EPFL, Lausanne
CERN, Geneva
Using B. Zotter's formalism, we present here a novel, efficient and exact matrix method for the field matching determination of the electromagnetic field components created by an offset point charge travelling at any speed in an infinitely long circular multilayer beam pipe. This method improves by a factor of more than one hundred the computational time with three layers and allows the computation for more layers than three. We also generalize our analysis to any azimuthal mode and finally perform the summation on all such modes in the impedance formulae. In particular the exact multimode direct space-charge impedances (both longitudinal and transverse) are given, as well as the wall impedances to any order of precision.
EPFL, Lausanne
CERN, Geneva
The exact formalism from B. Zotter to compute beam coupling impedances has been fully developed only in the case of an infinitely long circular beam pipe. For other two dimensional geometries, some form factors are known only in the ultrarelativistic case and under certain assumptions of conductivity and frequency of the pipe material. We present here a new and exact formalism to compute the beam coupling impedances in the case of a collimator-like geometry where the jaws are made of two infinite plates of any linear material. It is shown that the impedances can be computed theoretically without any assumptions on the beam speed, material conductivity or frequency range. The final formula involves coefficients in the form of integrals that can be calculated numerically. This way we obtain new generalized form factors between the circular and the flat chamber cases, which eventually reduce to the so-called Yokoya factors under certain conditions.
CERN, Geneva
EPFL, Lausanne
The kickers are major contributors to the CERN SPS beam coupling impedance. As such, they may represent a limitation to increasing the SPS bunch current in the frame of an intensity upgrade of the LHC. In this paper, CST Particle Studio time domain electromagnetic simulations are performed to obtain the longitudinal and transverse impedances/wake potentials of simplified models of ferrite loaded kickers. The simulation results have been successfully compared with some existing analytical expressions. In the transverse plane, the dipolar and quadrupolar contributions to the wake potentials have been estimated from the results of these simulations. For some cases, simulations have also been benchmarked against measurements on PS kickers. It turns out that the large simulated quadrupolar contributions of these kickers could explain both the negative total (dipolar+quadrupolar) horizontal impedance observed in bench measurements and the positive horizontal tune shift measured with the SPS beam.
EPFL, Lausanne
CERN, Geneva
In this study B. Zotter's formalism is applied to a circular infinitely long beam pipe made of a conductor of infinite thickness where an offset point-charge travels at any given speed. Simple formulae are found for the impedances and electromagnetic fields both at intermediate frequencies (recovering Chao's results) and in the low frequency regime where the usual classic thick wall impedance formula does not apply anymore due to the large skin depth compared to the pipe radius.
EPFL, Lausanne
CERN, Geneva
The SPS kickers are major contributors to the SPS transverse beam coupling impedance. The current "flat chamber" impedance model for a kicker is obtained by applying form factors to the theoretical impedance of an axisymmetric ferrite beam pipe. This model was believed to be acceptable for the vertical dipolar impedance, as two-wire measurements on SPS kickers revealed a satisfactory agreement. However, one-wire measurements on PS kickers suggested that this model underestimates the kickers' transverse quadrupolar (detuning) impedance. The longitudinal and transverse dipolar impedances of another kicker model that accounts for the metallic plates on each side of the ferrite were derived in the past by H. Tsutsui. The same formalism is used in this paper to derive the quadrupolar impedance. These formulae were then successfully benchmarked to electromagnetic simulations. Finally, simulating the interaction of an SPS bunch with the improved kickers' model results in a positive horizontal tune shift, which is very close to the tune shift measured with the SPS beam.
EPFL, Lausanne
CERN, Geneva
INFN/LNF, Frascati (Roma)
Honorary CERN Staff Member, Grand-Saconnex
The beam coupling impedance of the CERN SPS is expected to be one of the limitations to an intensity upgrade of the LHC complex. In order to be able to reduce the SPS impedance, its main contributors need to be identified. An impedance model for the SPS has been gathered from theoretical calculations, electromagnetic simulations and bench measurements of single SPS elements. The current model accounts for the longitudinal and transverse impedance of the kickers, the horizontal and vertical electrostatic beam position monitors, the RF cavities and the 6.7 km beam pipe. In order to assess the validity of this model, macroparticle simulations of a bunch interacting with this updated SPS impedance model are compared to measurements performed with the SPS beam.
CERN, Geneva
IHEP Protvino, Protvino, Moscow Region
TRIUMF, Vancouver
The LHC has two dedicated cleaning insertions: IR3 for momentum cleaning and IR7 for betatron cleaning. The collimation system has been specified and built with tight mechanical tolerances (e.g. jaw flatness ~ 40 μm) and is designed to achieve a high accuracy and reproducibility of the jaw positions. The practically achievable cleaning efficiency of the present Phase-I system depends on the precision of the jaw centering around the beam, the accuracy of the gap size and the jaw parallelism against the beam. The reproducibility and stability of the system is important to avoid the frequent repetition of beam based alignment which is currently a lengthy procedure. Within this paper we describe the method used for the beam based alignment of the LHC collimation system, its achieved accuracy and stability and its performance at 450GeV.
EPFL, Lausanne
CERN, Geneva
The exact formalism from B. Zotter to compute beam coupling impedances has been fully developed only in the case of an infinitely long circular beam pipe. For other two dimensional geometries, some form factors are known only in the ultrarelativistic case and under certain assumptions of conductivity and frequency of the pipe material. We present here a new and exact formalism to compute the beam coupling impedances in the case of a collimator-like geometry where the jaws are made of two infinite plates of any linear material. It is shown that the impedances can be computed theoretically without any assumptions on the beam speed, material conductivity or frequency range. The final formula involves coefficients in the form of integrals that can be calculated numerically. This way we obtain new generalized form factors between the circular and the flat chamber cases, which eventually reduce to the so-called Yokoya factors under certain conditions.
EPFL, Lausanne
CERN, Geneva
In this study B. Zotter's formalism is applied to a circular infinitely long beam pipe made of a conductor of infinite thickness where an offset point-charge travels at any given speed. Simple formulae are found for the impedances and electromagnetic fields both at intermediate frequencies (recovering Chao's results) and in the low frequency regime where the usual classic thick wall impedance formula does not apply anymore due to the large skin depth compared to the pipe radius.
EPFL, Lausanne
PSI, Villigen
CERN, Geneva
Wake fields in the CLIC Beam Delivery System (BDS) can cause severe single or multi-bunch effects leading to luminosity loss. The main contributors in the BDS are geometric and resistive wall wake fields of the collimators and resistive wall wakes of the beam pipe. The present work focuses only on the multi-bunch effects from resistive wall. Using particle tracking with wake fields through the BDS, we have established the aperture radius, above which the effect of the wake fields becomes negligible. Our simulations were later extended to include a realistic aperture model along the BDS as well as the collimators. The two cases of 3TeV and 500GeV have been examined in this paper.