Beam screen issues

In the High Energy LHC (HE-LHC), a beam energy of about 16.5 TeV is currently contemplated. The beam screen issues linked to the use of 20 T dipole magnets instead of 8.33 T are discussed, with a particular emphasis on two mechanisms, the magneto-resistance and the anomalous skin effect, assuming the nominal machine and beam parameters. The magneto-resistance effect always leads to an increase of the material resistivity (as the mean free path in the presence of a transverse magnetic field becomes smaller). As concerns the anomalous skin effect, the anomalous increase of surface resistance of metals at low temperatures and high frequencies is attributed to the long mean free path of the conduction electrons: when the skin depth becomes much smaller than the mean free path, only a fraction of the conduction electrons moving almost parallel to the metal surface is effective in carrying the current and the classical theory breaks down.Comment: 7 pages, contribution to the EuCARD-AccNet-EuroLumi Workshop: The High-Energy Large Hadron Collider, Malta, 14 -- 16 Oct 2010; CERN Yellow Report CERN-2011-003, pp. 83-8

Electromagnetic fields created by a macroparticle in an infinitely long and axisymmetric multilayer beam pipe

This paper aims at giving an as complete and detailed as possible derivation of the six electromagnetic field components created by an offset point charge travelling at any speed in an infinitely long circular multilayer beam pipe. Outcomes from this study are a novel and efficient matrix method for the field matching determination of all the constants involved in the field components, and the generalization to any azimuthal mode together with the final summation on all such modes in the impedance formulas. In particular the multimode direct space-charge impedances (both longitudinal and transverse) are given, as well as the wall impedance to any order of precision. New quadrupolar terms for the transverse wall impedance are found, which look negligible in the ultrarelativistic case but might be of significance for low-energy beams. In principle from this analysis the electromagnetic fields created by any particular source, with a finite transverse shape, can then be computed using convolutions

Multi-bunch simulations with HEADTAIL

The HEADTAIL code has been used for many years to study the interaction of a single bunch with a localized or lumped source of electromagnetic perturbation, usually self-induced (impedance, electron cloud or space charge). It models the bunch as macroparticles and at each turn slices up the bunch into several adjacent charged disks, which are made to subsequently interact with the perturbing agent. A first step toward the extension of HEADTAIL to multibunch simulations is presented in this paper. In this case, the bunches themselves are modeled as charged disks and are not sliced, which makes us lose information on the intra-bunch motion but can describe a zero mode interaction between different bunches in a train. The interaction of an SPS bunch train of 72 bunches with the resistive wall is studied as an example

SPS performance with PS2

The upgrade of the PS to the PS2 would allow injection into the SPS at higher energy (up to 70 GeV/c). Possible advantages deriving from a higher injection energy into the SPS include the improvement of space charge at flat bottom, absence of transition crossing for all proton beams and a higher threshold for the horizontal electron cloud coupled bunch instability. Transverse Mode Coupling Instability (TMCI) and vertical Electron Cloud Instability (ECI) thresholds are studied in greater detail. Their dependence on energy is defined in simulations with the HEADTAIL code and the results of this study are presented

Emittance sharing and exchange driven by linear betatron coupling in circular accelerators

The influence of linear betatron coupling due to constant-in-time skew quadrupolar fields on the transverse emittances is discussed using both a simplified model of a smooth circular accelerator and a more realistic strong-focusing lattice with localized sources of coupling (thin lens). New formulas for the coupled transverse emittances are derived that include the initial emittances, the coupling strengths, and the tune distance from the resonance. By using the more powerful Lie algebra and the resonance driving terms formalism, equivalent formulas are derived that provide a better understanding of some counterintuitive effects, otherwise not understandable in the smooth approximation. The new formulas have been tested both numerically and experimentally by using data of the CERN Proton Synchrotron showing a remarkable agreement

Resistive-Wall Impedance of an Infinitely long Multi-Layer Cylindrical Beam Pipe

The resistive-wall impedance of cylindrical vacuum chambers was first calculated more than forty years ago under some approximations. Since then many papers have been published to extend its range of validity. In the last few years, the interest in this subject has again been revived for the LHC graphite collimators, for which a new physical regime is predicted. The first unstable betatron line in the LHC is at 8 kHz, where the skin depth for graphite is 1.8 cm, which is smaller than the collimator thickness of 2.5 cm. Hence one could think that the resistive thick-wall formula would be about right. It is found that it is not, and that the resistive impedance is about two orders of magnitude lower at this frequency, which is explained by the fact that the skin depth is much larger than the beam pipe radius. Starting from the Maxwell equations and using field matching, a consistent derivation of both longitudinal and transverse resistivewall impedances of an infinitely long cylindrical beam pipe is presented in this paper. The results, which should be valid for any number of layers, beam velocity, frequency, conductivity, permittivity and permeability, have been compared to previous ones

Simulation study on the energy dependence of the TMCI threshold in the CERN-SPS

This paper concentrates on theoretical studies of Transverse Mode Coupling Instability (TMCI) at the SPS. It shows the expected thresholds based on the HEADTAIL tracking model and on impedance values estimated from previous measurements. First, the effect of space charge is addressed as an important ingredient at the low energies. Subsequently, the change of TMCI threshold possibly induced by a higher injection energy into the SPS (plausible according to the upgrade studies) is investigated and a scaling law with energy is derived

Review of impedance-induced instabilities and their possible mitigation techniques

In this paper a review of some important impedance-induced instabilities are briefly described for both the longitudinal and transverse planes. The main tools used nowadays to predict these instabilities and some considerations about possible mitigation techniques are also presented

Transverse mode coupling instability in the SPS: Headtail simulation and moses calculation

Since 2003, single bunches of protons with high intensity (~ 1.2 1011 protons) and low longitudinal emittance (~ 0.2 eVs) have been observed to suffer from heavy losses in less than one synchrotron period after injection at 26 GeV/c in the CERN Super Proton Synchrotron (SPS) when the vertical chromaticity is corrected (ξy ~ 0). Understanding the mechanisms underlying this instability is crucial to assess the feasibility of an anticipated upgrade of the SPS, which requires bunches of 4 1011 protons. Analytical calculations and particle tracking simulations had already agreed in predicting the intensity threshold of a fast instability. The aim of the present paper is to present a sensitive frequency analysis of the HEADTAIL simulations output using SUSSIX, which brought to light the fine structure of the mode spectrum of the bunch coherent motion. Coupling between the azimuthal modes “-2” and “-3” was clearly observed to be the reason for this fast instability