Random Errors induced by the Superconducting Windings in the LHC Dipoles

The problem of estimating the random errors in the LHC dipole is considered. The main contributions to random errors are due to random displacements of the coil position with respect to nominal design and to the variation of the magnetization of the superconducting cable. Coil displacements can be induced either by mechanical tolerances or by the manufacturing process. Analytical and numerical scaling laws that provide the dependence of the random errors due to random displacements on the multipolar order are worked out. Both simplified and more realistic models of the coil structure are analysed. The obtained scaling laws are used to extract from experimental field shape data the amplitude of the coil displacements in the magnet prototypes. Finally, random errors due to interstrand resistance variation during the ramp are estimate

Test of the Sorting Methods at the CERN-SPS

An external study of the effectiveness of the sorting strategies on the CERN Super-Proton-Synchrotron is proposed. The eight strong extraction sextupoles used for diffusion experiments can be independently powered to simulate random errors. Numerical computations show that a significant spread in the dynamic aperture can be obtained. A sorting strategy based on analytical quality factors allows a considerable improvement on the beam stability. A complete analysis of the possible permutations shows that the good configurations are rather abundant. The effectiveness of the ordering procedure is verified for long-term six-dimensional motion and different working points. Situations are presented where the beneficial effect of the sorting is expected to be large and well measurable in realistic conditions of operation

Long term estimates for sorting strategies of the LHC dipoles

Sorting strategies are investigated in view of improving the dynamic aperture of the CERN-LHC. Local and quasi-local compensation of the random field shape imperfections are discussed and applied to simplified model of the LHC lattice. The most promising strategies are further investigated on a realistic LHC model with particular emphasis on the analysis of the robustness of the dynamic aperture improvements including long term effects. First results on the application of the recently developed extrapolation law for the prediction of the dynamic aperture to the sorting problem are presented

PLATO: A Program Library for the Analysis of 4D Nonlinear Transverse Motion

The PLATO (Perturbative Lattice Analysis and Tracking tOols) program, a program library for analyzing four-dimensional betatronic motion in circular particle accelerators is presented. The routines included in this library provide both the resonant and the nonresonant 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. To ensure the highest flexibility, the code is fully compatible with standard tracking programs commonly used in the accelerator physics community

Modeling of random geometric errors in superconducting magnets with applications to the CERN Large Hadron Collider

Estimates of random field-shape errors induced by cable mispositioning in superconducting magnets are presented and specific applications to the Large Hadron Collider (LHC) main dipoles and quadrupoles are extensively discussed. Numerical simulations obtained with Monte Carlo methods are compared to analytic estimates and are used to interpret the experimental data for the LHC dipole and quadrupole prototypes. The proposed approach can predict the effect of magnet tolerances on geometric components of random field-shape errors, and it is a useful tool to monitor the obtained tolerances during magnet production