Innovative method to measure the extent of the stable phase-space region of proton synchrotrons

Abstract

The advent of circular accelerators based on superconducting magnets has revolutionized the field of beam dynamics, with particle motion turning from linear to nonlinear due to unavoidable high-order field errors generated by the ring magnets. Nonlinear dynamics was already well mastered, e.g., in the close field of celestial mechanics as similar problems had been considered and successfully tackled. Hence, several results were available to aid comprehension of the behavior of charged particle beams under the influence of nonlinear forces. Here, we discuss how concepts derived from the theory of dynamical systems, linked with the fundamental Kolmogorov-Arnold-Moser theory and Nekhoroshev theorem, can be successfully applied to the analysis of nonlinear motion of charged particles in a circular accelerator. Based on these ideas, an innovative method to measure the extent of the phase-space region within which bounded motion occurs is presented, which has been successfully tested for the first time at the CERN LHC.

Machine Learning Applied to the Analysis of Nonlinear Beam Dynamics Simulations for the CERN Large Hadron Collider and Its Luminosity Upgrade

“…This means that the knowledge of the evolution of the DA, i.e., a rather abstract quantity, can be directly linked to the evolution of the beam intensity in a circular particle accelerator, which is a fundamental physical observable. This approach has been already successfully applied in experimental studies [38] and intense efforts are devoted to refine and promote the proposed strategy.…”

Description of the luminosity evolution for the CERN LHC including dynamic aperture effects, Part I: The model

“…More importantly, such a scaling law was proposed to describe the time evolution of beam losses in a circular particle accelerator under the influence of non-linear effects [5], and the proposed model was verified experimentally, using data from CERN accelerators and the Tevatron. Note that such a scaling law for beam intensity as a function of time is at the heart of a novel method to measure experimentally the DA in a circular ring [6].…”

Analysis of the non-linear beam dynamics at top energy for the CERN Large Hadron Collider by means of a diffusion model

“…For the latter, the technique consists of blowing up both the horizontal and vertical emittances until beam losses can be detected. The beam intensity as a function of time is then recorded, fitted, and compared with the results of numerical simulations, usually showing a very nice agreement [33]. During these measurements, the strength of non-linear elements located in the regular cell of the accelerator (see Fig.…”