Cavities for $\pi$-mode operation are used in existing accelerators and are being built for many future systems. One of the steps in cavity construction is tuning individual cells within the cavity to ensure that the absolute values of relative peak on-axis electric field amplitudes in each cell are equal. This process may have multiple iterative steps: measuring the on-axis fields using bead-pull techniques, employing tuning methods to perturb the cells, making cell adjustments, and then repeating the process on the basis of the new results. This paper describes a one-step process for an $N$ cell cavity that provides the necessary adjustment for each cell to achieve equal field amplitude absolute values from one bead-pull measurement. In addition, a method is shown for inferring relative cell fields while a cavity is operational in an accelerator complex.

In a multipurpose cyclotron, it is convenient to use stripping extraction to extract selected positive ions in addition to the usual extraction by stripping of negative ions. The ions are specified as positive or negative according to the sign of their charge during acceleration. After stripping, positive ions travel not only through the pole edge magnetic field gradient, as is the case with negative ions, but can also pass more than once through regions of large sector edge magnetic field gradients. Influence of the magnetic field gradients on the trajectory of a stripped positive ion and on the extracted beam emittance is studied. It is shown that extraction efficiency depends on the position of the point of beam extraction from a cyclotron and on the ratio between ion charge after and before stripping. The position of the point of extraction also strongly affects the design parameters of the stripping extraction system. Extraction quality and design parameters cannot all be simultaneously optimized. The method of extraction system optimization is suggested and applied to the special case of the VINCY cyclotron.

In this paper we present two new techniques for frequency-resolved characterization of longitudinal impedances in storage rings. The first method is based on transient measurements of the growth rates and tune shifts of unstable coupled-bunch modes. In the second approach, estimates of the impedances are obtained from analysis of the steady-state synchronous phases of the bunches for uneven fill patterns. These techniques are applicable to measurements of both fundamental and higher-order mode (HOM) impedances and allow characterization of shunt impedances and quality factors of the HOMs. Methods presented here are complementary to laboratory bench measurements of rf cavities, in that the beam-based measurements directly sense the physical impedance in the installed configuration. Experimental results from the Advanced Light Source and BESSY-II are presented showing the use of these techniques to measure complex impedances.

A simple 1D model is proposed to explore the resonant extraction of intense beams from a synchrotron as performed in the SIS synchrotron in GSI (Darmstadt). The model Hamiltonian consists of a constant focusing, a thin sextupole, and a smooth space charge field. Hyperbolic normal forms are used to estimate the extraction times and the emittance of the extracted beam; the quality of the reconstruction is tested in absence of space charge. The effect of space charge on the dynamical behavior of the beam near the $1/3$ betatron resonance is numerically investigated using the frequency map analysis and qualitatively explained with perturbation theory. A polynomial approximation to the one turn map is obtained by replacing the exact space charge force with a sequence of polynomial kicks, and the resonant normal forms reproduce quite accurately the nonlinear tunes and the fixed points position. At low order an analytical estimate of the area of the stable region is proposed to recover the self-consistency of the model.

Extending the method of Warnock and Ellison for the simulation of the Vlasov-Fokker-Planck equation for bunched beams [in Proceedings of the 2nd ICFA Advanced Accelerator Workshop on the Physics of High Brightness Beams, Los Angeles, CA, 1999 (World Scientific, Singapore, 2000)], we analyze arbitrary radio-frequency potentials and high- $Q$ impedances and study instabilities in stretched bunches. Results for the microwave instability driven by a broadband impedance and instability driven by high- $Q$ rf modes in stretched bunches are compared with measurements of the vacuum ultraviolet ring at the National Synchrotron Light Source. A method for the calculation of response functions is developed, and simulated response functions are compared to experimental results.

We study a method of laser-Compton cooling of electron beams for future linear colliders. Using a Monte Carlo code, we evaluate the effects of the laser-electron interaction for transverse cooling. The optics with and without chromatic correction for the cooling are examined. The laser-Compton cooling for Japan Linear Collider/Next Linear Collider at $E_0=2\mathrm{}\mathrm{GeV}$ is considered.

Superconducting cavities presently used for acceleration of ions in velocity range $\sim 0.01c$ to $0.3c$ (where $c$ is the speed of light) are based on quarter-wave resonators. Currently there are several design proposals in nuclear physics laboratories for application of this type of cavity for acceleration of light and heavy ions. The operating frequencies of the cavities range from $\sim 50$ to 360 MHz to satisfy various specifications. Electrodynamics studies of the field distributions in the beam-cavity interaction area indicate appreciable dipole components of both electric and magnetic fields, especially for higher-frequency cavities. The dipole fields induce beam steering, which is a strong function of rf phase and which couples the longitudinal and transverse motion. This can result in growth in the transverse emittance of the beam. In this paper, we propose two possible methods for the correction of such dynamic beam-steering effects in quarter-wave resonators. We analyze and discuss the correction methods for the particular examples of two quarter-wave resonators operating at 57.5 and 115 MHz designed for the driver linac of the Rare Isotope Accelerator facility.

We recently used a prototype rf dipole magnet to study the spin flipping of a 669 MeV horizontally polarized electron beam stored in the presence of a nearly full Siberian snake in the new MIT-Bates storage ring. We flipped the spin by ramping the rf dipole's frequency through an rf-induced depolarizing resonance. After optimizing the frequency ramp parameters, we used multiple spin flipping to measure a spin-flip efficiency of $94.5\pm 2.5\%$. The spin-flip efficiency was apparently limited by the field strength in the air-core prototype rf dipole magnet. This unexpectedly high efficiency indicates that very efficient spin flipping of the ring's stored polarized electron beam should be possible using the much stronger ferrite spin flipper, which is now being built by the University of Michigan's Spin Physics Center.

We present 2D simulations of both beam-driven and laser-driven plasma wakefield accelerators, using the object-oriented particle-in-cell code XOOPIC, which is time explicit, fully electromagnetic, and capable of running on massively parallel supercomputers. Simulations of laser-driven wakefields with low $\backslash (\sim {10}^{16}\mathrm{W}/{\mathrm{cm}}^2\backslash )$ and high $\backslash (\sim {10}^{18}\mathrm{W}/{\mathrm{cm}}^2\backslash )$ peak intensity laser pulses are conducted in slab geometry, showing agreement with theory and fluid simulations. Simulations of the E-157 beam wakefield experiment at the Stanford Linear Accelerator Center, in which a 30 GeV electron beam passes through 1 m of preionized lithium plasma, are conducted in cylindrical geometry, obtaining good agreement with previous work. We briefly describe some of the more significant modifications to XOOPIC required by this work, and summarize the issues relevant to modeling relativistic electron-neutral collisions in a particle-in-cell code.

Detailed experimental results of staging two laser-driven, relativistic electron accelerators are presented. During the experiment called STELLA (staged electron laser acceleration), an inverse free-electron laser (IFEL) is used to modulate the electron energy, thereby, causing $\sim 3\mathrm{fs}$ microbunches to form separated by the laser wavelength at $10.6\mu \mathrm{m}$ (equivalent to a 35 fs period). A second IFEL accelerates the electrons depending upon the phase of the microbunches entering the second IFEL with respect to the laser beam driving the second IFEL. The data presented includes electron energy spectra as a function of the phase delay and laser power driving the first IFEL. Also shown is a comparison with the computer model, which includes space charge and misalignment effects.

This paper provides a systematic derivation of a guiding-center kinetic model that describes intense beam propagation through a periodic focusing lattice with axial periodicity length $S$, valid for sufficiently small phase advance (say, $\sigma <60\mathrm{}°$). The analysis assumes a thin $(a,b\ll S)$ axially continuous beam, or very long charge bunch, propagating in the $z$ direction through a periodic focusing lattice with transverse focusing coefficients ${\kappa }_x(s+S)={\kappa }_x\left(s\right)$ and ${\kappa }_y(s+S)={\kappa }_y\left(s\right)$, where $S=\mathrm{const}$ is the lattice period. By averaging over the (fast) oscillations occurring on the length scale of a lattice period $S$, the analysis leads to smooth-focusing Vlasov-Maxwell equations that describe the slow evolution of the guiding-center distribution function ${\overline{f}}_b(\overline{x},\overline{y},{\overline{x}}^{\prime },{\overline{y}}^{\prime },s)$ and (normalized) self-field potential $\overline{\psi }(\overline{x},\overline{y},s)$ in the four-dimensional transverse phase space $(\overline{x},\overline{y},{\overline{x}}^{\prime },{\overline{y}}^{\prime })$. In the resulting kinetic equation for ${\overline{f}}_b(\overline{x},\overline{y},{\overline{x}}^{\prime },{\overline{y}}^{\prime },s)$, the average effects of the applied focusing field are incorporated in constant focusing coefficients ${\kappa }_{x\mathrm{sf}}>0\mathrm{}$ and ${\kappa }_{y\mathrm{sf}}>0\mathrm{}$, and the model is readily accessible to direct analytical investigation. Similar smooth-focusing Vlasov-Maxwell descriptions are widely used in the accelerator physics literature, often without a systematic justification, and the present analysis is intended to place these models on a rigorous, yet physically intuitive, foundation.

We studied the electrostatic field due to a charged-particle beam with uniform particle density propagating inside an rf-shielding cage (rf cage) constructed from evenly spaced conducting wires. The beam and the rf cage are surrounded by a ceramic beam pipe positioned inside a conducting pipe concentric with the beam and the rf cage. The space-charge impedances in the long wavelength regime are investigated by considering the electrostatic fields due to the longitudinal and transverse perturbations on the density of the charged-particle beam. Shielding effects due to the rf cage are discussed and simple formulas are derived for estimating the space-charge impedances. Numerical examples are given for illustration. Comparisons between analytical estimates and the results produced by the field-solver computer program MAFIA show good agreement.

This paper outlines a formalism for the description of the linear transverse dynamics of charged particles in an axisymmetric ionization cooling channel. The particle trajectories in the absence of Coulomb scattering are described in terms of lattice functions à la Courant and Snyder, which depend only on the electric and magnetic fields in the channel. The process of multiple Coulomb scattering, which introduces stochastic terms into the particle equations of motion, is treated (in Gaussian approximation) by obtaining the distribution function in phase space as a solution of a Fokker-Planck equation. The distribution function is then used to obtain moment equations for the transverse variables and for combinations of variables such as the emittance and angular momentum. The distribution function is also used to obtain an expression for the peak four-dimensional phase space density and for the fraction of the beam that is within a certain area in phase space. The special case of a periodic channel is then considered and expressions for the asymptotic rms emittance and peak phase space density are obtained. Finally, the application of the general formalism to a numerical example, based on the reported design of a cooling channel for a neutrino source, is considered, and comparisons are made with numerical simulations of that channel.

In a recent Brief Comment, the results of an experiment to measure the refraction of a particle beam were reported [P. Muggli et al., Nature 411, 43 (2001)]. The refraction takes place at a passive interface between a plasma and a gas. Here the full paper on which that Comment is based is presented. A theoretical model extends the results presented previously [T. Katsouleas et al., Nucl. Instrum. Methods Phys. Res., Sect. A 455, 161 (2000)]. The effective Snell's law is shown to be nonlinear, and the transients at the head of the beam are described. 3D particle-in-cell simulations are performed for parameters corresponding to the experiment. Additionally, the experiment to measure the refraction and internal reflection at the Stanford Linear Accelerator Center is described.

Detailed experimental studies of the first operation of an $X$-band (8.547 GHz) rf photoinjector are reported. The rf characteristics of the device are first described, as well as the tuning technique used to ensure operation of the $1\frac{1}{2}$-cell rf gun in the balanced $\pi$-mode. The characterization of the photoelectron beam produced by the rf gun includes: measurements of the bunch charge as a function of the laser injection phase, yielding information about the quantum efficiency of the Cu photocathode ( $2\times {10}^{-5\mathrm{}}$ for a surface field of $100\mathrm{MV}/\mathrm{m}$); measurements of the beam energy (1.5–2 MeV) and relative energy spread ( $\Delta \gamma /{\gamma }_0=1.8\mathrm{}\pm 0.2\%$) using a magnetic spectrometer; measurements of the beam 90% normalized emittance, which is found to be ${\varepsilon }_n=1.65\mathrm{}\pi \mathrm{mm}\mathrm{mrad}$ for a charge of 25 pC; and measurements of the bunch duration ( $<2\mathrm{}\mathrm{ps}$). Coherent synchrotron radiation experiments at Ku-band and Ka-band confirm the extremely short duration of the photoelectron bunch and a peak power scaling quadratically with the bunch charge.

The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by a pencil beam. The nonlinearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.

We report on electron beam quality measurement results from the Massachusetts Institute of Technology 17 GHz RF gun experiment. The 1.5 cell RF gun uses a solenoid for emittance compensation. It has produced bunch charges up to 0.1 nC with beam energies up to 1 MeV. The normalized rms emittance of the beam after 35 cm of transport from the gun has been measured by a slit technique to be $3\pi \mathrm{mm}\mathrm{mrad}$ for a 50 pC bunch. This agrees well with PARMELA simulations at these beam energies. At the exit of the electron gun, we estimate the emittance to be about $1\pi \mathrm{mm}\mathrm{mrad}$, which corresponds to a beam brightness of about $80\mathrm{A}/(\pi \mathrm{mm}\mathrm{mrad}{)}^2$. Improved beam quality should be possible with a higher energy output electron beam from the gun.

A method for finding four-dimensional symplectic maps with an enlarged nearly integrable region is described. The method relies on solving for parameter values at which the linear stability factors of the fixed points (periodic orbits) of the map have the values corresponding to integer island tunes. This method is applied to accelerator lattices in order to increase dynamic aperture. The result shows a significant increase of the dynamic aperture after correction.