Undulators are the most advanced sources for the generation of synchrotron radiation. The photons generated by a single electron add up coherently along the electron trajectory. In order to do so, the oscillatory motion of the electron has to be in phase with the emitted photons along the whole undulator. Small magnetic errors can cause unwanted destructive interferences. In standard permanent magnet undulators, the magnetic errors are reduced by applying shimming techniques. Superconductive undulators have higher magnetic fields than permanent magnet undulators but shimming is more complex. In this paper it is shown that coupled superconductive loops installed along the surface of the superconductive undulator coil can significantly reduce the destructive effect of the field errors. This new idea might allow the building of undulators with a superior field quality.

The beam-beam effects have been the dominating sources of beam loss and lifetime limitations in the Tevatron proton-antiproton collider [V. Shiltsev et al., Phys. Rev. ST Accel. Beams 8, 101001 (2005)]. Electron lenses were originally proposed for compensation of electromagnetic long-range and head-on beam-beam interactions of proton and antiproton beams [V. Shiltsev et al., Phys. Rev. ST Accel. Beams 2, 071001 (1999).]. Results of successful employment of two electron lenses built and installed in the Tevatron are reported by Shiltsev et al. [Phys. Rev. Lett. 99, 244801 (2007); New J. Phys. 10, 043042 (2008)] and by Zhang et al. [X.-L. Zhang et al., Phys. Rev. ST Accel. Beams 11, 051002 (2008)]. In this paper we present design features of the Tevatron electron lenses (TELs), discuss the generation of electron beams, describe different modes of operation, and outline the technical parameters of various subsystems.

The longitudinal acceptance of the Spallation Neutron Source superconducting linac is computed with a longitudinal model. A beam current monitor and beam loss monitors are utilized in a new beam acceptance measurement technique, and the measured results show close agreement with the model. Based on the simulations and on the measurements of the superconducting linac acceptance, we developed a novel method to measure beam bunch shape, beam energy profile, and the longitudinal emittance at the entrance of the linac. The experimental measurements reveal that a large longitudinal beam halo exists in the injected beam to the superconducting linac, and the longitudinal rms emittance is approximately twice that of the nominal design. The simple measurement method is applicable to other superconducting linacs.

A detailed study of hardware related tolerances for the undulator system for the European x-ray free-electron laser (XFEL) has been performed. Various realistic error scenarios were taken into account. These included girder deformation under magnetic loads, the influence of temperature variation, errors caused by limited accuracy of the motion control system, and phase matching errors. Undulator errors are classified into periodic and random errors. For periodic errors, such as girder deformation, a close and universal correlation between rms phase shake and power degradation was established, while the results of random errors show more scatter in the results, which have to be evaluated statistically. For XFEL parameters the correlation is very good and can be used to evaluate the influence of different error sources without the need to do extended FEL simulations. The method was applied to reevaluate some critical tolerances on the XFEL undulator systems: girder deformation, accuracy for gap control, and the requirement on temperature stability. The results show that these tolerances could be relaxed as compared to earlier work.

Computer simulations using the 2D code POSINST were used to study the formation of the electron cloud in the wiggler section of the positron damping ring of the International Linear Collider. In order to simulate an $x\mathrm{\text{−}}y$ slice of the wiggler (i.e., a slice perpendicular to the beam velocity), each simulation assumed a constant vertical magnetic field. At values of the magnetic field where the cyclotron frequency was an integral multiple of the bunch frequency, and where the field strength was less than approximately 0.6 T, equilibrium average electron densities were up to 3 times the density found at other neighboring field values. Effects of this resonance between the bunch and cyclotron frequency are expected to be non-negligible when the beam bunch length is much less than the product of the electron cyclotron period and the beam velocity, for a beam moving at $v\approx c$. Details of the dynamics of the resonance are described.

Many particle accelerators are proposing the use of crab cavities to correct for accelerator crossing angles or for the production of short bunches in light sources. These cavities produce a rotation to the bunch in a well-defined polarization plane. If the plane of the rotation does not align with the horizontal axis of the accelerator, the bunch will receive a small amount of spurious vertical bunch rotation. For accelerators with small vertical beam sizes and large beam-beam effects, this can cause significant unwanted effects. In this paper we propose the use of a 2nd smaller crab cavity in the vertical plane in order to cancel this effect and investigate its use in numerical simulations.

Operation with natural chromaticity in a linear nonscaling fixed field alternating gradient (FFAG) accelerator causes crossing of the low order resonances such as integer and half-integer. Although those resonances are not systematic ones, small errors, such as a typical misalignment of $10\mu \mathrm{m}$ rms, significantly increase particle amplitude when the accelerator is operated with a slow acceleration rate. For example, there is practically no dynamic aperture if it takes 1000 turns to finish the whole acceleration cycle. Chromaticity correction with sextupole and octupole reduces the maximum available dynamic aperture in a lattice without errors. On the other hand, the accelerator becomes less sensitive to errors. To use a nonscaling FFAG for applications where, unlike a muon accelerator, the large acceptance is not a high priority demand (such as a proton driver or a particle therapy accelerator), chromaticity correction seems to be an essential ingredient.

We employ the so-called “spin response formalism,” which is a linear response theory applied to the spin dynamics in circular accelerators, to analyze recent measurements of spin-flip resonance widths. The data was taken using a radial field rf dipole spin flipper to flip the spins of stored polarized proton and deuteron beams at the COSY storage ring. Numerical calculations are presented, which provide a satisfactory fit to the data.

In a two-stage compression and acceleration system, where each stage compresses a chirped bunch in a magnetic chicane, wakefields affect high-current bunches. The longitudinal wakes affect the macroscopic energy and current profiles of the compressed bunch and cause microbunching at short wavelengths. For macroscopic wavelengths, impedance formulas and tracking simulations show that the wakefields can be dominated by the resistive impedance of coherent edge radiation. For this case, we calculate the minimum initial bunch length that can be compressed without producing an upright tail in phase space and associated current spike. Formulas are also obtained for the jitter in the bunch arrival time downstream of the compressors that results from the bunch-to-bunch variation of current, energy, and chirp. Microbunching may occur at short wavelengths where the longitudinal space-charge wakes dominate or at longer wavelengths dominated by edge radiation. We model this range of wavelengths with frequency-dependent impedance before and after each stage of compression. The growth of current and energy modulations is described by analytic gain formulas that agree with simulations.

Transverse emittance growth along the Alvarez drift tube linac (DTL) section is a major concern with respect to the preservation of beam quality of high current beams at the GSI UNILAC. In order to define measures to reduce this growth, appropriate tools to simulate the beam dynamics are indispensable. This paper is about the benchmarking of three beam dynamics simulation codes, i.e. DYNAMION, PARMILA, and PARTRAN against systematic measurements of beam emittances for different transverse phase advances along the DTL. Special emphasis is put on the modeling of the initial distribution for the simulations. The concept of rms equivalence is expanded from full intensity to fractions of less than 100% of the beam. The experimental setup, data reduction, preparation of the simulations, and the evaluation of the simulations are described. In the experiments and in the simulations, a minimum of the rms-emittance growth was observed at zero current phase advances of about 60°. In general, good agreement was found between simulations and experiment for the mean values of horizontal and vertical emittances at the DTL exit.

We report experiments at Jefferson National Accelerator Facility (Jlab) and computer simulations performed at the Naval Postgraduate School (NPS) designed to probe the small Rayleigh length regime. We compare the gain, power, and sensitivity to mirror and electron beam misalignments as a function of decreasing Rayleigh length. The agreement is quite good, with experiments and simulations showing comparable trends as the Rayleigh length is decreased. In particular, we find that the gain and power decrease substantially at short Rayleigh length, contrary to a common Gaussian-mode filling factor argument. Within currently achievable alignment tolerances, the gain and power are still acceptable for FEL operation.

A system for inspecting the inner surface of superconducting rf cavities is developed in order to study the relation between the achievable field gradient and the defects in the inner surface. The inspection system consists of a high resolution complementary metal-oxide-semiconductor camera and a special illumination system built in a cylinder that has a diameter of 50 mm. The camera cylinder can be inserted into the L-band 9 cell superconducting cavity. The system provides a resolution of about $7.5\mu \mathrm{m}/\mathrm{pixel}$. Thus far, there have been good correlations between locations identified by thermometry measurements and positions of defects found by this system. The heights or depths of the defects can also be estimated by measuring wall gradients using the reflection angle relation between the camera position and the strip illumination position. This paper presents a detailed description of the system and the data obtained from it.

In this paper we present a method for measuring the nonlinear errors in a circular accelerator by taking advantage of the feed-down effect of high order multipoles when the closed orbit is globally deformed. We devise a nonlinear tune response matrix in which the response to a closed orbit deformation is obtained in terms of change of machine tune and correlated with the strength of the local multipoles. A numerical example and a proof of principle experiment to validate the theoretical methods are presented and discussed.

We describe a dedicated electron cloud experiment which was installed in the CERN Proton Synchrotron in 2007. The setup comprises shielded button-type pickups, a fast vacuum logging, a dipole magnet, and a stripline electrode to experimentally verify the beneficial effect of electron cloud clearing. The electron cloud effect was observed within the last milliseconds before ejection of the nominal LHC proton beam consisting of 72 bunches with 25 ns spacing. Measurements of electron flux at the wall and vacuum pressure are presented for a set of magnetic fields and bias voltages on the clearing electrode, showing that efficient electron cloud suppression can be obtained for appropriate clearing voltages but revealing an unexpectedly complex dependence on magnetic field and voltage.

This paper proposes a new design of spin flipper for high-energy accelerators to obtain full spin flip with the spin tune staying at half integer. The traditional technique of using a single rf spin rotator with a fixed spin rotation axis and an oscillating spin rotation, either an rf dipole or solenoid, as spin flipper to achieve full spin flip in the presence of a full Siberian snake has been demonstrated [B. B. Blinov et al., Phys. Rev. Lett. 81, 2906 (1998); B. B. Blinov et al., Phys. Rev. Lett. 88, 014801 (2001); V. S. Morozov et al., Phys. Rev. ST Accel. Beams 7, 024002 (2004); R. A. Phelps, AIP Conf. Proc. 338, 361 (1994); Ya. S. Derbenev et al., Part. Accel. 8, 115 (1978)]. However, this technique requires one to change the snake configuration to move the spin tune away from half integer which is not practical for an operational high-energy polarized proton collider such as RHIC where beam and polarization lifetime are sensitive to small changes. Based on the conceptual designs to use rf dipoles to achieve full spin flip with the spin tune at half integer [T. Roser, BNL Report No. BNL-52453, 1994; R. A. Phelps, BNL Report No. BNL-52453, 1994], this paper presents a compact design of a spin flipper for a high-energy accelerator. The theory of the new spin flipper technique and numerical simulations are also presented.