We present the theoretical design and cold test of a 17 GHz photonic band gap (PBG) cavity with improved coupling from an external rectangular waveguide. The PBG cavity is made of a triangular lattice of metal rods with a defect (missing rod) in the center. The ${\mathrm{TM}}_{010}$-like defect mode was chosen as the operating mode. Experimental results are presented demonstrating that critical coupling into the cavity can be achieved by partial withdrawal or removal of some rods from the lattice, a result that agrees with simulations. A detailed design of the PBG accelerator structure is compared with a conventional (pillbox) cavity. One advantage of the PBG cavity is that its resonance frequency is much less perturbed by the input/output coupling structure than in a comparable pillbox cavity. The PBG structure is attractive for future accelerator applications.

In the past few years, the concept of a high intensity muon storage ring has been pursued as an option for the next generation neutrino source. To produce the high intensity muon beam needed for the successful operation of a neutrino source, on the order of ${10}^{20}$ muon decays per year, the phase space occupied by the muon beam must be significantly reduced before the beam is accelerated. The initial transverse emittance of the muon beam before acceleration is assumed to be $9\pi \mathrm{mm}\mathrm{rad}$. Because of the time limitation imposed by the muon lifetime, the technique employed to accomplish the desired emittance reduction is ionization cooling. In this paper we present two ionization cooling lattice designs, which use solenoidal focusing elements and liquid hydrogen absorbers to reduce the muon beam phase space. We discuss the design concepts and engineering constraints for these lattices and present simulation results obtained using a detailed tracing code with a complete model of muon-matter interactions. The reduction in transverse emittance is approximately a factor of 5. This result is within a factor of 2 of the total cooling requirements for a successful neutrino factory design and within a factor of 1.4 of the requirements for the main cooling section specified in the conceptual design of this machine.

Transverse stability with nonlinear space charge is studied within the context of coasting beams. For bare tune spreads originating from chromaticity or frequency slip, the space charge tune spread has a fairly small effect and the incoherent space charge force is well modeled by a transverse capacitance. For tune spreads due to octupoles or fringe fields, beams are more stable when the bare tune increases with betatron amplitude.

Two-beam accelerators (TBAs) have been proposed as efficient power sources for next generation high-energy linear colliders. Studies have demonstrated the possibility of building TBAs from $X$-band $\backslash (\sim 8–12\mathrm{GHz}\backslash )$ through Ka-band $\backslash (\sim 30–35\mathrm{GHz}\backslash )$ frequency regions. The relativistic klystron two-beam accelerator project, whose aim is to study TBAs based upon extended relativistic klystrons, is described, and a new simulation code is used to design the latter portions of the experiment. Detailed, self-consistent calculations of the beam dynamics and of the rf cavity output are presented and discussed together with a beam line design that will generate nearly 1.2 GW of power from 40 rf cavities over a 10 m distance. The simulations show that beam current losses are acceptable and that longitudinal and transverse focusing techniques are sufficiently capable of maintaining a high degree of beam quality along the entire beam line.

The nonlinear regime of the beam-beam instability for flat beams is considered. Excitation of coherent modes and mode interaction is studied above the threshold of instability. It is shown that the exponential growth of the linear approximation may saturate, leading to a finite growth of transverse emittance.

Stationary, self-consistent, and localized longitudinal density perturbations on an unbunched charged-particle beam, which are solutions of the nonlinearized Vlasov-Poisson equation, have recently received some attention. In particular, we address the case that space charge is the dominant longitudinal impedance and the storage ring operates below transition energy so that the negative mass instability is not an explanation for persistent beam structure. Under the customary assumption of a bell-shaped steady-state distribution, about which the expansion is made, the usual wave theory of Keil and Schnell for perturbations on unbunched beams predicts that self-sustaining perturbations are possible only (below transition) if the impedance is inductive (or resistive) or if the bell shape is inverted. Space charge gives a capacitive impedance. Nevertheless, we report numerous experimental measurements made at the CERN Proton Synchrotron Booster that plainly show the longevity of holelike structures in coasting beams. We shall also report on computer simulations of boosterlike beams that provide compelling evidence that it is space-charge force which perpetuates the holes. We shall show that the localized solitonlike structures, i.e., holes, decouple from the steady-state distribution and that they are simple solutions of the nonlinearized time-independent Vlasov equation. We have derived conditions for stationarity of holes that satisfy the requirement of self-consistency; essentially, the relation between the momentum spread and depth of the holes is given by the Hamiltonian—with the constraint that the phase-space density be high enough to support the solitons. The stationarity conditions have scaling laws similar to the Keil-Schnell criteria except that the charge and momentum spread of the hole replaces that of the beam.

Harmonic cavities have been used in storage rings to increase beam lifetime and Landau damping by lengthening the bunch. The need for lifetime increase is particularly great in the present generation of low to medium energy synchrotron light sources where the small transverse beam sizes lead to relatively short lifetimes from large-angle intrabeam (Touschek) scattering. We review the beam dynamics of harmonic radio-frequency systems and discuss optimization of the beam lifetime using passive harmonic cavities.

A draft scenario of optical stochastic cooling of muons is considered. Difficult places of this scenario are highlighted and constraints are explained. The parameters of a $2\mathrm{TeV}\times 2\mathrm{TeV}$ muon collider utilizing muons after optical stochastic cooling are presented.

We investigate algorithms for computing steady state electromagnetic waves in cavities. The Maxwell equations for the strength of the electric field are solved by a mixed method with quadratic finite edge (Nédélec) elements for the field values and corresponding node-based finite elements for the Lagrange multiplier. This approach avoids so-called spurious modes which are introduced if the divergence-free condition for the electric field is not treated properly. To compute a few of the smallest positive eigenvalues and corresponding eigenmodes of the resulting large sparse matrix eigenvalue problems, two algorithms have been used: the implicitly restarted Lanczos algorithm and the Jacobi-Davidson algorithm, both with shift-and-invert spectral transformation. Two-level hierarchical basis preconditioners have been employed for the iterative solution of the resulting systems of equations.

A vertical instability of the KEK-Photon Factory electron storage ring was observed in a multibunch mode with empty buckets (bunch gap) using a bunch-by-bunch beam diagnostic system that consisted of a high-speed light shutter and an optical betatron oscillation detector. It was clearly seen that vertical betatron frequencies of individual bunches varied along a bunch train. The dependence of the betatron frequencies on the bunch positions in the train was explained by modulation of trapped-ion density caused by passage of the beam. Agreement between experimental results and the theoretical prediction was quite good.

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.