In order to clarify the difference of outcomes between our recent work [Y. Yuri et al., Phys. Rev. ST Accel. Beams 10, 104001 (2007)] and the work done by Los Alamos National Laboratory in the 1990s outlined in the Comment [R. E. Shafer, Phys. Rev. ST Accel. Beams 11, 039001 (2008)], we briefly summarize the former progress of the research and development on beam uniformization by means of the nonlinear focusing method, and insist on the newness of our recent publication in this Reply.

We have developed 1D analytic and 2D fully electromagnetic models of radial transmission-line impedance transformers. The models have been used to quantify the power-transport efficiency and pulse sharpening of such transformers as a function of voltage pulse width and impedance profile. For the cases considered, we find that in the limit as $\Gamma \to 0$ (where $\Gamma$ is the ratio of the pulse width to the one-way transit time of the transformer), the transport efficiency is maximized when the impedance profile is exponential. As $\Gamma$ increases from zero, the optimum profile gradually deviates from an exponential. A numerical procedure is presented that determines the optimum profile for a given pulse shape and width. The procedure can be applied to optimize the design of impedance transformers used in petawatt-class pulsed-power accelerators.

Acceleration of ions from ultrathin foils irradiated by intense circularly polarized laser pulses is investigated using one- and two-dimensional particle simulations. A circularly polarized laser wave heats the electrons much less efficiently than the wave of linear polarization and the ion acceleration process takes place on the front side of the foil. The ballistic evolution of the foil becomes important after all ions contained in the foil have been accelerated. In the ongoing acceleration process, the whole foil is accelerated as a dense compact bunch of quasineutral plasma implying that the energy spectrum of ions is quasimonoenergetic. Because of the ballistic evolution, the velocity spread of an accelerated ion beam is conserved while the average velocity of ions may be further increased. This offers the possibility to control the parameters of the accelerated ion beam. The ion acceleration process is described by the momentum transfer from the laser beam to the foil and it might be fairly efficient in terms of the energy transferred to the heavy ions even if the foil contains a comparable number of light ions or some surface contaminants. Two-dimensional simulations confirm the formation of the quasimonoenergetic spectrum of ions and relatively good collimation of the ion bunch, however the spatial distribution of the laser intensity poses constraints on the maximum velocity of the ion beam. The present ion acceleration mechanism might be suitable for obtaining a dense high energy beam of quasimonoenergetic heavy ions which can be subsequently applied in nuclear physics experiments. Our simulations are complemented by a simple theoretical model which provides the insights on how to control the energy, number, and energy spread of accelerated ions.

This paper presents designs for four types of very-low-velocity superconducting (SC) accelerating cavity capable of providing several MV of accelerating potential per cavity, and suitable for particle velocities in the range $0.006<v/c<0.06$. Superconducting TEM-class cavities have been widely applied to cw acceleration of ion beams. SC linacs can be formed as an array of independently phased cavities, enabling a variable velocity profile to maximize the output energy for each of a number of different ion species. Several laboratories in the U.S. and Europe are planning exotic beam facilities based on SC linacs. The cavity designs presented here are intended for the front end of such linacs, particularly for the postacceleration of rare isotopes of low charge state. Several types of SC cavities have been developed recently to cover particle velocities above 0.06c. Superconducting four-gap quarter-wave resonators for velocities $0.008<\beta =v/c<0.05$ were developed about two decades ago and have been successfully operated at the ATLAS SC linac at Argonne National Laboratory. Since that time, progress in simulation tools, cavity fabrication, and processing have increased SC cavity gradients by a factor of 3–4. This paper applies these tools to optimize the design of a four-gap quarter-wave resonator for exotic beam facilities and other low-velocity applications.

For magnets arranged so closely that the distance between them is comparable to the magnet apertures, the field interference becomes important. This is the case in the injection region at the China Spallation Neutron Source (CSNS) where several bump magnets are used to create fixed and dynamic local orbit bumps for the beam injection using the ${\mathrm{H}}^{-}$ stripping and the phase space painting method. The reduction in the field integral due to the field interference will cause an orbit distortion, and the orbit bumps will be no longer localized. It is found that the end coil structure plays an important role in reducing the fringe field of a magnet. This has been analyzed by using both the image current method and three-dimensional magnetic field calculations. The saddle end coil instead of the compact end coil has been adopted at the CSNS. The relative reduction in the field integration after the optimization can meet the design requirement of about 1% or less.

The Linac Coherent Light Source is a SASE x-ray free-electron laser (FEL) project presently under construction at SLAC [J. Arthur et al., SLAC-R-593, 2002.]. The injector section, from drive laser and rf photocathode gun through first bunch compressor chicane, was installed in the fall of 2006. The initial system commissioning with an electron beam was completed in August of 2007, with the goal of a 1.2-micron emittance in a 1-nC bunch demonstrated. The second phase of commissioning, including second bunch compressor and full linac, is planned for 2008, with FEL commissioning in 2009. We report experimental results and experience gained in the first phase of commissioning, including the photocathode drive laser, rf gun, photocathode, S-band and X-band rf systems, first bunch compressor, and the various beam diagnostics.

There is a growing interest in producing intense, coherent x-ray radiation with an adjustable and arbitrary polarization state. In this paper, we study the crossed-undulator scheme [K.-J. Kim, Nucl. Instrum. Methods Phys. Res., Sect. A 445, 329 (2000)] for rapid polarization control in a self-amplified spontaneous emission (SASE) free electron laser (FEL). Because a SASE source is a temporally chaotic light, we perform a statistical analysis on the state of polarization using FEL theory and simulations. We show that, by adding a small phase shifter and a short (about 1.3 times the FEL power gain length), 90° rotated planar undulator after the main SASE planar undulator, one can obtain circularly polarized light—with over 80% polarization—near the FEL saturation.

Transition radiation (TR) and diffraction radiation (DR) has widely been used for both electron beam diagnostics and generation of intense radiation beams in the millimeter and the submillimeter wavelength range. Recently, it was theoretically predicted that TR and DR properties change either at extremely high energies of electrons or at long radiation wavelengths. This phenomenon was called a prewave zone effect. We have performed the first observation and detailed investigation of the prewave zone effect in optical diffraction radiation at 1.28 GeV electron beam at the KEK-Accelerator Test Facility (KEK-ATF). The beam energy at KEK-ATF is definitely not the highest one achieved in the world. Since we could easily observe the effect, at higher energies it might cause serious problems. We developed and applied a method for prewave zone suppression valid for optical wavelengths. Furthermore, a method for prewave zone suppression applicable for longer radiation wavelengths is discussed.

We show that, through careful control of noise sources, it is possible to determine the microbunching gain curve for the FERMI@ELETTRA linac using the particle tracking code elegant. In addition to using a sufficiently large number of particles ($60\times {10}^6$), use of a low-pass filter is very helpful in controlling noise and providing convenient intrabin interpolation. Gains of up to 1500 are seen for modulation wavelengths down to $25\mu \mathrm{m}$. Because of the high gain, very small initial modulations are needed to avoid saturation, which further motivates the use of a large number of particles. We also show, for the first time, how the density modulation evolves in detail inside the dipoles of a multichicane system.

A light source based on the combination of an energy-recovery linac (ERL) and a storage ring is a feasible scheme for next generation light sources. We propose a system with which a beam of an ERL circulates through two or four turns in a storage ring. The system consists of several deflecting cavities and static deflecting magnets. With this system, the average current of the ring can be two or four times higher than that of the ERL, thus easing the burden on the ERL. Resultant low bunch current can lead to a high quality ERL beam and low average current of the ERL can lead to a multipass scheme.

The new generation of linac injectors driving free electron lasers in the self-amplified stimulated emission (SASE-FEL) regime requires high brightness electron beams to generate radiation in the wavelength range from UV to x rays. The choice of the injector working point and its matching to the linac structure are the key factors to meet this requirement. An emittance compensation scheme presently applied in several photoinjectors worldwide is known as the “Ferrario” working point. In spite of its great importance there was, so far, no direct measurement of the beam parameters, such as emittance, transverse envelope, and energy spread, in the region downstream the rf gun and the solenoid of a photoinjector to validate the effectiveness of this approach. In order to fully characterize the beam dynamics with this scheme, an innovative beam diagnostic device, the emittance meter, consisting of a movable emittance measurement system, has been designed and built. With the emittance meter, measurements of the main beam parameters in both transverse phase spaces can be performed in a wide range of positions downstream the photoinjector. These measurements help in tuning the injector to optimize the working point and provide an important benchmark for the validation of simulation codes. We report the results of these measurements in the SPARC photoinjector and, in particular, the first experimental evidence of the double minimum in the emittance oscillation, which provides the optimized matching to the SPARC linac.

We will explore a method for measuring chromaticity by continuously kicking the beam transversely. This is called the continuous head-tail method for measuring chromaticity. The complete analytic approximation in terms of trigonometric functions is derived for zero transverse emittance beam. A simple formula for calculating chromaticity from experimental data is also shown. Finally, the theory is compared with experimental data.

The traditional process of designing and tuning the magnetic lattice of a particle storage ring lattice to produce certain desired properties is not straightforward. Often solutions are found through trial and error and it is not clear that the solutions are close to optimal. This can be a very unsatisfying process. In this paper we take a step back and look at the general stability limits of the lattice. We employ a technique we call GLASS (GLobal scan of All Stable Settings) that allows us to rapidly scan and find all possible stable modes and then characterize their associated properties. In this paper we illustrate how the GLASS technique gives a global and comprehensive vision of the capabilities of the lattice. In a sense, GLASS functions as a lattice observatory clearly displaying all possibilities. The power of the GLASS technique is that it is fast and comprehensive. There is no fitting involved. It gives the lattice designer clear guidance as to where to look for interesting operational points. We demonstrate the technique by applying it to two existing storage ring lattices—the triple bend achromat of the Advanced Light Source and the double bend achromat of CAMD. We show that, using GLASS, we have uncovered many interesting and in some cases previously unknown stability regions.

Diffraction radiation (DR) is one of the most promising candidates for electron beam diagnostics for International Linear Collider and x-ray free electron lasers due to its nonintercepting characteristic. One of the potential problems that may restrict its applications in real-time monitoring beam parameters is the wakefield generated by the presence of the DR target. In this paper, a comparative study of the wakefield and the backward DR (BDR) field is performed to clarify the relationship between them. The wakefield is studied with a particle-in-cell code MAGIC and the DR field is calculated based on virtual photon diffraction model. It is found that they have the same frequency spectrum and angular distribution, which indicates that the difference only exists in the subjective terminology. The longitudinal and transverse wake for a beam passing through a DR target is calculated for a general case when the beam’s velocity is smaller than that of light. The resulted emittance growth and energy spread growth due to the short range wakefield is estimated and found to be permissible. In real measurement where BDR propagates in the direction perpendicular to the trajectory, it may add a transverse kick to the beam as a requirement of momentum conservation. The kick is found to be large enough to degrade the performance of accelerator driven facilities and needs to be corrected.

Within the realm of classical electrodynamics, the curvature-induced bunch collective interaction in magnetic bends can be studied using effective forces in the canonical formulation of the coherent synchrotron radiation (CSR) effect. As an application of this canonical formulation, in this paper, for an electron distribution moving ultrarelativistically in a bending system, the dynamics of the particles in the distribution is derived from the Hamiltonian of the particles in terms of the bunch internal coordinates. The consequent Vlasov equation manifests explicitly how the phase-space distribution is perturbed by the effective CSR forces. In particular, we study the impact of an initial linear energy chirp of the bunch on the behavior of the effective longitudinal CSR force, which arises due to the modification of the retardation relation as a result of the energy-chirping-induced longitudinal-horizontal correlation of the bunch distribution (bunch tilt) in dispersive regions. Our study clearly demonstrates the time delay (or retardation) of the behavior of the effective longitudinal CSR force on a bunch in responding to the change of the bunch length in a magnetic bend. Our result also shows that the effective longitudinal CSR force for a bunch under full compression can have sensitive dependence on the transverse position of the test particle in the bunch for certain parameter regimes.

The problems of stripper target behavior in the nonstationary intense particle beams are considered. The historical sketch on studies of radiation damage failure of carbon targets under ion bombardment is presented. The simple model of target evaporation under intensive pulsing beam is supposed. Lifetimes of stripper targets under intensive nonstationary beams can be described by two failure mechanisms: radiation damage accumulation and evaporation of a target. At the maximal temperatures less than $2500°\mathrm{K}$ the radiation damage dominates; at temperatures above $2500°\mathrm{K}$ the mechanism of evaporation of a foil prevails. The proposed approach has been applied to the description of stripper foils behavior in Brookhaven National Laboratory linac and Spallation Neutron Source conditions.

Using the ORBIT code we study the sensitivity of electron cloud properties with respect to different proton beam profiles, the secondary electron yield (SEY) parameter, and the proton loss rate. Our model uses a cold proton bunch to generate primary electrons and electromagnetic field for electron cloud dynamics. We study the dependence of the prompt and swept electron signals vs the bunch charge and the recovery of electron clouds after sweeping on the beam loss rate and the SEY. The simulation results are compared with the experimental data measured at the proton storage ring at the Los Alamos National Laboratory. Our simulations indicate that the fractional proton loss rate in the field-free straight section may be an exponential function of proton beam charge and may also be lower than the averaged fractional proton loss rate over the whole ring.

We present the results of our investigation of lead as a suitable photocathode material for superconducting rf injectors. Quantum efficiencies (QE) have been measured for a range of incident photon energies and compared to predictions from the three-step model of photoemission. A variety of cathode preparation methods have been used, including various lead plating techniques on a niobium substrate. The effects of operating at ambient and cryogenic temperatures and different vacuum levels on the cathode QE have also been studied.

The Napoly integral is the very useful method for calculations of wake potentials in structures where parts of the boundary extend below the beam pipe radius or the radii of the two beam pipes at both ends are unequal. It reduces CPU time a lot by deforming the integration path so that the integration contour is confined to the finite length over the gap of the structures. However, the original Napoly method cannot be applied to the transverse wake potentials in a structure where the two beam tubes on both sides have unequal radii . In this case, the integration path needed to be a straight line and the integration is stretched out to an infinite, in principle. We generalize the Napoly integrals so that integrals are always confined in a finite length even when the two beam tubes have unequal radii, for both longitudinal and transverse wake potential calculations. The extended method has been successfully implemented to the ABCI code.