Measurements of the transverse beam-halo population at large amplitudes in the Large Hadron Collider (LHC) provide crucial insights into the stored beam energy near the LHC collimators. These particles do not contribute significantly to the luminosity but their loss could impose limitations on accelerator performance through sudden loss spikes or even collimator damage in case of fast beam failures. A thorough understanding of the beam halo formation, along with the physical mechanisms driving its behaviour and evolution throughout the final stage of the LHC injection chain and during the acceleration cycle, is essential to define appropriate mitigation strategies to ensure reliable operation in view of High Luminosity LHC beam parameters. In this study, we explore potential origins of the transverse beam halo by examining experimentally multiple contributing factors to halo formation, including electron cloud effects, beam injection dynamics from the Super Proton Synchrotron (SPS), and the energy ramping process within the LHC.

Employing octupole magnets for Landau damping of transverse single-bunch instabilities in synchrotrons often restricts the dynamic aperture due to the excitation of betatron resonances. The situation complicates in the presence of strong direct space charge fields. A notable case is the 1-second accumulation plateau of the heavy-ion synchrotron SIS100 at the Facility of Antiproton and Ion Research (FAIR), which is designed to operate at beam intensities near the space charge limit. This study presents numerical simulations that establish the proposed stabilisation scheme, incorporating self-consistent space charge effects, beam coupling impedance and full lattice tracking. The analysis combines requirements for Landau damping of the resistive-wall instability and tolerable octupole current in relation to dynamic aperture. The results demonstrate effective control of collective effects for the most demanding beam production scheme with ${}^{238}$U${}^{28+}$ beams.

Eddy currents induced by rippling magnets in axially asymmetric vacuum chambers are known to generate magnetic multipoles of higher orders, with a dynamic sextupole driven by a time-varying dipole being a common example. However, the inverse phenomenon—lower-order multipoles created by an oscillating higher-order multipole magnet, though consistent with Maxwell’s equations—has not been explored to our knowledge. In this paper, we present an analytical derivation of the kick for the driving magnetic multipole of any order and the vacuum chamber of arbitrary shape. We then validate our findings using FEM simulations. Finally, we demonstrate the relevance of this effect to the Electron Storage Ring (ESR) of the Electron-Ion Collider. The ESR has very stringent orbit stability requirements at the interaction point, which demand rigorous evaluation of all potential dipolar kick contributions. Our findings reveal that the dipolar kicks generated by rippling sextupoles are sufficiently strong to require the ESR sextupole power supply ripple specification to be tightened from an otherwise sufficient 100 parts per million (ppm) rms to 20 ppm.