Future facilities at PSI, the High-Intensity Muon Beams (HIMB) project

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Introduction
High-intensity proton-driven meson factories have contributed to stringent tests of the current Standard Model (SM) of particle physics with a number of precision experiments.Within this framework, high-intensity muon beams have been employed as sensitive probes of Beyond SM (BSM) physics by searching for SM highly suppressed muon decays, such as µ + → e + γ, µ + → e + (e + e − ) and µ − N → e − N. These so-called golden channels in the charged Lepton Flavor Violation (cLFV) sector, if detected, would be a direct signal of BSM physics. Antimuons have also found applications outside of particle physics such as aiding solid-state physics, chemistry and material science by using the muon spin spectroscopy method (µSR) to probe magnetic properties of matter down to nanometer scales.
At PSI, the High Intensity Proton Accelerator (HIPA) facility delivers one of the most powerful proton beams to target stations, 1.4 MW, to produce the most intense continuous muon beams in the world, with rates up to few 10 8 µ + /s, granting PSI the lead at the intensity frontier in both particle physics [1] and condensed matter research with muons [2][3][4][5][6][7]. Such high rates are possible by exploiting 'surface muons', which are anti-muons generated by π + decay at rest inside the production target within a very narrow momentum range. This is due  . Calculated muon stopping ranges in Copper (Cu) as a function of the incoming muon energy. Plot modified from [9]. Typically used muon energies for µSR measurements restrict the probed ranges to either < 200 nm (low-energy muons, LE-µ + ) or ≥ 100 µm (surface-and decay-muon beams).
to the fact that they are created in a two-body decay, where the energy of the outcoming muon is only determined by the material budget it encounters inside the target. In addition, these muons are fully polarized.
The High-Intensity Muon Beams project (HIMB) at PSI aims at further pushing the current muon rates by two orders of magnitude up to 10 10 µ + /s, thus boosting reachable sensitivities for next-generation cLFV searches ( Figure 1). Such high rates could be also exploited to improve limitations of the current µSR technique, such as the lack of intensity in the subsurface region (see Figure 2), decreased measurement time and the possibility of probing multiple samples at once [9].
While next-generation proton drivers still require significant research and development to exceed the current limits, HIMB focuses on boosting surface muon yields with a new target station by increasing both capture and transport efficiency by building two new solenoidbased beamlines.
The HIMB project is part of the Isotope and Muon Production using Advanced Cyclotron and Target Technologies project [10] (IMPACT), whose other goal is the construction of a new radionuclide production target for an online isotope separation facility: the Targeted Alpha Tumour Therapy and Other Oncological Solutions (TATTOOS) project.

Target upgrade
Muons are produced at PSI by impinging the HIPA proton beam on two polycrystalline graphite rotating wheels: target M (TgM), which is 5.2 mm thick, and target E (TgE), which is 40 mm thick and devoted to high-intensity production. The rotation is used for radiative cooling and to distribute the heat load over the target rim.
To increase the surface muon yield, TgM station will be substituted with a high-intensity version, target H (TgH) with a slanted target geometry. Introducing a slanting angle while keeping the proton path length constant increases the surface muon yield as the pion production depends only on the material budget met by the protons in the target, while the surfaceto-volume ratio of the target is increased as opposed to no slanting angle. TgH is going to be 20 mm thick in the proton beam direction, with a 10 deg slanting angle (see Figure 3):   these parameters result in surface muon yields comparable to a 40 mm thick non-slanted target [11]. The slanted geometry has already been successfully tested at TgE, improving the surface muon yield by 40-50% depending on the beamline. The particles are planned to be extracted at 90 deg to the proton beam axis.
The proton beam will impinge on the back of the target, passing through a water-cooled copper plate acting as local shielding. A Densimet® (tungsten alloy) protection collimator will be used in order to protect the cooling plate.
To allow for such a configuration, the proton beam trajectory has to be lower than the rotation axis of the target, or it would intersect the rotation shaft. Additionally, a lower trajectory allows the use of a flat target, providing more usable space and further reducing the heat and radiation load on the target insert. Figure 4 shows a more detailed view of the TgH design.
The insert of TgH will fit into the existing TgE remote-controlled exchange flask (Figure 5). All elements that experience high radiation exposure along PSI beamlines are organised in inserts to allow for easier handling and maintenance. The extraction of those elements from the beamlines is performed using exchange flasks that provide shielding while moving the inserts in the experimental hall. The flasks are thick steel cases equipped with grippers and motors to insert and extract the different elements of the beamline. The possibility of handling both target stations with the same exchange flask allows for easier operations and reduces the number of needed spare components.

Capture
When using solenoids to capture particles produced at a target, the common approach is to have the target completely enclosed inside the solenoid aperture, as this provides maximum acceptance for the created particles. This solution is not straightforward to apply in the HIMB project as the proton beam is not going to be stopped at TgH: the proton beam must pass through both TgH and TgE to then be fully stopped in the spallation source of the Swiss Spallation Neutron Source SINQ. In order to avoid major changes to the proton beam optics to compensate for the high magnetic fields required for capture, our approach is to have two different capture solenoids sideways to the target. Figure 6 shows a schematic of the 'capture solenoid' together with the TgH.
Because of the high radiation exposure, the capture solenoids are chosen to be normal conducting. Mineral-insulated coils are used to withstand the high radiation load, and the water cooling is indirect to avoid the corrosion of the coils. The design is going to be similar to that already used in the µE4 beamline at PSI [12].  The central field of the capture solenoids is planned to be ∼ 0.45 T, and, to maximize capture, they are going to be positioned as close to the target as possible. Such a configuration will induce non-negligible fringe fields at TgH, and a dipole chicane will provide correction to the proton beam trajectory.

Particle production
The proton beam is accelerated to 590 MeV to impact TgH first and subsequently TgE. At such an energy, the only particles produced, together with the remnants of the nuclear reactions in the target, are electrons, muons and pions. Figure 7 shows the momentum spectrum of the relevant species produced at TgH.
As already introduced in Section 1, muons are produced through pion decay: the peak in the µ + spectrum in Figure 7 is caused by the surface muon production, while at higher energies, the muons come from pion decay-in-flight. In the case of µ − , the surface muon feature is not present as there are no pion decays at rest: any stopped pion undergoes nuclear capture, and no muon is produced. Analogously, µ + stopped in the target decay at rest, producing a peak in the positron spectrum close to the Michel edge at 52.8 MeV/c [13].
The HIMB project focuses on increasing the delivered surface muon rates, but it will be possible as well to deliver the other particle species to the experimental areas. In order to do so, the dipoles will be designed to accept momenta up to 80 MeV/c, but transmission at momenta higher than that of surface muons, 28 MeV/c, will be limited by the maximum excitation currents of the solenoids.

Beamlines
Two new muon beamlines will be built within the HIMB project: MUH2 and MUH3. The main feature of these high-intensity muon beamlines is the extensive use of solenoids as focusing elements, as opposed to quadrupoles. The latter focus the beam in one transverse direction and defocus it in the other, solenoids provide focusing in both transverse directions simultaneously. This leads to higher capture capabilities, but usually, the required magnetic fields are much higher than for quadrupoles. For the momentum of the surface muons,   the required maximum fields for the capture and transport solenoids are ∼ 0.45 T, which is achievable with normal conducting solenoids. Figure 8 shows the layout of the HIPA experimental area, including the HIMB beamlines. The proton beam is bunched at 50 MHz and accelerated by the cyclotron Injector 2 (INJ2), then it is transported to the RING cyclotron for the final acceleration to reach 590 MeV energy. From there, the proton beam is transported to TgH. Additionally, the full beam can be kicked to the UCN facility or up to 100 µA can be scraped off to be delivered to TATTOOS. The HIMB beamlines will be oriented perpendicularly to the proton beamline. After TgH the proton beam impinges on TgE and is stopped at SINQ.

The MUH2 beamline
The MUH2 beamline is designed to deliver beams to fixed target experiments, e.g. Mu3e phase II [14]. It will be located at the left-hand side of the target station in the proton beam direction, with the beamline starting at a distance of 250 mm from TgH.
Being dedicated to particle physics, the most important figure of merit for MUH2 is transmission to be pushed as high as possible. To do so, the focusing elements along the full chan-  MUH2 beamline model in G4beamline [16] including the double Wien filter separation scheme and the graded-field capture solenoid. TgH is positioned at the intersection of the axes on the right. The muon beam (green lines) is captured from the capture solenoid and transported to the entrance of the experimental area located on the downstream side of the last transport solenoid on the left. MUH3 beamline model in G4beamline [16]. TgH is positioned between the two capture solenoids on the left. The muon beam (blue lines) is delivered to the entrance of the experimental area by the solenoid-only section, to then continue through the quadrupole channels. The two branches MUH3.2 and MUH3.3 are served by a septum magnet. nel will be solenoids. Another requirement for the layout of the beamline is to avoid a direct line of sight to the target due to the high radiation and neutron flux coming from the target: two 40 deg bends are included in the beam trajectory with two dipoles, leading to a stretched Z-layout. The initial optical model and design were studied using the matrix-based code Graphics Transport [15]. Then a G4beamline [16] model based on high-fidelity fieldmaps for each element was implemented.
The model reported in the Conceptual Design Report (CDR) published in January 2022 [10] is able to deliver 1.22 × 10 10 µ + /s at a proton current of 2.4 mA at the entrance of the experimental area at the surface muon momentum. The beam spot size and the average polarization at the end of the channel are σ x = 40 mm, σ y = 42 mm and 88 %.
As previously shown in Figure 7, at the target, the positron yield is roughly the same as that of anti-muons at 28 MeV/c, leading to non-negligible positron contamination at the entrance of the experimental area. Setting the MUH2 optics for surface muons leads to 1.94× 10 10 e + /s at a proton current of 2.4 mA. The pion yield for the considered momentum instead is negligible. Figure 11 shows the delivered rates at the entrance of the experimental area at different momenta.  A double Wien filter scheme is currently under study to keep the positron contamination under control: the length of a single Wien filter to be effective in separating positrons and muons would not allow for an optimal transmission, leading to a muon rate reduction of 74 % [10]. By employing two Wien filters, separated by a solenoid to refocus the diverging beam, it is possible to reduce their lengths and increase the overall transmission. Detailed studies are still ongoing to find the optimal solution between contamination and transmission.
Another feature under study is the possibility of powering the coils of the capture solenoids independently to increase the absolute transmission of the beamlines. The current design of such a magnet, the 'graded-field solenoid', envisages three coils that can be excited independently to increase the degs of freedom at capture. Figure 9 shows the version of MUH2, including the double Wien filter scheme and the graded-field capture solenoid.

The MUH3 beamline
The MUH3 beamline aims at delivering muon beams for muon spin rotation spectroscopy (µSR). It will be located on the right-hand side of the target station in the proton beam direction, with a distance of 250 mm from TgH to the up-stream face of the coils in the capture solenoid. As introduced above, higher rates would be beneficial for such a technique to cover the sub-surface gap and increase the low energy muon (LEµ) rates. For such an application, the full 10 10 µ + /s rate is not required, as the needed statistics are lower than for particle physics experiments. Hence, the increase in rate with respect to the current µSR beamlines is provided by a first solenoid-only section up to the second bend, analogously to MUH2, while transmission to the experiments is given by a conventional quadrupole tuplet scheme. The MUH3 beamline will serve two experimental areas MUH3.2 and MUH3.3, that will be exploited alternatively or concurrently by employing a septum magnet. The studies on MUH3 optics are performed on Graphics TRANSPORT [15] and COSY INFINITY [17], while transport simulations are performed with a G4beamline [16] model including high-fidelity fieldmaps for each element. Figure 10 shows the G4beamline model of MUH3, including both branches.
The solenoid section delivers more than 10 10 µ + /s to the entrance of the experimental area at a proton current of 2.4 mA. Both MUH3.2 and MUH3.3 channels can deliver 3 × 10 8 µ + /s to the experiments at the surface muon momentum, 3×10 7 µ + /s at 15 MeV/c and 6×10 6 µ + /s at 10 MeV/c, providing high enough rates for µSR measurements in the sub-surface gap. The polarizations in the considered cases are 97 %, 96 % and 95 %, respectively -comparable to that of the beams currently available at PSI [18] [19]. The final focus optics are still under study, but we expect the final beam spots to be σ x ∼ 20 mm and σ y ∼ 20 mm.
The main focus for MUH3 will be on the surface and sub-surface muons. We are studying the beam properties at different momenta, such as rates and polarization.

Conclusions
The HIMB project is currently in a planning phase, with one out of three approval stages passed. Figure 12 shows the main milestones of our program: • end of the preparation phase and publication of the Technical Design Report -end 2024 The current design of the beamlines meets the primary goal of exceeding 10 10 µ + /s delivered rates, and we aim to prepare a final beamline layout with corresponding particle rates and envelopes by the end of 2022.