor, \(\bar{I}\) is the average beam current in the ring, and \(\Delta p/p\) is the momentum spread. For the current design, the incoming energy spread would be about 0.2%, at minimum. With \(|\eta |=0.04\), \(\bar{I}=27\) A (at extraction) and \(F=1\), the longitudinal impedance threshold is \(|Z_{||}|=21\,\Omega\) for a momentum spread of 0.2%, and 48 \(\Omega\) if the momentum spread is 0.3%. Above these values, the beam may become unstable. The extraction kicker magnets are expected to be the primary impedance contributor, and it is crucial that the impedance of the ring is estimated in the technical phase of the project, along with its resulting effects.

5.4 Collimation

In the operation of a high-intensity proton accumulator such as this, it is of paramount importance to minimise uncontrolled beam loss to reduce component activation and to make hands-on maintenance possible. This is done by designing a collimation system that will be used for controlled beam loss. In other words, the collimation system gets rid of beam particles that before they can damage sensitive equipment elsewhere in the ring.

A two-stage collimation system has been designed for the \({\text {ESS}}\nu {\text {SB}}\) accumulator. It consists of a thin scraper to scatter halo particles, followed by a set of secondary collimators to absorb those scattered particles. Phase advances between scraper and secondary collimators, together with the type, the material, the thickness of collimators, and the relationship with the physical acceptance, have been studied in detail and numerical simulations have been performed to evaluate the performance of the collimation system.

Given that 5 MW of average beam power would be stored in the ring, the total fractional uncontrolled beam loss in the ring must be less than \(10^{-4}\), for which a collimation system with a collimation efficiency beyond 90% is required, according to experience from similar accelerators, e.g., SNS [155] and J-PARC [156].

5.4.1 Two-stage collimation system

The two-stage collimation system chosen for the \({\text {ESS}}\nu {\text {SB}}\) accumulator includes a thin scraper, which is the primary collimator that increases the scattering angle of the beam halo particles. This is followed by four thick collimators, two in the horizontal plane and two in the vertical plane; these are the secondary collimators which absorb the scattered beam-halo particles. The main advantage compared to the traditional single-stage collimation system is an increase in the impact parameter of particles hitting the front of the secondary collimators. This effect can dramatically improve the collimation efficiency, which is defined as the ratio of particles lost on the collimators to the total particle loss in the ring.

The straight section following the injection section will accommodate the collimation system, see Fig. 40. To leave enough room for downstream placement of secondary collimators, the primary collimator is located before the centre of the straight section, where \(\beta _x=\beta _y\). Figure 55 shows the lattice function for one lattice super-period and the location of the primary collimator.

Fig. 55
figure 55

Optical beta functions \(\beta _x\) and \(\beta _y\) and horizontal dispersion \(D_x\) in one lattice super-period. The blue line at the top marks the location of the primary collimator

The optimal phase advance between the primary and the secondary collimator, for maximum interception efficiency, can be calculated as [157]

$$\begin{aligned} \mu _{\mathrm{opt}}=\arccos \left( \frac{n_{\mathrm{prim}}}{n_{\mathrm{sec}}}\right) , \end{aligned}$$

where \(n_{\mathrm{prim}}\) and \(n_{\mathrm{sec}}\) are half apertures of primary and secondary collimators normalised to RMS beam size. For the \({\text {ESS}}\nu {\text {SB}}\) accumulator, considering the acceptance of primary and secondary collimators as \(70\pi\) mm mrad and \(120\pi\) mm mrad, respectively, we have \(n_{\mathrm{prim}}=2.35\), \(n_{\mathrm{sec}}=3.07\), and the optimal phase advance from Eq. (5.2) is approximately \(40^\circ\). Thus, the secondary collimators are ideally located at \(40^\circ\) and its complementary location \(140^\circ\). Considering the real lattice situation, the phase advances of the secondary collimators are listed in Table 10.

Table 10 A list of the collimator elements and the phase advance, with respect to the primary collimator, at which they are located

5.4.2 Material and thickness of primary collimator

The material choice of the primary collimator normally follows two rules: (1) small energy loss, and (2) large multi-Coulomb scattering angle. Figure 56 shows a comparison of RMS scattering angle along with energy loss for a 2.5 GeV proton beam interacting with a variety of materials. After also considering availability, heat tolerance, melting point, and thermal conductivity, tantalum, tungsten, and platinum have been identified as acceptable choices for the primary collimator.

The choice of thickness for the primary collimator is also a balance between scattering angle and energy loss in the proton beam. A thick scraper increases the probability of large-angle scattering, which may cause particle loss downstream before reaching the first secondary collimator. Figure 57 shows an example of the RMS scattering angle and energy loss for a 2.5 GeV proton beam interacting with tantalum collimators of different thicknesses. With a desired RMS scattering angle larger than, e.g., 4 mrad and energy loss less than roughly 1%, a thickness of 6–20 \({\text {g/cm}}^{2}\) is expected to be suitable.

Fig. 56
figure 56

RMS scattering angle and energy loss for 2.5 GeV protons interacting with different materials, each having a thickness of 10 \({\text {g/cm}}^{2}\)

Fig. 57
figure 57

RMS scattering angle and energy loss for 2.5 GeV protons interacting with different thicknesses of tantalum

5.4.3 Numerical simulations

Multi-particle simulations have been performed with the PyORBIT code [143] to evaluate the performance of the collimation system.

The collimation system only affects the beam halo particles; thus, to simplify the simulation process, initial particles are give a larger amplitude than the primary collimator aperture, starting at the front of the primary collimator. This means that all simulated particles hit the primary collimator first. The initial particle distribution is an “L” type in real space, with a typical width of \(10\,\upmu {\text {m}}\) and a uniform distribution, which matches the shape of the primary collimator. Space charge effects are not included in the simulation.

Tantalum with 10 \({\text {g/cm}}^{2}\) thickness is chosen for the primary collimator and tungsten with 1.5 m length for the secondary collimators. To compare the particle loss rate for different collimator types, three configurations have been studied:

  1. 1.

    All collimators of two-sided type

  2. 2.

    The first collimator of rectangular type; the others of two-sided type

  3. 3.

    All collimators of rectangular type.

Figure 58 shows the particle loss rate in the collimation section for the different configurations. For Option 1, the major particle loss in the collimation section but not in the absorber blocks appears just after the first secondary collimator. Changing the first secondary collimator to a rectangular type (Option 2) reduces the beam loss after the first secondary collimator from around 7% to less than 1%. For Option 3, beam loss after the other secondary collimators can also be reduced. Figure 59 shows the beam loss map for the full ring using Option 3. Here, the collimation efficiency reaches 97%, which is 2% higher than Option 2 and 12% higher than Option 1.

Fig. 58
figure 58

Particle loss rate in collimation sections with different collimator types

Fig. 59
figure 59

Beam-loss map for the accumulator ring for Option 3 (all rectangular-type collimators)

Studies of the relationship between collimation efficiency, ring acceptance, and primary collimator thickness have also been performed. Figure 60 shows the relationship between collimation efficiency and ring acceptance. The collimation efficiency increases with the ring acceptance and comes to a quasi-flat top when the acceptance reaches approximately \(200\pi\) mm mrad. Figure 61 shows collimation efficiency and power loss before reaching the secondary collimators as a function of primary-collimator thickness. The collimation efficiency rises to a quasi-flat top when the thickness of primary collimation reaches roughly 6 \({\text {g/cm}}^{2}\), while power loss continues increasing due to the large-angle scattering of the primary collimator.

Fig. 60
figure 60

Relationship between collimation efficiency and ring acceptance

Fig. 61
figure 61

Collimation efficiency and the power loss before reaching secondary collimators as a function of the primary-collimator thickness

In conclusion, a 97% collimation efficiency can be achieved using a two-stage collimation system where the primary collimator consists of an 10 \({\text {g/cm}}^{2}\) thick, L-shaped scraper of tantalum, and the secondary collimator consists of four tungsten absorber blocks, 1.5 m long each. The primary collimator acceptance is \(70\pi\) mm mrad, the secondary collimator acceptance \(120\pi\) mm mrad, and the machine acceptance is \(200\pi\) mm mrad. Position acceptance mechanisms in the horizontal and vertical planes are foreseen for the collimator elements.

5.5 Single-turn extraction

Once the accumulator ring has been filled, the now-compressed beam pulse is transferred to the ring-to-target (R2T) transfer line through fast, single-turn extraction. The pulse at this point is \(1.2\,\upmu {\text {s}}\) long, in compliance with the target and horn requirements, and carries an energy of nearly 90 kJ.

The extraction system is located in the straight section on the opposite side of the ring from the injection region (at the bottom in Fig. 40). The extraction system, illustrated in Fig. 62 consists of four sets of fast kicker magnets, located around the central quadrupole pair in the straight section extraction, and a septum magnet. Each kicker provides a small kick in the vertical direction, so that when the beam arrives at the septum magnet it encounters a horizontally deflecting field (see Fig. 63). Such a scheme was successfully implemented in the accumulator ring at SNS to extract the 1.3 GeV proton beam with 24 kJ per pulse [135]. The scheme suits the \({\text {ESS}}\nu {\text {SB}}\) well, since the beam, when arriving at the target, must be directed \(2.29^\circ\) downwards in order for the neutrino super-beam to point towards the far detector. Therefore, there is no need for cancelling the vertical angle provided by the kicker magnets, and there is no need of having a tilted septum magnet, which is the case in the SNS accumulator ring.

For simplicity, a horizontal deflection angle of \(16.8^\circ\) is used, matching that of the SNS septum magnet. A 3 m-long magnet at 1.0 T gives a beam separation of approximately 50 cm at the exit. This means that the septum magnet can be placed at a minimal distance to the subsequent quadrupoles, thus maximising the available space in the straight section for placing the kickers. A large distance between kicker and septum magnet means that the kick provided can be smaller, which facilitates the kicker magnet design in terms of impedance, aperture, and ramping speed.

Fig. 62
figure 62

Schematic of the extraction system

Fig. 63
figure 63

Schematic view of the Lambertson septum magnet [158]: The beam encounters no magnetic field while injection is ongoing. Once the injection is complete, the kicker magnets are powered and steer the beam towards the other side of the septum blade, where the magnetic dipole field deflects the beam horizontally

The total vertical deflection \(\theta _y\) is determined from the desired vertical position y of the closed orbit at the entrance of the septum, through

$$\begin{aligned} \theta _y=\frac{y}{\sqrt{\beta _{y,k}\beta _{y,s}}\sin \mu _y}, \end{aligned}$$

where \(\beta _{y,k}\) and \(\beta _{y,s}\) are the vertical beta functions at the location of the kicker and septum, respectively, and \(\mu _y\) is the phase-advance between the two points. To minimise the kicker deflection angle, the phase advance between the kicker and the septum should be close to \((2n+1)\pi /2\), where n is an integer. In addition, the septum should be placed as far away from the kicker as possible. Furthermore, to reduce the individual kicker strength, and minimise the impact of an element failure, a larger number of shorter kickers is considered.

The vertical distance from the closed orbit to the extracted beam is calculated from

$$\begin{aligned} y_{\mathrm{extr}}=\sigma _0+\sigma _{\mathrm{extr}}+2\cdot y_{\mathrm{m}} + a, \end{aligned}$$

with \(\sigma _0\) and \(\sigma _{\mathrm{extr}}\) being the full beam width of the circulating and extracted beam, respectively, at the entrance of the septum, estimated from the optical functions

$$\begin{aligned} \sigma _{0, {\mathrm{extr}}}=\sqrt{\beta _{\mathrm{s}}J_{\mathrm{s}}}+\delta \cdot \Delta _y, \end{aligned}$$

where \(\beta _{\mathrm{s}}\) is the value of the optical beta function at the entrance of the septum magnet and \(J_{\mathrm{s}}\) is the septum acceptance of the circulating and extracted beams. For a septum-blade width of \(a=10\) mm, and an aperture margin of \(y_{\mathrm{m}}=10\) mm, we obtain a value \(y_{\mathrm{extr}}= -161.0\) mm.

In the proposed configuration, 16 kickers, in groups of four, are placed around the central quadrupole doublet in the extraction straight section. Each of the 16 kickers has a length of 0.3 m. In order to simplify their design, each element in a given group has the same aperture and strength. Since the aperture of the kickers is expected to increase towards the extraction point (to accommodate the beam deflection) their strength is scaled accordingly. Based on these conditions, using MAD-X [159], the strength of the kickers was matched to the desired \(y_{\mathrm{extr}}\)-coordinate for the extracted beam (at the entrance of the septum) as defined above.

The apertures of all the elements in the extraction section were calculated to enclose the full beam envelope, plus a 1 cm contingency margin. This is to account for possible variations of kicker fields during extraction or single-element failures. Table 11 includes the apertures of the extraction kickers, as well as designated kick angles and field strengths. The beam envelopes of the circulating and the extracted beam are shown in Fig. 64. The 16 kickers are shown in groups of 4 in different shades of green; the Lambertson septum is illustrated in magenta; and the lattice quadrupoles are shown in brown. A \(180\pi\) mm mrad beam acceptance has been used in this calculation—a value that has been explicitly chosen to be larger than the acceptance of the secondary collimators, which define the maximum beam envelope—to have a safety margin in the design.

A septum blade thickness of 1 cm is assumed to be sufficient for ensuring that no field penetrates into the field-free opening. The circulating beam requires an aperture in the field-free region of about 120 mm in the horizontal plane and 148 mm in the vertical plane. The extracted beam will require a similar vertical aperture, but more than half a meter in the horizontal plane, where the \(16.8^\circ\) deflection takes place.

Fig. 64
figure 64

Beam envelopes in the extraction region

Table 11 Kicker design parameters. The total deflection angle is − 21.9 mrad

5.5.1 Extraction kickers

As described in Sect. 5.3, the kicker must be able to deflect the entire circulating beam in a single turn. This means that the ramping of the magnetic field in the kicker magnets must be done within the duration of the beam-free extraction gap (100 ns). To this end, a kicker-field rise-time is defined as the time it takes for the kicker to go from 2 to 98% of the nominal field strength, as depicted in Fig. 65. There may be remaining ripple in the pulse, but it should remain below \(\pm 2\%\) of the nominal field strength. The fall time of the kicker pulse is defined by the interval between the extraction of a pulse and the start of injection for the next pulse (i.e., a maximum of \(100\,\upmu {\text {s}}\)). The pulse duration should be around \(1.5\,\upmu {\text {s}}\).

Fig. 65
figure 65

Illustration of the extraction kicker ramping

The specifications described above will serve as input to an engineering study for kicker-magnet optimisation and construction. However, the required parameters are comparable to those of kickers already constructed for the SNS accumulator [160] and the CERN Proton Synchrotron Booster extraction region [161]. Development of the \({\text {ESS}}\nu {\text {SB}}\) extraction kickers will also include the pulse-forming network needed for powering the magnets. Since the time between pulses is short, it may be necessary to use two power supplies per magnet.

5.5.2 Failure scenarios

Two different failure scenarios have been studied: (a) a \(\pm \, 2\%\) variation in the kicker field, and (b) the failure of a single kicker element in the 16-kicker assembly.

The first case simulates a possible uncorrected ripple in the kicker field strength as explained above until it is stabilised to the nominal value. To take a conservative estimate, the error is assigned in all 16 kickers (which in reality can be compensated automatically among the four power supplies). Simulations indicate that the chosen apertures are sufficient to provide clearance and avoid losses even in this pessimistic case.

The second case was simulated in MAD-X by setting the field strength to zero for one kicker at a time. Also in this case, the chosen apertures provide sufficient margin for the beam to pass without losses. For both cases, the resulting trajectory variations and resulting losses in the beam transfer line up to the target have not been studied.

5.6 Generation of short neutron pulses

The \({\text {ESS}}\nu {\text {SB}}\) accumulator ring could, in principle, serve an important purpose also for the neutron community. The ESS facility itself provides long neutron pulses to the users, but some users wish for high-intensity short pulses of epithermal neutrons, i.e., neutrons in the energy range 0.025–0.4 eV. Considering the typical moderating time of about \(100\,\upmu {\text {s}}\) [162] for these neutrons, there is no great advantage of using the compressed \(1.2\,\upmu {\text {s}}\) pulse to generate the neutrons, since this would require a specialised target to handle such a pulse [163]. As an alternative, a compressed pulse at lower intensity could be used, but at the cost of a subsequently reduced neutron flux. The other alternative is to use the \({\text {ESS}}\nu {\text {SB}}\) accumulator to produce a proton pulse of 50–100 \(\upmu {\text {s}}\) through slow extraction from the ring. In this way, the delivered neutron pulse duration would be of the same order, but the instantaneous power delivered to the neutron target, and thus the levels of induced mechanical stress, is limited. Thus, the \({\text {ESS}}\nu {\text {SB}}\) infrastructure could also be highly impactful for the neutron user community, as a complement to the long pulses of ESS [162, 164].

The most promising scenario for the \({\text {ESS}}\nu {\text {SB}}\) accumulator is the use of slow resonant extraction at a half-integer or integer resonance. The more commonly used third-order resonance, employed at the J-PARC Main Ring [165], the SPS at CERN[166], and at GSI [167] takes place over several seconds (on the order of 1000 turns or more), and would be too slow to extract the beam in \(100\,\upmu {\text {s}}\). An extraction time of \(50\,\upmu {\text {s}}\) corresponds to about 38 turns in the accumulator ring, since the revolution time is about \(1.3\,\upmu {\text {s}}\). Resonant extraction with as few as 40 turns has been demonstrated at SPS using integer resonance [168, 169], which indicates that this should be a feasible approach.

Resonant extraction will be designed with a dedicated electrostatic septum, using an identical Lambertson septum as that used in fast extraction. To minimise losses, it is also important to, for example, keep the so-called step size at the extraction sufficiently large. Moreover, there are a number of special techniques to reduce losses for resonant extraction, such as dynamic bump, bent-crystal diffusers, and carbon wires [169]. J-PARC has reached impressive extraction efficiencies of 99.5% with careful optimisation employing a dynamic bump [170]. More realistic loss levels for the \({\text {ESS}}\nu {\text {SB}}\) accumulator ring are estimated to be approximately 5–10%.

As slow, resonant, extraction is inherently lossy, the losses cannot be eliminated entirely if resonant extraction is to be employed for neutron production. Mitigation measures should include careful beam optics design, electrostatic septum design, and careful optimisation at beam operation. Most of the unavoidable losses will happen on the septum at the point of extraction. This will have the undesired effect of activation, which limits the feasibility of handling in terms of repair and preventive maintenance. Remote handling, including robotics, could be introduced to reduce the dose levels to personnel. Ultimately, the only way to limit the average power to an acceptable level is by reducing the duty cycle for resonant extraction. If, for example, every tenth pulse is extracted for short pulse neutron production, this yields an average loss of 50 kW, at 90% extraction efficiency. Further analysis of the activation levels and shielding requirements are needed to determine the acceptable duty cycle for neutron production.

The moderation of the neutrons produced by the medium-duration proton pulse will have the effect that any variation in the proton intensity during the pulse is smeared. Thus, the extraction spill quality, which is usually an important parameter for slow extraction, is of less importance in this case. This gives more degrees of freedom in terms of the excitation of the extraction, and therefore more possibilities to reduce the beam loss during the spill.

Another approach that has been considered employs a target design which is capable of handling short high-power pulses on the order of \(1\,\upmu {\text {s}}\), similarly to the case at SNS following the Proton Power Upgrade [171]. In such a scenario, the same fast-kicker extraction as for neutrino production, with the same low losses, could be used for the neutron production. This is an interesting alternative, which—with a specially adapted neutron moderator design—could give comparable neutron-flux levels, at about the same duty cycle; but this would require more research and development to ensure its technical feasibility.

5.7 Injection beam dump

Straight behind the ring injection, see Fig. 40, there will be a short beam line towards a beam dump, here referred to as the injection beam dump. The purpose of the beam dump is to safely dispose of incoming particles that are not fully stripped. A stripping efficiency of about 98% can be expected, which leaves an average beam power of 100 kW to be handled by the dump. The dump is designed to handle up to 10% of the average beam power, mostly coming from \(H^-\) ions which miss the stripping foil, or from foil defects, or from partially stripped \(H^0\). Radiation shielding is required on top of the beam dump for radiation safety, both at operation, and during service, to reduce the radiation levels to acceptable limits. Shielding towards the ground is required to prevent activation of soil and groundwater, primarily from tritium, which could potentially be transported through the groundwater.

In the conceptual design of the \({\text {ESS}}\nu {\text {SB}}\) injection dump, the design and experience of the SNS injection beam dump has been carefully studied. Comparing the parameters, SNS has an \(H^-\) beam of 1 GeV, and 1.44 mA average current. This gives a power of 1.44 MW, with the injection beam dump designed for losses up to 150 kW. In comparison, the beam parameters for \({\text {ESS}}\nu {\text {SB}}\), with an upgrade to 2.5 GeV, and an average \(H^-\) beam current of 2 mA are set to reach 5 MW average power and a loss level of 10%, which corresponds to 500 kW. The design of the beam transport around the injection region will be conceptually similar to the SNS design, see Fig. 66. Further details on the SNS injection beam dump can be found in [172] and [173].

Fig. 66
figure 66

SNS injection section, shown schematically, where F1 is the stripper foil; F2 is a second, thick stripper foil to fully strip \(H^-\) and \(H^0\) to protons; IDSM is the Injection Dump Septum Magnet; and Q is a defocusing quadrupole. From: [174]

5.7.1 Energy deposition in the beam dump

The levels of heat deposition and activation have been simulated using the FLUKA code [175,176,177]. The model of the beam dump in FLUKA consists of a copper cylinder of 25 cm radius and 120 cm length, with an effective density set to 90% of nominal to model cooling water channels. In the simulation, the proton beam energy is 2.5 GeV, and the current is 0.2 mA corresponding to losses of 10%. The beam is assumed to be Gaussian, with size \(\sigma _x, \sigma _y = 25\) mm, (59 mm FWHM) and an angular divergence of 1 mrad FWHM. In the simulations, no time structure of the pulses is considered.

Fig. 67
figure 67

Distribution of energy deposition in the copper beam dump

The resulting energy deposition in the beam dump is shown in Fig. 67. Here, a 2D radial projection, integrated over the polar coordinate, is shown in (a); a one-dimensional projection, integrated over the radial and polar coordinates, is shown in (b). The maximum energy deposition is about 30 \({\text {W/cm}}^{3}\) and occurs at \(z\approx 9\) cm.

For comparison, the SNS beam dump has a radius of 15 cm and a length of 80 cm and is built up of copper disks which are stacked into a cylinder with the thickness adapted, so that each disk does not take a heat load exceeding 5 kW. Further details are available in [178]. Due to the higher energy at \({\text {ESS}}\nu {\text {SB}}\), the dimensions have to be increased for the primary and secondary particles to be deposited in the dump. Because of this higher energy, the energy deposition will be spread out over a larger depth, which is an advantage compared to SNS in terms of local heating.

Different dimensions have been tested and it has been concluded that a 25 cm radius is required and a length of 120 cm would be sufficient. A larger radius gives more margin and less heating and activation to the outer shielding, which should be considered when optimising the overall structure.

5.7.2 Shielding calculations

In the present analysis of the shielding, the focus has been on the shielding atop the injection beam dump. Here, there is need for a service area—both for the beam window to the injection dump and for the injection dump itself.

The attenuation of the shielding can be calculated semi-empirically using the Moyer model [179, 180] or a similar approach. Such models are generally valid above 1 GeV; with, for example, a point loss in a target, and thick shielding (more than three mean free paths for inelastic nuclear interactions—in order for the nuclear cascade to develop and average over the energy loss from secondary particles.) Iron has been chosen as the main shielding material, since it performs well in terms of shielding high-energy neutrons. However, iron has fairly low attenuation of low-energy neutrons, which dominate the particle fluence after a few attenuation lengths. Therefore, a concrete layer has been added outside the iron shielding, since concrete has a high attenuation of low-energy neutrons. The effective density of iron has been set to 95% to allow for water cooling to compensate for heating from deposited energy due to prompt radiation and activation. A model of the shielding is shown in Fig. 68, with the beam entering from the left.

Fig. 68
figure 68

Schematic layout of the injection beam dump with shielding

For a point source, the dose-rate outside the shielding can be calculated from [179]

$$\begin{aligned} H=H_0\frac{e^{-d/\lambda }}{R^2}\,{{\mathrm {Sv/h}}}, \end{aligned}$$

where \(H_0\) is the source term in \({\text {Sv/m}}^{2}\), d is the thickness of shielding, \(\lambda\) is the attenuation length (mean free path) for nuclear inelastic interactions, and R is the distance from the source.

The data for the attenuation lengths, \(\lambda\), are taken from [181]. For iron, \(\lambda = 132\) \({\text {g/cm}}^{2}\), corresponding to \(\lambda =16.7\) cm at a nominal density of 7.87 \({\text {g/cm}}^{2}\). Assuming a density of 95% to compensate for cooling channels, this gives \(\lambda =17.6\) cm. Concrete has an attenuation coefficient of \(\lambda =43\) cm at a density of 2.3 \({\text {g/cm}}^{3}\). The attenuation varies with specific concrete composition but with these numbers a first estimate can be made.

The total attenuation factor in Eq. (5.6), \(e^{-d/\lambda }/R^2\), for a shielding consisting of 3 m iron and 1 m concrete at 90\(^\circ\), and a distance 5 m from the source, then becomes \(1.0\times 10^{-10}\).

5.7.3 Source-term calculations

The source term, \(H_0\), has been calculated using FLUKA [175,176,177], again using a copper cylinder of radius 25 cm and 120 cm length as a target surrounded by vacuum, with a beam of \(1.25\times 10^{15}\) particles per second (0.2 mA) consisting of 2.5 GeV protons; and again assuming a density of 90% of the nominal value to compensate for cooling water channels.

The proton beam matches the parameters used in the heat deposition calculations: Gaussian, with size \(\sigma _x, \sigma _y = 25\)  mm, (59 mm FWHM), and an angular divergence of 1 mrad FWHM. The dose-rate distribution is shown in 2D, Fig. 69, integrated over the polar coordinate, and in 1D, integrated over the polar and the radial coordinates, and averaged over \(z=30\)–40 cm, where the dose rate has its highest values.

As can be seen from Fig. 69b, the calculated dose rate at 1 m radius is \(1.9\times 10^5\) Sv/h, which corresponds to a source term \(H_0\) of \(1.9\times 10^5\)\(/{\text {Sv/h/m}}^{2}\). This can be compared to semi-empirical source term calculations following Ref. [179], which gives \(1.6\times 10^5\) \(/{\text {Sv/h}}/{\text {m}}^{2}\).

The dose rate outside the shielding at \(R = 5\) m is then attenuated with a factor \(1.0\times 10^{-10}\) according to Eq. (5.6) giving a dose rate directly outside the shielding of \(19\,\upmu {\text {Sv/h}}\). This dose rate would be acceptable for a radiation worker (corresponding to 6 mSv per year at 300 h occupancy), and depending on the classification of the area, and occupancy, one could possibly reduce the shielding to some extent.

The present calculation should be confirmed with FLUKA simulations or other another Monte Carlo code; this should be complemented with activation calculations, and radiation levels at various cool-down times, i.e., elapsed time after beam shut-off. As mentioned above, the shielding towards the ground, and possible effects of tritium production will have to be studied.

Fig. 69
figure 69

Distribution of dose rate for source term calculations

5.7.4 Summary and outlook

The conceptual design of the injection beam dump consists of a water-cooled copper cylinder of 25 cm radius and 120 cm length, surrounded by 3 m of iron inner shielding and 1 m of concrete outer shielding. The power loss and prompt radiation levels have been calculated for a beam loss of 0.5 MW, 0.2 mA average beam, 10% beam loss. Under normal operation, a lower beam loss is expected—on the order of 2%. The power loss reaches 30 \({\text {W/cm}}^{3}\) at a depth of 9 cm, and the resulting dose rate directly atop the dump is \(19\,\upmu {\text {sV/h}}\), as calculated by performing source-term calculations with FLUKA along with semi-empirical calculations of the attenuation of the shielding.

The heating resulting from the power loss can be handled reasonably well by water cooling, but the detailed thermal and mechanical response has yet to be studied in detail, to make sure that the temperature in the beam dump is kept below \(400\,^\circ {\text {C}}\) to avoid softening of the copper. Such a study will include the actual pulse structure of the beam. One should also keep in mind corrosion problems for copper, owing to radiolysis of water; and possibly consider copper-alloys for mitigation. High neutron flux can also lead to material damage, such as swelling, creep, or embrittlement [182].

The injection beam dump has been designed to be able to handle up to 10% losses. A sustained loss level of 10% is not expected under long-term operation. However, as experience at SNS shows, it is important that the dump is designed with a sufficient margin to handle radiation levels and thermal stresses of up to 10% [183]. One of the problems experienced at SNS—which is an additional constraint for increasing the average beam power—is thermal stress in the concrete and consequent risk of cracking, which reduce the radiation-shielding effectiveness. Alternatives to consider for reducing the beam dump size are temperature monitoring and active cooling of the concrete.

Careful 3D simulations of beam transport are essential, particularly for minimising losses [184], and should be carried out as part of a technical-design phase of the project. However, we do not foresee this issue to be seriously prohibitive: it is more a matter of careful magnet design with full control of the 3D fields, including fringe fields.

A strategy to manage the convoy electrons must also be made. At 5 MW average beam power the convoy electrons carry about 5 kW. A water-cooled electron collector was designed at SNS [145]. A similar system could be envisaged for the \({\text {ESS}}\nu {\text {SB}}\).

5.8 Transfer line from the ring to the beam switchyard

As the compressed pulses are extracted from the accumulator, they are transported through a beam line leading up to the switchyard that feeds the target station. The purpose of this beamline, called the ring-to-switchyard (R2S), is to bring the protons, with as little losses as possible, into correct alignment with the desired neutrino beam direction.

Fig. 70
figure 70

Overview drawing showing the location of the accumulator and the target station, connected by the R2S beam line [185]

In the latest \({\text {ESS}}\nu {\text {SB}}\) layout [185, 186], a line drawn from the beam target through the decay tunnel makes an angle of \(16.8^\circ\) in the horizontal plane with the straight section of the accumulator containing the extraction. In addition, the target station should point at an angle of \(2.29^\circ\) vertically with respect to the horizon. These angles must be respected while designing the R2S beam line to ensure the particles produced by the target to follow their way up in the direction of the beam dump and on to the near and far detectors. From Ref. [185], the coordinates of the exit of the extraction septum magnet and those of the centre of the target station are found to be (101.9; − 280.3; − 12.5) m and (249.1; − 127.4; − 22.35) m, respectively, see Fig. 70. The distance between the target station and the accumulator is then estimated to be 212.40 m, with the depth of the target station at 22.35 m below the ground level (9.85 m below the extraction point at the exit of the septum). All of these values confirm the need for a transfer line with unfolding of the horizontal and vertical planes.

The protons will exit the extraction septum magnet at an angle of \(16.80^\circ\) and \(1.14^\circ\) in the horizontal and vertical planes, respectively, seen from the accumulator reference orbit. Having a transfer line pointed in the intended neutrino-beam direction will ease the subsequent design of the switchyard. This transfer line must be as short as possible to minimise the cost of the equipment comprising it. Figure 71 shows the first suggested layout of the beamline [185] together with the direction of the neutrino beam in the (xy) plane (left) and the (xz) plane (right).

Fig. 71
figure 71

Horizontal and vertical plots of the R2S from [185] and slopes of the neutrino direction. To simplify the simulations, the extraction of the beam at the exit of the septum has the coordinates xyz (0; 0; 0)

5.8.1 Design of the R2S beamline

The particle distributions used in the design process of the R2S beam line are presented in Fig. 72. These distributions come from the anti-correlated painting process and contain 240500 macroparticles. Table 12 contains the main characteristics of the incoming beam.

Fig. 72
figure 72

Transverse phase space of the particles used in the design of the R2S transfer line (240500 macroparticles)

Table 12 Beam parameters of the input beam

The transfer line must contain both vertical and horizontal bends. To minimise the necessary magnetic field per magnet, several dipoles were used to bend the protons in steps. Simulations show that three vertical and eight horizontal bends, 2 m long each, are sufficient for constructing the transfer line. Table 13 presents the main characteristics of the dipole magnets.

Table 13 Main parameters of the dipoles composing the R2S

Quadrupole doublets are then placed in between the dipole magnets for maintaining a small beam envelope and ensure a good transmission. The lattice layout with dipoles and quadrupoles is shown in Fig. 73, whereas Fig. 74 shows the geometric layout of the R2S compared to the original suggestion and the neutrino direction.

Fig. 73
figure 73

Horizontal (left) and vertical (right) synoptics of the R2S beam line

Fig. 74
figure 74

Coincidence of the end of the R2S beam line, designed with TraceWin, and the neutrino beam direction in the horizontal (left) and vertical (right) planes

By adjusting the values of the different quadrupoles composing the beam line, a minimum beam size is achieved and maintained all along the transfer line as displayed in Fig. 75. In the final design the R2S measures 72 m in length and meets all the initial requirements.

Fig. 75
figure 75

RMS transverse beam envelopes along the R2S beam line

5.9 Beam switchyard

Once the proton beam is aligned with the neutrino-beam direction by the R2S beamline, it will be distributed to the four targets by a beam switchyard (BSY). The BSY will not only transport and distribute the protons onto the targets but also focus them to the desired shape and size centred on the target, ideally a circular beam with a radius not larger than 1.5 cm.

Figure 76 shows the layout of the target station. The distance between the centres of the targets is 3 m. The distance was later changed to 2.5 m, but since switchyard designs have been made for the distances 2 m and 3 m, there is no doubt that a good design can be made for values within this range, if the baseline changes.

Fig. 76
figure 76

Face view of the target station layout. The four targets are named T1, T2, T3, and T4

In the baseline pulsing scheme, the linac is pulsed at 14 Hz. As a result the accumulator will deliver a set of compressed pulses or batches to the BSY at 14 Hz, but where the batch-to-batch frequency is 1.1 kHz. Each compressed pulse or batch has a \(1.2\,\upmu {\text {s}}\) duration and the spacing, which leaves less than 0.9 ms for the beam switching from target to target.

5.9.1 Design of the BSY

A previous design suggested diagonally splitting the proton beam onto the target station [187]. However, due to a change in the baseline parameters of the beam (i.e., time structure) coming out from the accumulator, it was no longer feasible to use this configuration. In addition, this design carries a weakness in terms of safety, where a beam dump would be needed to protect the system in cases of dipole magnet failure. Therefore, a new layout was investigated. This new layout suggests driving the protons from one section to the next using conventional dipoles (Fig. 77).

Fig. 77
figure 77

Schematic layout of the beam switchyard. D1 and D2 are dipoles that bend the beam in the horizontal plane. D3, D4, D5, and D6 bend the beam in the vertical plane

Figure 78 shows the working principle of the switching scheme. The switchyard contains six dipoles to bend the beam in both the horizontal and the vertical planes. Sets of quadrupoles maintain minimal transverse envelops of the beam as it propagates through the beamlines. Each branch of the BSY will be equipped with a collimator at its exit.

Fig. 78
figure 78

Time structure of the incoming beam in relation to the dipoles of the BSY

5.9.2 From D1 to T1

The first branch of the BSY transports and focuses the beam onto the target named “T1”. The T1 axis is the main axis of the beam upon exiting the R2S line. To reach T1, the dipoles D1 and D3 act as a drift tube. In other words, no induced magnetic field is needed from their magnets. Figure 79 shows the beam envelopes for the T1 branch. According to these simulations, this branch has a transmission of 100% and is achromatic at its extremity. The radii of the beam in the middle of the target are expected to be 14.90 mm and 14.94 mm in x and y, respectively. Table 14 presents the main beam parameters at the target location.

Table 14 Beam parameters at the target T1
Fig. 79
figure 79

RMS transverse beam envelopes and dispersion along the T1 branch of the BSY

5.9.3 From D1 to T2

The second branch of the BSY transports and focuses the beam onto the target T2. The dipoles D1 and D2 must induce a magnetic field to bend the protons horizontally. The designated angle of deflection must require both a moderate magnetic field in the dipole magnets (less than 1 T, capable of switching on/off with respect to the time structure of the incoming beam) and a sufficient space downstream to allow for positioning equipment. To this end, an angle of 244 mrad was selected. To deflect the beam with such an angle, a magnetic field of 890 mT for a 3 m-long dipole would be necessary. Such dipoles have an inductance of around 15 mH, an intensity consumption of 58 kAt (kilo-Amp-turns), and a 40 mm-radius gap. Figure 80 shows the transverse beam envelops in the xy plane through the T2 branch. The maximum radii for the beam at the centre of the target are expected to be 14.66 mm and 14.98 mm in x and y, respectively. Table 15 presents the main beam parameters at the target location.

Fig. 80
figure 80

RMS transverse beam envelopes and dispersion along the T2 branch of the BSY

Table 15 Beam parameters at the middle of the target T2

5.9.4 From D1 to T3

The third branch of the BSY transports and focuses the beam onto the target T3. This beam line is the most complicated of the system, since four dipoles should be active simultaneously: D1 and D2, as well as D5 and D6 to, respectively, bend the beam horizontally and vertically. Dipoles D5 and D6 are similar to D5 and D6. Figure 81 shows the transverse beam envelops in the xy plane through the T3 branch. The maximum radii of the beam at the middle of the target are expected to be 12.58 mm and 14.99 mm in x and y, respectively. Table 16 presents the main beam parameters at the target location.

Table 16 Beam parameters at the middle of the target T3
Fig. 81
figure 81

RMS transverse beam envelopes and dispersion along the T3 branch of the BSY

5.9.5 From D1 to T4

The fourth branch of the BSY transports and focuses the beam onto target T4. Two dipoles are necessary to bend the beam vertically. Figure 82 shows the transverse beam envelops in the xy plane through the T4 branch. The maximum radii of the beam at the middle of the target are expected to be 14.38 mm and 14.99 mm in x and y, respectively. Table 17 presents the main beam parameters at the target location.

Table 17 Beam parameters at the middle of target T4
Fig. 82
figure 82

RMS transverse beam envelopes and dispersion along the T4 branch of the BSY

5.9.6 Overall layout of the BSY

Figures 83 and 84 show the overall synoptics and 3D views of the BSY, respectively. The system has a total length of 45 m.

Fig. 83
figure 83

Horizontal (left) and vertical (right) synoptics of the BSY

Fig. 84
figure 84

Overall 3D views of the BSY: top, side (middle), and isometric (bottom) projections. Possible locations for adding diagnostics capable of measuring several characteristics of the beam (i.e., size, position, energy, etc.) are identified with boxes

Although simulations show 100% transmission of the beam along the four branches of the BSY, collimators will be placed at the terminus of each beam line. These protect the horns in case of unwanted fluctuations of the beam before it reaches the targets. It must be capable of handling beam halo as well as losses due to any malfunction in the operation of the upstream system. The baffles are mainly made of graphite. Its dimensions would be 2 m in length with an outer radius of 70 cm. A conical aperture with a downstream radius of 1.5 cm, as depicted in Fig. 85, is an option to be considered. The distance between the end of the collimators and the targets is 1025 mm. Following the amount of heat load that is expected to be deposited in the collimator, the use of He (or even air) cooling in closed circuit may be feasible here.

Fig. 85
figure 85

Section plane of the collimators

5.9.7 Alternatives to dipoles

The feasibility of having adequate rise and fall times for dipoles must be tested with respect to the operating frequency. Alternatively, dipoles D1, D3, and D5 could also be a combination of a kicker and a septum. Indeed, according to simulations, a pair of fast kickers of 0.5 m long each could be used to kick the beam for a total angle of 1\(^\circ\), then the septum would further deflect the beam. Each kicker would require a peak current of 383 A to induce the necessary magnetic field of 193 mT. Such kickers can have rise and fall times of less than \(10\,\upmu {\text {s}}\) and operate at frequencies up to 10 kHz [188]. Figure 86 shows the time structure of the BSY when kickers are used. Detailed investigations on such technology shall be performed during the technical design phase.

Fig. 86
figure 86

Time structure of kickers for the BSY

5.9.8 Failure scenarios

Several failure scenarios are possible when operating the BSY. In this report, two of these are discussed. In case of failure of one of the dipoles, the protons would travel straight to the branch leading to the target T1. In addition, the BSY contains enough quadrupoles, so that in case of failure of one of them, the beam envelop would be corrected automatically to match as closely as possible the required beam parameters at the target location. For example, if two quadrupoles of the T3 branch fail at the same time, preliminary calculations show that focusing the beam onto the target is still possible, and achromaticity can be achieved (Fig. 87). In this case the beam would measure 12.48 mm (horizontal) and 14.95 mm (vertical) within the target (Table 18). Nevertheless, according to these preliminary results, this specific scenario would lead to 0.2% losses in the collimators.

Table 18 Beam parameters at the middle of the target T2 when two quadrupoles of the branch are not functioning (failure scenario)
Fig. 87
figure 87

RMS transverse beam envelopes and dispersion along the T3 branch of the BSY when two quadrupoles, Q34 and Q37, are not functioning (failure scenario)

5.10 Vacuum system

The beam vacuum requirements of the \({\text {ESS}}\nu {\text {SB}}\) accelerator complex are mostly expected to be in line with similar operating machines. Due to their single-pass nature, the vacuum level in the transfer lines, both before and after the ring, is expected to be of the order of \(10^{-7}\) mbar. This means that at the point of extraction from the linac, the two beam lines will have comparable vacuum levels, so that there is no need for differential pumping.

A higher vacuum level, about \(10^{-8}\) mbar, will be needed in the ring where the head of each injected batch will spend about 0.8 ms making 600 turns of revolution. Even though the beam will be extracted immediately after the injection is complete, there is a risk of instabilities arising in the ring. At this high beam intensity, and an almost coasting beam, the biggest concern is likely to be the instability caused by the interaction of beam protons with electrons released from the inner side of the vacuum chamber [189]. The risk can be mitigated by suppressing the emission of secondary electrons by coating the inner surface with a ceramic material, titanium nitride (TiN).

A TiN coating forms a barrier that prevents outgassing, primarily of hydrogen from the stainless-steel vacuum chamber. This helps to maintain an acceptable vacuum level. Such a coating also suppresses the emission of secondary electrons, which is an important measure against the formation of electron clouds. It is these electron clouds that can, in combination with the high-current proton beam, give rise to electron–proton instabilities as the proton bunch interacts with the electron could coherently on a turn-by-turn basis.

The emission and reflection of blackbody radiation in the vacuum chamber is also suppressed by the TiN coating. Studies of \({\text {H}}^-\) stripping processes indicate that stripping due to blackbody radiation can be an issue in the transfer line (see Sect. 4.10), unless the emission and reflection is mitigated through coating or cooling of the vacuum chamber. It is therefore expected that the vacuum chamber in the linac-to-ring transfer line will have to be coated (although polishing of the beam-pipe may also be a feasible alternative).

5.11 Safety

The design of the accumulator ring and transfer lines is governed by one major safety aspect: that the uncontrolled beam loss must not supersede 1 W/m (see also Sect. 4.10). This is the empirical limit below which the activation of the accelerator equipment is low enough to allow hands-on maintenance 1 h after a beam stop. The large curvature of the linac-to-ring-transfer line, the two-stage collimation system, and the generous machine acceptance in the ring are a few results of this limitation. The loss limit is thus important both for the machine availability and for the safety of the personnel.

It is already apparent at this stage that certain sectors in the accelerator chain will have a elevated risk of beam loss. These sectors will suffer more activation which may restrict human intervention. The injection and extraction regions, the injection dump line, and the vicinity of the collimators are such sectors. Note that a large fraction of the losses in these regions are considered controlled, and therefore may be higher than the 1 W/m limit.

A detailed understanding of beam-loss patterns in the beam lines will require further study, where instabilities, magnet position and field errors, correction technique, and further effects are modelled. Only then will it be possible to fully judge the activation risks, and determine the need for extra shielding near to the accelerator. As with all particle accelerators, a global radiation monitoring system will be employed to control the radiation levels. In addition, dosimetry for any personnel entering the accelerator area will be necessary.

An extensive system of beam diagnostics and instrumentation will also be necessary. Several hundreds of beam loss monitors will be distributed along the beam line, combining two main types: fast monitors, to detect fast losses that could harm the machine; and slow varieties, to monitor losses over longer term. The former will be connected to a machine protection system with feedback to the \({\text {H}}^-\) source. If an error occurs which results in a rapid spike in losses, the source must be stopped on the next pulse. Roughly 200 beam position and current monitors will be employed in the beam-loss control and machine-protection scheme.

Longitudinal and transverse beam profile monitors, a diagnostic system to measure the particle tune in the ring, and a system to detect particles in the extraction gap will be crucial tools to safely operate the complex at 5 MW (along with a variety of other instruments and methods). The commissioning of the machine will be done in stages, heavily relying on the beam diagnostics, by slowly increasing the number of injected turns and the total intensity passing through the beam lines.

The 900 m of new beam line is a challenge in terms of safety preparations—in the sense that a plan must be made for a multitude of different failures. A study of such failure scenarios will be left to a later stage in the project. The existing systems at ESS, and the experience of the ESS staff will help in facilitating the planning and the implementation of all the \({\text {ESS}}\nu {\text {SB}}\) safety systems.

5.12 Summary

The accumulator ring detailed in this section is a prerequisite for the use of the unique beam power of the ESS linac for the production of a neutrino super-beam. By compressing the long pulses from the linac, through multi-turn charge-exchange injection and single-turn extraction, pulses on the order of a microsecond can be delivered to the target station and its neutrino horn. Through this, the beam is compliant with the power restrictions of the horn, while, at the same time, the background level in the far neutrino detector is suppressed.

The accumulator ring consists of four short arcs with an FODO cell structure, connected by long straight sections. The arcs provide the proper phase advance for the straight sections to be free from dispersion. Five sextupole magnets, with which the natural chromaticity can be corrected, are included in each arc. Each straight section will contain systems to ensure a good performance.

The first straight section will house the injection system where the \({\text {H}}^-\) beam is stripped and merged with the circulating proton beam. The injection system consists of four dipole magnets forming a permanent orbit bump, \(2\times 4\) fast kicker magnets to generate a fast bump that is varied to provide phase space painting. At the first stages of the project, foil stripping will be used.

It is essential that the thermal load on the stripper foil is limited, something that is a challenge at 5 MW average beam power and high batch-to-batch repetition rate. An injection process using anti-correlated phase space painting has been designed, so that the final beam distribution is uniform and so as to minimise the number of stray foil hits. Instead of a single stripper foil, a sequence of thinner foils will be used. This increases the radiating area and speeds up the cooling between pulses. In addition, a mismatched injection, where the optical function of the injected beam is larger than the one of the circulating beam, will be used. This measure dilutes the beam spot at injection and thus reduces the peak temperature. By combining these three techniques, the steady-state, peak temperature can be kept at just above 1900 K.

The second straight section downstream from the injection contains a two-stage collimation system consisting of a thin scraper followed by four long absorber blocks. The collimator elements will have a position-adjustment mechanism so as to be able to respond to variations in the beam trajectory and size. A 97% collimation efficiency is expected from this system and the machine acceptance is estimated to \(200\pi\) mm mrad.

Barrier RF cavities will be employed to preserve the beam-free gap needed for the extraction. If RF cavities are included also in the linac-to-ring transfer line, the incoming energy spread can be kept low and the required RF voltage becomes moderate, around 10 kV. If the energy spread is allowed to grow from space charge in the transfer line at least 20 kV is needed to keep the gap clean.

The compressed pulse will be extracted in a single turn using a combination of fast kicker dipoles, that provide a vertical kick, and a horizontal septum magnet that deflects the beam horizontally into the ring-to-target transfer line. The extraction kickers consists of four groups of four identical kickers in each, to minimise the sensitivity to the failure of a a single kicker. The extraction system has been designed with a margin so as to reduce losses at extraction.

The ring-to-switchyard transfer line includes quadrupoles for beam focusing and a dog-leg structure in each plane, to bring the beam into the correct direction as it arrives at the switchyard. The beam switchyard consists of four beam lines, each one leading to one of the four targets. Every pulse from the linac is transformed into four short pulses in the accumulator. Each pulse will be delivered to a different target by six dipole magnets. Three of these dipole magnets are fast-switching. A detailed report of the switchyard design, including beam envelopes and final beam sizes as well as first considerations for the switching dipoles, has been given here.

The \({\text {ESS}}\nu {\text {SB}}\) accumulator could be used for producing very short and intense pulses of neutrons for the neutrons community. However, it is uncertain if this can be done through multi-turn extraction with tolerable loss-levels, simultaneously with the \({\text {ESS}}\nu {\text {SB}}\) operation. A study of neutron targets that can tolerate the fully compressed pulse extracted in a single turn is an alternative solution.

A conceptual design of the injection beam dump was presented, as well as a discussion of vacuum parameters. The section ended with a discussion of safety aspects required for the \({\text {ESS}}\nu {\text {SB}}\).

6 Target station

The target station facility is a key element of the \({\text {ESS}}\nu {\text {SB}}\) project, which will convert the \(5\,{\text {MW}}\) proton beam with a \(14\,{\text {Hz}}\) frequency into an intense neutrino beam. These particles are produced by the decay-in-flight of secondary mesons (mostly pions), which are created by the interaction of the proton beam within the target and focused into a decay tunnel by a hadronic collector. The technology chosen is based on a solution already studied in the framework of the European design study EUROnu [190], and it consists of four solid targets, each embedded in a magnetic horn. This hadronic collector, termed a “four-horn system” and shown in Fig. 88, is supplied by a custom design power unit, producing a high magnetic field capable of focusing the pions inside the decay tunnel.

Fig. 88
figure 88

Overview of the target station facility including the four-horn system, the decay tunnel, the beam dump, as well as the hot cell used for manipulating/repairing the hadron collector

The revision of the baseline parameters with respect to EUROnu [190] imposes significant changes on the present project. Most of the elements must be refined; in particular, the shape of the individual horns of the target station and the dimensions of the facility. From a technical point of view, the high-power deposition inside the target imposes more stringent constraints on the granular target in terms of cooling and mechanical performance. The consequence of the change of the horn shape and the fast commutation between the four horns imposes a need for a new power-supply-unit scheme based on a modular approach.

In addition, the facility building hosting the target station will be subject to an intense flux of radiation, producing high-energy deposition and high activation levels in the surrounding materials. This facility will also be equipped with essential elements including a hot cell to repair the hadronic collector, a morgue to store radioactive elements, and a beam dump to stop remaining particles. The design of such a facility represents a considerable challenge in terms of physics and engineering, and has to be compliant with Swedish safety regulations. In the following text, separate sections will address the aforementioned evolution of elements, starting with the defining factors of the target station and followed by the proposed technological solutions.

6.1 Hadronic collector

In all neutrino Super Beam experiments, neutrinos are produced by the decay-in-flight of mesons inside the decay tunnel of the facility, through the following reactions:

$$\begin{aligned} \begin{array}{lcl} \pi ^+ &{} \longrightarrow &{} \mu ^+ + \nu _\mu \\ \\ \pi ^- &{} \longrightarrow &{} \mu ^- + \overline{\nu }_\mu . \end{array} \end{aligned}$$

The magnetic horns surrounding the target focus \(\pi ^+\) (\(\pi ^-\)) and defocus \(\pi ^-\) (\(\pi ^+\)) particles, thanks to the toroidal magnetic field generated by a short-pulse electric current running through the horn skin, to ultimately produce the \(\nu _\mu\) (\(\overline{\nu }_\mu\)) beam. The polarity of the current allows for the selection between \(\nu _\mu\) (positive polarity) and \(\overline{\nu }_\mu\) (negative polarity) modes. Other types of neutrino flavors are also produced by the decay of other types of particles (like kaons) at lower rates.

The four-horn system, shown in Fig. 89, allows for an effective reduction of the incoming beam power of \(5\,{\text {MW}}\) delivered by the linac to a more acceptable level of \(1.25\,{\text {MW}}\) per target, with \(2.5\,{\text {GeV}}\) proton kinetic energy, \(1.3\,\upmu {\text {s}}\) pulse duration, and a \(14\,{\text {Hz}}\) repetition rate. Each pulse will therefore deliver \(2.23 \times 10^{14}\) protons/pulse/target. The transverse beam profile is characterised by a quasi-uniform distribution formed by the anti-correlated painting technique in the accumulator ring (see Sect. 5.2).

Fig. 89
figure 89

The target station for \({\text {ESS}}\nu {\text {SB}}\)

The beam distribution on the targets is obtained after the transport of the proton beam to the switchyard, its profile in the transverse plane has a diameter of \(\sim 2.8\,{\text {cm}}\) and a divergence of 5 mrad. Due to the high power and short pulse duration of the proton beam, the \({\text {ESS}}\nu {\text {SB}}\) target will therefore be operating under severe conditions.

6.1.1 Horn shape optimisation

Due to the relatively low energy of the protons from the ESS linac, the pions exiting the target are expected to have a large angular spread. The shape of the horns was determined using a deep-learning method based on a genetic algorithm. This technique is an evolutionary algorithm, in which a set of different geometric configurations of the system to be optimised is allowed to evolve towards the best figure of merit (FoM), which is taken to be the fraction of \(\delta _{{\mathrm{CP}}}\). The configuration with the best FoM value after several iterations, known as “generations”, is taken as the optimised configuration of the system (Fig. 90).

Fig. 90
figure 90

Optimisation of the horn profile

A simplified geometry consisting of the four targets, together with the horn assembly and the decay tunnel has been considered and simulated with FLUKA [176]. The system is characterised by a parameter set defining the geometry of the horn and the length of the decay tunnel. Each parameter has been allowed to evolve within a range scaling between 0.5 and 1.5 times the initial reference values. The results of these calculations suggest an overall increase in size for the target station, as shown in Fig. 91.

Fig. 91
figure 91

Definition of the horn parameters and their values obtained after optimisation

This physics optimisation procedure resulted in a nearly finalised horn shape. However, some additional modifications—the most important of which was the diameter of the horn neck (the part directly encircling the target)—were determined by the target cooling requirements. The final horn dimensions, for which the results are discussed below, are shown in the technical drawing in Sect. 6.1.3. The neutrino fluxes obtained for the final horn shape are represented in Fig. 92 with the flavor composition given in Table 19.

Fig. 92
figure 92

The initial neutrino fluxes for the two horn polarities

Table 19 Neutrino flux composition at \(100\,{\text {km}}\)

6.1.2 Granular target design

A granular target solution was proposed in the early 2000s by P. Sievers at CERN [191, 192], and was then adopted in the context of the EUROnu project [190]. The main advantage of such a design in comparison with a monolithic target lies in its possibility of the cooling medium flowing directly through the target, which allows for a better heat removal from the target regions with the highest power deposition (specifically, from the centre of the target co-aligned with the axis of the impinging proton beam). In addition, the stress levels are much lower in a granular target compared to a monolithic design. This target concept has been studied in the frame work of the \({\text {ESS}}\nu {\text {SB}}\) project.

Fig. 93
figure 93

3D model of the target concept based on a packed bed of titanium spheres Target cooling concept

The conceptual model of a helium-cooled target is shown in Fig. 93. The granular target under consideration is a rod of \(78\,{\text {cm}}\) length and \(3\,{\text {cm}}\) diameter, consisting of titanium spheres with a mean diameter of \(3\,{\text {mm}}\), placed within a container made of titanium. It has been assumed for the purpose of this study that the porosity of the target is equal to 0.34, so that 66% of the target volume includes titanium spheres, while the space between the spheres is filled with the coolant (gaseous helium).

The impinging beam will consist of \(1.3\,\upmu {\text {s}}\) proton pulses, repeated at a frequency of \(14\,{\text {Hz}}\). As a result of the interaction of the beam with the target spheres, an estimated \(138\,{\text {kW}}\) will be deposited in each target as heat. A map of the average power deposition inside the target is shown in Fig. 94. Due to the high power deposited (almost three times higher than in the EUROnu project), efficient heat removal is a critical issue.

Fig. 94
figure 94

Map of power deposition inside a titanium granular target

Heat energy is deposited by the beam into the spheres during a short time at the beginning of each cycle; afterwards, it is transferred to the surrounding medium over the remainder of the cycle (\(t_c=1/f=0.071\,{\text {s}}\)). The principal mechanism of heat transfer is the transmission of heat from the surface of the spheres to the helium flowing outside, known as forced heat convection. Because of the large amount of energy released in the titanium spheres, a high-helium mass-flow rate is required. Passing such a big quantity of gas in the axial direction through the target is not feasible, not only due to the target length and its small diameter, but particularly as a result of the high sphere-packing ratio. This is the main reason for selecting transverse target cooling, as shown in Fig. 93.

To facilitate the study of granular target cooling, an analytical model has been proposed in [193]. This model allows for a rapid estimation of the influence of different parameters, such as the target geometry, the packing ratio, and the flow rate on target cooling. Figure 95 presents the average temperature \(T_a\), pressure p, velocity u, and density \(\rho\) of helium within the first target sector (the first \(8\,{\text {cm}}\) of the target length) plotted against the transverse coordinate \(y_{\mathrm{s}}\), obtained using this model (full details are given in [193]). The results of the maximum sphere temperature \((T_{\mathrm{s}})_{{\mathrm{max}}}\), minimum sphere temperature \((T_{\mathrm{s}})_{\mathrm{min}}\), and \(\Delta T_{\mathrm{s}}\) vs. the transverse coordinate \(y_{\mathrm{s}}\) are shown in Fig. 96.

Fig. 95
figure 95

Helium-flow parameters obtained from the analytical approach for transverse flow (first sector)

Fig. 96
figure 96

\((T_{\mathrm{s}})_{{\mathrm{max}}}\), \((T_{\mathrm{s}})_{{\mathrm{min}}}\) and \(\Delta T_{\mathrm{s}}\) of spheres in each beam cycle (first sector)

Figure 97 shows steady-state results from a CFD (Computational Fluid Dynamics) analysis performed using ANSYS Fluent [194], for a helium global mass flow rate \(\dot{m} =\) \(0.3\,{\text {kg/s}}\) (mass flow for the whole target) and with the power distribution inside the target given in Fig. 94. The numerical calculations for the packed-bed target are used a porous-medium approach, as proposed by Ergun [195]. The superficial velocity shown in Fig. 97 is a related to the local velocity u and the porosity of the porous medium. The profiles shown do not change significantly along the target length, but since the most proton beam power is released in the initial part of the target, the temperature (apart from the target initial part) decreases downstream from the point of beam impact.

Fig. 97
figure 97

Distribution of superficial velocity [\({\text {m/s}}\)] (a), temperature [K] (b), absolute pressure [\({\text {Pa}}\)] (c), and density [\({\text {kg/m}}^{3}\)] (d) of helium flowing upwards in the transverse direction through the first two sectors of the target under constant helium mass flow \(300\,{\text {g/s}}\) and with the non-homogeneous power deposition inside the target having a total value of \(\dot{Q} = 138.53\,{\text {kW}}\)

Both the analytical and the CFD simulations show that the velocity of the flowing gas decreases in the vicinity of the target axis, where the beam power density is the highest, and is higher at the outlet (Figs. 95, 97a). The decrease in the gas velocity in regions near the target axis results in a significant reduction in the heat transfer coefficient there, which in turn reduces heat exchange between the spheres and the gas. As a result, there is a considerable increase in the temperature of the spheres in this region. The maximum temperature of the spheres has been found to be approximately \(750\,{\text {K}}\), well below the melting point of titanium (about \(2000\,{\text {K}}\)). Static and dynamic stress in the target spheres

The power density averaged over the region of the “hottest” sphere is about \(2.8 \times 10^{9}\,{\text {W/m}}^{3}\) (compare Fig. 94). Taking into account that the power is deposited only in the titanium spheres, which occupy 0.66% of the volume, the power density used in the calculations is \(4.25 \times 10^{9}\,{\text {W/m}}^{3}\). For the material properties specified in Table 20, the maximum value of the steady-state stress components and the von Mises stress is equal to \(50.6\,{\text {MPa}}\), for a sphere with \({1.5}\,{\text {mm}}\) radius. The steady-state stress is lower for smaller sphere radii. It is reduced to \(22.5\,{\text {MPa}}\) and \(12.7\,{\text {MPa}}\), for sphere radii of \(1\,{\text {mm}}\) and \(0.75\,{\text {mm}}\), respectively. The stress in a sphere can be shown to be independent on the heat transfer coefficient on the sphere surface.

Table 20 Material properties of titanium spheres used in stress calculations

However, the temperature on the spheres depends on the heat transfer coefficient. This has been calculated in the previous section, and it is equal to about \({4600}\,{\text {W (m}}^{2}\,{\text {K}})\)), for spheres of \(1.5\,{\text {mm}}\) radius. Using this value, the maximum temperature increase above the temperature of cooling helium at the titanium sphere core is equal to: \(555.7\,^{\circ }{\text {C}}\), \(349.6\,^{\circ }{\text {C}}\) and \({254.4}\,^{\circ }{\text {C}}\), respectively, for the sphere radii of \(1.5\,{\text {mm}}\), \(1\,{\text {mm}}\) and \(0.75\,{\text {mm}}\). The last two values are expected to be even lower, since the heat transfer coefficient tends to decrease with the sphere radius.

Thermal shock in the spheres that make up the target is an important issue. Analytical models that make use of wave propagation in solids have been studied for rods, discs, and cylinders in [196]. These analytical solutions provide the necessary insight into the complex phenomena resulting from thermal shock. The numerical study of thermal shock, e.g., using the finite element method, calls for much care, in terms of the size of the elements used and the integration time [197]. As a rule, unrealistically low stress levels are obtained if the mesh is not fine enough or the integration time step is too large. To obtain reliable results, a code using explicit integration schemes can be used. The results discussed below have been calculated using ANSYS LSDyna.

The energy released during each pulse by the proton beam in \(1\,{\text {g}}\) of titanium that makes up the spheres is estimated, based on the above steady-state value and taking into account that the proton beam pulses are repeated every \(14\,{\text {Hz}}\), to be about \(67\,{\text {J/g}}\) per cycle. For the specific heat value used (\(c_p={600}\,{\text {J/(kg K)}}\)), this results in a linear temperature increase of the “hottest” titanium spheres during the duration of a pulse by \(112\,{\text {K}}\).

Fig. 98
figure 98

Dynamic stress at the sphere core

Figure 98a shows the dynamic stress at the sphere centre, where the stress is the highest, over a time interval three times the pulse length, for a sphere with a radius of \(1.5\,{\text {mm}}\). The sphere is free to deform everywhere on its surface. The principal stress components, which are equal to the stress components in the spherical coordinate system \(\sigma _{\mathrm{r}}\), \(\sigma _\phi\) and \(\sigma _ \theta\), coincide for this point. One can see from this figure that the beam pulse length of \(1.3\,\upmu {\text {s}}\) is longer than the period of oscillations of a sphere. The maximum value of dynamic stress is equal to \(83\,{\text {MPa}}\). For comparison, about half of this value would be found at a point located at a distance of one-half radius from the centre. Additive superposition of the stress wave at the end of the pulse appears in the plot, as has been discussed for discs in [196]. Since the dynamic stress has an oscillatory character, it will combine with the static stress, irrespective of the sign of the latter. The maximum static plus dynamic stress is below the tensile strength of titanium (\(220\,{\text {MPa}}\)), and especially that of some titanium alloys (the mechanical properties of which can, however, deteriorate significantly with temperature). Material and fatigue issues in the presence of high temperature and radiation will require additional study.

As a general rule, the stress due to thermal shock of a given pulse length tends to decrease for smaller radii, but the additive superposition mentioned above can also play an important role. Figure 98b shows the stress components for a sphere with radius equal to \(0.75\,{\text {mm}}\). The maximum value of dynamic stress in this case is equal to \(52\,{\text {MPa}}\). The packing fraction is equal to 0.66, the same as for the spheres with \(1.5\,{\text {mm}}\) radius.

The value of radius equal to \(1.5\,{\text {mm}}\) has been used when studying target cooling to allow for an efficient flow of helium gas through a packed-bed target. Reducing the sphere size imposes more severe conditions on the cooling system performance, since smaller radii lead to a higher pressure drop of helium. For this reason, the radius of the spheres was kept equal to \(1.5\,{\text {mm}}\) as a baseline. Concerning the stress in the spheres, it would be advantageous to reduce the sphere size. To make the final selection of the sphere radius, some experimental results will be required, primarily to test how the sphere size affects the flow of cooling helium through a packed-bed target.

6.1.3 Magnetic horn design

Figure 99 shows the final optimised shape of the \({\text {ESS}}\nu {\text {SB}}\) horn.

Fig. 99
figure 99

Sketch of the magnetic horn proposed for \({\text {ESS}}\nu {\text {SB}}\)

Different aspects must be considered in a horn design, including the magnetic field calculation, horn cooling, as well as the mechanical stresses due to magnetic, mechanical, and thermal loading. All results discussed below have been obtained using the ANSYS finite element code.

Magnetic field due to current pulsing The magnetic field is generated when the horn undergoes a \(100\,\upmu {\text {s}}\) current pulse of magnitude \(350\,{\text {kA}}\). A semi-sinusoidal current pulse will be provided by a power supply unit, which is discussed in detail in Sect.  6.2. Figure 100 shows the magnetic flux density inside a magnetic horn at time \(t=50\,\upmu {\text {s}}\), when the current takes on its maximum value. The maximum calculated magnetic flux density is about \(2.1\,{\text {T}}\).

Fig. 100
figure 100

Magnetic flux density in tesla inside a horn and surrounding space, at time \(50\,\upmu {\text {s}}\) when the value of current is equal to \(350\,{\text {kA}}\) (after the current discharge)

Power deposition inside the magnetic horn The power deposited inside the magnetic horn during each cycle comes primarily from two sources: the secondary particles leaving the target during a beam impact (Fig. 101) and the Joule heat losses caused by the high-amplitude current pulsing through the horn skin (Fig. 102). In calculating Joule heat losses, an electromagnetic analysis has been performed, which accounts for the skin effect in the horn wall. A summary of the power deposited in different horn sections can be found in Table 21.

Fig. 101
figure 101

Power density in \({\text {kW/cm}}^{3}\) inside the magnetic horn skin due to secondary particles

Fig. 102
figure 102

Joule power density per unit volume in \({\text {W/m}}^{3}\) in the horn skin, at time \(50\,\upmu {\text {s}}\) (horn outer skin is not shown)

Table 21 Power deposition inside the horn by secondary particles and Joule heat losses

Estimation of the required water mass flow rates Based on the balance of energy transferred to the water from each of the separate horn sections and the increase in the internal energy of cooling water, the mass flow rate of water required for the operation of the cooling system can be calculated from the formula

$$\begin{aligned} \dot{m} = \frac{P_{\mathrm{SP}}+ P_{\mathrm{JH}}}{c_{\mathrm{w}} \Delta T_{\mathrm{w}}}, \end{aligned}$$

in which: \(P_{\mathrm{SP}}\) and \(P_{\mathrm{JH}}\) is the power from the secondary particles and from Joule heat losses in a given section, respectively; \(c_{\mathrm{w}}\) is the specific heat of water; and \(\Delta T_{\mathrm{w}}\) is an increase in the water temperature.

Assuming the specific heat of water \(c_{\mathrm{w}}=4193\,{\text {J/(kg K)}}\) and the increase in water temperature due to the transmission of energy from the cooled surface equal to \(\Delta T_{\mathrm{w}} = 10\,^{\circ }{\text {C}}\), the mass flow rate for each section of the horn can be estimated as listed in Table 22, and sketched in Fig. 103.

Table 22 Mass flow rate for different horn sections, assuming a water temperature increase of \(\Delta T_{\mathrm{w}} = 10\,^{\circ }{\text {C}}\)
Fig. 103
figure 103

Model of the horn with values for each section of power deposition, required mass flow rate, and temperature

Horn average temperature in steady-state operation Given the power deposition by the secondary particles and Joule heat losses included in Table 21, the average temperature of each horn section has been estimated analytically. The value of the heat transfer coefficient \({\text {H}}=3000\,{\text {W/(m}}^{2}\,{\text {K}})\) has been used for the entire horn surface. The results are collected in Table 23.

Table 23 Average horn temperature for each section of the horn, assuming a heat transfer coefficient \(h=3000\,{\text {W/(m}}^{2}\,{\text {K}})\) and water temperature \(T_{\mathrm{w}} = 25\,^{\circ }{\text {C}}\)

Assuming a cooling water temperature of \(T_{\mathrm{w}} = 25\,^{\circ }{\text {C}}\), the highest temperature (\(51.40\,^{\circ }{\text {C}}\)) is expected to occur on the horn walls in the direct vicinity of the integrated target (the “Inner1” section in Fig. 103).

Numerical analyses have also been performed with respect to the cooling of the horn, using the same values of deposited power. The temperature calculated using ANSYS is \(51.26\,^{\circ }{\text {C}}\), which is comparable to the results obtained using the simplified analytical approach.

Mechanical stresses in the horn Figure 104 gives the results of the structural analysis of a magnetic horn under a single current pulse. The maximum stress in the horn shell is equal to \(28.2\,{\text {MPa}}\) and the maximum longitudinal displacement is equal to \(0.1\,{\text {mm}}\). The maximum values occur at different horn locations, but also at different times. These values fall entirely within the acceptable limits.

Fig. 104
figure 104

Results of horn structural analysis due to magnetic forces

The steady-state stress levels due to the calculated thermal load are shown in Fig. 105, for the heat transfer coefficient of \(3000\,{\text {W/(m}}^{2}\,{\text {K}})\). The maximum steady-state stress is low (below \(10\,{\text {MPa}}\)).

Fig. 105
figure 105

Thermal stress in a magnetic horn, assuming heat transfer coefficient between horn and water \(h = 3000\,{\text {W/(m}}^{2}\,{\text {K}})\)

6.1.4 Target-horn integration issues

Figure 106 shows the direction of gas flow through the target shell, with the gas inlet located at the bottom and the gas outlet at the top of the shell. Figure 107 shows the cross-section of the proposed integration concept of a target inside a horn. The design consists of: the granular target spheres placed inside a \(2\,{\text {mm}}\)-thick titanium container (in red), the outer \(2\,{\text {mm}}\)-thick shell (also in red), two \(2\,{\text {mm}}\)-thick plates which connect the target container to the outer shell, and the horn inner conductor (in violet). There is a \(1\,{\text {mm}}\) thick layer of gaseous helium (in blue) between the outer shell and the horn inner conductor, which provides thermal insulation. The location of the attachment of the plates has been chosen for two reasons: First, they separate the lower channel, into which cooling helium is pumped, from the upper channel, from which hot helium will be extracted. Second, they act as a link between the target container, target shell, and the horn wall. They are also placed in a region of a relatively low temperature, which ensures the acceptable levels of thermal stress.

Fig. 106
figure 106

Direction of helium inflow and outflow

Fig. 107
figure 107

Cross-section of the proposed horn–target integration (horn in purple, target container, target shell and connecting plates in red, thermal isolation in blue) used for the calculations

Initially, three gas inlet and three gas outlet channels were considered for cooling the target, as was proposed in the EUROnu project. However, the calculations have shown that for such a layout most of the gas tends to flow directly towards the outlets, omitting the central area of the target located around the z-axis, where the most power is deposited. For this reason, to ensure the flow of the gas through the centre of the granular target, a design has been proposed in which the gas inlet is located on the opposite side of the gas outlet, as shown in Fig. 106.

Figure 108 shows the top–down view of a layout of the openings in the target container, to allow for the transverse flow of helium through the granular target. The width of each opening is \(1.5\,{\text {mm}}\), the distance between them is \(4.59\,{\text {mm}}\)(there are 128 holes along the shell length of \(78\,{\text {cm}}\)), and the total surface of the holes is equal to twice the overall cross-section area of the gas inlet and outlet channels. The size and distribution of the openings at the bottom (gas inlet) and the top (gas outlet) of the target container are the same.

Fig. 108
figure 108

Pattern of helium entry and exit openings of uniform size in the target container

Figure 109 shows the numerical results obtained with inner horn diameter \(d = 80\,{\text {mm}}\), helium mass flow rate \(\dot{m} = 0.3\,{\text {kg/s}}\), power deposition \(P = 138.53\,{\text {kW}}\), and the titanium granular target modelled as a porous medium. It has also been assumed in these calculations that the heat transfer coefficient at the surface of the horn sprayed by water jets is \(3000\,{\text {W/(m}}^{2}{\text { K}})\), and that the space between the shell and the horn is filled with helium.

Figure 110a shows the temperature in the outer shell, under the conditions specified above. Assuming that the container and the outer shell are connected by plates along their length, and that the plates are fixed on their outer edges, the maximum deflection of 0.28 mm occurs at the end of the outer shell, whereas the maximum von Mises stress in the outer shell is around \(100\,{\text {MPa}}\). This is the maximum value of stress, except for very localised stress concentrations at both ends of the plates, which will depend on the plate-attachment configuration. The plots of the displacement and von Mises stress are shown in Fig. 110b, c, respectively.

As far as the electrical insulation is concerned, the horns will be insulated from both the support frame and the cooling manifold. Additionally, the target must not be grounded.

Fig. 109
figure 109

Numerical results for helium flow under a steady-state power deposition condition for titanium spheres, inner horn diameter \(d=80\,{\text {mm}}\), and the pattern of shell holes of uniform size

Fig. 110
figure 110

Mechanical analysis of the shell and target container

6.1.5 Four-horn support system

Fig. 111
figure 111

a General view of four horn support system, b side view

The static and dynamic analyses of the four-horn support frame are discussed in the following subsections. Static analysis of the four-horn support system

Figure 111 shows the general concept of a four-horn support frame. The proposed solution takes into account both the assembly and operation conditions. For this purpose, a frame system was proposed which provides a relatively easy access to the horns and their additional equipment (water jets, drain pipes, etc.), as well as sufficient stiffness resulting in minimum vertical deflections of the horns themselves (y-direction). In the proposed approach, each horn is directly supported on two saddle supports, which are located at positions in the z-direction that ensure equalisation of the maximal values of the bending moment distributed along the z-axis. These points are taken at \(z_1=570\,{\text {mm}}\) and \(z_2=2100\,{\text {mm}}\), measured from the inner edge of the collar of the horn, at the upstream end of the horn. All the elements of the frame will be made of aluminium. It is also assumed that the frame will be rigidly supported at several location on its top and bottom, including the corner points.

The saddle supports are placed on a horizontal supporting plate, which is attached to channel sections at both ends parallel to the x-axis. These are joined by means of welding in the four corners to the frame system. Taking into account the mass of the horn and its surrounding equipment (not modelled), the stiffness of the plate alone is too low to keep the vertical deflections within the required range. Therefore, to increase the plate stiffness, a set of three vertical ribs is introduced, welded to the bottom of the plate.

For the supporting frame, a channel section has been chosen. The proposed aluminium channel section has the standard dimensions (C-cross section: \(250\,{\text {mm}} \times 150\,{\text {mm}} \times {18}\,{\text {mm}}\)), and it consists of commercially accessible elements. The numerical results obtained for the designed structure are as follows:

  • The maximum absolute value of vertical deflection for the horn assembly: \(u_y=2.06\,{\text {mm}}\); (Fig. 112)

  • The maximum absolute value of vertical deflection for the support system: \(u_y=1.85\,{\text {mm}}\); (Fig. 113)

  • The maximum value of equivalent stress for the horn assembly: \(\sigma _{{\mathrm{eqv}}}=39.3\,{\text {MPa}}\);

  • The maximum value of equivalent stress in the supporting plate: \(\sigma _{{\mathrm{eqv}}}=18.8\,{\text {MPa}}\);

Fig. 112
figure 112

Distribution of vertical deflections in four-horn assembly—results in \({\text {mm}}\)

Fig. 113
figure 113

Distribution of vertical deflections in supporting frame—results in mm

The results illustrating the discrepancies from the perfect horizontal position of the top and bottom horn axes, defined by the vertical deflections in two chosen points (see Fig. 114) are as follows:

  • Top horn: \(\Delta u_y = \left| -1.58 + 1.21 \right| {\text {mm}} = {0.37}\,{\text {mm}}\)

  • Bottom horn: \(\Delta u_y = \left| -1.57 + 1.22 \right| {\text {mm}} = {0.35}\,{\text {mm}}\).

Fig. 114
figure 114

Control point K and L location Dynamic analysis of the frame with four horns

Table 24 gives the lowest natural frequencies of a frame with the four horns. The thickness of the plates of the saddle supports is equal to \(20\,{\text {mm}}\)—the value was also used for the static analysis. These frequencies have been obtained under the condition that the frame is restrained at its top and bottom. It is important to ensure that this condition will be met in the final design. Should either the top or the bottom part of the frame be flexibly attached, much lower frequencies will result, which would lead to unacceptably high frame displacement due to the magnetic pulses.

Table 24 Ten lowest natural frequencies of the frame with the four horns

The frame has been designed, so that its natural frequencies with the four horns are not near the pulse-repetition frequency of \(14\,{\text {Hz}}\), to avoid the risk of resonance. However, the natural frequencies may change if additional elements add substantial mass or stiffness to the structure. To avoid this effect, both the striplines and the cooling water pipes need to be connected flexibly to the horns (for the pipes, a flexible connection has been proposed using bellows which surround the water jet nozzles). Figure 115 shows the mode shapes of the lowest vibration mode (Fig. 115a), as well as that of a higher mode, with a frequency of \(23.93\,{\text {Hz}}\) (Fig. 115b), the first mode that displays a substantial deformation of the frame.

Fig. 115
figure 115

Mode shapes of the frame with the four horns

The analysis of the stress in the horn discussed in Sect. 6.1.3 used the Lorentz forces obtained from a finite-element magnetic analysis. All components of the displacement of the nodes that are in contact with the cradle supports have been set to zero in this calculation. To estimate the displacement and stress due to a current pulse for a horn mounted in the support frame and for the frame itself, an approximate approach is used here. This is unavoidable, due to the very large finite-element model used.

It has been assumed that the magnetic field everywhere within a horn is toroidal, so that it can be approximated by a magnetic flux \(B_\varphi (r)=\mu _0I/(2\pi r)\). It has been verified, by comparing with the finite-element electromagnetic results, that this is a reasonable approximation of the field everywhere inside the horn, including the region near its end. The Maxwell stress tensor formula is used to account for the action of the magnetic forces on the horn skin. In this approach, the traction (force per unit area) acting on a surface element with the normal \({\mathbf{n}}\) is equal to

$$\begin{aligned} {\textbf {T}}_n=\frac{1}{\mu _0}\left[ ({\textbf {B}}\circ {\textbf {n}}){\textbf {B}}-\frac{1}{2}B^2{\textbf {n}}\right] . \end{aligned}$$

Here, \({\textbf {n}}\) is a unit vector that points from the horn skin towards the horn interior, where \({\textbf {B}}\) is the magnetic induction vector as the horn skin is approached from the inside. It has been verified analytically, that with the assumed direction of the magnetic induction vector, the first component disappears everywhere on the horn surface, including the toroidal end part. As a result, the surface traction reduces to a negative pressure \(-\frac{1}{2\mu _0}B^2(r)\).

Fig. 116
figure 116

Components of displacements at a point on the horn neck, under a single pulse of current of amplitude \(350\,{\text {kA}}\) and \(100\,\upmu {\text {s}}\) duration

Figure 116 shows the three components of displacement at a point on the horn neck, resulting from a single pulse with a current of amplitude \(350\,{\text {kA}}\) and a \(100\,\upmu {\text {s}}\) duration. The curve with the highest amplitude oscillations corresponds to the axial displacement, with a maximum value of about \(0.25\,{\text {mm}}\). This displacement is determined by the magnetic forces that act on the curved end part of the horn, as well as by the stiffness of the cradle supports. The transverse displacements are small, which is important from the point of view of beam alignment. It has also been found that the dynamic displacement of the frame is considerably smaller than that of the horn, so that the vibration transmitted from the horn to the frame appears to be at an acceptable level. Higher amplitudes can appear under a sequence of pulses, but these should still be acceptable in the absence of resonance.

The maximum calculated von Mises stress during a single pulse is about \(24.5\,{\text {MPa}}\), and it occurs in the horn inner conductor. This value is comparable to the more accurate result given in Sect. 6.1.3 (the smaller value of stress and greater displacement is consistent with the flexibility of the support). Considerably lower values of stress are found on the support frame. These values should be feasible for aluminium, also when the four horns are pulsed simultaneously. Additional studies are still needed to confirm this conclusion.

6.2 Power supply unit

The magnetic field in each horn is produced by a power supply unit (PSU), which delivers \(350\,{\text {kA}}\) peak-current pulses to each of the four horns, synchronised with the proton beam pulses coming from the switchyard (see Fig. 117).

Fig. 117
figure 117

Proton pulsing scheme

The power supply unit has been developed in accordance with the following main requirements:

  • Each horn is pulsed by a half-sinusoid current waveform of \(100\,\upmu {\text {s}}\) width and \(350\,{\text {kA}}\) peak current, with a very high RMS current of \(9.3\,{\text {kA}}\). The magnetic horn behaves as a “shunt” with a very low inductance of \({1.24}\,\upmu {\text {H}}\) and a low resistance value of \(0.414\,{\text {m}}\Omega\).

  • The pulses will be generated at a high operating frequency of \(14\,{\text {Hz}}\) for each horn, with a \(750\,\upmu {\text {s}}\) delay time between each horn.

  • The maximum operating voltage is restricted by electrical insulation and technical constraints to \(<\,20\,{\text {kV}}\).

  • The proposed electrical solution must reduce the thermal dissipation in the horns to a minimum.

  • The PSU electrical consumption is minimised by developing a solution that allows for maximal energy recovery.

  • The components have been designed to accept very stringent electrical constraints during their operation.

  • A water cooling system will be implemented to improved durability.

The delivery of such high-intensity pulses and the fast commutation between the horns at the level of \(750\,\upmu {\text {s}}\) imposed by the linac presents serious constraints in terms of lifetime for the electrical components. The proposed design is based on a modular approach, and it should guarantee a reasonable stability of the PSU with the minimum of maintenance for the duration of the experiment.

6.2.1 Principle of \(\upmu\)s pulse generation

The power supply unit consists of 16 modules connected in parallel, capable of delivering \(350\,{\text {kA}}\) to each horn, with \(100\,\upmu {\text {s}}\) duration, at \(14\,{\text {Hz}}\). The principle of generating short pulses by each module is based on an oscillating circuit, which consists of two parts, as shown in Fig. 118.

Fig. 118
figure 118

Electrical diagram for delivering \(350\,{\text {kA}}\) peak current during \({100}\,\upmu {\text {s}}\) half period (left), and electrical values of the components (right)

The charger circuit supplies \(+14\,{\text {kV}}\) and will charge the main capacitor C, which is common to the discharge circuit. It also contains a recovery circuit with a resistor \(R_{\mathrm{r}}\), diode \(D_{\mathrm{r}}\) and the coil \(L_{\mathrm{r}}\), ensuring good energy recovery. Once the capacitor is charged, the discharge big switch is turned on and a \(+44\,{\text {kA}}\) pulse with \(100\,\upmu {\text {s}}\) duration is delivered by the discharge circuit, which consists of a resistor \(R_d\) and a coil \(L_d\) representing the electrical properties of the stripline and the horn.

Fig. 119
figure 119

Principle of delivering \(350\,{\text {kA}}\) peak current during a \(100\,\upmu {\text {s}}\) half period