In the context of future accelerators and, in particular, the beam vacuum of the Large Hadron Collider (LHC), a 27 km circumference proton collider to be built at CERN, VUV synchrotron radiation (SR) has been used to study both qualitatively and quantitatively candidate vacuum chamber materials. Emphasis is given to show that angle and energy resolved photoemission is an extremely powerful tool to address important issues relevant to the LHC, such as the emission of electrons that contributes to the creation of an electron cloud which may cause serious beam instabilities and unmanageable heat loads on the cryogenic system. Here we present not only the measured photoelectron yields from the proposed materials, prepared on an industrial scale, but also the energy and in some cases the angular dependence of the emitted electrons when excited with either a white light (WL) spectrum, simulating that in the arcs of the LHC, or monochromatic light in the photon energy range of interest. The effects on the materials examined of WL irradiation and /or ion sputtering, simulating the SR and ion bombardment expected in the LHC, were investigated. The studied samples exhibited significant modifications, in terms of electron emission, when exposed to the WL spectrum from the BESSY Toroidal Grating Monochromator beam line. Moreover, annealing and ion bombardment also induce substantial changes to the surface thereby indicating that such surfaces would not have a constant electron emission during machine operation. Such characteristics may be an important issue to define the surface properties of the LHC vacuum chamber material and are presented in detail for the various samples analyzed. It should be noted that all the measurements presented here were recorded at room temperature, whereas the majority of the LHC vacuum system will be maintained at temperatures below 20 K. The results cannot therefore be directly applied to these sections of the machine until measurements at cryogenic temperatures, i.e., in the presence of cryosorbed gas layers, are obtained. However, these results are directly relevant to all the warm regions of the LHC vacuum system, such as the experimental vacuum chambers and warm element vacuum chambers in the insertion regions.

The inductance of the vacuum chamber of the Proton Storage Ring at Los Alamos National Laboratory was intentionally increased by the introduction of ferrite rings to counteract the longitudinal space-charge effect of the intense beam. The magnetic permeability of the ferrite could be adjusted by introducing current into solenoids wound around the ferrite. Results show that the minimum rf voltage necessary to stabilize the beam against $e-p$ instability may be reduced over that previously measured. The injected bunch length was observed to be longer when the ferrite was heavily biased so that its effect was reduced.

In an x-ray free electron laser like the Linear Coherent Light Source being designed at SLAC, electron bunches about $70\mu \mathrm{m}$ FWHM long are sent into a beam tube only 5 mm in internal diameter and more than 100 m in length. Because of the surface roughness of the beam tube, wakefields can be generated that catch up to the bunch and interact with it, causing energy spread and emittance growth. The strength of this effect depends on the details of the roughness of the surface. We present here a study in which the roughness of the beam tube was measured and the longitudinal impedance of the tube was calculated. Our result shows that a commercially available beam tube can be made smooth enough so the resulting wakefield effects are within the tolerance determined by the requirement that the induced relative energy spread of the beam be less than $5\times {10}^{-4\mathrm{}}$.

We examine the transverse impedance of a periodic array of cavities in a beam pipe at high frequency. The calculation is an extension of a previous one for the longitudinal impedance of a periodic array of azimuthally symmetric pillboxes, for which only TM modes were needed. In the present case, we must include TE modes as well. In addition, we extend the applicability of the previous calculation by including an extra term in the coupling kernel so that the results are valid for all values of the ratio of the cavity length to the period of the structure (all values of the ratio of iris thickness to structure period). In spite of the presence of TE modes, we find that the high frequency limit of the transverse impedance is simply $\left(2/{\mathrm{ka}}^2\right)$ times the corresponding limit of the longitudinal impedance, just as it is for the resistive wall impedances, a relation which occurs frequently for azimuthally symmetric structures. Finally, we present numerical results as well as approximate expressions for the impedance per period, valid for all ratios of cavity length to structure period.

We recently created a snake depolarizing resonance using an rf solenoid magnet in a ring containing a nearly 100% Siberian snake. We found that the primary snake rf resonance also had two weaker synchrotron sidebands, which are second-order snake resonances; they were probably caused by the energy-dependent strength of the solenoid snake due to the Lorentz contraction of its longitudinal $\int Ḃ\mathrm{dl}$. This was the first observation of an rf synchrotron-sideband depolarizing resonance in the presence of a nearly full Siberian snake.

We discuss a new layout of a cavity chain (called superstructure) allowing, we hope, a significant cost reduction due to a simplification of the rf system of the TESLA linear collider. The proposed scheme increases the fill factor and thus makes an effective gradient of the accelerator higher. In this paper computations and preliminary measurements on existing copper models of the TESLA Test Facility accelerating structures are presented. A new copper model of the scheme has been ordered, made of four 7-cell standing wave cavities, which according to the results of computations and measurements seems to be the most promising version. Experiments with a beam will be necessary to prove that the proposed layout can be used for the acceleration.

Bent solenoids can transmit charged particle beams while providing momentum dispersion. While less familiar than quadrupole and dipole systems, bent solenoids can produce superficially simple transport lines and large acceptance spectrometers for use at low energies. Design issues such as drift compensation and coupling sections between straight and bent solenoids are identified, and aberrations such as shears produced by perpendicular error fields are discussed. Examples are considered which provide the basis for the design of emittance exchange elements for the cooling system of a muon collider.

Simulations of the longitudinal instability in the $50\mathrm{GeV}\times 50\mathrm{GeV}$ muon collider ring have been performed. Operation of the ring close to the slippage factor ${\eta }_1\simeq {10}^{-6\mathrm{}}$, such that synchrotron motion is frozen, minimizes the need for rf to maintain the bunch length. However, there is still an energy spread due to the bunch wake. For design parameters of the ring, this induced energy is too large and must be controlled. This paper demonstrates that the bunch wake may be compensated for by two rf cavities with low rf voltages. These studies were made at the nominal design point, and sensitivities to errors were explored. It is seen that the small energy spread of the beam ($\delta E/E=3\mathrm{}\times {10}^{-5\mathrm{}}$) in the $50\mathrm{GeV}\times 50\mathrm{GeV}$ muon collider ring can be maintained during the 1000 turn lifetime of the muons. Controlled beam dynamics requires proper choice of rf parameters (rf voltage, rf frequency, and phase offset) for two cavities; these parameters depend on the ring design through the impedance, beam pipe radius, and momentum compaction. The simulation also shows that the computation of wake field using bins of variable width (each with a constant number of macroparticles in each bin) gives an accurate wake and also yields reduced computing time compared to an evaluation of the wake as the direct sum over the wakes of all preceding macroparticles.

Beam halo formation issues are important for the design of high current linear ion accelerators. Various mechanisms can potentially cause beam halo. Some recent studies suggested that Coulomb collisions in the beam bunch can contribute significantly to beam bunch growth and halo development in linear accelerators. Despite the general belief that collisions are not important, it is clear that a rigorous treatment of this question is needed. In an effort to explore this issue in detail we have undertaken an analysis of the effects of Coulomb scattering between ions in a self-consistent spherical bunch.

The present analysis makes use of the Vlasov-Maxwell equations to develop a fully kinetic description of the electrostatic, electron-ion two-stream instability driven by the directed axial motion of a high-intensity ion beam propagating in the $z$ direction with average axial momentum ${\gamma }_b{m}_b{\beta }_{b}c$ through a stationary population of background electrons. The ion beam has characteristic radius $r_b$ and is treated as continuous in the $z$ direction, and the applied transverse focusing force on the beam ions is modeled by ${\mathbf{F}}_{\mathrm{foc}}^b=-{\gamma }_b{m}_b{\omega }_{\beta b}^{0^2}{\mathbf{x}}_{\perp }$ in the smooth-focusing approximation. Here, ${\omega }_{\beta b}^0=\mathrm{const}$ is the effective betatron frequency associated with the applied focusing field, ${\mathbf{x}}_{\perp }$ is the transverse displacement from the beam axis, $({\gamma }_b-1\mathrm{})m_b{c}^2$ is the ion kinetic energy, and $V_b={\beta }_{b}c$ is the average axial velocity, where ${\gamma }_b=(1-{\beta }_b^2{)}^{-1\mathrm{}/2}$. Furthermore, the ion motion in the beam frame is assumed to be nonrelativistic, and the electron motion in the laboratory frame is assumed to be nonrelativistic. The ion charge and number density are denoted by ${+Z}_{b}e$ and $n_b$, and the electron charge and number density by $-e$ and $n_e$. For $Z_b{n}_b>n_e$, the electrons are electrostatically confined in the transverse direction by the space-charge potential $\phi$ produced by the excess ion charge. The equilibrium and stability analysis retains the effects of finite radial geometry transverse to the beam propagation direction, including the presence of a perfectly conducting cylindrical wall located at radius ${r=r}_w$. In addition, the analysis assumes perturbations with long axial wavelength, $k_z^2{r}_b^2\ll 1$, and sufficiently high frequency that $|\omega /k_z|\gg v_{\mathrm{Tez}}$ and $|\omega /k_z{-V}_b|\gg v_{\mathrm{Tbz}}$, where $v_{\mathrm{Tez}}$ and $v_{\mathrm{Tbz}}$ are the characteristic axial thermal speeds of the background electrons and beam ions. In this regime, Landau damping (in axial velocity space $v_z$) by resonant ions and electrons is negligibly small. We introduce the ion plasma frequency squared defined by ${\hat{\omega }}_{\mathrm{pb}}^2=4\mathrm{}\pi {\hat{n}}_b{Z}_b^2{e}^2/{\gamma }_b{m}_b$, and the fractional charge neutralization defined by $f={\hat{n}}_e/Z_b{\hat{n}}_b$, where ${\hat{n}}_b$ and ${\hat{n}}_e$ are the characteristic ion and electron densities. The equilibrium and stability analysis is carried out for arbitrary normalized beam intensity ${\hat{\omega }}_{\mathrm{pb}}^2/{\omega }_{\beta b}^{0^2}$, and arbitrary fractional charge neutralization $f$, consistent with radial confinement of the beam particles. For the moderately high beam intensities envisioned in the proton linacs and storage rings for the Accelerator for Production of Tritium and the Spallation Neutron Source, the normalized beam intensity is typically ${\hat{\omega }}_{\mathrm{pb}}^2/{\omega }_{\beta b}^{0^2}\lesssim 0.1$. For heavy ion fusion applications, however, the transverse beam emittance is very small, and the space-charge-dominated beam intensity is much larger, with ${\hat{\omega }}_{\mathrm{pb}}^2/{\omega }_{\beta b}^{0^2}\lesssim 2{\gamma }_b^2$. The stability analysis shows that the instability growth rate $\mathrm{Im}\omega$ increases with increasing normalized beam intensity ${\hat{\omega }}_{\mathrm{pb}}^2/{\omega }_{\beta b}^{0^2}$ and increasing fractional charge neutralization $f$. In addition, the instability is strongest (largest growth rate) for perturbations with azimuthal mode number $\ell =1\mathrm{}$, corresponding to a simple (dipole) transverse displacement of the beam ions and the background electrons. For the case of overlapping step-function density profiles for the beam ions and background electrons, corresponding to monoenergetic ions and electrons, a key result is that there is no threshold in beam intensity ${\hat{\omega }}_{\mathrm{pb}}^2/{\omega }_{\beta b}^{0^2}$ or fractional charge neutralization $f$ for the onset of instability. Finally, for the case of continuously varying density profiles with parabolic profile shape, a semiquantitative estimate is made of the effects of the corresponding spread in (depressed) betatron frequency on stability behavior, including an estimate of the instability threshold for the case of weak density nonuniformity.

In this paper we discuss the self-stabilization of the so-called fast ion instability of an electron beam in the case when coherent oscillations of bunches can be described in the linear approximation. Such a possibility occurs due to an increase in the number of ions along the electron beam and a proportional increase in the betatron tune shifts of electrons in subsequent bunches. The tune variation along the beam results in the BNS damping of the coherent oscillations of electron bunches.

We have studied the beam dynamics in a high field separated-sector cyclotron to establish conditions required to achieve single-turn extraction. Extraction efficiency above 99% is aimed to avoid beam-induced damages. A sufficient last-turn separation and a preservation of beam quality throughout the acceleration are the prerequisites. The last-turn separation can be enhanced with the orbital precession induced by an off-centering injection as in existent lower field separated-sector cyclotrons. The beam qualities, on the other hand, are affected by the resonances traversed or approached during the acceleration. Acceleration of light nuclei to the energies of 300–400 MeV/u was especially disturbing because of the broadening of radial beamwidth upon crossing the ${\nu }_r=3\mathrm{}/2$ resonance. Tolerance to the third harmonic gradient field, which causes the resonance in lowest order, is set to be 0.1 G/cm. The integer resonance ${\nu }_z=1\mathrm{}$ can be avoided with a proper design of the yoke. The longitudinal space charge forces were also investigated to estimate the intensity limits determined by the energy spreads of beam assuming simplified charge distributions. Moreover, beam preparations for injection matching are described in view of reducing the beam losses into the extraction elements.

An essential feature of third generation storage ring based light sources is the magnetic lattice is designed with a high degree of periodicity. Tracking simulations show that if the periodicity is perturbed (by focusing errors, for example), nonlinear resonances become excited, which causes a reduction in the dynamic aperture. Therefore it is important to have a method to measure and correct perturbed periodicity. In this paper we study the effect of broken and restored periodicity at an actual third generation light source: the Advanced Light Source at Lawrence Berkeley National Laboratory. First, we show that it is possible to accurately determine the storage ring optic and thus the perturbation of the periodicity by fitting measured orbit response matrices. This method allows us to determine individual field gradient errors in quadrupoles and closed orbit errors in sextupoles. By varying individual quadrupole field strengths it is possible to correct the optic, largely restoring the lattice periodicity. A comparison is made of the performance of the storage ring before and after the optic is corrected. Measurements of the electron beam tails and the synchrotron light image reveal a large suppression in resonance excitation after the optic is corrected. Correcting the optic also improves the injection efficiency.

We study single bunch stability with respect to monopole longitudinal oscillations in electron storage rings. Our analysis is different from the standard approach based on the linearized Vlasov equation. Rather, we reduce the full nonlinear Fokker-Planck equation to a Schrödinger-like equation which is subsequently analyzed by perturbation theory. We show that the Haissinski solution [Nuovo Cimento Soc. Ital. Fis. 18B, 72 (1973)] may become unstable with respect to monopole oscillations and derive a stability criterion in terms of the ring impedance. We then discuss this criterion and apply it to a broadband resonator impedance model.

In future linear collider schemes, energy loss, as well as deterioration of the beam due to long-range wakefields, is a severe problem to be overcome. The wakefield effects in accelerator sections for these colliders are thought to be reduced either by damping, by detuning, or by a combination of both. While, in principle, damping is possible by selective coupling to dangerous higher order modes (HOMs), an alternative way is to prevent coherent excitation of these wakes by modifying a constant gradient accelerator tube in such a way that each following cell is progressively detuned in relation to the preceding ones (“detuned” or “stagger-tuned” structure). This should result in low transit time factors for the higher order modes. However, the disturbed longitudinal symmetry of the structure induces trapped modes especially in the lower dipole bands, which are again dangerous for the beam. The process of detuning suppresses the synchronous dipole modes with their extreme high loss factors, but it also produces many other HOMs with significant loss factors. Experimental results were compared with the predictions of MAFIA field calculations.

This paper deals with the evaluation of the longitudinal coupling impedance due to a charged particle traveling along the axis of an iris in a circular waveguide. The solution of the electromagnetic problem is given in terms of a dual series expansion, and some interesting developments of this technique are presented in this paper.

This work deals with the design of the Institute of Physics of the University of São Paulo (IFUSP) main racetrack microtron accelerator end magnets. This is the last stage of acceleration, comprised of an accelerating section (1.04 m) and two end magnets (0.1585 T), in which a 5.10 MeV beam, produced by a racetrack microtron booster has its energy raised up to 31.15 MeV after 28 accelerations. Poisson code was used to give the final configuration that includes auxiliary pole pieces (clamps) and auxiliary homogenizing gaps. The clamps create a reverse fringe field region and avoid the vertical defocusing and the horizontal displacement of the beam produced by extended fringe fields; Ptrace code was used to perform the trajectory calculations in the fringe field region. The auxiliary homogenizing gaps improve the field uniformity as they create a “magnetic shower” that provides uniformity of $\pm 0.3\%$, before the introduction of the correcting coils that will be attached to the pole faces. This method of correction, used in the IFUSP racetrack microtron booster magnets, enabled uniformity of $\pm 0.001\%$ in an average field of 0.1 T and will also be employed for these end magnets.

Measured angular and energetic distributions of neutrons obtained by bombarding Be, C, and U thick targets with ${}^2\mathrm{H}$ at 17, 20, and 28 MeV incident energies are reported. The data were obtained using the time-of-flight method. The energetic distributions of neutrons were determined at 0°, 5°, 10°, and 20°. The data are compared with a modelization based on stripping formalism extended for thick targets.

Beam energy loss in a cavity can be easily computed for a relativistic bunch using time-domain codes like MAFIA or ABCI. However, for nonrelativistic beams the problem is more complicated because of difficulties with its numerical formulation in the time domain. We calculate the cavity loss factors for a bunch in frequency domain as a function of its velocity and compare results with the relativistic case.

The KEK Accelerator Test Facility (KEK-ATF) was constructed to develop technologies for producing a low-emittance beam which will be required by future linear colliders. The KEK-ATF consists of an injector linac, a damping ring, and a beam extraction line. The basic optical structure of the damping ring is a FOBO lattice, which reduces the horizontal dispersion at the center of the bending magnets and, as a consequence, can produce an extremely small emittance beam. To verify the performance of such a unique, low-emittance lattice, it is crucial to measure the horizontal emittance. The horizontal emittance was measured using wire scanners in the beam extraction line. Since the horizontal beam position was not stable, we established a method to correct the measured beam size for position fluctuation (“jitter”) and we succeeded in the observation of the so far smallest horizontal emittance in any accelerator. The measured horizontal emittance was $1.37\pm 0.03\mathrm{nm}$ at a beam energy of 1.285 GeV and a bunch population of $\backslash (3–5\backslash )\times {10}^9$, in agreement with the design value of 1.27–1.34 nm at the beam energy and the bunch population.