HL-LHC nominal scenario at the end of the luminosity leveling. (a) The minimum DA difference from the case without wire (Δ DA min ) for different dc wire configurations and (b) DA values vs angles for the wire configurations that guarantee DA min ≥ DA min (no wire). (c) Δ DA min for PACMAN bunches using different wire configurations. (d) Δ DA min for different wire configurations and zero Landau octupoles (I o ¼ 0 A).

HL-LHC nominal scenario at the end of the luminosity leveling. (a) The minimum DA difference from the case without wire (Δ DA min ) for different dc wire configurations and (b) DA values vs angles for the wire configurations that guarantee DA min ≥ DA min (no wire). (c) Δ DA min for PACMAN bunches using different wire configurations. (d) Δ DA min for different wire configurations and zero Landau octupoles (I o ¼ 0 A).

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Several configurations of the High Luminosity Large Hadron Collider, whose performance at collision is mainly limited due to the strong beam-beam long-range interactions, are studied in the presence of dc wire compensators. This analysis is based on analytical and numerical calculations where the main observables are the dynamic aperture (correlate...

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... with half crossing angle at IP1 and IP5 Φ 1=5 2 ¼ 250 μrad, Landau octupoles set at I o ¼ −300 A for partial compensation of the leading order octupolelike TSA χ from the BBLR kicks (as it is shown in [41] for LHC) and optimized working point Q ¼ ð62.315; 60.32Þ [22], the DA min without the use of dc wires is DA min (no wire) ¼ 6.1σ as shown in Fig. 4(a). Making use of the dc wires, the DA min can be improved up to Δ DA min ¼ 0.7σ with configurations that comply with the machine protection restrictions (D w > 10.4σ). The extra gain at the DA min can provide the margin for a flawless operation even in the presence of unexpected detrimental effects (like electron cloud formation). The ...
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... order to better appreciate the dc wires impact on different particles, the DA values for different phase angles (different initial conditions) are plotted in Fig. 4(b). The different wire configurations that guarantee DA min ≥ DA min (no wire) are plotted with different colors while the case without compensators is plotted in black. As can be seen, the DA improvement across the different angles can be quite more significant than the Δ DA min . The largest DA improved with wire compensators can be ...
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... nominal scenario and simulating a PACMAN bunch that experience only the left BBLR interactions of the IR1 and IR5 (the last bunch of the last train before the abort gap with minimum number of BBLR kicks N PACMAN ¼ N BBLR 2 ), the Δ DA min for the same wire configurations as before (baseline scenario with the full set of BBLR kicks) can be seen in Fig. 4(c). The DA min not only is not degraded with the good wire configurations but it is actually improved compared to the case without compensation. Focusing on the configurations indicated with green asterisks that are the ones that give the best conditional DA min at the baseline scenario with full set of BBLR kicks, the DA min is up to ...
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... mitigation of the leading order octupole-like tune spread with amplitude generated by the BBLR kicks. In order to calculate the compensation effect related only to the dc wires, the DA scans for the nominal scenario at the end of the luminosity leveling but with zero Landau octupoles (I o ¼ 0 A) are repeated and the Δ DA min is presented in the Fig. 4(d). The DA min without dc wire is less than 6σ (DA min (no wire) ¼ 5.5σ) but with the use of dc wires there are many configurations with D w > 10.4σ that guarantee DA min > 6σ. The best of them, that are indicated with green stars, can guarantee DA min up to 7.8σ (2.3σ improvement over the case without wire). From the results in Figs. ...
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... in the Fig. 4(d). The DA min without dc wire is less than 6σ (DA min (no wire) ¼ 5.5σ) but with the use of dc wires there are many configurations with D w > 10.4σ that guarantee DA min > 6σ. The best of them, that are indicated with green stars, can guarantee DA min up to 7.8σ (2.3σ improvement over the case without wire). From the results in Figs. 4(a) and 4(d), it is clear that the DA gain is higher when only wire compensators are used (zero octupole current). The reason for this difference, is the overcompensation of the octupolelike component generated by the BBLR kicks in the case with non zero octupole current. Despite this overcompensation, the different configurations with DA min ≥ 6σ ...
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... clear that the DA gain is higher when only wire compensators are used (zero octupole current). The reason for this difference, is the overcompensation of the octupolelike component generated by the BBLR kicks in the case with non zero octupole current. Despite this overcompensation, the different configurations with DA min ≥ 6σ and D w > 10.4σ in Fig. 4(a), indicates that some choices of the octupole current can be destructive for the wire performance but not catastrophic. On the other hand, with an appropriate choice of the octupole current, the dc wire performance can be enhanced as it is shown in a following ...

Citations

... The second reason for assessing multiple DA values is that optimising the ring configuration is a crucial aspect of the circular accelerator design and operation. This is usually achieved by evaluating numerous machine configurations and examining the hyper-surface that represents the DA as a function of the machine parameters, identifying regions that maximise the DA and produce minimal DA variation close to the peak (see, e.g., Ref. [22,23]). ...
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Understanding the concept of dynamic aperture provides essential insights into nonlinear beam dynamics, beam losses, and the beam lifetime in circular particle accelerators. This comprehension is crucial for the functioning of modern hadron synchrotrons like the CERN Large Hadron Collider and the planning of future ones such as the Future Circular Collider. The dynamic aperture defines the extent of the region in phase space where the trajectories of charged particles are bounded over numerous revolutions, the actual number being defined by the physical application. Traditional methods for calculating the dynamic aperture depend on computationally demanding numerical simulations, which require tracking over multiple turns of numerous initial conditions appropriately distributed in phase space. Prior research has shown the efficiency of a multilayer perceptron network in forecasting the dynamic aperture of the CERN Large Hadron Collider ring, achieving a remarkable speed-up of up to 200-fold compared to standard numerical tracking tools. Building on recent advancements, we conducted a comparative study of various deep learning networks based on BERT, DenseNet, ResNet and VGG architectures. The results demonstrate substantial enhancements in the prediction of the dynamic aperture, marking a significant advancement in the development of more precise and efficient surrogate models of beam dynamics.
... The crab cavities introduce a closed-orbit dependency on the longitudinal position within the bunch, allowing for a maximization of the bunches overlap at the IP. With a 10.5σ beam-beam separation, but a doubled bunch intensity, the effect of the BBLR interactions is expected to be reduced, although not negligible [15]. A proposed solution to cope with the residual BBLR interactions and their possible implications is the use of direct current (dc) wires to mitigate the detrimental effect of such phenomena. ...
... III, the observables of the experimental campaign together with the strategies adopted in order to demonstrate the mitigation of the BBLR interactions using wires are discussed. Some of the tracking simulations results [15,30,31] are shown in Sec. IV. ...
... The dimensioning of the wire compensators was also supported by numerous tracking simulations, whose results are reported in details in [15,30,31]. In this section, we report part of those results, focusing on the effect of the wire currents and the beam-wire distance on the dynamic aperture (DA). ...
Article
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In high intensity and high energy colliders, such as the CERN Large Hadron Collider (LHC) and its future high-luminosity upgrade, interactions between the two beams around the different interaction points impose machine performance limitations. In fact, their effect reduces the beam lifetime, and therefore, the collider’s luminosity reach. Those interactions are called beam-beam long-range (BBLR) interactions, and a possible mitigation of their effect using dc wires was proposed for the first time in the early 2000’s. This solution is currently being studied as an option for enhancing the HL-LHC performance. In 2017 and 2018, four demonstrators of wire compensators have been installed in the LHC. A 2-yearlong experimental campaign followed in order to validate the possibility to mitigate the BBLR interactions in the LHC. During this campaign, a proof-of-concept was completed and motivated an additional set of experiments, successfully demonstrating the mitigation of BBLR interactions effects in beam conditions compatible with the operational configuration. This paper reports in detail the preparation of the experimental campaign, including the corresponding tracking simulations and the obtained results, and draws some perspectives for the future. Published by the American Physical Society 2024
... Beam-Beam Long Range (BBLR) interactions are well recognized as one of the machine performance restrictions in hadron colliders like the LHC [1]. Their influence decreases the beam lifetime and the collider integrated luminosity [2]. ...
Article
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Beam-Beam Long-Range Compensators employing current-carrying wires are considered as valuable options in hadron colliders to increase dynamic aperture at small crossing angles. This paper presents a simple design proposal for application at CERN LHC. The preliminary design allows for a certain scalability of the number of modules, current flowing in the wire, and dimensions. It complies with two key requirements: (a) the use of a thin, bare metal wire that allows for movement as near to the beam as necessary while minimizing interactions with beam particles and meeting the specified DC current target; and (b) a wire support that is both an electrical insulator and a thermal conductor (ceramic). A molybdenum wire, vacuum brazed on an aluminium nitride support, is proposed, and the design is conceptually proved through the realization and extensive test of a demonstrator device. The wire brazing validation, as well as the system’s heat management, which are the most critical aspects, are given particular regard.
... Using these compensators in different experimental studies (that are accompanied by numerical ones), it was shown a significant improvement in beam lifetime [77]. These results encouraged using the wire demonstrators in the upcoming Run 3 of the LHC and are also under study for their eventual implementation in the HL-LHC [78]. ...
Preprint
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of fixed points in their topology and dynamics, the motion close to a resonance is presented, with simple non-linear map examples. The onset of chaotic motion and the modern methods used for their detection are detailed with a focus on frequency map analysis and concrete examples for a variety of rings and non-linear effects.
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