Ultimate Hadron-Beam Brightness

I.FAST Innovation Fostering in Accelerator Science and Technolog y Horizon 2020 Research Infrastructures GA n° 101004730 MILESTONE REPORT ULTIMATE HADRON-BEAM BRIGHTNESS MILESTONE: MS19 Document identifier: IFAST-MS19 Due date of deliverable: End of Month 1 (September 2025) Report release date: 30/09/2025 Work package: WP5: SMART, Task 2: PAF Lead beneficiary: CERN Document status: Final ABSTRACT The activity of Task 5.2 “Pushing Accelerator Frontiers” (PAF) supports the community effort in pushing the hadron-beam brightness. Bright hadron beams are fundamental for atomic and nuclear physics experiments as well as for achieving novel ultra-precise nuclear clocks (HITHOR). Multispecies beams in storage rings are foreseen as a novel intriguing possibility for collisions in a moving frame, and new insights into nuclear reactions. Space-charge forces and intra-beam scattering are two fundamental mechanisms that limit the ultimate beam brightness. Pushing Accelerator Frontiers has co-organized the “Space Charge 2024” workshop where the state of the art in this domain has been reviewed. ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 2 / 21 I.FAST Consortium, 2025 For more information on IFAST, its partners, and contributors, please see https://ifast-project.eu/ This project has received funding from the European Union’s Horizon 2020 Research and Innovation programme under Grant Agreement No 101004730. IFAST began in May 2021 and will run for 4 years. Delivery Slip Name Partner Date Authored by G. Franchetti, F. Zimmermann GSI, CERN 30/09/2025 Reviewed by M. Vretenar [on behalf of Steering Committee] CERN 30/09/2025 Approved by Steering Committee 30/09/2025 ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 3 / 21 TABLE OF CONTENTS 1 Executive summary ..................................................................................................................... 4 2 Brightness limitations of hadron beams..................................................................................... 4 3 Coherent and incoherent effects of space charge ...................................................................... 5 4 Collective effects ........................................................................................................................ 10 5 Intrabeam Scattering and mitigation measures: beam cooling .............................................. 11 5.1 Electron Cooling ........................................................................................................................... 12 5.2 Stochastic cooling ......................................................................................................................... 15 5.3 Advanced schemes ........................................................................................................................ 16 6 The path towards the ultimate brightness ................................................................................ 18 7 Conclusion ................................................................................................................................. 19 8 References ................................................................................................................................. 20 9 Annex: Glossary ........................................................................................................................ 21 ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 4 / 21 1 Executive summary This report focuses on the results of the Space Charge Workshop held in Dongguan and on ongoing initiatives aimed at achieving ultimate hadron-beam brightness. The demand for higher-brightness hadron beams spans several key facilities, including the storage rings at GSI (ESR, CRYRING), the future HESR ring at FAIR, CERN's accelerator complex (LEIR, PSB, PS, SPS, LHC), and the Lanzhou rings at the IMP facility in China. CERN also operates the AD and ELENA rings for lowenergy antiprotons, while the HIAF project in China plans constructing the SRring for storing exotic beams. Producing high-brightness beams in these existing and future accelerators presents significant challenges, including limitations from lattice structures, beam intensity, intrabeam scattering (IBS), and collective effects. Brightness can be enhanced through advanced injection techniques—such as two or three-plane injection schemes (HIAF, GSI)—while space charge and resonance effects are being managed via lattice optimization and space-charge compensation strategies (e.g., at J-PARC). Collective effects are mitigated using chromaticity control and feedback systems. Emittance growth due to IBS is addressed through active beam cooling techniques, including electron, stochastic, and laser cooling, implemented in accelerator facilities at GSI, CERN, and HIAF. The report also highlights the global deployment of these technologies. Additionally, we sketch the progress on advanced concepts such as optical stochastic cooling, currently tested at Fermilab’s IOTA facility, and laser cooling developments at GSI. Finally, we conclude with a discussion of the roadmap towards achieving the ultimate beam brightness. 2 Brightness limitations of hadron beams The ultimate goal of hadron beam production is to bring ions into collision with a fixed target or with another beam. A high-brightness beam is connected to luminosity, and the higher the luminosity, the more collisions occur. Brightness is defined as the beam current “I” divided by the 4D phase space volume occupied by the beam. Therefore, a high-brightness beam requires a large beam current in a small phase space volume. Producing high-brightness beams is challenging mainly due to the repulsive Coulomb force among the hadron particles. The electric fields created by many particles generate a space-charge effect that opposes the focusing forces of the accelerator. This effect includes both incoherent and coherent responses. The unavoidable nonlinearities of the accelerator couple with the space charge, causing either a rapid coherent beam response or a slow incoherent increase in emittance, due to the interaction between amplitude-dependent detuning and magnet error resonances. These mechanisms complicate the production of a high-density beam and hinder maintaining it over time without special mitigation techniques. Coulomb forces originate from point-like charged particles. During beam production, creating small phase space volumes inevitably increases the beam's intrinsic collisionality with other particles—a process known as intrabeam scattering (IBS). This fundamental process results in Coulomb collisions that exchange energy and momentum among particles, transferring potential and kinetic energies within different parts of the phase space. Over time, IBS causes emittance growth or "heating," which reduces the beam's brightness. Without cooling techniques, achieving ultimate brightness is impossible. ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 5 / 21 The transition from intrabeam scattering between individual ion pairs and ion motion in the coarsegrained Coulomb potential of the particle ensemble is not captured by most of the accelerator simulation codes or the corresponding analytical descriptions. For physics based on storage rings, the ultimate brightness is of the main actors in the global scenario are the storage rings of GSI (ESR, CRYRING), along with the future HESR part of the FAIR plan, the rings at CERN (LEIR, PSB, PS, SPS, LHC) as well as the IMP China facility with the Lanzhou storage rings. CERN also features the AD and ELENA with antiprotons at low energy. In addition, the HIAF project in China foresees the construction of the SRring for the storage of exotic beams. Because of the broad and joint interest of both IMP and IHEP in China, and also the “Helmholtz Forschungsakademie für FAIR” (HFHF), the Pushing Accelerator Frontiers task of iFAST coorganized, in September 2024, the international Space Charge 2024 workshop in Dongguan, China. 3 Coherent and incoherent effects of space charge At HIAF, it is planned to deliver intense beams to targets. The SRing will be realized through linac acceleration and two-plane injection into the Bring [1]. The design intensity is 2.0 × 10^11 ppp, which will be accelerated in a cutting-edge facility with a fast-ramping rate of 12 T/s and a high repetition rate of 3-5 Hz. The beam will be longitudinally stacked when transferring from the Bring to SRing. In these rings, the effect of the incoherent space charge in the presence of lattice nonlinearities is critical, especially in view of the potential 4th-order structure resonances driven by space charge in the Bring, as is illustrated in Fig. 1 Fig.1. Fourth-order structure resonances predicted by the CISP simulation for the HIAF Bring [1]. The strategy for mitigating the space charge effect is to employ a high, fast ramping mode, 12T/s, ±38,000 A/s, with a peak power of ±230 MW at full load, relying on new technology based on a MA (Magnetic alloy) RF system [1], as is illustrated in Fig. 2. ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 6 / 21 Fig.2. Schematic of the concept and network implementation of the MA core for the HIAF BRing [1]. At JPARC, the RCS relies on the Hmultiturn injection. This machine is highly space-charge dominated, which poses a serious obstacle to fulfilling multiple demands simultaneously. Routine operation with 1 MW has started at the MLF since April 2024. The space charge and resonance effects complicate simultaneous beam optimizations at high intensities. Systematic beam studies and numerical simulations are conducted for the optimisation of many parameters and their pulse-bypulse switching to minimise beam loss and beam emittance at both the RCS/MLF and the MR. The incoherent space charge tunespread is ~0.5, and this large a spread leads to an overlap with important machine resonances, leading to beam degradation and beam loss. The major resonances in the RCS are 1) Qx – 2Qy = -6, which is a structure resonance excited by the sextupole field component intrinsic to the bending magnets (BMs): K2 = 0.1006 m-2 (1/4 strength of full x correction). This resonance affects operation at lower beam energies due to the large tune spread. It also produces larger emittance growth in the vertical plane. For the MLF beam, this resonance is corrected by sextupoles, as the latter are not being used for chromaticity correction. 2) 3Qx = 19 is a 3rd order random resonance excited by the not-cancelled sextupole field component (K2 = 0.0012 m-2) in the injection chicane magnets (SB). This resonance causes horizontal emittance growth when the SBs are ON during the beam injection. The effect can be partially mitigated by reducing the magnetic fields of the SB by 20%. 3) Qx + 2Qy = 19 is a 3rd order random resonance that arises from the sextupole fields in the BMs and chromatic correction sextupole magnets. It is also additionally excited by a distortion of the lattice super-periodicity due to a beta beating caused by the chicane during injection. It leads to twice larger emittance growth in the vertical plane. Currently,  ~ 10% as Qy is set far from the Qy = 6.5, and the beating is further decreased by reducing SB fields. 4) The Montague resonance 2Qx-2Qy = 0 is a 4th-order systematic resonance excited by skewquadrupole errors, the 2nd-order effect of the sextupolar field, and also by the octupole component in the space charge field. It is critical when Qx and Qy are close to each other. This resonance causes an emittance exchange between the horizontal and vertical planes. Its effect is mitigated with a careful choice of injection painting. The anti-correlated painting is favourable for a larger transverse painting [2]. ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 7 / 21 The 3-GeV RCS of J-PARC shows that the space charge effect at injection energy excites many resonances, resulting in beam emittance growth and beam losses. Beam handling, machine properties, and errors have been incorporated into the simulations in order to obtain precise results, allowing the identification of each resonance effect and developing the corresponding countermeasures. Recently, the SC effect has been sufficiently mitigated at 1 MW operation by combining several appropriate measures. The beam loss and the beam emittance have been minimized. The residual beam loss of 1 MW is <<0.1% and this loss occurs almost entirely during the injection period, where about half of the total loss is attributed to the foil scattering. The beam loss power at the collimator is ~0.1 kW (small compared with the collimator capacity of 4 kW). The simulation results are well consistent with the measurements. Improvements of the RCS beam quality have also been well recognized at the downstream facilities. The machine activation is well suppressed, achieving a sustainable operation with more than 98% availability. Another important task to reach a high-brightness beam is the injection. The development of an efficient method to accumulate as much beam as possible is necessary. The standard approach to inject a hadron beam from a linac into a synchrotron is via a multi-turn injection. This approach is usually implemented in one plane and requires the creation of a local bump to fill the horizontal phase space up to the machine acceptance. For proton and ion multiturn injection via magnetic or electrostatic septum, Liouville’s theorem applies and severely restricts the number of turns, typically to ~15 turns for single plane injection with optimized conditions. The specific results depend on the machine acceptance and the emittance of the injected beam coming from the linac. To increase the brightness also the vertical plane can be exploited, increasing the number of injected turns to ~100. At HIAF, the two-plane injection scheme is studied and will be implemented for the BRing [3]. They estimate a 20% beam loss over 100 turn injection to achieve a stable intensity of 1.3x1010 particles. Figure 3 shows a simulation of the full process. ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 8 / 21 Fig. 3. Two-plane injection at HIAF from a multiparticle simulation obtained via CISP-GPU [3]. At GSI, the demand for increasing the brightness is also pushing the studies for the implementation of the two-plane injection, as is illustrated in Fig. 4. In general, horizontal-longitudinal and three-dimensional x-y-z injection schemes are also feasible. These can be implemented with a nonzero dispersion at the injection point by varying the beam energy from the linac. Fig. 4. Characteristic efficiency of the standard multiturn injection. [4]. Two-plane injection studies at GSI [5]; the study shows the dependence of a two-plane injection scheme efficiency as a function of the machine working point. ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 9 / 21 At CERN, the LHC Injector Upgrade greatly increased the beam brightness and pushed the intensity. The space charge force is limiting the emittance in the PSB, the PS, and in the SPS, as is illustrated in Fig. 5. Resonance crossing is the mechanism behind beam loss or emittance growth caused by space charge in all these machines. In PS and SPS, the space charge condition is applied in the form Qy <0.31, 0.21, respectively. These limits were found empirically. Ideally, they should both be near 0.25 (i.e. the space available between the 0.25 and integer resonances), but due to uncertainty in the beam distributions and width of the stop bands, plus possible influence from other resonance lines (e.g., the coupling resonance line) the values chosen seem to better represent the actual limits in the two accelerators under some simplified assumptions. In Fig. 5, the rounded shape of the curves approaches zero, followed by a linear behaviour is because for very low emittances the dispersive part of the beam transverse size dominates, while for larger emittances it is the emittance part. PS and SPS have both bunch-to-bucket injection. On the other hand, in the PSB, the beam is injected by Hcharge exchange and chopped longitudinally from Linac4 over several turns. The “brightness line” shown is the best line that can be measured, and it also roughly fits the simulation of the injection process. In reality, the line should reduce its slope for low intensities (when the emittance blow-up becomes dominated by the scattering on the stripping foil) and eventually level off to 0.4 m even for the limit of zero intensity (because this is the emittance from Linac4). This is indicated by the green curve in Fig. 5. The so-called 8b4e bunch pattern, consisting of trains of 8 bunches spaced by 25 ns, followed by 4 “empty” 25-ns buckets, is limited by space charge in the SPS and, therefore, is expected to perform exactly like the bunch compression, merging, and splitting (“BCMS”) scheme. In mid-August 2025, a normalised rms emittance of ≤1.5 m was measured at PS extraction with 2.6×1011 protons per bunch extracted, consistent with the diagram, and also with measurements right at SPS injection. Under the LHC Injector Upgrade program, PS longitudinal instabilities have been successfully overcome by installing a wide-band longitudinal feedback system (Finemet cavity) and reducing the impedance of the 10 MHz RF system. Hence, the limit corresponding to the vertical red line in Fig.5 has been removed. At present, more than 3×1011 protons per bunch can stably be extracted from the PS in trains of 72 bunches. The requirement on the longitudinal emittance, however, which should be small enough not to exceed the bunch length of 3.8 ns at the SPS injection (for ensuring horizontal beam stability in the SPS), makes intensities above 2.9×1011 protons per bunch hardly usable. ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 16 / 21 5.3 ADVANCED SCHEMES The advantages of stochastic cooling are particularly significant for colliders. At RHIC, the 3D stochastic cooling for Uranium-on-Uranium collisions has increased the integrated luminosity per store by a factor of 5. Often, the stochastic cooling is used in combination with electron cooling to reach the best beam performance. The combination of electron and stochastic cooling is proposed for fast cooling at the highest energies through a novel scheme called the “Coherent Electron Cooling” system. The Coherent Electron Cooling system has three major subsystems. 1) modulator: the ions of the beam imprint a “density bump” on the electron distribution; 2) amplifier based on a high-gain free electron laser, on the microbunching instability, or a plasma cascade; each of these interactions amplifies a density bump by orders of magnitude; 3) kicker: the amplified & phase-shifted electron charge distribution is used to correct the velocity offset of the ions. Such a “strong hadron cooling” scheme is considered for possible deployment at the Electron Ion Collider (Fig. 11). Fig. 11. The Electron Ion Collider. In this project, the brightness of the colliding beams is planned to be increased through advanced electron cooling systems. The four main challenges for realizing Coherent Electron Cooling are: (1) high-current ERL, (2) a low-noise electron beam, (3) longitudinal alignment of 1 micron over 100 m distance, and (4) the controlled amplifier [11]. A concept similar to Coherent Electron Cooling is also used for the Optical Stochastic Cooling. Here, a Pickup Wiggler makes the beam emit synchrotron radiation, on which the characteristic features of the beam distribution are imprinted. The beam is transported through the accelerator, and at the same time, the radiation emitted by the beam at the Pickup Wiggler is amplified through an optical amplifier and then injected into a Kicker wiggler, where it interacts with the beam and applies the correction for cooling. This concept has been demonstrated with an electron beam at the IOTA facility in ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 17 / 21 Fermilab in 2022 (Fig. 12), and it is considered an interesting option for cooling hadron beams at the highest energy. Fig. 12. Scheme of the optical stochastic demonstration [12]. Among the novel concepts for advanced cooling, Laser Cooling is now receiving attention as it is proposed as a main tool for experimental physics. In particular, a special laser cooling scheme for particular stripped ion beams is a key ingredient of the Gamma Factory project [13]. Laser cooling is also foreseen in the FAIR project. Figure 13 shows the Schottky noise during the laser sweep. In this picture, the relative frequency width is df/f=2x10-5 Fig. 13. Schottky spectra at the ESR, during laser cooling of C3+. (left) and the Argon ion laser (257.3 nm), frequency doubled, utilized for this experiment (right). The laser cooling is being prepared and set up for the SIS100 in a dedicated laser cooling area, also dedicated to laser spectroscopy [14]. ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 18 / 21 6 The path towards the ultimate brightness The path towards ultimate brightness requires: 1) The creation of a bright beam at the linac section. The injection to a synchrotron should minimize the dilution factor, and a non-Liouvillian injection method should be employed. 2) Controlling the effect of space charge on beam degradation. This is reached by resonance compensation and proper choice of the machine working point. Additionally, space charge compensation techniques could be developed, such as electron lenses and “electron columns” for space charge compensation. For specific mechanisms degrading the beam quality, such as the space charge-induced periodic crossing of resonances, the longitudinal bunch shaping via multi-harmonics RF systems may lead to significant benefit and greatly reduce the resulting beam loss. 3) Collective effects must be controlled via proper feedback systems and with proper design of components to stay within an acceptable impedance budget. 4) The Beam Cooling remains a fundamental tool to reach high-brightness beams. In particular, the future of beam cooling will be shaped by two types of development: 1) Cooling at higher energies • Laser cooling in SIS100 is one example • The Electron-Ion Collider (EIC) will significantly benefit from beam cooling options: • electron beam from a linac (energy recovery linac) • coherent electron cooling • merging of electrons circulating in a storage ring 2) The high brightness beam will be relevant for two emerging Heavy Ion and Secondary Beam Facilities: FAIR (Germany) and HIAF (China). These projects will need more traditional cooling systems, but operating over a large energy range and with a large particle variety. The highest brightness could be achieved with 1D, 2D, or 3D crystalline beams. 3D crystalline beams up to helix structures surrounding a linear string were created at the RF quadrupole storage ring PALLAS in Germany [15]. An ion-cloud confined in a Paul trap acquires Coulomb crystalline state when cooled near absolute zero, the normalized emittance of a Coulomb crystal can be in the sub-femtometer range. Ongoing efforts at Hiroshima University aim at demonstrating an ultimate single-ion source with rms emittance of order 10−16 m from a two-component Coulomb crystal. Experiments have already generated a Coulomb crystal consisting of calcium and nitrogen ions. The image of a two-component Coulomb crystal taken by an intensified charge coupled device (ICCD) camera in Fig. 14. The bright area of ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 19 / 21 the outer part of the crystal is the laser-induced fluorescence from calcium ions. The dark area of the inner part is considered to include nitrogen ions, which do not emit light [16]. Fig. l4. Image of a two-component shell Coulomb crystal at Hiroshima University [16]. If the beam particles are bosons, e.g., He nuclei (alpha particles), potentially also a Bose-Einstein condensate could be generated through cooling; see Ref. [17] and articles cited therein. 7 Conclusion Beam brightness is compromised and diluted by Liouville’s theorem, by incoherent and coherent space charge effects, and by intrabeam scattering. The transition between space charge and scattering is presently not fully captured in simulations or theories. The brightness of hadron beams is advanced worldwide by major new projects in Nuclear Physics, including HIAF in China, FAIR in Germany, and the EIC in the US. These flagship projects. Along with the Gamma factory proposed at CERN, drive forward more complex and more efficient injection schemes, such as 2or 3-plane injection, as well as advanced beam cooling methods. Emerging and evolving cooling techniques are more flexible and/or more powerful, with high-energy bunched-beam electron cooling, optical stochastic cooling, laser cooling, and coherent electron cooling figuring among the frontier techniques. Crystalline beams or Bose-Einstein-condensate beams could reach an ultimate level of brightness. Bright beams are also fundamental for realizing a nuclear clock as foreseen in the HITHOR project [18], where, by using highly charged 229Th ions—especially the one-electron state 229Th⁸⁹⁺—the nuclear hyperfine mixing is exploited, which enhances nuclear excitation rates by up to a millionfold. This approach, enabled by the advanced trapping facilities at GSI, will allow the first laser excitation of a nucleus, ushering in a new era of precision timekeeping and fundamental physics exploration. ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 20 / 21 8 References [1] Jiancheng Yang, High intensity challenges in the HIAF project, Space Charge 2024; https://indico.ihep.ac.cn/event/21466 [2] H. Hotchi, PRAB 23, 2020 [3] Guodong Shen, Study on two-plane painting injection scheme for HIAF Bring, https://indico.ihep.ac.cn/event/21466 [4] R.W. Hasse, I. Hofmann Space-charge limits of multiturn injection in HIDIF, NIM A, Volume 415, Issues 1–2, 21 September 1998, Pages 478-483 [5] O. Dolinskyy et al., Enhancing beam intensity in sis18 by a two-plane multi-turn injection approach, MOPS141, IPAC25 [6] Liangsheng Huang, Source of instability in the RCS of CSNS, Space Charge 2024; https://indico.ihep.ac.cn/event/21466 [7] Markus Steck, Beam Cooling, Space Charge 2024; https://indico.ihep.ac.cn/event/21466 [8] HFHF Helmholtz Forschunsakademie Hessen für FAIR https://hfhf-hessen.de/en/ [9] A. Engeda, G. Franchetti, Intrabeam Scattering in a 3D Poisson solver, Proc. of IPAC2023, 7-12 May 2023, Venice, Italy; Alexander Engeda and Giuliano Franchetti, Macroparticle collisionality in PIC solver, 2024 J. Phys.: Conf. Ser. 2687 062028 [10] J. Y. Du, X. N. Du, X. G. Liu, and Y. S. Yuan, 3D Space Charge Solver Based on Tensor Decomposition for High-Intensity Beams, Progress of Theoretical and Experimental Physics, Vol. 2025, pp. 1-20, DOI: https://doi.org/10.1093/ptep/ptaf047 [11] S. Nagaitsev, private communication (2025) [12] Experimental demonstration of optical stochastic cooling, J. Jarvis, V. Lebedev, et al. Nature 608 287-292 (2022) [13] Witek Krasny, The Gamma Factory Project, “Gigahertz Rate and Rapid Muon Acceleration”, Bern 2023 [14] Danyal Winters, Laser cooling taken to the extreme: cold relativistic intense beams of highlycharged heavy, TUOGA2, IPAC23, TUOGA2.pdf, 2023, Venice [15] U. Schramm, T. Schätz, and D. Habs, Three-dimensional crystalline ion beams, Phys. Rev. E 66, 036501 (2002) [16] K. Muroo, K. Ito, H. Okamoto, An Ultimate Single-Ion Source Using a Coulomb Crystal in a Paul Trap. IPAC24, MOPR71 (2024) [17] L.M. Satarov, I.N. Mishustin, and H. Stoecker, Bose-Einstein condensation in finite drops of 𝛼 particles, Phys. Rev. C 106, 014301 (2022) [18] Highly Ionized Trapped 229-Thorium: A New Paradigm Towards a Nuclear Clock https://cordis.europa.eu/project/id/101142155 ULTIMATE HADRON-BEAM BRIGHTNESS Milestone: MSxx Date: 30/09/2025 Grant Agreement 101004730 PUBLIC 21 / 21 9 Annex: Glossary Acronym Definition AD Antiproton Decelerator at CERN BNL Brookhaven National Laboratory on Long Island, U.S.A. CERN European Organization for Nuclear Research in Geneva, Switzerland CSNS Chinese Spallation Neutron Source in Guangdong, P.R. China CSR Cryogenic Storage Ring at MPI Heidelberg ESR Experimental Storage Ring at GSI FAIR Facility for Antiproton and Ion Research at GSI HIAF High Intensity Heavy-ion Accelerator Facility at IMP IBS Intrabeam Scattering IMP Institute of Modern Physics – Chinese Academy of Science IHEP Institute of High Energy Physics - Chinese Academy of Science LINAC4 Hlinac at CERN PALLAS Paul laser cooling acceleration system at Munich’s Ludwig-Maximilians University PS Proton Synchrotron at CERN PSB Proton Synchrotron (PS) Booster at CERN RCS Rapid Cycling Synchrotron RF Radiofrequency RHIC Relativistic Heavy Ion Collider at BNL SPS Super Proton Synchrotron at CERN