An autoresonance electron acceleration phenomenon in the combined steady-state inhomogeneous magnetic and microwave fields is analytically studied. Equations describing the evolution of the phase shift between the particle velocity and the microwave electric field, total energy, and longitudinal velocity of the electron are obtained. Linear and parabolic profiles of the magnetic field are examined. It is shown that the proper choice of the magnetic heterogeneity degree, the microwave electric field value, and initial electron velocity can retain the electron in the acceleration phase band. The results obtained in this work show a complete agreement with our previous autoresonance results obtained through simulations of the relativistic Newton-Lorentz equation.

Coherent transition radiation (CTR) in the THz regime is an important diagnostic tool for analyzing the temporal structure of the ultrashort electron bunches needed in ultraviolet and x-ray free-electron lasers. It is also a powerful source of such radiation, covering an exceptionally broad frequency range from about 200 GHz to 100 THz. At the soft x-ray free-electron laser FLASH we have installed a beam transport channel for transition radiation (TR) with the intention to guide a large fraction of the radiation to a laboratory outside the accelerator tunnel. The radiation is produced on a screen inside the ultrahigh vacuum beam pipe of the linac, coupled out through a diamond window and transported to the laboratory through an evacuated tube equipped with five focusing and four plane mirrors. The design of the beamline has been based on a thorough analysis of the generation of TR on metallic screens of limited size. The optical propagation of the radiation has been computed taking into account the effects of near-field (Fresnel) diffraction. The theoretical description of the TR source is presented in the first part of the paper, while the design principles and the technical layout of the beamline are described in the second part. First experimental results demonstrate that the CTR beamline covers the specified frequency range and preserves the narrow time structure of CTR pulses emitted by short electron bunches.

The rf accelerating structures of the Compact Linear Collider (CLIC) require a material capable of sustaining high electric field with a low breakdown rate and low induced damage. Because of the similarity of many aspects of dc and rf breakdown, a dc breakdown study is underway at CERN in order to test candidate materials and surface preparations, and have a better understanding of the breakdown mechanism under ultrahigh vacuum in a simple setup. Conditioning speeds and breakdown fields of several metals and alloys have been measured. The average breakdown field after conditioning ranges from $100\mathrm{MV}/\mathrm{m}$ for Al to $850\mathrm{MV}/\mathrm{m}$ for stainless steel, and is around $170\mathrm{MV}/\mathrm{m}$ for Cu which is the present base-line material for CLIC structures. The results indicate clearly that the breakdown field is limited by the cathode. The presence of a thin cuprous oxide film at the surface of copper electrodes significantly increases the breakdown field. On the other hand, the conditioning speed of Mo is improved by removing oxides at the surface with a vacuum heat treatment, typically at $875°\mathrm{C}$ for 2 hours. Surface finishing treatments of Cu samples only affect the very first breakdowns. More generally, surface treatments have an effect on the conditioning process itself, but not on the average breakdown field reached after the conditioning phase. In analogy to rf, the breakdown probability has been measured in dc with Cu and Mo electrodes. The dc data show similar behavior as rf as a function of the applied electric field.

We report the results of theoretical and experimental studies on passive spatiotemporal shaping of cw mode-locked picosecond laser pulses for driving the photocathode of a high-brightness, high-current energy recovery linear accelerator. The temporal pulse shape is modified using birefringent crystals, while a refractive optical system is used to generate a flattop spatial beam profile. An optical transport system is designed and implemented to deliver the flattop pulse onto a photocathode sited 9 m away from the shapers. The alignment tolerances on the beam shaper and the temporal pulse stacker have been studied both theoretically and experimentally. The experimental results agree well with theoretical simulations.

Coherent Smith-Purcell (SP) radiation originating from three different gratings has been measured at End Station A, SLAC, and has been used to reconstruct the time profile of the electron bunches. The beam energy during these experiments was 28.5 GeV ($\gamma \cong 55773$) and the number of electrons in the bunch was $0.9–1.4\times {10}^{10}$. The spectral distribution of the radiated energy was measured by means of an array of 11 pyroelectric detectors. Typical values of the FWHM of the bunch length are about 2.5 ps, but sharper peaks with FWHM less than 2.0 ps have also been observed. The longitudinal profile also varies with accelerator conditions and can best be approximated by a superposition of 3–4 Gaussian curves. Some typical profiles are presented, together with a discussion of the limitations and strengths of coherent SP radiation as a diagnostic tool. It is concluded that SP radiation offers excellent prospects in this respect, not only in the picosecond range, but potentially in the femtosecond range as well.

In order to reach the high peak current required for an x-ray free electron laser, two separate magnetic dipole chicanes are used in the Linac Coherent Light Source accelerator to compress the electron bunch length in stages. In these bunch compressors, coherent synchrotron radiation (CSR) can be emitted either by a short electron bunch or by any longitudinal density modulation that may be on the bunch. In this paper, we report detailed measurements of the CSR-induced energy loss and transverse emittance growth in these compressors. Good agreement is found between the experimental results and multiparticle tracking studies. We also describe direct observations of CSR at optical wavelengths and compare with analytical models based on beam microbunching.

Precise measurements of the temporal profile of ultrashort electron bunches are of high interest for the optimization and operation of ultraviolet and x-ray free-electron lasers. The electro-optic (EO) technique has been applied for a single-shot direct visualization of the time profile of individual electron bunches at FLASH. This paper presents a thorough description of the experimental setup and the results. An absolute calibration of the EO technique has been performed utilizing simultaneous measurements with a transverse-deflecting radio-frequency structure that transforms the longitudinal bunch charge distribution into a transverse streak. EO signals as short as 60 fs (rms) have been observed using a gallium-phosphide (GaP) crystal, which is a new record in the EO detection of single electron bunches and close to the physical limit imposed by the EO material properties. The data are in quantitative agreement with a numerical simulation of the EO detection process.

The beam-beam interaction is one of the dominant sources of emittance growth and luminosity lifetime deterioration. A current-carrying wire has been proposed to compensate long-range beam-beam effects in the LHC and strong localized long-range beam-beam effects are experimentally investigated in the RHIC collider. Tune shift, beam transfer function, and beam loss rate are measured in dedicated experiments. In this paper, we report on simulations to study the effect of beam-wire interactions based on diffusive apertures, beam loss rates, and beam transfer function using a parallelized weak-strong beam simulation code (bbsimc). The simulation results are compared with measurements performed in RHIC during 2007 and 2008.

Neutrino factory and muon collider cooling lattices require both high gradient rf cavities and strong focusing solenoids. Experiments have shown that there may be serious problems operating rf in the required magnetic fields. Experimental observations using vacuum rf cavities in magnetic fields are discussed, current published models of breakdown with and without magnetic fields are briefly summarized, and some of their predictions compared with observations. A new theory of magnetic field dependent breakdown is presented. It is proposed that electrons emitted by field emission on asperities on one side of a cavity are focused by the magnetic field to the other side where they induce mechanical fatigue leading to cavity surface damage in small spots. Metal is then electrostatically drawn from the molten spots, becomes vaporized and ionized by field emission from the remaining damage, and causes breakdown. The theory is fitted to existing 805 MHz data and predictions are made for performance at 201 MHz. The model predicts breakdown gradients significantly below those specified for either the International Scoping Study neutrino factory or a muon collider. Possible solutions to these problems are discussed, including designs for magnetically insulated rf in which the cavity walls are designed to be parallel to chosen magnetic field contour lines and consequently damage from field emission is expected to be suppressed. An experimental program that could study these problems and their possible solution is outlined. We also mention the use of high pressure gas as an alternative possible solution.

A ceramic chamber with Cu stripes is usually used as the vacuum chamber in a rapid cycling synchrotron. The Cu stripes terminate at either end as capacitors, and provide the low impedance for the circulating beam, and the high impedance for the induced current with the frequency components of the external time-dependent magnetic field (for example, injection bump magnets, bending magnets, etc.). It is important to be able to precisely estimate the field modulations inside the chamber when the field is excited, because any such field modulations can cause the beam characteristics to deteriorate. In this paper a theoretical approach to evaluate the field modulations in a quick and precise manner is developed.

We demonstrate that a wide variety of current-pulse shapes can be generated using a linear-transformer-driver (LTD) module that drives an internal water-insulated transmission line. The shapes are produced by varying the timing and initial charge voltage of each of the module’s cavities. The LTD-driven accelerator architecture outlined in [Phys. Rev. ST Accel. Beams 10, 030401 (2007)] provides additional pulse-shaping flexibility by allowing the modules that drive the accelerator to be triggered at different times. The module output pulses would be combined and symmetrized by water-insulated radial-transmission-line impedance transformers [Phys. Rev. ST Accel. Beams 11, 030401 (2008)].

Beam injection and extraction in the delay loop of the CLIC Test Facility 3 (CTF3) for recombination of adjacent bunch trains, is performed by a specially designed rf deflector. A standing wave structure has been chosen for this purpose. Three possible solutions have been investigated, and a comparative analysis is presented. All of them satisfy the essential requirements of the system up to the maximum foreseen energy with the existing klystron. The final design of the rf deflector consists of two identical cavities connected to the rf power source through a hybrid junction that equally splits the power and isolates the klystron from reflections. The rf deflector design, the results of electromagnetic simulations, and the low level rf measurements are illustrated. The impact of beam loading in the rf deflectors on the transverse beam dynamics is also analyzed. The general expression of the single passage transverse wakefield is obtained and a dedicated tracking code has been written to study the multibunch multiturn effects. A complete analysis for different machine parameters and injection errors is presented and discussed. These numerical simulations indicate a tolerable beam emittance growth due to the transverse wakefield in the rf deflectors.

It is desirable to optimize (minimizing both the inductance and electron flow) the magnetically insulated vacuum sections of low impedance pulsed-power drivers. The goal of low inductance is understandable from basic efficiency arguments. The goal of low electron flow results from two observations: (1) flowing electrons generally do not deliver energy to (or even reach) most loads, and thus constitute a loss mechanism; (2) energetic electrons deposited in a small area can cause anode damage and anode plasma formation. Low inductance and low electron flow are competing goals; an optimized system requires a balance of the two. While magnetically insulated systems are generally forgiving, there are times when optimization is crucial. For example, in large pulsed-power drivers used to energize high energy density physics loads, the electron flow as a fraction of total current is small, but that flow often reaches the anode in relatively small regions. If the anode temperature becomes high enough to desorb gas, the resulting plasma initiates a gap closure process that can impact system performance. Magnetic-pressure driven ($z$ pinches and material equation of state) loads behave like a fixed inductor for much of the drive pulse. It is clear that neither fixed gap nor constant-impedance transmission lines are optimal for driving inductive loads. This work shows a technique for developing the optimal impedance profile for the magnetically insulated section of a high-current driver. Particle-in-cell calculations are used to validate the impedance profiles developed in a radial disk magnetically insulated transmission line geometry. The input parameters are the spacing and location of the minimum gap, the effective load inductance, and the desired electron flow profile. The radial electron flow profiles from these simulations are in good agreement with theoretical predictions when driven at relatively high voltage (i.e., $V\ge 2\mathrm{MV}$).

An x-ray free-electron laser oscillator proposed recently for hard x rays [K. Kim, Y. Shvyd’ko, and S. Reiche, Phys. Rev. Lett. 100, 244802 (2008)] can be made tunable by using an x-ray cavity composed of four crystals, instead of two. The tunability of x-ray energy will significantly enhance the usefulness of an x-ray free-electron laser oscillator. We present a detailed analysis of the four-crystal optical cavity and choice of crystals for several applications: inelastic x-ray scattering, nuclear resonant scattering, bulk-sensitive hard x-ray photoemission spectroscopy, other high-energy-resolution ($\lesssim 1\mathrm{meV}$) spectroscopic probes, and for imaging with hard x rays at near-atomic resolution ($\simeq 1\mathrm{nm}$).

In this paper, we systematically study the echo-enabled harmonic generation (EEHG) free electron laser (FEL). The EEHG FEL uses two modulators in combination with two dispersion sections that allow one to generate in the beam a high harmonic density modulation starting with a relatively small initial energy modulation of the beam. After presenting an analytical theory of the phenomenon, we address several practically important issues, such as the effect of incoherent synchrotron radiation in the dispersion sections, and the beam transverse size effect in the modulator. Using a representative realistic set of beam parameters, we show how the EEHG scheme enhances the FEL performance and allows one to generate a fully (both longitudinally and transversely) coherent radiation. As an example, we demonstrate that 5 nm coherent soft x rays with GW peak power can be generated directly from the 240 nm seeding laser using the proposed EEHG scheme.

By analyzing the pulse to pulse intensity fluctuations of the radiation emitted by a charge particle in the incoherent part of the spectrum, it is possible to extract information about the spatial distribution of the beam. At the Advanced Light Source of the Lawrence Berkeley National Laboratory, we have developed and successfully tested a simple scheme based on this principle that allows for the absolute measurement of the rms bunch length. A description of the method and the experimental results are presented.

Coherent radiation emitted from a compressed electron bunch as it traverses the sharp edge regions of a magnetic chicane has been investigated at the Brookhaven National Laboratory Accelerator Test Facility. Electron beam measurements using coherent transition radiation interferometry indicate a 100 fs rms bunch accompanied by distinct distortions in energy spectrum due to strong self-fields. These self-fields are manifested in emitted high power THz radiation, which displays signatures of the phenomenon known as coherent edge radiation. Radiation characterization studies undertaken include spectral analysis, far-field intensity distribution, polarization, and dependence on the electron bunch length. The observed aspects of the beam and radiation allow detailed comparisons with start-to-end simulations.

Transverse beam stability is strongly affected by the beam space charge. Usually it is analyzed with the rigid-beam model. However, this model is only valid when a bare (not affected by the space charge) tune spread is small compared to the space charge tune shift. This condition specifies a relatively small area of parameters which, however, is the most interesting for practical applications. The Landau damping rate and the beam Schottky spectra are computed assuming that validity condition is satisfied. The results are applied to a round Gaussian beam. The stability thresholds are described by simple fits for the cases of chromatic and octupole tune spreads.