Optics Issues for Phase 1 and Phase 2 Upgrades

A review of the main issues of the upgrade scenarios of the LHC performance is presented. According to recent proposals, the upgrade of the LHC insertions is staged in two parts, which will be considered and discussed in some detail in this report

Principle and Analysis of Multiturn Injection Using Stable Islands of Transverse Phase Space

By applying a time reversal to the multiturn extraction method recently proposed, a novel approach to perform multiturn injection is described. It is based on the use of stable islands of the horizontal phase space generated by means of sextupoles and octupoles. A particle beam can be injected into stable islands of phase space, and then a slow tune variation allows merging the beam trapped inside the islands. The results of numerical simulations will be presented and discussed in detail, showing how to use the proposed approach to generate hollow bunches in the transverse phase space, and how different resonances can be used. The dependence of the final beam parameters on the key quantities of the proposed approach, such as emittance of the initial beam and the way the resonance is crossed, is investigated. Furthermore, a comparison of the proposed approach against the classical multiturn injection without the use of stable islands is carried out

NERO: a code for evaluation of nonlinear resonances in 4D symplectic mappings

A code to evaluate the stability, the position and the width of nonlinear resonances in four-dimensional symplectic mappings is described. NERO is based on the computation of the resonant perturbative series through the use of Lie transformation implemented in the code ARES, and on the analysis of the resonant orbits of the interpolating Hamiltonian. The code is aimed at studying the nonlinear moti on of a charged particle moving in a circular accelerator under the influence of nonlinear forces

Experimental Evidence of Beam Trapping with one-third and one-fifth Resonance Crossing

Beam trapping in stable islands of the horizontal phase space generated by non-linear magnetic fields is realized by means of a given tune variation so to cross a resonance of order n. Whenever the resonance is stable, n + 1 beamlets are created whereas if the resonance is unstable, the beam is split in n parts. Experiments at the CERN Proton Synchrotron showed protons trapped in stable islands while crossing the one-third and one-fifth resonance with the creation of 3 and 6 stable beamlets, respectively. The results are presented and discussed

Stability change of Fourth-Order Resonance with application to Multi-Turn Extraction Schemes

Recently, a novel multi-turn extraction scheme was proposed, based on particle trapping inside stable resonances. Numerical simulations and experimental tests conirmed the feasibility of such a scheme for low order resonances. While the 3rd order resonance is generically unstable and those higher than 4th order are generically stable, the 4th order resonance can be either stable or unstable depending on the details of the system under consideration. By means of the normal form approach a general formula to control the stability of the 4th order resonance is derived. Numerical simulations confirm the analytical results and show that by crossing the unstable 4th order resonance the region around the centre of phase space is depleted and particles are trapped only in the four stable islands. This indicates that a four-turn extraction could be envisaged based on this technique

Simultaneous matching of dispersion function and Twiss parameters in a transfer line

Dispersion matching in a beam transfer line is an important issue in order to avoid blow-up and luminosity reduction. This is the case for the LHC beam, due to its small emittance and relatively large momentum spread. The dispersion matching can be performed with quadrupoles, but one has to impose the additional constraint of leaving the Twiss parameters unchanged, to preserve the betatron matching. A first order pertubative approach, using the MICADO solver, has been applied to the problem of simultaneous betatron and dispersion matching. A theoretical derivation of the correction matrix as well as simulated and experimental results are presented. (8 refs)

Progress in the Beam preparation for the Multi-Turn Extraction at the CERN Proton Synchrotron

A new type of extraction based on beam trapping inside stable islands in the horizontal phase space will become operational during 2008 at the CERN Proton Synchrotron. A series of beam experiments was carried out to prove lossless capture with high intensity and multi-bunched beams, up to $1.5 × 10^{13}$ protons per pulse, in preparation of the extraction commissioning. These fundamental steps for the new Multi-turn Extraction are presented and discussed in details

Analysis of adiabatic trapping phenomena for quasi-integrable area-preserving maps in the presence of time-dependent exciters

In this paper, new results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps with a time-dependent exciter are presented and discussed in detail. The applicability of the results about trapping efficiency for Hamiltonian systems to the maps considered is proven by using perturbation theory. This allows determining explicit scaling laws for the trapping properties. These findings represent a generalization of previous results obtained for the case of quasi-integrable maps with parametric modulation as well as an extension of the work by Neishtadt \textit{et al.} on a restricted class of quasi-integrable systems with time-dependent exciters