The Tevatron in Collider Run II (2001–present) is operating with 6 times more bunches, many times higher beam intensities and luminosities than in Run I (1992–1995). Electromagnetic long-range and head-on interactions of high intensity proton and antiproton beams have been significant sources of beam loss and lifetime limitations. We present observations of the beam-beam phenomena in the Tevatron and results of relevant beam studies. We analyze the data and various methods employed in operations, predict the performance for planned luminosity upgrades, and discuss ways to improve it.

We investigate multipass beam breakup (BBU) in a recirculating linear accelerator in the framework of a single cavity model. We present expressions for the beam breakup threshold current for various situations derived from a perturbative solution of BBU equations. These formulae should serve as a guide to understand the BBU phenomenon for a particular system and also as a tool to estimate the BBU threshold current quickly. Many of the results presented are more general than previous considerations because they include the effects of coupling between the two transverse polarizations in each dipole higher order mode.

An electron cloud induces a wake force on a charged particle beam which creates correlations between bunches—i.e., a small displacement of a bunch creates a perturbation of the electron cloud, which affects the motions of the following bunches, with the result that a coupled-bunch instability is caused. The coupling mode of the instability is determined by the motion of the electrons in the cloud—that is, it depends on which electrons, moving in a drift space, a weak solenoid field or a strong bending field, are dominant for the instability. We discuss the coupled-bunch instability focusing on the relation between the mode spectrum and the electron motion.

A new procedure has been developed for automatic longitudinal tuning of a multiple-charge-state heavy-ion beam. It uses a matrix-based code to track the beam centroids and Twiss parameters of the individual charge state beams and a minimization code to minimize a goal function by adjusting the synchronous phases and field levels in the accelerating cavities. The procedure has been successfully tested in the case of the Rare Isotope Accelerator driver linac and proven to improve an original manual tune by significantly reducing beam losses. The procedure was also applied for fast retuning of the linac after one or more cavity failure and restoring the beam with limited beam loss.

The dependence of path length on betatron motion in a storage ring is analytically calculated from equations of motion using curvilinear coordinates. It is demonstrated that the change of average path length for one revolution is expressed by a sum of the products of invariant of betatron motion and chromaticity in both the horizontal and vertical directions. Because of this effect, a quasi-isochronous electron storage ring should have a considerable momentum spread when the chromaticities are large.

A 1.5-dimensional model of Compton/Raman free-electron laser (FEL) amplifiers with helical wigglers has been composed by using the helical-trajectory approach. This model has been used to analyze results of earlier experimental investigations of Compton/Raman millimeter-wavelength FEL amplifiers. The results of the 1.5D simulation are in reasonable agreement with 3D simulation and experimental results obtained in the regimes with reversed and zero guide magnetic fields. Thus a convenient tool has been developed to determine basic amplification parameters for possible experiments in the future.

We show that the formula of the strength of the spin resonance driven by a rf dipole in the commented paper is incorrect. A derivation of the resonance strength due to direct spin rotation from a rf dipole is shown. The result of a numerical simulation to verify our derivation is also presented.

It seems improper to publish a theoretical Comment about an experimental Article without mentioning the Article’s referenced theoretical paper, which derived the equation that the Comment claims is incorrect. Our experimental collaboration declines to offer any opinion about which factor of 2 is correct.

We present the detailed description of the successful design and cold test of photonic band gap (PBG) resonators and traveling-wave accelerator structures. Those tests provided the essential basis for later hot test demonstration of the first PBG accelerator structure at 17.140 GHz [E. I. Smirnova, A. S. Kesar, I. Mastovsky, M. A. Shapiro, and R. J. Temkin, Phys. Rev. Lett., 95, 074801 (2005).]. The advantage of PBG resonators is that they were built to support only the main, ${\mathrm{TM}}_{01}$-like, accelerator mode while not confining the higher-order modes (HOM) or wakefields. The design of the PBG resonators was based on a triangular lattice of rods, with a missing rod at the center. Following theoretical analysis, the rod radius divided by the rod spacing was held to a value of about 0.15 to avoid supporting HOM. For a single-cell test the PBG structure was fabricated in X-band (11 GHz) and brazed. The mode spectrum and $Q$ factor ($Q=5000$) agreed well with theory. Excellent HOM suppression was evident from the cold test. A six-cell copper PBG accelerator traveling-wave structure with reduced long-range wakefields was designed and was built by electroforming at Ku-band (17.140 GHz). The structure was tuned by etching the rods. Cold test of the structure yielded excellent agreement with the theoretical design. Successful results of the hot test of the structure demonstrating the acceleration of the electron beam were published in E. I. Smirnova, A. S. Kesar, I. Mastovsky, M. A. Shapiro, and R. J. Temkin, Phys. Rev. Lett., 95, 074801 (2005).

One of the main sources of electrons in the Spallation Neutron Source’s Accumulator Ring is the stripped electrons in the injection region. A magnetic field guides the stripped electrons to the bottom of the beam pipe, where an electron catcher with overhanging surface traps them. This paper describes the stripped electrons’ motion, the optimization of the catcher, and the build up of an electron cloud in this region.

Modulation of the bunch length in an electron storage ring appears with the combination of a high rf voltage derivative and large dispersion in the dipoles, producing drifting of the longitudinal phase plane along the closed orbit. The comparison is done between two different regimes: the one corresponding to high momentum compaction structures, in which the drifting in all dipoles has always the same direction, and the other one corresponding to low momentum compaction in which the drifting changes sign along the ring. Expressions for the longitudinal Twiss functions, energy spread and longitudinal emittance are given. The generalization to multiple rf systems is mentioned.

The passage of a finely focused electron beam near the surface of a periodic metallic grating produces radiation known as Smith-Purcell radiation. This paper presents an analysis of the role of the grating profile in the case of echelle-type gratings whose period consists of two facets only. Particular emphasis is placed on the ultrarelativistic regime and a comparison is made with recent experimental results in this region. It is shown that the details of the profile of the grating play an important role in the optimization of the radiated energy. The behavior of higher order modes and the limitations of the surface current description of the radiative process are also discussed briefly.

We report experimental studies of the spectral linewidth and chirp characteristics of the mm-wave rf radiation of the Israeli Electrostatic-Accelerator free electron laser (EA-FEL), along with theory and numerical simulations. The simulations, matching the experimental data, were carried out using a space-frequency-domain model. EA-FELs have the capacity to generate long pulses of tens microseconds and more, that in principle can be elongated indefinitely (cw operation). Since a cold beam FEL is by nature a “homogeneously broadened laser,” EA-FEL can operate, unlike other kinds of FELs, at a single longitudinal mode (single frequency). This allows the generation of very coherent radiation. The current status of the Israeli Tandem Electrostatic-Accelerator FEL, which is based on an electrostatic Van de Graaff accelerator, allows the generation of pulses of tens microseconds duration. It has been operated recently past saturation, and produced single-mode coherent radiation of record narrow inherent relative linewidth $\sim \Delta f/f={10}^{-6}$ at frequencies near 100 GHz. A frequency chirp was observed during the pulses of tens of microseconds ($0.3–0.5\mathrm{MHz}/\mathrm{ms}$). This is essentially a drifting “frequency-pulling effect,” associated with the accelerator voltage drop during the pulse. Additionally, damped relaxation of the FEL oscillator was experimentally measured at the beginning and the end of the lasing pulse, in good correspondence to our theory and numerical simulations. We propose using the chirped signal of the pulsed EA-FEL for single pulse sweep spectroscopy of very fine resolution. The characteristics of this application are analyzed based on the experimental data.

Dynamics of interaction of longitudinal modes in a FEM oscillator with a broad-frequency-band feedback system and a klystronlike interaction region is studied. It is shown that the use of the klystronlike interaction region results both in increasing the efficiency of electron energy extraction and decreasing the number of competing modes. The latter provides a significant increase of the electron-current threshold of stability of the single-mode operation.

A method for direct momentum correction of a selected beam particle using a controllable induction-voltage modulator is proposed for a low-flux ion beam. The corrected ion beam has a small momentum error restricted by a detection error at a kinetic energy analyzer and a voltage fluctuation at the induction-voltage modulator. Numerical simulations indicate that the scheme using a multiturn correction in a storage ring can considerably reduce the requirement of the amplitude and the tolerance level of the correction voltage. The results also show the final momentum error of the order of ${10}^{-5}$ can be rapidly achieved at total flight time of $30\mu \mathrm{s}$ when repetitive correction voltages are applied during the revolutions in the ring.

Currently ongoing at Los Alamos National Laboratory is a program to develop high-power, planar 100–300 GHz traveling-wave tubes. A necessary part of this effort is a sheet electron beam source. Previously, we have described a novel asymmetric solenoid lens concept for transforming the circular beam from a high-perveance electron gun to a planar configuration. The lens is a standard electromagnetic solenoid with elliptical, instead of circular, pole apertures. The elliptical pole openings result in asymmetric focusing, which in turn forms an elliptical sheet beam suitable for our planar structures. Here we report the first experimental demonstration of this lens.

We consider an ultrarelativistic particle traveling on axis in an infinitely long cylindrical metallic beam pipe with azimuthally varying conductivity. For a circular geometry, a semianalytical solution is obtained using the Green functions and applying approximate boundary conditions for conductors. The theory predicts an image current distribution on the pipe walls practically independent of the azimuth, at least in the frequency range relevant for future machines such as the LHC. Numerical electromagnetic simulations and bench measurements confirm the theoretical predictions. Implications for the beam-induced heating in the copper-coated, welded LHC beam screen are also addressed.

We derive completely integrated formulas for emittance growth times due to intrabeam scattering for charged particle beams in the high energy limit, including the effect of lattice parameters that vary around the accelerator ring. Using accelerator lattices for the prototype damping ring called the Accelerator Test Facility at KEK and those for two proposed International Linear Collider damping rings, we compare our results with other calculations.