In the study of a high-energy linear collider such as the CERN Compact Linear Collider (CLIC), there are domains of activities where analytical developments are useful guides before doing fully numerical calculations or using standard accelerator design programs. The purpose of this report is to illustrate the interest of such an approach in designing rarely used magnetic insertions, such as isochronous modules or tunable achromats which are required in several locations of the CLIC complex. Algorithmic codes have been written in this context. They give global information or guidance among a variety of approximated solutions and help the user in selecting the most promising one before fully numerical calculations and, eventually, optimizations are carried out to obtain the solution consistent with the physical model.

A numerical simulation of a possible coherent beam-beam instability of the head-tail type is presented. The studied model employs a linearized coherent beam-beam interaction and takes complete account of the bunch length, including the deformation of the colliding bunches during their overlap. Measured head-tail mode spectra from the VEPP-2M collider are compared with the results of the analytical model and tracking. A computer code for evaluation of the coherent mode increments, which was used for analysis of possible ways to stabilize the beam-beam system, is described.

We present an analysis of shielding of electromagnetic fields excited by beams of charged particles surrounded by thin conducting layers or metal stripes inside an external structure of finite length. The ability of shielding by a layer thinner than the skin depth is explained and expressions for the impedance are derived. A previous result showing preferential penetration through the shielding layer at the resonant frequencies of the surrounding structure is verified and extended to include finite resistivity of the outer structure. Integration over the spectrum of the beam bunch shows that penetration is (nearly) independent of the quality factors of the resonances. The transition of these results to those for a geometry of infinite length requires numerical evaluation.

We describe the first measurement of an electron beam size in the accelerator test facility damping ring at KEK with a laser wire beam profile monitor. This monitor is based upon the Compton scattering process of electrons with a laser light target, which is produced by injecting a cw laser beam into a Fabry-Pérot optical cavity. We have observed clear signals of the Compton scattered photons and confirmed that the observed energy spectrum as well as the count rate agree with the expected ones. From the measurement, we have deduced the vertical beam size ${\sigma }_b$ to be $9.8\pm 1.1\pm 0.4\mu \mathrm{m}$, where the first (second) error represents statistical (systematic) uncertainty. Various improvements are in progress to enhance the signal-to-noise ratio, which is essential for the detailed study of the beam dynamics.

We present the results of an experimental study of the longitudinal beam dynamics at injection in the advanced light source, an electron storage ring. By measuring the longitudinal bunch distribution following injection using a streak camera, we were able to study several useful and interesting effects as well as improve overall injection efficiency. These include measurement and correction of the phase and energy offsets at injection, measurement of the injected bunch length and energy spread, direct observation of phase space filamentation due to the spread in synchrotron frequencies, and measurement of the effective damping rate of the bunch shape including radiation damping and decoherence. We have also made some initial studies of the decay of an uncaptured beam at injection which may provide a novel means of measuring the radiation loss per turn.

A design process is described for damping rings in a linear collider where the competing requirements of small equilibrium emittance and fast damping of the injected phase space are needed. A systematic approach to the determination of the basic ring parameters is described. In addition, qualitative consideration is given to minimizing the system cost. The approximate interdependencies of the various lattice parameters are derived and arguments for the parameter choices are presented. In addition, many useful expressions are derived for a theoretical minimum emittance lattice. The design of the damping rings for the Next Linear Collider design are used as examples throughout.

In order to further understand phenomena observed during studies of adiabatic excitation of longitudinal bunch shape oscillations [M. Bai et al., Phys. Rev. ST Accel. Beams 3, 064001 (2000)], we have developed a simulation using a one-turn map. In this report we will present the physical foundations for the simulation and the methods used in the simulator. We will present simulation results using parameters of actual experiments, along with the corresponding experimental results.

The Cornell Electron-Positron Storage Ring (CESR) has a longitudinal dipole-coupled-bunch instability that limits the total amount of current that can be stored in the ring without feedback. As a result, it is one of the major limitations for higher stored current and luminosity. This paper reports the measurements of multiple bunch longitudinal dynamics done on CESR with a streak camera. The camera was used to measure the dependence of the bunch distribution on current and accelerating rf voltage, for multiple bunches stored in CESR, as well as the effects of the longitudinal instability on the bunch distribution. Measurements of the beam's longitudinal bunch distribution with multiple bunches present in the ring help give an understanding of the instability, how it affects the bunch distribution, and possibly give insight into a cure of the instability.

A highly accurate self-consistent particle code to simulate the beam-beam collision in $e^{+}{e}^{-}$ storage rings has been developed. It adopts a method of solving the Poisson equation with an open boundary. The method consists of two steps: assigning the potential on a finite boundary using Green's function and then solving the potential inside the boundary with a fast Poisson solver. Since the solution of Poisson's equation is unique, our solution is exactly the same as the one obtained by simply using Green's function. The method allows us to select a much smaller region of mesh and therefore increase the resolution of the solver. The better resolution makes more accurate the calculation of the dynamics in the core of the beams. The luminosity simulated with this method agrees quantitatively with the measurement for the PEP-II B Factory ring in the linear and nonlinear beam current regimes, demonstrating its predictive capability in detail.

The collimation system for the Spallation Neutron Source accumulator ring is designed for a capture efficiency close to 95% of the proton beam halo, dissipating about 2 kW of beam power. The collimation system consists of a two-stage collimation system (one scraper and two absorbers) cleaning the transverse halo and a beam-in-gap kicker system cleaning the gap residual and longitudinal halo. Preliminary studies indicate that a maximum level of uncontrolled loss of 0.01% of the total beam is achievable. On the other hand, the energy lost in the primary scraper may kick protons outside the rf bucket concentrating uncontrolled losses in areas of maximum dispersion. We use Monte Carlo simulations to clarify some beam dynamic issues that may compromise the high efficiency required. The material interacting with the beam and the shape of the scraper and absorbers have been carefully chosen to maximize the collimation efficiency and to minimize radioactivation. Furthermore, a realistic distribution of losses around the machine is used to identify potential hot areas. Finally, we determine the sensitivity of the collimation efficiency to misalignments and closed orbit errors. This paper describes the latest design of the collimation system and summarizes the results of these numerical studies.

This comment takes up the suggestion of the authors that it could be informative to model the excitation of the bunch shape oscillations using multiparticle tracking. The experiment they report employs an 80% modulation of the rf amplitude at approximately twice the synchrotron frequency; the first-order perturbation analysis given in the paper is not suitable for quantitative comparison to the experimental observations. The tracking code ESME is used to model the conditions of the experiment. The potential well distortion arising from image charge and current and a broadband longitudinal impedance of $Z_{\parallel }/n=6\mathrm{}\Omega$ was considered as an additional perturbation which also varies at the modulating frequency.

Response is made to J. A. MacLachlan's preceding Comment [Phys. Rev. ST Accel. Beams 4, 017001 (2001)]. We are gratified to see that high quality simulations, as presented by MacLachlan, verify our experimental results.

Photoemission and secondary emission are known to give rise to a quasistationary electron cloud inside the beam pipe through a beam-induced multipacting process. We investigate the electron-cloud build up and related effects via computer simulation. In our model, macroparticles representing photoelectrons are emitted synchronously with the passing proton or positron bunch and are subsequently accelerated in the field of the beam. As they hit the beam pipe, new macroelectrons are generated, whose charges are determined by the energy of the incoming particles and by the secondary emission yield of the beam pipe. A quasistationary state of the electron cloud is eventually reached due to space charge. The equilibrium density is used as an input parameter for a second program that analyzes the electron-cloud driven single-bunch instability. The electron cloud simulation also allows the evaluation of the heat load on the cold Large Hadron Collider beam screen, which must stay within the available cooling capacity, and the electron charge deposited on or emitted from the electrodes of the beam-position monitors.

A new computer code for simulation of multipacting phenomenon in axisymmetrical radio frequency structures is presented. The existence of resonant electron trajectories can lead to electron multiplication under given field and surface conditions and can damage these accelerator components or prevent their use. The goal of the simulation is to detect such occurrences. Therefore, large parameter sets have to be tested; a parallel version of the code has been developed to reduce computing time while dealing with highly demanding cases in terms of accuracy and parameter sweeping. Both superconducting cavities and power coupler components have been studied. Simulation results are compared with experimental measurements.

In a circular accelerator, a horizontal-vertical coupling can occur as a purely geometrical effect, in the absence of any coupling device (skew-quadrupole magnets, etc.). The coupling between horizontal and vertical coordinates (and momenta) is represented by a rotation [SO(2)]. The rotation angle is called the twist angle. It comes from the geometry of the reference orbit, and is related to the possible nonintegrability of parallel transport on it. We give an analytic expression of the twist and discuss some simple dynamical consequences of the twist on betatron tune.

Estimates of random field-shape errors induced by cable mispositioning in superconducting magnets are presented and specific applications to the Large Hadron Collider (LHC) main dipoles and quadrupoles are extensively discussed. Numerical simulations obtained with Monte Carlo methods are compared to analytic estimates and are used to interpret the experimental data for the LHC dipole and quadrupole prototypes. The proposed approach can predict the effect of magnet tolerances on geometric components of random field-shape errors, and it is a useful tool to monitor the obtained tolerances during magnet production.

We report the development of different algorithms for the calculation of quality factors of eigenmodes in accelerating cavities, which have resonance frequencies above the cutoff frequency of the beam tubes. The analysis is based on a discretization of such cavity structures by the finite integration technique, and the radiation at the open boundaries is systematically taken into account by different approaches in time and frequency domain. Results indicate that even single cell cavities of the TESLA type show $Q$ values of ${10}^3$ and multicell cavities values in excess of ${10}^4$. Thus these modes may cause considerable beam instabilities. Comparison with the conventional method of analyzing closed cavities and identifying modes with little change in frequency as a function of boundary condition shows qualitative differences. Some modes from the closed cavity model do not exist in the open structure and thus would be misinterpreted as trapped modes when only a closed cavity analysis is employed.

The six-dimensional beam-beam interaction as developed in 1992 by Hirata, Moshammer, and Ruggiero has been extended to include linear coupled motion and an arbitrary crossing plane. The technique of symplectic mapping in the six-dimensional phase space, called synchrobeam mapping, is applied to investigate the beam-beam kick within a solenoid. A linear beam-beam model including coupling is discussed in detail, also in the framework of a six-dimensional symplectic dispersion formalism.

In this paper, we present a series of analytic expressions to predict the beam dynamics in a long linear accelerator. These expressions can be used to model the linac optics, calculate the magnitude of the wakefields, estimate the emittance dilution due to misaligned accelerator components, and estimate the stability and jitter limitations. The analytic expressions are based on the results of simple physics models and are useful to understand the parameter sensitivities. They are also useful when using simple codes or spreadsheets to optimize a linac system.