Ezio Todesco

PLATO: A program library for the analysis of nonlinear betatronic motion☆

Abstract We present PLATO (Perturbative Lattice Analysis and Tracking tOols), a program library for analysing four-dimensional betatronic motion in circular particle accelerators. The 136 included routines provide both the resonant and the non-resonant perturbative series that approximate nonlinear motion (normal forms); standard numerical tools such as the Lyapunov exponent, frequency analysis and evaluation of the dynamic aperture are also available. The aim of the library is to apply these techniques, originally developed for the analysis of nonlinear dynamic systems, to realistic models of particle accelerators. To ensure the highest flexibility, the code is fully compatible with standard tracking programs commonly used in the accelerator physics community.

GIOTTO: A CODE FOR THE NONLINEAR ANALYSIS OF AREA-PRESERVING MAPPINGS

An interactive code for the analysis of nonlinear area-preserving mappings is described; several facilities allow the user to draw phase portraits, make zooming, and use colors. The perturbative approach of normal forms and all the standard tools for the analysis of the nonlinear dynamics (Fourier spectra, Lyapunov exponents, fixed points …) are implemented in a user-friendly graphic environment based on X-window and OSF-Motif. Both simple models and more involved mappings which describe the betatronic motion in a particle accelerator can be implemented.

Performance of CERN LHC main dipole magnets on the test bench from 2008 to 2016

Throughout 2015 and 2016, the LHC is operated with a current in the main dipoles of 10980 A, equivalent to a proton–proton collision energy of 13 TeV in the center of mass. A total of 175 training quenches were needed in 2014 in the 1232 main dipole magnets installed in the LHC at CERN to reach operational conditions. Since 2008, a number of dipole magnets have been removed from the LHC and were, sometimes after repairs of nonconformities, retested in the CERN based SM18 magnet test facility up to ultimate current. Other magnets have been retested after long storage. The results confirm earlier findings that some magnets series are more prone to quenching than others after thermal cycle. The correlation between a short and long thermal cycle is under investigation. Special cases with many thermal cycles will be highlighted and a new magnet series, fully produced at CERN is introduced. Results of a quench heater fatigue test, assessing the long-term reliability of the quench heaters, will be given. The results of repairs following high internal splice resistances are discussed.

Normal forms and invariants in the description of a magnetic lattice

Abstract We summarize some mathematical methods used in the description of magnetic lattices for hadrons, based on the discrete formalism of symplectic maps. We first generalize the perturbative approach of normal forms to the resonant case; then we analyze the structure of the singularities of the conjugating function in the nonresonant case, making an analytic continuation of the perturbative series using Pade approximants. A nonperturbative method, which computes the invariants of the motion from the iterates of the map using a variational principle, is outlined. Two applications of the nonresonant normal forms to the physics of hadron accelerators are shortly discussed: the analysis of the dynamic aperture experiment carried out at the SPS in 1988 and the correction of the nonlinearities due to errors in the superconducting magnets in the LHC.

Accelerator Magnet RD in the Perspective of a LHeC and HE-LHC - Synergy or Competion?

Beyond HL-LHC, CERN has a number of physics options that offer potential and challenges. This contribution dwells on the long-term projects HE-LHC and LHeC to put the magnet R&D at CERN (resistive and superconducting, slow and fast) in a long-term perspective. In particular synergies and parallel roadmaps will be highlighted. We will show how the on-going development (2012-2015) on low-field, high-field, and low-loss magnets can be used towards longer term objectives.