An innovative method for slow extraction in circular hadron accelerators with resonance islands and bent crystals

Contents lists available at ScienceDirect Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima An innovative method for slow extraction in circular hadron accelerators with resonance islands and bent crystals Dóra Erzsébet Veres a,b,∗, Massimo Giovannozzi a, Giuliano Franchetti b,c aCERN, Esplanade des Particules 1, 1211, 23 Geneva, Switzerland bGoethe University Frankfurt, Theodor-W.-Adorno-Platz 1, 60629, Frankfurt am Main, Germany cGSI Helmholtzzentrum fur Schwerionenforschung GmbH, Planckstraße 1, 64291, Darmstadt, Germany ARTICLE INFO Keywords: Hadron accelerators Nonlinear beam dynamics Single-particle dynamics Beam injection and extraction Slow extraction Crystal Channelling Crystal extraction ABSTRACT Recent developments in accelerator physics and nonlinear beam dynamics have broadened the range of techniques for manipulating charged-particle beams. The effective use of adiabatic trapping and beam transport in resonance islands within the CERN Proton Synchrotron has been the basis for multiturn extraction. Moreover, the effective deployment of bent crystals in the CERN Large Hadron Collider has improved the efficiency of the collimation system and within the CERN Super Proton Synchrotron, it has significantly minimised losses at the extraction septum during slow extraction. We discuss the potential synergy of using resonance islands and bent crystals together to create a novel approach for slow extraction in circular hadron accelerators. 1. Introduction Slow extraction (see, e.g., Refs. [1–9] and references therein) is the standard method for delivering charged-particle beams to fixed-target experiments from circular accelerators. It relies on exciting an unstable third-integer resonance strongly driven by sextupoles, which induces the stochastic motion of particles along unbounded separatrix arms in the horizontal phase space. At the point of extraction, the thin foil of an electrostatic septum cuts the distribution of particles along one of the separatrix arms and deflects particles into the extraction channel. Thus, slow extraction is characterised by inherent beam loss on the septum, which poses a risk of damaging and irradiating accelerator components, reducing their lifetime and affecting maintenance [10,11]. All this ultimately limits the number of protons on target delivered by the machine. Loss reduction during slow extraction is therefore an active field of study within accelerator physics. Bent crystals have been explored to shadow the electrostatic septum [12–17] or to non-resonantly slowextract the beam halo [18] in the Super Proton Synchrotron (SPS). In fact, extensive research [19–39] at many research institutions around the world such as CERN in Switzerland, INFN in Italy, FERMILAB in the USA, and IHEP in Russia over many decades has established bent crystals as a valuable tool in many other areas of accelerator physics, as illustrated by them being an integral part of the collimation system of the CERN Large Hadron Collider (LHC) [40–42], as well as their planned use for future fixed target experiments in the LHC [43–50] ∗Corresponding author at: CERN, Esplanade des Particules 1, 1211, 23 Geneva, Switzerland. E-mail addresses: [email protected] (D.E. Veres), [email protected] (M. Giovannozzi), [email protected] (G. Franchetti). considered in the framework of the Physics Beyond Colliders studies at CERN [51–53]. In recent years, several advanced techniques exploiting nonlinear effects in accelerators have emerged providing new and improved ways to control and manipulate charged-particle beams. A notable example is Multi-Turn Extraction (MTE) [54,55] developed at the CERN Proton Synchrotron (PS), which has become the standard method of extracting high-intensity proton beams destined for fixed target experiments at the SPS [56–59]. Further examples include the combined use of nonlinearities and external exciters for particle trapping in stable islands [60], the crossing of 2D nonlinear resonances to achieve emittance exchange [61,62], and the use of transverse exciters to cool an annular beam distribution [63]. In this paper, we extend the novel concept of [64] that exploits the combined use of resonance islands and bent crystals to achieve a lowloss alternative to standard resonant slow extraction. We present 6D simulations using a realistic accelerator lattice of an alternative version of the method. 2. Basic principle of the resonance island and bent crystal approach The principle of this novel approach is illustrated in Fig. 1. A bent crystal creates an angular separation between particles circulating in the machine and those to be extracted in a given turn by means https://doi.org/10.1016/j.nima.2025.170286 Received 14 December 2024; Received in revised form 24 January 2025; Accepted 2 February 2025 Nuclear Instruments and Methods in Physics Research A 1073 (2025) 170286 Available online 10 February 2025 0168-9002/© 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies. D.E. Veres et al. Fig. 1. Illustration of the principle of the novel slow-extraction approach. Particles are steadily transported to a bent crystal at large amplitude close to the separatrix (blue) of stable islands generated by sextupole and octupole magnets close to the third-order resonance. At the crystal (a) particles receive a kick due to planar channelling, which allows them to jump the septum blade (b) later on leading to low-loss extraction. The crystal is shaded in grey, the septum blade and aperture are shown in red and the field region of the septum is shown in green. Fig. 2. Angular deflection received by 400 GeV∕cprotons upon a single pass through a2.8 mm-long bent silicon strip crystal with a bending radius of 28 m, simulated using xcoll [65]. The regimes corresponding to various coherent interactions are indicated in red. of planar channelling. With an optimal phase advance between the crystal and the septum, this angular separation at the crystal location translates into a spatial separation at the septum location, creating a depleted beam intensity region at the foil of the electrostatic septum, thus reducing beam losses. The transport of particles from the beam core to the bent crystal is achieved by exciting the third-order unstable resonance. However, contrary to standard techniques, the particle motion remains regular as a result of the presence of stable islands, controlled by sextupole and octupole magnets. This phase-space topology opens up the possibility of multiple passes through the crystal, which enhances multi-turn channelling efficiencies, leading to low-loss slow extraction. Furthermore, it also allows for good control of the particle flow to the crystal, and by careful control of the islands’ shape at the crystal location, we can limit the angular spread of the beam at the crystal, which is key to ensuring that the particles interact with the crystal within the critical angular acceptance (see below). The beam can be brought into resonance either by changing the machine tune or by changing the field of the main dipoles (and quadrupoles) in the presence of non-zero chromaticity. An elegant method to achieve this is Constant Optics Slow Extraction (COSE) [66]. Note that while changing the machine tune during the extraction process changes the machine optics, thus affecting phase advances between elements of interest, COSE involves scaling the machine settings according to the beam momentum. This leaves optics and phase advances unchanged and ensures the invariance of the phase-space topology at the crystal and septum locations from the particle momentum (and hence, extraction time). COSE is therefore the method chosen for our studies. 3. Stable islands as a means of controlled transport to large amplitudes In a time-independent system, the separatrix is an impenetrable boundary. By scaling the machine settings during the extraction process, the particles can cross the separatrix. If the system variation is adiabatic, the movement of particles between different regions of the phase space is described by well-established probabilistic rules [60,67– 72]. In this case the particles approach the resonance such that the rate of increase of the island surface surpasses the rate of decrease of the core surface, which leads to particles being trapped in stable islands only and not in the region outside them. However, the slow extraction timescale, albeit relatively long, is often still too short for all momenta to be extracted adiabatically. Hence, particles leaving the core may enter the stable islands or the region outside them. In either case, they move close to the growing separatrix delimiting the stable islands until they reach the bent crystal. Since the COSE approach selects particles for extraction on the basis of their momentum, a non-zero chromaticity is necessary, and the larger the chromaticity, the smaller the range of 𝛿𝑝=𝑝−𝑝0 𝑝0for which particles see the resonance at a given time. This allows for a steady spill of particles out of the core region. However, the larger the chromaticity, the less time a single particle spends close to the resonance. Combined with the stability of the phase space outside the core region, this can induce particle recapture in the growing core region on the opposite side of the resonance, thus preventing the particles from reaching the crystal and being extracted. This is a key difference of this novel approach to standard methods, and needs to be compensated for by creating a large amplitude detuning and kicking the beam before starting the extraction process to deplete the very centre of the phase space. 4. Channelling by bent crystals The method presented here relies mainly on the planar channelling of a bent Si crystal [73,74]. This can occur when a particle enters the crystal at a small angle with respect to the crystal planes (i.e. below the critical angle 𝜃𝑐=√2𝑈max 𝑝𝑣 (1 −𝑅c 𝑅), where 𝑈max is the crystal potential, 𝑝𝑣 is the particle energy and 𝑅𝑐is the critical bending radius below which channelling is not possible) and is trapped in the potential wells formed by the electric fields of the atomic planes. It then travels between the atomic planes following the crystal curvature and emerges at an angle close to the crystal bending angle. The impact angle above which channelling cannot occur, called the critical angle, Nuclear Inst. and Methods in Physics Research, A 1073 (2025) 170286 2 D.E. Veres et al. Fig. 3. 𝛽-functions (top) and dispersion (bottom) of the lattice used in simulations. Key elements located in dispersion-free straight sections are indicated in grey and their optical functions are given in the table on the right. depends on the particle energy and is approximately 10 μr ad for 400 GeV protons. In addition to channelling, particles may undergo several other coherent interactions with the crystal, as shown in Fig. 2(for a detailed description of the physics, see [73,74]). Due to the stability of the phase space both inside and outside the islands, undesired interactions such as a small kick owing to volume reflection or slight amorphous scattering pose little risk to the efficiency of the proposed slow-extraction method, as particles continue to move along stable orbits in relative proximity to the separatrix and have the chance to come back to the crystal and channel at a later turn. This results in a high multi-pass channelling efficiency compared to the lower single-pass efficiency of standard methods that rely on crystal shadowing. The other key difference with respect to crystal shadowing is that all extracted particles interact with the crystal. Scattering at large angles due to amorphous interactions can, however, contribute to losses, but the primary source of the remaining losses in the septum is de-channelling, which occurs when particles lose channelling conditions due to scattering from electrons, crystal nuclei, or defects. 5. Simulation model The simulations presented here were performed on an accelerator lattice inspired by the SPS and illustrated in Fig. 3. The lattice was constructed with four dispersion-free straight sections housing an insertion for changing the tune, a sextupole and octupole magnet in close proximity to each other to control islands, a bent crystal, and an extraction septum. The nonlinear elements, the crystal and the extraction septum are positioned in dispersion-free regions to ensure that any momentumdependent offset of the closed orbit does not degrade the performance of the method. In addition, the nonlinear elements are located at a large horizontal 𝛽-function to minimise the coupling between the transverse planes. The crystal parameters were chosen to be similar to those of the crystals installed in the SPS: 2.8 mm length, 2 mm width, 100 μr ad bend. The septum foil was modelled as a500 μm thick black absorber, which is a pessimistic estimate of the apparent width of the SPS electrostatic septum with sub-optimal alignment of the tanks [15,75]. The horizontal septum gap, where the particles were considered extracted, was taken to be 10 mm wide. The beam energy was assumed to be 400 GeV to match that of the SPS fixed-target beam at extraction. The machine and beam parameters used in the tracking simulations are collected in Table 1. The momentum distribution of the beam was chosen to be uniform. Hence, to achieve a uniform spill, a linear ramp of the reference energy was applied. In the presence of significant nonlinear chromaticity and a highly non-uniform momentum distribution, the change of the magnetic field of the machine simply needs to take a different, appropriate functional form to ensure a uniform extraction spill. This is easily achieved in real time using feed-forward control of machine settings, as is already done in the SPS [66,76]. The tracking of particles through the electromagnetic elements of the lattice was performed with the xtrack package of Xsuite [77, Table 1 Parameters used in tracking simulations (inspired by the CERN SPS). Parameter Value Spill length ∼3.5 s Revolution period (𝑇0)13.6 μs Machine ramp rate (𝛥𝑝0𝑐)4.77 k eV/turn Momentum (𝑝0)400 GeV∕𝑐 Momentum spread (𝛿𝑝) [−1.5, 1.5] ‰ Horizontal emittance (norm.) (𝜀∗ 𝑥)1 μm Vertical emittance (norm.) (𝜀∗ 𝑦)1 μm Horizontal tune (𝑄𝑥) 10.68 Vertical tune (𝑄𝑦) 10.58 Horizontal chromaticity (𝑄′ 𝑥) 10 Vertical chromaticity (𝑄′ 𝑦) 0.5 Table 2 Percentage of particles in various states at the end of the extraction. Particle state at end of tracking % Circulating 0.2 Extracted 98.5 Lost in septum 0.4 Lost in crystal 0.5 Lost in global aperture (5 cm) 0.4 78] simulation framework. The particle-crystal interaction was simulated using the xcoll [65] package of Xsuite, which implements the same crystal routine in C programming language that has been available in Fortran as part of SixTrack [79–81] and that was compared with the results of beam tests carried out in the CERN North Experimental Area and measurements in the LHC [40,80,82–85] and the SPS [82]. 6. Simulation results Fig. 4shows the time evolution of the particle distribution in the horizontal phase space at the crystal location. The initial smallemittance beam is first displaced and allowed to filament into a hollow beam, then the reference energy is ramped to induce the spill of particles from the core region into the stable islands and finally to the crystal shaded in grey. The use of stable islands not only ensures the possibility of multiple passes through the crystal but can also be exploited to achieve a condition where almost all particles hitting the crystal are within the channelling acceptance, as illustrated in Fig. 5. The percentage of particles extracted or lost at the different elements over the 2.6 × 105turns (approximately 3.5 s) process is given in Table 2. The extraction efficiency of 98.5% achieved exceeds the measured slow extraction efficiencies of 96.6% in the SPS in 2016– 2017 [86] before the introduction of crystal shadowing, and the 0.4% Nuclear Inst. and Methods in Physics Research, A 1073 (2025) 170286 3 D.E. Veres et al. Fig. 4. Beam distribution in the horizontal phase space at the crystal location at different moments during the extraction process. The phase-space structure with three stable islands is clearly visible. The crystal is shown in grey. Fig. 5. Simulated beam spot on the crystal. The crystal alignment angle is shown in red and the channelling acceptance is shaded in grey. Almost all particles fall within the acceptance. Fig. 6. Distribution of 𝑥, 𝑝𝑥of extracted particles at the septum location. septum losses are well below even the values achieved after the local shadowing was made operational with a 40% loss reduction [15], resulting in about 2% septum losses if projected from the 2016–2017 measurements [86]. The 0.2% of particles still circulating at the end of the extraction process were mainly those recaptured in the core and can be extracted by increasing the initial beam displacement. Fig. 6shows the position and angle distribution of the extracted particles. Sparsely populated tails can form as a result of the rare large-angle scattering by the crystal. However, the extracted distribution exhibits a more focused profile and reduced horizontal spread compared to the typically narrow, elongated distribution obtained using standard slow-extraction methods. This can also facilitate a more effective matching to the subsequent transfer line. 7. Conclusions and outlook A novel slow-extraction concept was developed that provides a new application of bent crystals, combining them with the use of stable islands as a means of particle transport to large amplitude. This enables multiple passes through the crystal, enhancing channelling efficiency and providing precise control over the angular spread of the beam at the crystal. The novel concept is combined with the COSE technique, further enhancing the overall performance. Numerical simulations demonstrate improved extraction efficiency and reduced septum losses compared to current SPS slow extraction performance. Further simulation studies are planned to evaluate the potential challenges of a real machine, such as closed-orbit jitter. Proof-of-principle tests are already underway at the SPS. 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 The authors would like to thank the colleagues of the CERN BEABP-NDC section, in particular B. Lindström and F. van der Veken for support with simulations and P. Hermes and S. Redaelli for their helpful insights on crystal physics. We also thank colleagues from the CERN SY-ABT-BTP section for many useful discussions on slow extraction. 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