Non-Gaussian beam tails producing low beam lifetimes and background to the experimental detectors can be a serious performance limitation in colliding beam facilities. We describe simulations and measurements of non-Gaussian beam tails performed on the $e^{+}{e}^{-}$ collider LEP that revealed the importance of inelastic particle scattering as launching processes of particles to large amplitudes.

The conventional method of spin flipping a stored polarized beam is based on slowly crossing an rf induced depolarizing resonance. This paper discusses a different approach where the polarization reversal is achieved by trapping the beam polarization into a stable spin-flipping motion on top of rf induced resonance at a half-revolution frequency.

Measurement of the betatron phase in the vertical and horizontal planes as well as the transverse horizontal-vertical coupling is a standard procedure now used at the Cornell Electron/Positron Storage Ring. The measurement is made by shaking the beam and observing the phase of oscillation at detectors located around the ring. The measurements allow quadrupolar errors to be corrected.

This paper summarizes the low-loss design for the Spallation Neutron Source accumulator ring [“Spallation Neutron Source Design Manual” (unpublished)]. A hybrid lattice consisting of FODO arcs and doublet straights provides optimum matching and flexibility for injection and collimation. For this lattice, optimization focuses on six design goals: a space-charge tune shift low enough (below 0.15) to avoid strong resonances, adequate transverse and momentum acceptance for efficient beam collimation, injection optimized for desired target beam shape and minimal halo development, compensation of magnet field errors, control of impedance and instability, and prevention against accidental system malfunction. With an expected collimation efficiency of more than 90%, the uncontrolled fractional beam loss is expected to be at the ${10}^{-4\mathrm{}}$ level.

It is shown that energy conservation in the longitudinal envelope equation can be used to derive analytic expressions to model fast bunch compression and the effect of space charge in terms of a dimensionless Coulomb parameter $\Sigma$ $(\propto 1/\eta$, with $\eta$ the slip factor). For small $|\eta |$ (below transition, hence $\Sigma \gg 1$), the rf voltage required is nearly independent of $\eta$ and dominated by space charge repulsion. The extra voltage generates the coherent momentum spread $\delta \propto 1/\sqrt{|\eta |}$ required to compensate the increasing space charge force gradient during compression. This sets a clear limit to the useful approach to transition. An $\eta$ jump scheme is discussed to minimize this effect. Particle-in-cell computer simulation confirms the validity of our results also for more realistic beam distributions. Noticeable tails in momentum space due to the nonlinear space charge force are found for Gaussian line density bunches and $\Sigma \gg 1$.

Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST) code is used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton ($e-p$) two-stream instability observed in the Proton Storage Ring (PSR) experiment. Detailed simulations in a parameter regime characteristic of the PSR experiment show that the dipole-mode two-stream instability is stabilized by a modest spread (about 0.1%) in axial momentum of the beam particles.

The use of ${\mathrm{TE}}_{12}$ in circular waveguide with smooth walls was suggested for low-loss transport of rf signals in multimoded systems [S. G. Tantawi et al., in Advanced Accelerator Concepts: Eighth Workshop, edited by Wes Lawson, AIP Conf. Proc. No. 472 (AIP, New York, 1999), pp. 967–974]. Such systems use the same waveguide to transport different signals over different modes. In this report we detail a series of experiments designed to measure the characteristics of this mode. We also describe the different techniques used to generate it and receive it. The experiments were done at $X$ band around a frequency of 11.424 GHz, the frequency of choice for future linear colliders at $X$ band [The NLC Design Group, Report No. LBNL-PUB-5424, SLAC Report No. 474, Report No. UCRL-ID 124161, 1996; The JLC Design Group, KEK-REPORT-97-1, 1997]. The transportation medium is 55 m of highly overmoded circular waveguide. The design of the joining flanges is also presented.

The dynamics of particles in laser pulse-driven wakefields over multistages in a collider is studied. A map of phase space dynamics over a stage of wakefield acceleration induced by a laser pulse (or electron beam) is derived. The entire system of a collider is generated with a product of multiple maps of wakefields, drifts, magnets, etc. This systems map may include offsets of various elements of the accelerator, representing noise and errors arising from the operation of such a complex device. We find that an unmitigated strong focusing of the wakefield coupled with the alignment errors of the position (or laser beam aiming) of each wakefield stage and the unavoidable dispersion in individual particle betatron frequencies leads to a phase space mixing and causes a transverse emittance degradation. The rate of the emittance increase is proportional to the number of stages, the energy of the particles, the betatron frequency, the square of the misalignment amplitude, and the square of the betatron phase shift over a single stage. The accelerator with a weakened focus in a channel can, therefore, largely suppress the emittance degradation due to errors.

We have used 2D cylindrically symmetric particle-in-cell simulations to investigate the dynamics of a high energy electron beam propagating through an underdense plasma. The simulation parameters are relevant to a recent plasma wakefield experiment conducted at the Stanford Linear Accelerator Center [R. Assmann et al., Stanford Linear Accelerator Center Proposal, 1997]. We model the dynamic development of the beam and wakefield excitation over meters of propagation length. To most clearly illustrate the dynamics of both the beam and the wakefield, a video of the simulation data is presented. The main observation is that the beam dynamics, i.e., its betatron motion in the resulting ion channel, agree well with the theoretical predictions while the plasma wake remains almost invariant over the entire propagation distance. The video illustrates subtle details regarding the interplay between the beam dynamics and wakefield generation. The results presented here complement results published separately [S. Lee et al., Phys. Rev. E 61, 7014 (2000)].

By modulating the rf voltage at near twice the synchrotron frequency, the longitudinal bunch shape can be modulated. This method can be used to shorten bunches. We show experimentally that the bunch shape can be modulated while preserving the longitudinal emittance when the rf voltage modulation is turned on adiabatically. Experimental measurements will be presented along with theoretical predictions.

In this paper we present a study of beam halo based on a three-dimensional particle-core model of an ellipsoidal bunched beam in a constant focusing channel including the effects of nonlinear rf focusing. For an initially mismatched beam, three linear envelope modes—a high frequency mode, a low frequency mode, and a quadrupole mode—are identified for an azimuthally symmetric bunched beam. The high frequency mode has three components all in phase; the low frequency mode has the transverse components in phase and the longitudinal component 180° out of phase; the quadrupole mode has no longitudinal component, and the two transverse components in the mode are 180° out of phase. We also study the case of an ellipsoidal bunched beam without azimuthal symmetry and find that the high frequency mode and the low frequency mode are still present but the quadrupole mode is replaced by a new mode with transverse components 180° out of phase and a nonzero longitudinal component. Previous studies, which generally addressed the situation where the longitudinal-to-transverse focusing strength is roughly 0.6 or less, conclude that the oscillation of the high frequency mode is predominantly transverse, and that of the low frequency mode is predominantly longitudinal. In this paper we present a systematic study of the features of the modes as a function of the longitudinal-to-transverse focusing strength ratio. We find that, when the ratio is greater than unity, the high frequency mode may contain a significant longitudinal component. Thus, excitation of the high frequency mode in this situation can be responsible for the formation of longitudinal beam halo. Furthermore, while previous studies have observed halo amplitudes roughly 2–3 times the matched beam edge, for the present parameters we observe much larger amplitudes (5 times or more). This is due to the fact that the longitudinal-to-transverse focusing ratio used here is greater than that of previous studies. The finding of large transverse halo amplitude can have significant impact on the design of high-intensity ion accelerators where the longitudinal-to-transverse focusing ratio is slightly greater than unity in some parts of the linac.

Beam-based alignment of quadrupoles by variation of quadrupole strength is a widely used technique in accelerators today. We describe the dominant systematic limitation of such algorithms, which arises from the change in the center position of the quadrupole as the strength is varied, and derive expressions for the resulting error. In addition, we derive an expression for the statistical resolution of such techniques in a periodic transport line, given knowledge of the line's transport matrices, the resolution of the beam position monitor system, and the details of the strength variation procedure. These results are applied to the Next Linear Collider main linear accelerator, an 11 km accelerator containing 750 quadrupoles and 5 000 accelerator structures. We find that, in principle, a statistical resolution of $1\mu \mathrm{m}$ is easily achievable, but the systematic error due to variation of the magnetic centers could be several times larger.

The present paper takes one step beyond the single-resonance theory for betatron motion by summing all the members of a given resonance family and expressing the joint influence in a single driving term. As a demonstration and confirmation of this work, the family driving terms are used to derive the classic closed-orbit and betatron-modulation equations of Courant and Snyder. A more serious demonstration is made by applying the family driving terms to the compensation of linear coupling and showing how numerical matrix-based and resonance compensation schemes are related. In a final phase, the Hénon map is used to compare the efficiency of different coupling compensation schemes with respect to dynamic aperture.

We point out that, the way it is reported, the solution to the equation of motion of a relativistic electron in the field of two electromagnetic waves advanced recently by Amatuni and Pogorelsky [Phys. Rev. ST Accel. Beams 1, 034001 (1998)] does not handle the case of two copropagating waves differing in frequency. An equivalent form for that solution is rigorously developed.

Response is made to Y. I. Salamin's preceding Comment [Phys. Rev. ST Accel. Beams 3, 059001 (2000)]. We confirm the areas of applicability of the original and Salamin's general solutions and discuss new applications of the developed formalism.

In the 2.5-GeV Photon Factory storage ring at KEK, we have found that the beam lifetime can be improved by modulating the phase of an rf accelerating voltage at a frequency of 2 times the synchrotron oscillation frequency. By applying this phase modulation with a peak-to-peak amplitude of 3.2°, the beam lifetime could be improved, typically, from 22 to 36 h under a beam current of about 360 mA. At the same time, the longitudinal coupled-bunch instability could be considerably suppressed. The improvement in the beam lifetime can be explained as an improved Touschek lifetime, which was caused by a quadrupole-mode longitudinal oscillation of the stored bunches.

The transverse coherent motion of two colliding proton beams at the Large Hadron Collider is studied by multiparticle tracking. We use the beam-beam force for a Gaussian beam distribution with variable barycenters and rms beam sizes, and optionally include the effect of long-range collisions and external impedance. The simulation yields the coherent and incoherent oscillation frequencies, the emittance growth of either beam, and evidence for the existence or lack of Landau damping. For head-on collisions of beams with equal sizes, we find that the $\pi$-mode frequency lies outside of the continuum frequency spread, if the ratio of the beam-beam parameters exceeds 0.6, in accordance with predictions. For smaller ratios of the beam-beam parameters, or if, for equal beam-beam parameters, the beam sizes are widely different, the $\pi$ mode is Landau damped. When long-range collisions are also included, undamped coherent modes do still exist outside the continuum, both with and without alternating crossing planes at two interaction points. However, separating the tunes of the two beams restores the Landau damping, provided the external impedance is sufficiently small.

We recently studied the spin flipping of a 202.7 MeV vertically polarized proton beam stored in the Indiana University Cyclotron Facility cooler ring during the first polarized run with its new cooler injector synchrotron and its new cooler injector polarized ion source. We first set the vertical betatron tune to avoid the measured ${\nu }_y$ value of the $G\gamma =7-{\nu }_y$ intrinsic depolarizing resonance in the cooler ring. We then flipped the spin by ramping the frequency of an rf dipole through an rf-induced depolarizing resonance. After optimizing the rf dipole's frequency ramp parameters, we used multiple spin flips to measure a maximum spin-flip efficiency of $97.5\pm 1\%$.

The design of a detuned and damped accelerating structure implies variations in the geometry which induce, in turn, a variation of the group velocity $v_g$ and the impedance per unit length $R^{\prime }$, divided by the quality factor $Q$. The resulting differential equation for the longitudinal electric field (fundamental mode) contains coefficients that depend on the distance $z$ along the structure. This report describes a possible method to solve this nonlinear, first-order differential equation analytically and how to obtain approximate closed algebraic forms, by using the sequence of Gauss integration methods. Analytical expressions of the longitudinal field profile in a loaded or unloaded accelerating section are deduced for both linear and arbitrary variations of $v_g$ and $R^{\prime }/Q$. Simple relations between the average field $〈E〉$ and the field at the entrance of the structure $E\left(0\right)$ make it possible to provide the dependence of the field function $E\left(z\right)$ on the design value for $〈E〉$ and on the structure parameters. The results are in good agreement with the direct numerical integration. Applications are presented for particular structure designs.