The recent IPAC’23 conference was an ideal opportunity to present and discuss within our community the status of the beam dynamics simulations for Run 4, marking the start of HL-LHC operation. At top energy, proton beams will circulate in the machine for about 10 hours, covering inside the LHC ring about half the distance of the Voyager 1 space probe, the most distant human-made object from Earth. The proton journey will however be perturbed by strong non-linear fields. In fact, the main goal of the collider is to maximize the inelastic interaction between the beams (i.e., the collider luminosity) but this comes at the price of electromagnetic interactions between them, known as the beam-beam effect.
Our goal and challenge is to find the best compromise between the instantaneous luminosity and the lifetime of the beam in relation to the machine settings and the beam parameters. This is possible via an iterative process based on the invaluable input from the different HL WPs (optics and luminosity leveling strategy, magnet field quality, alignment tolerance, noise of power supplies and crab cavities, impedance and machine protection considerations, cryogenic limits, experiments pile-up constraints…) and by building on the experience from the present LHC Run. The intensity limitations due to electron cloud confirmed in 2022 might require using lower beta* values, higher pile-up and pushed bunch intensity to reach the integrated luminosity goal, possibly in addition to mixed filling schemes already in use in today’s LHC since the 2023 Run.
Despite the great progress in speeding up the numerical tracking, simulating the beam lifetime in a multiparametric space (e.g., varying bunch intensity, filling schemes, beta*, crossing angles, tunes, chromaticity, octupoles…) is computationally too intensive. For this reason, an indirect observable is considered: the dynamic aperture (DA), that is the minimum transverse amplitude of the "surviving" particles after one million turns (corresponding to about 90 seconds of time inside the LHC ring). DA benchmarking during LHC runs showed its good correlation with beam lifetime and allowed us to define the minimum DA target, set to 6 sigma.
In Figure 1, we show an example of DA dependence versus the horizontal and vertical tunes of the machine at the end of the beta* leveling (assuming in this case a flat optics, betax* > betay*). One can see that there is a relatively large region (enclosed by the green line) with DA>6 sigma. Given the residual transverse coupling constraints, only a small subset of this region can be considered as a valid working point (the region with QY > QX+0.005).
In Figure 1, simulations were performed considering the beam-beam encounters of a specific bunch. However, the impact of beam-beam effects varies depending on the number of long-range interactions and bunch-by-bunch variations of the DA are expected. Figure 2 (top) shows the simulated DA for the first 3000 bunch slots of the so-called ‘8b4e’ filling scheme (interleaving 8 nominal bunches with 4 empty slots to mitigate the electron cloud formation). The selected bunch for DA analysis of Figure 1 is highlighted in green. A specific optimized working point is selected for this analysis (QX, QY = 62.316, 60.321). For each bunch, the number of long-range encounters in ATLAS/CMS (red) and LHCb (blue) are illustrated in the bottom part of the figure. The results of the analysis indicate that the selected bunch, despite having the maximum number of beam-beam interactions, does not result in the worst DA among all the bunches, demonstrating the relevance of bunch-by-bunch DA studies.
Operating with optimized working points, reducing chromaticity and reversing octupole polarity at the end of the luminosity leveling have been found to be the most promising mitigation measures to enhance the collider’s performance. At present, together with other relevant aspects, the effect of the reduced chromaticity and negative sign of the octupoles on the beam stability is being scrutinized within the HL-WP2, aiming to converge to a sound proposal for the Run 4 cycle configuration by the end of the year. Stay tuned.