Frequency maps of LHC models

The frequency map analysis method is applied in models of LHC optics versions 5 and 6 in order to study their non-linear dynamics. The maps present a global picture of the resonance structure of the phase space. They enable us to view the dangerous zones tracing the limits of the dynamic aperture. This approach, assisted by detailed resonance analysis, is used as a guide for exploring possible correction schemes, which are subsequently verified by long-term tracking

Correction Schemes for the Normal Octupole and Decapole Errors in the LHC Dipoles

Different correction schemes for curing the effect of the normal octupole and decapole multipole errors of the LHC main dipoles, at injection, are investigated. Frequency and diffusion maps are constructed and compared for two working points and for different values of the momentum deviation. The excitation of individual resonant driving terms is estimated through high order normal form construction techniques. The resonance analysis results are finally verified through short-term element by element tracking

Operational beams for the LHC

The variety of beams, needed to set-up in the injectors as requested in the LHC, are reviewed, in terms of priority but also performance expectations and reach during 2015. This includes the single bunch beams for machine commissioning and measurements (probe, Indiv) but also the standard physics beams with 50 ns and 25 ns bunch spacing and their high brightness variants using the Bunch Compression Merging and Splitting (BCMS) scheme. The required parameters and target performance of special beams like the doublet for electron cloud enhancement and the more exotic 8b$\oplus$4e beam, compatible with some post-scrubbing scenarios are also described. The progress and plans for the LHC ion production beams during 2014-2015 are detailed. Highlights on the current progress of the setting up of the various beams are finally presented with special emphasis on potential performance issues across the proton and ion injector chain.Comment: Submitted for publication in a CERN Yellow Report (YR

Weak-strong beam-beam simulations for the Large Hadron Collider

A weak-strong simulation code is used to study the single-particle stability in the presence of triplet field errors, head-on collisions, and long-range beam-beam interactions at the Large Hadron Collider. We present the dependence of the simulated transverse diffusion rate on various parameters, such as starting amplitude, working point in tune diagram, crossing angle, beta function at the interaction points (IPs), beam current, triplet nonlinearities, tune modulation, and a transverse offset at one of two IPs. For several examples, we perform a frequency map analysis a la Laskar, to obtain tune footprints and the tune variation in time. A cursory look at the effect of a Mobius lattice is also reported. (17 refs)

Study of the Non-linear Behaviour of the LHC using Normal Forms

Normal form tools are used in view of understanding the causes of dynamic aperture limitations in the LHC optics versions 4 and 5. To this end, maps up to 11th order have been produced and analysed by means of Lie algebraic methods, for all models and 60 different realisations of the accelerator, at injection energy. The resonances up to 12th order are systematically analysed and correlated with the dynamic aperture. It has been of particular interest to establish the link between the individual multipole coeffcients and the higher order contributions to a specific resonanc

Normal Form Approaches and Resonance Analysis of LHC Models

In order to understand the dynamic aperture limitations in LHC optics versions 4 and 5 at injection energy (450 GeV), a thorough resonance analysis is performed through Lie perturbation methods and Normal Form construction. In this respect, a simple numerical tool has been developed, the Graphical Representation of Resonances (GRR), allowing the evaluation and graphical representation of the resonance strengths and detuning, up to a desired order. The resonance analysis performed by means of GRR enabled us to understand the effect of the large errors in some special quadrupoles of LHC optics version 5. We were also able to identify and minimise the resonance which was correlated with the drop of the dynamic aperture, following the introduction of a large skew octupole bias in the LHC optics version 5, using the "target" error table. As shown by subsequent tracking studies, the proposed correction procedures led to a considerable improvement of the dynamic aperture of the studied LHC models

Sorting strategies for the arc quadrupoles of the LHC

The variation in the field gradient of the LHC arc quadrupoles can not be corrected by the dedicated trim quadrupole circuits. This may result to a beta function beating larger than the one accepted by the machine budget. In this respect, sorting strategies for the installation of these magnets were implemented in order to eliminate this effect, as locally as possible. Special care was taken for quadrupoles whose warm measurements showed large gradient errors due to an excessive magnetic permeability. The figures of merit used in the sorting and the results obtained for all 8 sectors of the LHC are detailed. The global optics function beating foreseen, as computed by analytical estimates are finally presented

Optics Design Considerations for the CLIC Pre-Damping Rings

The CLIC pre-damping rings have to accommodate a large emittance beam, coming in particular from the positron source and reduce its size to low enough values for injection into the main damping rings. Linear lattice design options based on an analytical approach for theoretical minimum emittance cells are presented. In particular the parameterisation of the quadrupole strengths and optics functions with respect to the emittance and drift lengths is derived. Complementary considerations regarding constraints imposed by positron stacking and input momentum spread are also considered

Preliminary Change Request for the Chromatic Sextupoles and Trim Quadrupole Elements of the SNS Accumulator Ring

In view of the adopted modified design for the 1.3 GeV compatible accumulator ring of the SNS [1], complementary studies have been undertaken, in order to justify the need of high-field chromatic sextupoles for chromaticity correction. Furthermore, as these chromatic sextupoles introduce a first order quadrupole ``feed-down'' effect, the trim quadrupole elements specifications had to be reviewed in order to accommodate this change