A method for computing driving and detuning beam coupling impedances of an asymmetric cavity using eigenmode simulations

We propose a method for numerical calculation of driving and detuning transverse beam coupling impedances of an asymmetric cavity. The method relies on eigenmode simulations and can be viewed as an alternative to time domain wakefield simulations. A similar procedure is well-established for symmetric cavities, and this paper extends it to the case of an asymmetric cavity. The method is benchmarked with time-domain wakefield simulations and its practical implementation is discussed

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

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

Chromaticity dependence of the transverse effective impedance in the CERN Proton Synchrotron

The current knowledge of the transverse beam coupling impedance of the CERN Proton Synchrotron (PS) has been established with beam-based measurements at different energies. The transverse coherent tune shift as a function of the beam intensity has been measured in order to evaluate the total effective imaginary part of the transverse impedance in the accelerator at the energies of 7, 13 and 25 GeV. Measurements have been performed changing the vertical chromaticity for each vertical tune scan with intensity. The data analysis revealed an increase of impedance with chromaticity for all the considered energies. The transverse impedance can be compared with the previously evaluated theoretical impedance budget taking into account the individual contribution of several machine devices

An update of Zbase, the CERN impedance database

A detailed knowledge of the beam coupling impedance of the CERN synchrotrons is required in order to identify the impact on instability thresholds of potential changes of beam parameters, as well as additions, removals or modifications of hardware. To this end, an update of the impedance database was performed, so that impedance results from theoretical calculations using new multilayer models, impedance results from electromagnetic field simulations and impedance results from bench measurements can be compiled. In particular, the impedance database is now set to separately produce the dipolar and quadrupolar transverse impedance and wakes that the Headtail simulation code needs to accurately simulate the effect of the impedance on the beam dynamics

Comparison between Laboratory Measurements, Simulations and Analytical Predictions of the Resistive Wall Transverse Beam Impedance at low frequencies

The prediction of the resistive wall transverse beam impedance at the first unstable betatron line (8 kHz) of the CERN Large Hadron Collider (LHC) is of paramount importance for understanding and controlling the related coupled-bunch instability. Until now only novel analytical formulas were available at this frequency. Recently, laboratory measurements and numerical simulations were performed to crosscheck the analytical predictions. The experimental results based on the measurement of the variation of a probe coil inductance in the presence of i) sample graphite plates, ii) stand-alone LHC collimator jaws and iii) a full LHC collimator assembly are presented in detail. The measurement results are compared to both analytical theories and simulations. In addition, the consequences for the understanding of the LHC impedance are discussed

Bench measurements of the Low Frequency Transverse Impedance of the CERN LHC Beam Vacuum Interconnects with RF Contacts

The low frequency longitudinal and transverse impedances of the CERN Large Hadron Collider (LHC) have to be specifically minimized to prevent the onset of coherent instabilities. The LHC beam vacuum interconnects were designed as Plug In Modules (PIMs) with RF contacts to reduce their coupling impedances, but the resulting contact resistance is a concern, as this effect is difficult to estimate. High sensitivity measurements of the transverse impedance of a PIM at low frequency using a coil probe are presented. In particular, the increase of the transverse impedance of the PIM when it is elongated to its operating position is discussed in detail. Finally, the issue of non-conforming contact resistance is also addressed

Impedance Studies for the Phase 2 LHC Collimators

The LHC phase 2 collimation project aims at gaining a factor ten in cleaning efficiency, robustness and impedance reduction. From the impedance point of view, several ideas emerged during the last year, such as using dielectric collimators, slots or rods in copper plates, or Litz wires. The purpose of this paper is to discuss the possible choices, showing analytical estimates, electromagnetic simulations performed using Maxwell, HFSS and GdFidL, and preliminary bench measurements. The corresponding complex tune shifts are computed for the different cases and compared on the stability diagram defined by the settings of the Landau octupoles available in the LHC at 7 TeV

Measurement of the longitudinal and transverse impedance of kicker magnets using the coaxial wire method

Fast kicker magnets are used to inject beam into and eject beam out of the CERN SPS accelerator ring. These kickers are generally ferrite loaded transmission line type magnets with a rectangular shaped aperture through which the beam passes. Unless special precautions are taken the impedance of the ferrite yoke can provoke significant beam induced heating, even above the Curie temperature of ferrite. In addition the impedance can contribute to beam instabilities. In this paper different variants of the coaxial wire method, both for measuring longitudinal and transverse impedance, are briefly discussed in a tutorial manner and do's and don'ts are shown on practical examples. In addition we present the results of several impedance measurements for SPS kickers using the wire method and compare those results with theoretical models