Bruno W Zotter

The Large Hadron Collider (LHC) in the LEP tunnel

After the remarkable start-up of LEP, the installation of a Large Hadron Collider, LHC, in the LEP tunnel will open a new era for the High Energy Physics. This report summarizes the main LHC parameters and subsytems and describes the more recent studies and developments.

A generalized method for calculating wake potentials

Abstract We describe a generalized method to compute wake potentials created in axisymmetric structures. It relies on expressing the wake potentials, of any multipole order, as integrals over the e.m. fields along an arbitrary one-dimensional contour spanning the structure longitudinally. For perfectly conducting structures, the integration along the axis can then be replaced by choosing a contour beginning and ending on the beam tubes. Thus it generalizes the former method of calculating the wake potentials by integrating along a straight line at the beam tube radius. Its usefulness is illustrated with the computer code ABCI which permits calculation of wake potentials in structures extending to the inside of the beam tube radius, or having unequal beam tube radii at the two sides.

Measurements of impedance distributions and instability thresholds in LEP

The distribution of reactive and resistive components of the transverse impedance around the circumference of LEP has been obtained by exciting the beam and measuring the variations of phase advance and of closed orbit displacements with beam current. Tune shifts with current and instability thresholds were determined for two machine lattices with different beta functions and momentum compaction for various values of bunch length and synchrotron frequency. These measurements are particularly interesting for LEP2, which will require larger bunch currents to achieve the design luminosity.

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 resistive- wall 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.

CLIC-a compact and efficient high energy linear collider

We discuss the RF system, the drive linac, drive beam generation, the isochronous ring drive beam scheme, the main linac injector system, machine parameters, beam dynamics and final focus studies and the alignment test facility and beam monitor test results.

A Computer Code for the Calculation of Beam Stability in Circular Electron Machines

A computer program is presented which assists the designer of a circular electron accelerator or storage ring in finding out the limits of beam stability. The most prominent longitudinal and transverse instabilities are taken into account with emphasis on coherent bunch oscillations.

Measurement of Beam Stability and Coupling Impedance by RF Excitation

The transverse stability limit and coupling impedance of proton beams in the CERN Intersecting Storage Rings have been measured by external excitation of the beam. The impedance values at low frequencies thus obtained are in good agreement with the sum of the skin-effect and the wall-inductance which has been measured previously. The method can be extended to higher frequencies if the beam can be stabilized against low-frequency oscillations, e.g. by feedback.

Experimental Investigation of the Coherent Longitudinal Instability of Relativistic Particle Beams

In order to verify the theoretical predictions of stability of relativistic proton beams against coherent longitudinal oscillations driven by interaction with the surrounding vacuum chamber wall, a special high-Q cavity was built with remotely controlled tuning and damping. Already the first experiments with the cavity were successful, and the beam was driven unstable at thresholds quite close to those calculated for simplified models. These results also confer more credibility to the claim that it is necessary to continue the costly efforts of keeping the wall impedance low.

Longitudinal and transverse impedances of bellows in the low frequency range

Abstract The longitudinal and transverse impedances of bellows are found for both the axially symmetric and the dipole mode. Expressions for impedances, which were obtained previously by other authors using perturbation techniques or field matching methods, agree with our formulae in the regions of their applicability. Numerical results are presented and are in good agreement with those from the program TBCI.

Analytic models for the broad band impedance

In order to overcome the limitations of the broadband resonator impedance model, two different models are proposed which have more realistic properties at both very high and very low frequencies. For each model two types are specified which are proportional to either omega /sup -1/2/ or omega /sup -3/2/ at high frequencies. At low frequencies, the real part of the first impedance model rises quadratically or-for a special choice of the parameters-with the fourth power of frequency. In the second model it is identically zero up to a chosen cutoff frequency, and thereby yields the very fast decrease of the loss factor with bunch length which is always found by direct solution of Maxwells equations for lossless structures. Although not quite as simple as the broadband resonator, both models have impedances and Green functions which can be expressed by analytic functions and depend only on a few parameters. Thus, they should lead to improved estimates of beam stability limitations in particle accelerators and storage rings.<<ETX>>