A particle beam is a collection of a large number of charges and represents an electromagnetic potential for other charges, therefore exerting forces on itself (space charge) and other beams (Beam-Beam Interactions, BBIs). The control of the BBIs in particle colliders is fundamental to preserve beam stability and achieve the optimum collider performance. In the case of the Large Hadron Collider (LHC) at CERN, these forces are experienced as localized periodic distortions when the two beams cross each other in the four experimental areas. The forces are most important for high density beams, i.e. high intensity and small beam sizes. Each LHC beam is composed of 2808 bunches, each containing 1011 protons and with a transverse size of 16 µm at the interaction points. These extreme parameters are the key to obtain high "luminosity", i.e. the number of collisions per second needed to study \rare" physics phenomena. The BBI is therefore often the limiting factor for the luminosity of colliders. Within all BB effects, this thesis covers coherent and incoherent beam-beam effects in hadron colliders with particular emphasis on those with a large number of bunches, like the LHC. Complementary numerical tools have been developed to study the effects of BBIs on the particle beams. The use of new parallel algorithms was fundamental to allow the scale of the calculations. The objectives are a better understanding of these effects and if necessary to propose changes to the LHC beam parameters to keep detrimental effects small. We have demonstrated the numerical predictibility of bunch to bunch differences and for the first time compared the results to analytical predictions and experimental data from the Relativistic Heavy Ion Collider (RHIC). Beam-beam transfer function measurements had been reproduced and understood in terms of coherent beam-beam modes. An implementation of the measurement devices had been suggested in order to avoid misinterpreted diagnostics. An emittance growth caused by the BBIs had been observed and characterized with numerical studies and explained with a simple physical picture. A study of the parametrical dependency of this effect defines qualitatively the expected limiting factors to avoid detrimental deterioration of the beams. The variation of the LHC tune spectra for different collision symmetries and in the presence of long range as well as head-on collisions had been presented and explained. This will be of fundamental importance to correctly interprete the observations of single bunch measurements during the operation of the collider and to improve the performances.

A study of beam-beam effects in hadron colliders with a large number of bunches

Superconducting magnets have played a key role in advancing the energy reach of proton synchrotrons and enabling them to play a major role in defining the Standard Model. The problems encountered and solved at the Tevatron are described and used as an introduction to the many challenges posed by the use of this technology. The LHC is being prepared to answer the many questions beyond the Standard Model and in itself is at the cutting edge of technology. A description of its magnets and their properties is given to illustrate the advances that have been made in the use of superconducting magnets over the past 30 years.

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The Development of Superconducting Magnets for Use in Particle Accelerators: From the Tevatron to the LHC

The decay of the sextupole component in the bending dipoles during injection and the subsequent snapback at the start of beam acceleration are issues of common concern for all superconducting colliders built or in construction. Recent studies performed on LHC and Tevatron dipole magnets revealed many similarities in the snapback characteristics. Some are expected, e.g. the effect of operational history. One particular similarity, however, is striking and is the subject of this paper. It appears that there is a simple linear relation between the amount of sextupole drift during the decay and the magnet current (or field) change during the ramp required to resolve the snapback. It is surprising that the linear correlation between snapback amplitude and snapback field holds very well for all magnets of the same family (e.g. Tevatron or LHC dipoles). In this paper we present the data collected to date and discuss a simple theory that explains the scaling found.

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A scaling law for the snapback in Superconducting accelerator magnets

This report presents the stability and control of the Large Hadron Collider’s (LHC) two beam orbits and their particle momenta using beam-based feedback systems. The LHC, presently being built at CERN, will store, accelerate and provide particle collisions with a maximum particle momentum of 7TeV/c and a nominal luminosity of L = 10 cms. The presence of two beams, with both high intensity as well as high particle energies, requires excellent control of particle losses inside a superconducting environment, which will be provided by the LHC Cleaning and Machine Protection System. The performance and function of this and other systems depends critically on the stability of the beam and may eventually limit the LHC performance. Environmental and accelerator-inherent sources as well as failure of magnets and their power converters may perturb and reduce beam stability and may consequently lead to an increase of particle loss inside the cryogenic mass. In order to counteract these disturbances, control of the key beam parameters – orbit, tune, energy, coupling and chromaticity – will be an integral part of LHC operation. Since manual correction of these parameters may reach its limit with respect to required precision and expected time-scales, the LHC is the first proton collider that requires automatic feedback control systems for safe and reliable machine operation. The aim of this report is to help and contribute towards these efforts. Why lovest thou so this brittle world’s joy? Take all the mirth, take all the fantasies, Take every game, take every wanton toy, Take every sport that men can thee devise: And among them all on warrantise Thou shalt no pleasure comparable find To th’ inward gladness of a virtuous mind.

http://inspirehep.net/record/887250/files/thesis-2007-058.pdf

LHC Beam Stability and Feedback Control - Orbit and Energy -

The decay and snap-back of sextupole in the bending dipoles are issues of common concern, albeit at different levels of criticality, for all superconducting colliders built (Tevatron, HERA, RHIC) or in construction (LHC) to date. The main difficulty is the correction of the relatively large and fast sextupole change during snap-back. Motivated by the above considerations, we have pursued an extended study of sextupole snap-back on two different magnet families, the Tevatron and the LHC bending dipoles, using the same measurement method. We show here that it is possible to generalise the results obtained by using a simple, exponential scaling law. Furthermore, we show that for magnets of the same family the parameters of the scaling law correlate linearly. This finding could be exploited during accelerator operation to produce accurate forecast of the snap-back correction based solely on beam-based measurements.

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A scaling law for predicting snap-back in superconducting accelerator magnets

During beam injection the components of the magnetic field inside the magnets decay in time. At the re-start of the ramping, this decay is cancelled resulting in a fast change of the harmonics called "snapback". This sudden variation affects mainly the sextupole and decapole components and can induce significant changes in the machine chromaticity, thus causing particle beam loss. Standard magnetic measurements with rotating coils do not have a sufficient time resolution to properly characterize the snapback phenomenon. A system based on Hall probes has been developed from an existing prototype to measure with a moderate acquisition frequency (3-10 Hz) the decay and snapback of the sextupole and, for the first time, of the decapole fields. The present system also provides local measurements of these field harmonics along a wavelength of the superconducting cable twist pitch. In this paper, we describe the assembly features of this detector and of the measurement chain. The performances are demonstrated based on preliminary measurements performed on the LHC pre-series dipoles in operating conditions.

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E. Effinger

Papers

Field decay and snapback measurements using a fast Hall probe sensor