Linear coupling’s action-angle parametrization is convenient for interpretation of turn-by-turn beam position monitor (BPM) data. We demonstrate how to apply this parametrization to extract Twiss and coupling parameters in interaction regions (IRs), using BPMs on each side of a long IR drift region. Example data were acquired at the Relativistic Heavy Ion Collider, using an ac dipole to excite a single transverse eigenmode. We have measured the waist of the $\beta$ function and its Twiss and coupling parameters.

The effect of a higher-order mode upon longitudinal beam stability in an electron storage ring is modeled analytically and with simulations. Narrow band parasitic modes and broadband impedance are considered for the Aladdin and MAX-II electron storage rings. The simulations confirm that a passive harmonic cavity strongly suppresses parasitic coupled-bunch instabilities, in agreement with the analytic model. In the long-bunch regime where the bunch length exceeds the vacuum pipe radius, analytic modeling and simulations indicate that a harmonic cavity also suppresses the microwave instability. In the short-bunch regime where the bunch length is smaller than the vacuum pipe radius, analytic modeling and simulations indicate that tuning in a harmonic cavity may worsen the microwave instability.

Contrary to the claim of the recent publication by Barber, Ellison, and Heinemann [Phys. Rev. ST Accel. Beams 7, 124002 (2004).], we explain in this Comment that (1) the snake resonances are spin depolarizing resonances just like other spin depolarizing resonances and (2) the perturbed spin tune is useful to understand depolarization phenomena.

We reply to Lee and Mane’s foregoing Comment [Phys. Rev. ST Accel. Beams 8, 089001 (2005)]. In particular, we discuss how an adherence to certain notions of spin-orbit resonance and spin tune can limit the analysis and understanding of phenomena. Since the Comment has very little to do with the main thrust of our paper we take the opportunity to point out the main features of the “proper uniform precession rate,” a concept introduced in our paper and based on the concept of quasiperiodicity. We also respond to other material in the Comment.

The multipass, multibunch beam breakup (BBU) instability imposes a potentially severe limitation to the average current that can be accelerated in an energy-recovery linac. Simulation results for Jefferson Lab’s free electron laser (FEL) upgrade driver are presented which predict the occurrence of BBU below the nominal operating current of the machine. In agreement with simulation, BBU was observed and preliminary measurements to identify the higher-order mode causing the instability are shown. In addition, measurements performed to experimentally determine the threshold current are described. Using a newly developed two-dimensional BBU simulation code, we study the effect of optical suppression techniques, first proposed in 1980 [R. E. Rand and T. I. Smith, Part. Accel. 11, 1 (1980)], on the threshold current of the FEL. Specifically we consider the effect of (1) reflecting the betatron planes about an axis that is at 45° between the vertical and horizontal axes and (2) rotating the betatron planes by 90°. In two-pass recirculators, a 90° rotation can be effective at increasing the threshold current for BBU. The successful installation of a five skew-quadrupole reflector in the backleg of the FEL has been shown to be effective at suppressing the instability and comments on preliminary operational experience will be given.

The Beijing Electron-Positron Collider (BEPC) will be upgraded to BEPCII, and the luminosity will be about 100 times higher. We developed a three-dimensional strong-strong PIC code to study the beam-beam effects in BEPCII. The transportation through the arc is the same as that in Hirata’s weak-strong code. The beam-beam force is computed directly by solving the Poisson equation using the Fourier analysis and cyclic reduction method, and the boundary potential is computed by circular convolution. The finite bunch length effect is included by longitudinal slices. An interpolation scheme is used to reduce the required slice number in simulations. The standard message passing interface is used to parallelize the code. The computing time increases linearly with $(n+1)$, where $n$ is the slice number. The calculated luminosity of BEPCII at the design working point is $\sim 50\%$ of the design value. The best area in the tune space is near (0.505,0.57) according to the survey, where the luminosity is $\sim 80\%$ of the design.

For many damped-accelerating cavities for high-intensity beams, classifications of eigenmodes according to azimuthal indices are generally insufficient due to a lack of their axial symmetry. To classify the eigenmodes in such cavities having general symmetry, the application of group theory is studied. By taking basis functions from a complete set of eigenmodes, one can form a representation of the symmetry group of the cavity. The eigenmodes can then be classified according to irreducible representations of the symmetry group. This method is particularly useful for classifying the eigenmodes in complicated cavities, and for understanding the effects of perturbations on the eigenmodes.

A detailed analytical study of plasma wakefield generation in a wide parabolic plasma channel is reported. A perturbative technique involving orders of the incident laser beam and the effects of inhomogeneity of the plasma density is used to obtain explicit electric as well as magnetic wakefields. The axial and transverse forces acting on a test electron due to the wakefields have been evaluated.

A Bragg waveguide consisting of multiple dielectric layers with alternating index of refraction becomes an excellent option to form electron accelerating structure powered by high power laser sources. It provides confinement of a synchronous speed-of-light mode with extremely low loss. However, laser field cannot be coupled into the structure collinearly with the electron beam. There are three requirements in designing input coupler for a Bragg electron accelerator: side coupling, selective mode excitation, and high coupling efficiency. We present a side-coupling scheme using a distributed grating-assisted coupler to inject the laser power into the waveguide. Side coupling is achieved by a grating with a period on the order of an optical wavelength. The phase matching condition results in resonance coupling thus providing selective mode excitation capability. The coupling efficiency is limited by profile matching between the outgoing beam and the incoming beam, which has normally a Gaussian profile. We demonstrate a nonuniform distributed grating structure generating an outgoing beam with a Gaussian profile, therefore, increasing the coupling efficiency.

Advanced high-brightness beam applications such as inverse-Compton scattering (ICS) depend on achieving of ultrasmall spot sizes in high current beams. Modern injectors and compressors enable the production of high-brightness beams having needed short bunch lengths and small emittances. Along with these beam properties comes the need to produce tighter foci, using stronger, shorter focal length optics. An approach to creating such strong focusing systems using high-field, small-bore permanent-magnet quadrupoles (PMQs) is reported here. A final-focus system employing three PMQs, each composed of 16 neodymium iron boride sectors in a Halbach geometry has been installed in the PLEIADES ICS experiment. The field gradient in these PMQs is $560\mathrm{T}/\mathrm{m}$, the highest ever reported in a magnetic optics system. As the magnets are of a fixed field strength, the focusing system is tuned by adjusting the position of the three magnets along the beam line axis, in analogy to familiar camera optics. This paper discusses the details of the focusing system, simulation, design, fabrication, and experimental procedure in creating ultrasmall beams at PLEIADES.

We describe a fast and robust global decoupling scheme, coupling angle modulation. This novel technique introduces an extra rotating coupling coefficient into the coupled optics to determine the global decoupling strengths. The eigentune split is used as the observable during the modulation. The two eigentunes are tracked with a high-resolution phase locked loop tune measurement system. In the article, the principle of coupling angle modulation is presented, followed by its application to the Relativistic Heavy Ion Collider (RHIC). Coupling angle modulation coupling correction has been used for the global coupling correction on the nonstop RHIC ramp.

We present detailed simulations and analysis of Zholents’s [A. Zholents, P. Heimann, M. Zolotorev, and J. Byrd, Nucl. Instrum. Methods Phys. Res., Sect. A 425, 385 (1999).] concept for using deflecting cavities in a synchrotron light source storage ring for the purpose of producing short x-ray pulses. In particular, we look at the optimization and performance of such a system for the Advanced Photon Source. We find the concept is practical and that x-ray pulse durations of about 1.5 ps FWHM should be achievable with more than 15% of the original intensity retained. Issues covered include lattice design, emittance degradation, lifetime, photon beam modeling, errors, and optimum choice of rf parameters.

The linear accelerator based on a superconducting structure with a high accelerating gradient accordingly has a strong rf defocusing factor. Usually, a quadrupole or solenoid focusing system is used in such accelerators. Both of these systems complicate the linear accelerator. The quadrupoles are located outside the cavity and a transition between the cold and the warm systems is required. Therefore an additional drift space between cryostats is needed, which can cause parametric resonance in the longitudinal plane in the energy range of $(3–20)\mathrm{MeV}$. In the system with the solenoid the high magnetic field can affect the superconductivity. We consider the novel superconducting H resonator based on the TE211 mode with a slot and rf finger, providing the high-intensity beam focusing in the large range of low energy of $(3–50)\mathrm{MeV}$. Above 50 MeV we suggest using the slot structure with the external quadrupoles.

Smith-Purcell radiation (SPR), generated by an electron beam traveling above a grating, is characterized by a broad range of frequencies. The radiated wavelength depends on the angle of observation according to the SPR resonance relationship and the bandwidth is inversely proportional to the number of the grating grooves. A rigorous theoretical model of SPR from a three-dimensional bunch of relativistic electrons passing above a grating of finite length is presented by an electric-field integral equation method. The finite-length grating results are compared with the case of an infinitely long grating assumption in which periodic boundary conditions are rigorously applied and with a model based on the image-charge approximation. The SPR resonance relationship is the same in all three formalisms. Significant errors in the strength of the radiated energy are introduced by the two approximations. In particular, for gratings with less than $\sim 20$ periods, the image-charge approximation and the infinitely long grating assumption result in an order of magnitude too high and too low radiated energy per groove, respectively, in the plane transverse to the grating groove lines. Numerical examples are calculated for an $\sim 18\mathrm{MeV}$ bunch traveling above different finite-length gratings with a period of 2.5 mm.

We have measured the effects of high (0–4.5 T) magnetic fields on the operating conditions of 805 MHz accelerating cavities, and discovered that the maximum accelerating gradient drops as a function of the axial magnetic field. While the maximum gradient of any cavity is governed by a number of factors including conditioning, surface topology and materials, we argue that $\mathbf{J}\times \mathbf{B}$ forces within the emitters are the mechanism for enhanced breakdown in magnetic fields. The pattern of emitters changes over time and we show an example of a bright emitter which disappears during a breakdown event. We also present unique measurements of the distribution of enhancement factors, $\beta$, of secondary emitters produced in breakdown events during conditioning. We believe these secondary emitters can also be breakdown triggers, and the secondary emitter spectrum helps to determine the maximum operating field.

The validity of the Gaussian approximation of the distribution function in the study of the equilibrium bunch length in electron storage rings is considered with specific reference to the inductive wake. The Gaussian approximation can be used to describe not only localized wakes, but also uniformly distributed wakes, for which the longitudinal profiles at equilibrium are ruled by the potential-well-distortion (Haissinski) equation. Comparison of Gaussian approximation based results with those obtained from Haissinski equation shows good qualitative agreement in their common range of validity, while shedding light on the nature of the unstable regimes.

Small-angle multiple intrabeam scattering (IBS) emittance growth rates are normally expressed through integrals, which require a numeric evaluation at various locations of the accelerator lattice. In this paper, I demonstrate that the IBS growth rates can be presented in closed-form expressions with the help of the so-called symmetric elliptic integral. This integral can be evaluated numerically by a very efficient recursive method by employing the duplication theorem. Several examples of IBS rates for a smooth-lattice approximation, equal transverse temperatures and plasma temperature relaxation are given.

A sheet-beam traveling-wave amplifier has been proposed as a high-power generator of rf from 95 to 300 GHz, using a microfabricated rf slow-wave structure [Carlsten et al., IEEE Trans. Plasma Sci. 33, 85 (2005)], for emerging radar and communications applications. The planar geometry of microfabrication technologies matches well with the nearly planar geometry of a sheet beam, and the greater allowable beam current leads to high-peak power, high-average power, and wide bandwidths. Simulations of nominal designs using a vane-loaded waveguide as the slow-wave structure have indicated gains in excess of $1\mathrm{dB}/\mathrm{mm}$, with extraction efficiencies greater than 20% at 95 GHz with a 120-kV, 20-A electron beam. We have identified stable sheet-beam formation and transport as the key enabling technology for this type of device. In this paper, we describe sheet-beam transport, for both wiggler and periodic permanent magnet (PPM) magnetic field configurations, with natural (or single-plane) focusing. For emittance-dominated transport, the transverse equation of motion reduces to a Mathieu equation, and to a modified Mathieu equation for a space-charge dominated beam. The space-charge dominated beam has less beam envelope ripple than an emittance-dominated beam, but they have similar stability thresholds (defined by where the beam ripple continues to grow without bound along the transport line), consistent with the threshold predicted by the Mathieu equation. Design limits are derived for an emittance-dominated beam based on the Mathieu stability threshold. The increased beam envelope ripple for emittance-dominated transport may impact these design limits, for some transport requirements. The stability of transport in a wiggler field is additionally compromised by the beam’s increased transverse motion. Stable sheet-beam transport with natural focusing is shown to be achievable for a 120-kV, 20-A, elliptical beam with a cross section of 1 cm by 0.5 mm, with both a PPM and a wiggler field, with magnetic field amplitude of about 2.5 kG.

Two-plane focusing of sheet electron beams will be an essential technology for an emerging class of high-power, 100 to 300 GHz rf sources [Carlsten et al., IEEE Trans. Plasma Sci. 33, 85 (2005)]. In these devices, the beam has a unique asymmetry in which the transport is emittance dominated in the sheet’s thin dimension and space-charge dominated in the sheet’s wide dimension. Previous work has studied the stability of the transport of beams in the emittance-dominated regime for both wiggler and periodic permanent magnet (PPM) configurations with single-plane focusing, and has found that bigger envelope scalloping occurs for equilibrium transport, as compared to space-charge dominated beams [Carlsten et al., this issue, Phys. Rev. ST Accel. Beams 8, 062001 (2005)]. In this paper, we describe the differences in transport stability when two-plane focusing is included. Two-plane wiggler focusing degrades the transport stability slightly, whereas two-plane PPM focusing greatly compromises the transport. On the other hand, single-plane PPM focusing can be augmented with external quadrupole fields to provide weak focusing in the sheet’s wide dimension, which has stability comparable to two-plane wiggler transport.

High-current ${\mathrm{Cu}}^{+}$ ion beams were extracted from a laser-produced plasma using a pulsed high-voltage multiaperture diode driven by an induction cavity. The amplitude and the duration of the extraction voltage were 130 kV and 450 ns, respectively. During the extraction, explosive beam divergence due to the strong space-charge force was suppressed by the focusing action of the gap between concentric hemispheres. Modulation of the extracted beam flux due to the plasma prefill in the gap has been eliminated by using a biased control grid put on the anode holes. By means of this extraction scheme we obtained a rectangular beam pulse with a rise time as short as $\approx 100\mathrm{ns}$. The beam current behind the cathode was limited to $\approx 0.1\mathrm{A}$, owing to space-charge effects, as well as to poor geometrical transmission through the cathode sphere. From the measurement of the extracted beam current density distribution along the beam axis and the beam profile measurement, we found a beam waist slightly downstream of the spherical center of the diode structure. The measured beam behavior was consistent with numerical results obtained via a 3D particle code. No serious degradation of the beam emittance was observed for the grid-controlled extraction scheme.