In the last two decades, numerical and experimental studies have extensively explored the impact of the space charge on bunched beams in both linear accelerators and storage rings. However, fully accounting for space charge effects over the entire accelerator is computationally intensive, especially in storage rings, where simulations must track beam dynamics over many turns and extended time periods. In many cases, space charge forces cannot be neglected, motivating the development of an alternative computational model. Here, we explore space charge-induced nonlinear dynamics using a model that approximates the Coulomb force by concentrating its effects at discrete locations along the accelerator. This approach enables efficient analyses of the full six-dimensional phase space evolution under space charge effects. Future work will apply this model to further investigate the interplay between space charge and beam-beam interactions in colliders, as well as to assess long-term stability criteria in ring accelerators.

The ion injector complex at CERN supplies ions for collisions at the Large Hadron Collider (LHC) and for fixed-target physics programmes at the Super Proton Synchrotron (SPS) and Proton Synchrotron (PS). In recent years, there has been growing interest in experiments with lighter ions than lead within the ion-physics community. The NA61/SHINE collaboration has requested beams of oxygen, magnesium, and boron for Run 4 (2030-2033), while the HEARTS++ project proposal aims to enable switching between four ion species, with each transition occurring within 15 minutes. Additionally, LHC experiments are considering lighter-than-lead ion beams for Run 5 (2036-2041), pending an assessment of which particle species collisions offer higher nucleon-nucleon luminosity. Consolidating these future scenarios demands an evaluation of the light-ion performance of the present injector complex. This contribution discusses the challenges of the present injector complex in view of light-ion operation and a proposed ion complex upgrade to address future needs.

While human operators are very good at finding the optimal conditions that maximize the luminosity in RHIC, maintaining those conditions can be a demanding task. There is also no metric that can measurably determine if those optimal conditions are truly optimal, given the degrees of freedom are very high and there are multiple and competing objectives. In this talk we will describe how we use machine learning and improved physics models to build systems for optimizing the beam brightness during injection at the BNL Booster and AGS synchrotrons and efforts to maintain maximum luminosity in RHIC.

The extraction system of the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory has been modified to enable single-bunch extraction. This is achieved by increasing the voltage of the first deflector to oversteer the beam, halting extraction, and then selectively switching it off using a high-voltage chopper to synchronize the deflector’s operational voltage with the transit time of a single bunch, enabling its extraction. A pre-chopper positioned before the cyclotron limits the beam available for acceleration, minimizing activation and sputtering damage from discarded bunches. This cost-effective technique is crucial for time-sensitive experiments and provides precise control over dose delivery, broadening the cyclotron’s range of applications. Future efforts will focus on increasing extraction frequency by optimizing the deflector electronics for faster recovery times, and exploring sequential switching of two deflectors to reduce the required oversteering voltage.

Measurements of the transverse beam halo in the LHC showed that it contains a non-negligible portion of the total stored beam energy, with implications for both collimation system performance and overall machine protection. As the HL-LHC era, with a significant increase in stored beam energy approaches, the understanding and modelling of the beam halo distribution becomes even more important. This applies particularly for the risk quantification in view of new failure scenarios. This contribution summarizes the recent progress in beam halo measurement, new findings from refined analysis methods, an overview of the employment of key measurement techniques, and advancements in experiments aiming to quantify the origin of beam halo. We describe the latest halo models and how they affect the performance of potential active halo control mechanisms in simulations. These developments form a critical input to HL-LHC machine protection strategies.

Beam-beam long-range interactions are known to be a strong source of non-linearities in hadron colliders, undermining the performance of the LHC during proton-proton collisions. In order to enhance the luminosity production of the machine and increase the tolerance of the working point after the High Luminosity upgrade of the LHC (HL-LHC), dedicated correctors such as beam-beam wire compensators can be used. In this paper, the beam dynamics of this compensation problem is studied in details, ultimately showing that the linearity of the machine can be significantly improved throughout the beam core --- and up to several sigmas --- leading to an improvement of the Dynamic Aperture (DA) of the machine. This conclusion is shown to be supported by analytic calculations, dynamic aperture simulation studies, as well as experimental results presented in earlier work. Both nominal and pacman bunches are shown to benefit from the compensation. In the proposed approach, wire compensators can be positioned according to the collimation settings, simplifying their practical implementation in the machine for the HL-LHC era.

Beam matching is a common accelerator design and operation technique to minimize beam losses. Although widely used, a full theoretical understanding of beam matching in 6D remains elusive. In this paper, we present an analytical treatment of 6D beam matching of a high-intensity beam in RF structures. We start within the framework of a linear model and apply the averaging method to a set of 3D beam envelope equations. Accordingly, we obtain a matched solution that is comprised of smoothed envelopes and periodic terms, describing envelope oscillations with the period of the focusing structure. We then consider the nonlinear regime, where the beam size is comparable with the separatrix size. Starting with a Hamiltonian analysis in 6D phase space, we attain a self-consistent beam profile, showing that it significantly differs from the commonly used ellipsoidal shape. Subsequently, we analyze the special case of equilibrium with equal space charge depression between all degrees of freedom. A comparison of beam dynamics for equipartitioned, equal space charge depression, and equal emittances beams is given. Finally, we present experimental results on beam matching in the LANSCE linac.