Nonlinear effects in particle accelerators have historically been treated as harmful influences that necessitate various mitigation schemes. Therefore, the simulation tools available are largely focused on identifying and correcting resonances. However, recent advances proved that nonlinear beam dynamics enables new techniques for manipulating particle beams and can characterise diffusion and chaos in particle accelerators. The simulation tools currently available for these purposes are difficult to integrate across different frameworks. This paper presents Xnlbd, a new Python package extending the Xsuite simulation framework, which aims to provide a unified set of tools for analysing nonlinear beam dynamics phenomena. It allows the visualisation of highly nonlinear phase spaces, the efficient finding of both stable and unstable fixed points and separatrices, the calculation of resonance driving terms and normal forms, and the computation of dynamic indicators for the detection of chaotic motion.

In recent years, several new beam manipulation techniques have been proposed that exploit the crossing of nonlinear resonances and the use of stable islands of the transverse phase space. One such manipulation is a novel approach to slow extraction, which combines particle trapping in stable islands with the use of bent crystals to reduce losses on the extraction septum. As a first step towards testing this approach, measurements were performed at the CERN Super Proton Synchrotron (SPS) to demonstrate beam splitting using stable islands of the third-order resonance generated and controlled by sextupole and octupole magnets. The phase-space topology was reconstructed by displacing the beam and observing the turn-by-turn evolution of the signal of the beam position monitors. The beam splitting was achieved by varying both the machine tune and the radial steering of the beam. The measurement results were found to be in excellent agreement with the tracking simulations.

In the context of the High Luminosity Large Hadron Collider (HL-LHC) project, two configurations of collimator settings are being considered. A set of relaxed settings were conceived to address potential limitations due to the impedance contribution of the collimation system with the initially foreseen settings, and to increase the primary betatron cut in case of over-populated beam tails. A significant simulation campaign has been conducted, utilising Xsuite-FLUKA coupling for the first time, to estimate the cleaning performance for each of these settings with the latest optics and layout scenarios. In addition, experiments in the current LHC have been carried out to experimentally study the cleaning performance with HL-LHC settings and to validate the simulated predictions. This paper presents and examines the results of these studies, aiming to determine which collimation settings are more suitable for implementation.