Possible crystal application for FCC and beyond

Contents lists available at ScienceDirect Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima Possible crystal applications for FCC and beyond Frank Zimmermann CERN, Esplanade des Particules 1, 1211 Geneva 23, Geneva, Switzerland ARTICLE INFO Keywords: Future Circular Collider Lepton collider Hadron collider Muon collider Crystal channeling Positron source Collimation Electric dipole moment Magnetic dipole moment Synchrotron radiation Crystal collider ABSTRACT This article first describes the status and plans for the proposed Future Circular Collider (FCC), and then surveys possible crystal and channeling applications for the FCC. The latter range from crystal-based positron production, over crystalline undulators, to crystal collimation. Finally, a long-term perspective is presented, where, in the far future, crystals or crystal-like structures could enable the construction of ultimate colliders. 1. Future circular collider integrated project & its possible extensions The FCC ‘‘integrated project’’ [1] is inspired by the successful past Large Electron Positron collider (LEP) and Large Hadron Collider (LHC) projects at CERN. It represents a comprehensive long-term programme maximizing physics opportunities. The first stage of the FCC integrated project is an e+e−collider with 91 km circumference, called FCC-ee, which will serve as Higgs, electroweak and top factory at highest luminosities, and run at four different centre-of-mass energies, namely on the Z pole, at the WW threshold, at the ZH production peak, and at the t tthreshold. Key parameters are compiled in Table 1. The FCC-ee would allow for the start of a new, major facility at CERN within a few years of the end of HL-LHC. FCC-ee would be followed by a highest-energy proton collider, FCC-hh with a centreof-mass energy of about 100 TeV, that would naturally succeed the LHC at the energy frontier. Hadron-collider parameters are shown in Table 2. The FCC-hh could also accommodate ion and lepton–hadron collisions [2]. The overall timeline is sketched in Fig. 1. The lepton and hadron colliders would profit from a common civil engineering and from sharing technical infrastructures. In addition, the FCC would build on and reuse CERN’s existing infrastructure. For example, the existing chain of hadron accelerators, from Linac4 over PSB, PS, and SPS to the LHC, can serve as an injector complex for the FCC-hh. The FCC-ee and FCC-hh also support a highly synergetic and complementary physics programme, thereby, boosting the physics reach of both colliders. Fig. 1illustrates the FCC integrated programme. E-mail address: [email protected]. A third stage, or an alternative second stage, could be a muon collider, FCC-𝜇 𝜇, with a centre-of-mass energy of 14–30 TeV. The FCC-hh, or a modified version thereof, could be used as accelerator ring, and the smaller LHC tunnel for the collider proper [3]. The muons required for FCC-𝜇 𝜇could be generated through the LEMMAscheme [4] using 45 GeV positrons from FCC-ee to create muon pairs by positron annihilation, via the production and decay of pions from the LHC-based Gamma Factory [5], or by means of a proton driver. An ultimate incarnation of the third collider stage, FCC-𝜇 𝜇, might be in the combined form of the LEMMA scheme fed by intense positron beams from the Gamma factory, and using a plasma target for the positron annihilation [6,7]. The first stage FCC-ee would already allow many important proofof-principle tests in preparation for FCC-𝜇 𝜇. E.g. 45 GeV positrons extracted from the booster would be optimum for demonstration experiments and beam tests for the LEMMA low-emittance muon-beam production scheme. Various targets and accumulation schemes could be studied. The emittance of the generated muons could be characterized. The FCC-ee injector complex will go into operation first, and provide electron and positrons beams at a high rate, above 1013 particles per second, up to an energy of 20 GeV, which is the injection energy of the full energy booster. This injector complex comprises an electron linac up to 2.86 GeV, a positron target at 2.86 GeV and a positron linac to reach again 2.86 GeV, a damping ring for both e+and e−at 2.86 GeV, and the high energy linac to reach 20 GeV. The latest proposal is to construct this injector complex on the CERN Prévessin site with https://doi.org/10.1016/j.nima.2025.170371 Received 13 January 2025; Received in revised form 21 February 2025; Accepted 24 February 2025 Nuclear Instruments and Methods in Physics Research A 1075 (2025) 170371 Available online 4 March 2025 0168-9002/© 2025 Published by Elsevier B.V. F. Zimmermann Fig. 1. Timeline and scope of the FCC integrated project. The last stage, FCC-𝜇 𝜇, is not (yet) part of the FCC baseline. Table 1 Parameters of FCC-ee. Peak luminosity values are given per interaction point (IP), for a total of 4 IPs, Integrated luminosities refer to the sum over four IPs. Bunch lengths including beamstrahlung (BS) are shown. For the integrated luminosity, 185 days of operation per year, and luminosity production at 75% efficiency is assumed. Collider FCC-ee running mode Z W ZH t t Number of IPs 4 4 4 4 Beam energy (GeV) 45.6 80 120 182.5 Bunches/beam 11200 1780 440 60 Beam current [mA] 1283 135 26.8 5.1 Luminosity/IP [1034 cm−2s−1] 145 20 7.5 1.41 Energy loss/turn [GeV] 0.039 0.369 1.86 9.94 Rms bunch length (with BS) [mm] 15.7 5.28 5.59 2.33 Rms horizontal emittance 𝜀𝑥[nm] 0.71 2.16 0.66 1.51 Rms vertical emittance 𝜀𝑦[pm] 2.3 2.0 1.0 1.4 Longitudinal damping time [turns] 1171 218 65.4 19.6 Hor. IP beam size 𝜎∗ 𝑥[𝜇m] 9 22 13 37 Vert. IP beam size 𝜎∗ 𝑦[nm] 40 45 32 44 Total int. annual luminosity [ab−1/yr] 68 9.6 3.6 0.67 Table 2 Parameters of FCC-hh compared with the HL-LHC and LHC. For the integrated luminosity, 160 days of operation per year, and luminosity production at 75% accelerator availability is assumed. Collider FCC-hh HL-LHC LHC Centre-of-mass energy [TeV] 85 14 Circumference [km] 90.7 26.7 Dipole field [T] 14 8.33 Beam current [A] 0.5 1.1 0.58 Bunch Intensity 1011 1.0 2.2 1.15 No. bunches/beam 9500 2760 2808 Bunch spacing [ns] 25 Synchr. radiation power [kW] 2400 15 7 Longit. emit. damping time [h] 0.75 12.9 IP beta function 𝛽∗ 𝑥,𝑦 [m] 0.3 0.15 (min.) 0.55 Normalized rms emittance [𝜇m] 2.2 2.5 3.75 Peak luminosity [1034 cm−2s−1] 20 5 (lev.) 1 Peak no. events/bunch crossing 700 132 27 Integrated annual luminosity/IP [ab−1/yr] 0.94 0.25 0.05 the high energy linac next to North Area and Beam Dump Facility. A connection tunnel could be built to reach BA4 of the SPS, while the transfer to the FCC-ee booster is envisaged with a direct tunnel from the end of the high energy linac to the FCC tunnel. The FCC-ee injectors could support many other applications [8]. For example, the FCC-ee injector beams (including also the damping ring) could be used to carry out R&D for accelerator components and beam diagnostics for FCC-ee or the injector itself; to feed an irradiation facility (e.g., for testing electronics components); to support medical research; to provide beams for plasma & nanotube/crystal wakefield acceleration test facilities; to drive an X-ray photon source, e.g. with crystalline undulators; or to supply a neutron source with e−beam from the linac. FCC-ee injector complex could also be of interest for the AWAKE plasma wakefield expeiments. If an FCC-ee beam line passes through SPS BA4, it would directly reach the SPS extraction point of protons for the plasma wakefield acceleration experiment AWAKE. This would offer the unique opportunity to perform proton driven plasma wakefield acceleration of 20 GeV electrons and positrons. Also electron-driven wakefield acceleration experiments would become feasible. Finally, this would provide a unique possibility for studying the plasma acceleration of positrons. 2. Crystal applications for FCC Possible important applications of crystals and channeling processes [9–11] for the FCC include (1) crystal-based positron production for the FCC-ee (and for FCC-𝜇 𝜇) and other e+science applications; (2) crystalline undulators with FCC–ee positron beams; (3) crystal collimation for FCC-ee and FCC-hh; (4) crystal extraction for FCC-hh; and (5) crystal steering for FCC-𝜇 𝜇. Crystal-based positron production, first proposed in 1989 [12], exploits coherent lattice effects in oriented crystals, in particular the channeling process and over-barrier motion. The typical angular range or divergence required for the channeling is a few mrad at 6 GeV for the <111 >axis in W crystals. This production scheme for positrons relies on the enhancement of photon generation in oriented crystals, implying enhanced pair production and higher total e+charge, with, at the same time, lower energy deposition (ED) and reduced peak ED density (PEDD) inside the target. In consequence, heating and thermo-mechanical stress are predicted to be reduced [13]. Indeed, in a pioneering experiment at KEKB, a 10.5 mm thick single-crystal W positron target increased the positron yield by ∼25% compared to a conventional amorphous 14-mm thick tungsten target, whereas the steady-state heat load on the crystal target decreased by ∼20%. After a two-month period of operation, no degradation of the positronproduction efficiency was observed, and the crystal target was still stably operating at KEKB. Presently, efforts are underway to develop a crystal-based positron source for the FCC-ee [13,14]. In a crystalline undulator [17–19], the period of the crystal bending can be orders of magnitude shorter than for a conventional magnetic undulator. Positrons are better suited than electrons for this kind of device as their channeling path is between planes of nuclei, while electrons channel near the nuclei, leading to a much higher probability of interaction and particle loss. Simulations of a 10-GeV positron beam interacting with a crystalline undulator show at least a factor 20 higher emission rates in the 0.1–10 MeV range than for an equally thick amorphous Si sample, considering a radiation collimation half-angle of 0.5∕𝛾, with 𝛾the Lorentz factor [20]. In electron beam tests at MAMI in Mainz, two theoretical predictions were compared with experimentally measured radiation yields obtained by a 855 MeV beam and a crystal target of undulator period 𝑎= 0.12 Å. Significant radiation was recorded at least up to 30 MeV photon energies [21]. The ‘‘screened Coulomb potential’’ provided Nuclear Inst. and Methods in Physics Research, A 1075 (2025) 170371 2 F. Zimmermann Fig. 2. Sketch of crystal or nanotube with approximate channel dimension 𝑑; modified images from Ref. [15]. Fig. 3. Schematic of a circular crystal proton collider, from Ref. [16]. predictions in better agreement with the experimental data than the ‘‘continuum potential’’. Radiation spectra of electrons at a few hundred MeV were calculated with the screened Coulomb potential for different periods 𝑎[21]. Crystals are also effective elements for primary collimators. They could be deployed to address the FCC-ee [22] and FCC-hh machine protection and collimation challenges, through bent crystal-assisted collimation. In case of the FCC-hh, one can directly learn from relevant experience with crystal collimation at the LHC and HL-LHC [23]. Crystal based fixed-target experiments are another intriguing opportunity. In one proposal, a set-up with two bent crystals is considered [24], where a first crystal deflects beam-halo particles onto an in-vacuum target, and a second crystal deflects the short-lived baryons created inside the target, thus inducing spin precession [25]. This set up is sensitive to the electric and magnetic dipole moments of these unstable particles [26–29]. A proof-of-principle experiment at the LHC [24] is planned for 2025; a later deployment at the FCC-hh has been suggested. In a similar spirit, beam-halo particles could be fully extracted. A possible scheme of beam halo extraction from the FCC-hh with a bent crystal has been elaborated [30]. A bent crystal can be installed in a horizontal dogleg upstream of the Lambertson septum. This crystal intercepts, e.g., the vertical beam halo, and deflects the halo particles into the Lambertson septum. The conceptual study of Ref. [30] concluded that extraction of a natural beam halo from a collider of 50 TeV protons using a bent crystal is possible and may be efficient if a precise goniometer with an angular accuracy of 0.1 𝜇rad can be realized. The scheme of crystal extraction can also be combined with, or enhanced by, resonance islands [31]. Crystal assisted steering uses bent silicon or germanium crystals for deflecting high-energy charged-particle beams [32]. An assessment and optimization of the crystal-deflection efficiency for high-energy muons are being carried out [33]. Finally, strong field quantum electrodynamics (QED) can be studied using crystals. Namely, the combination of strong crystalline field and ultrarelativistic electrons allows reaching the Schwinger critical field in the electron rest frame [25]. An example experiment would consist of sending 180 GeV electrons from the FCC-ee through a thin silicon crystal. The implicated Feynman diagrams include double fermion lines, which correspond to positron solutions of the Dirac equation in the background field of the interplanar crystal potential [34]. Observing the so-called ‘‘one-step’’ contribution (where two photons are emitted ‘‘simultaneously’’) appears to be easier in a crystal than in a laser experiment [34]. 3. Beyond FCC: Future crystal-based colliders Crystals promise to become the basis for ultimate accelerators, since they support electromagnetic fields much higher than plasmas. A linear X-ray crystal muon collider has been proposed [35]. Possible ways to excite plasma wakefields in crystals or/and nanostructures are [15]: (a) by short X-ray laser pulses; (b) by short high-density bunches of charged particles; (c) by heavy high-𝑍ions; (d) by modulated high current beams; (e) by longer bunches experiencing self-modulation instability in the media. It is interesting to note that crystals could suppress the emission of synchrotron radiation [36]. Indeed, for a standard vacuum chamber, the synchrotron radiation emission is suppressed at wavelengths 𝜆 >2√𝑑3∕𝜌, where 𝜌denotes the bending radius, and 𝑑the pipe diameter [37]. Therefore, miniature accelerators with extremely small beam pipe on the micron or nanometre scale, combined with a large bending radius 𝜌(such as in the FCC tunnel) could suppress almost all radiation. An extreme case would be the use of nanotubes or bent crystals, where 𝑑becomes comparable to the inter-atom distance in the crystal lattice; see Fig. 2. Bent crystals exhibit a high effective field, amounting to 1000’s of Tesla, unreachable by superconducting magnet technology. The next hadron collider in the FCC tunnel, following the FCC-hh (and possibly the FCC-𝜇 𝜇), could be a circular crystal (or bent nanotube) proton collider; as sketched in Fig. 3. With an effective crystal field ≫1000 T, this collider could exceed the FCC-hh collision energy by a factor 100 or more [16]. Cryogenic crystals would minimize the ‘‘dechanneling’’ probability. As the effective dipole field of the bent crystals cannot be varied, the energy ramp may need to be accomplished by induction acceleration. Nuclear Inst. and Methods in Physics Research, A 1075 (2025) 170371 3 F. Zimmermann Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements I would like to thank S. 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