We applied frequency map analysis (FMA)—a method that is widely used to explore dynamics of Hamiltonian systems—to study beam-beam effects in a novel crab waist collision approach. The “crab” focusing of colliding beams results in significant suppression of betatron coupling resonances induced by beam-beam interaction. Application of FMA provides visible information about all working resonances, their widths, and locations in the planes of betatron tunes and betatron amplitudes, so the process of resonances suppression due to the beams crabbing is clearly seen. However, our numerical simulations and further analysis showed that effectiveness of crab waist is considerably restricted in the cases when the colliding beams are not flat. The FMA technique turned out to be very helpful in these studies, as it gave us the key information which would be difficult to obtain in a different way.

It was predicted that, when a fast electron beam with some angular spread is normally incident on a resistivity gradient, magnetic field generation can occur that can inhibit beam propagation [A. R. Bell et al., Phys. Rev. E 58, 2471 (1998)]. This effect can have consequences on the laser-driven ion acceleration. In the experiment reported here, we compare ion emission from laser irradiated coated and uncoated metal foils and we show that the ion beam from the coated target has a much smaller angular spread. Detailed hybrid numerical simulations confirm that the inhibition of fast electron transport through the resistivity gradient may explain the observed effect.

A neutrino factory, which can deliver an intense flux of $\sim {10}^{21}$ neutrinos per year from a multi-GeV stored muon beam, is seemingly the ideal tool for studying neutrino oscillations and $CP$ violations for leptons. The front end of this facility plays a critical role in determining the number of muons that can be accepted by the downstream accelerators. Delivering peak performance requires transporting the muon beams through long sections of a beam channel containing high-gradient rf cavities and strong focusing solenoids. Here, we propose a novel scheme to improve the performance of the cavities, thereby increasing the number of muons within the acceptance of the accelerator chain. The key element of our new scheme is to apply a tangential magnetic field to the rf surfaces, thus forcing any field-emitted electrons to return to the surface before gaining enough energy to damage the cavity. We incorporate this idea into a new lattice design for a neutrino factory, and detail its performance numerically. Although our proposed front-end channel requires more rf power than conventional pillbox designs, it provides enough beam cooling and muon production to be a feasible option for a neutrino factory.

In this paper we introduce, for the first time, an analytical solution (up to the third order) for a multistage bunch compression and acceleration system without collective effects. The solution for the system with collective effects is found by an iterative procedure based on this analytical result. The developed formalism is applied to the two-stage Free Electron Laser in Hamburg (FLASH) and to the three-stage European XFEL. Analytical estimations of rf tolerances are given and a simple formula for the optimal compression factor in the first bunch compressor is derived.

Recent work has shown the possibility of generating self-shaped ellipsoidal beams with properties commensurate with the requirements of future light sources such as free-electron lasers and inverse Compton sources. In this so-termed “blowout” regime, short laser bunches are transformed via photoemission into short electron bunches which then self-consistently evolve into nearly uniform-density ellipsoids under space-charge forces. We report here on the first blowout studies conducted in collaboration between the UCLA Particle Beam Physics Lab and the Photo Injector Test Facility, Zeuthen (PITZ). The measurements conducted at the PITZ photoinjector facility examine the evolution of 750 pC, 2.7 ps FWHM electron bunches born in an L-band photoinjector and subsequently accelerated through a nine-cell L-band booster for a resulting energy of 12 MeV. These measurements represent the first observations of self-shaped ellipsoid evolution under postinjector acceleration, a key step in demonstrating the utility of such self-shaped beams at higher energy, where the advantages in both transverse and longitudinal and transverse phase space may be exploited in creating very high brightness beams.

Based on the parabolic equation approach to Maxwell’s equations, we have derived scaling properties of impedance that apply either to (1) structures of general shape at high frequencies, or (2) small angle transitions at all frequencies. Applying these scaling properties to impedance/wakefield calculation of long, small angle, beam pipe transitions, like one often finds in insertion regions of storage rings, one can greatly reduce the computer resource required. We have tested the scaling with wakefield simulations of 2D and 3D models of such transitions, and have found that it appears to work well.

Acceleration gradient is a critical parameter for the design of future TeV-scale linear colliders. The major obstacle to higher gradient in room-temperature accelerators is rf breakdown, which is still a very mysterious phenomenon that depends on the geometry and material of the accelerator as well as the input power and operating frequency. Pulsed heating has been associated with breakdown for many years; however, there have been no experiments that clearly separate field and heating effects on the breakdown rate. Recently, such experiments have been performed at SLAC with both standing-wave and traveling-wave structures. These experiments have demonstrated that pulsed heating is limiting the gradient. Nevertheless the $X$-band structures breakdown studies show damage to the iris surfaces in locations of high electric field rather than of high magnetic field after thousands of breakdowns. It is not yet clear how the relative roles of electric field, magnetic field, and heating factor into the damage caused by rf breakdown. Thus, a dual-moded cavity has been designed to better study the electric field, magnetic field, and pulsed heating effects on breakdown damage.

In linear accelerators, the transverse beam orbit is induced by tilts of accelerating cavities (deviation of accelerating field direction from designed beam direction) and transverse offset of quadrupole magnets. Estimating induced orbit and emittance growth due to such random errors is important for evaluation of performance of linacs, especially where stable and low emittance beam is required, such as linear colliders. Usually, such estimations are performed using tracking simulations, including the Monte Carlo method, which tends to take a long time. Here, a much faster and simpler method of quantitative estimation of beam orbit and emittance growth is reported. This method is valid for very long linacs with many components, where statistical treatment of errors is justified. It is shown that the results from the method agree well with tracking simulations for the ILC (International Linear Collider) main linac.

An algorithm for spectral reconstructions (unfolds) and spectrally integrated flux estimates from data obtained by a five-channel, filtered x-ray-detector array (XRD) is described in detail and characterized. This diagnostic is a broad-channel spectrometer, used primarily to measure time-dependent soft x-ray flux emitted by $z$-pinch plasmas at the $Z$ pulsed-power accelerator (Sandia National Laboratories, Albuquerque, New Mexico, USA), and serves as both a plasma probe and a gauge of accelerator performance. The unfold method, suitable for online analysis, arises naturally from general assumptions about the x-ray source and spectral properties of the channel responses; a priori constraints control the ill-posed nature of the inversion. The unfolded spectrum is not assumed to be Planckian. This study is divided into two consecutive papers. This paper considers three major issues: (a) Formulation of the unfold method.—The mathematical background, assumptions, and procedures leading to the algorithm are described: the spectral reconstruction $S_{\mathrm{unfold}}(E,t)$—five histogram x-ray bins $j$ over the x-ray interval, $137\le E\le 2300\mathrm{eV}$ at each time step $t$—depends on the shape and overlap of the calibrated channel responses and on the maximum electrical power delivered to the plasma. The x-ray flux ${\mathcal{F}}_{\mathrm{unfold}}$ is estimated as $\int S_{\mathrm{unfold}}(E,t)dE$. (b) Validation with simulations.—Tests of the unfold algorithm with known static and time-varying spectra are described. These spectra included—but were not limited to—Planckian spectra $S_{bb}(E,T)$ ($25\le T\le 250\mathrm{eV}$), from which noise-free channel data were simulated and unfolded. For Planckian simulations with $125\le T\le 250\mathrm{eV}$ and typical responses, the binwise unfold values $S_j$ and the corresponding binwise averages $⟨S_{bb}{⟩}_j$ agreed to $\sim 20\%$, except where $S_{bb}\ll \max \{S_{bb}\}$. Occasionally, unfold values $S_j\lesssim 0$ (artifacts) were encountered. The algorithm recovered $\gtrsim 90\%$ of the x-ray flux over the wider range, $75\le T\le 250\mathrm{eV}$. For lower $T$, the test and unfolded spectra increasingly diverged as larger fractions of $S_{bb}(E,T)$ fell below the detection threshold ($\sim 137\mathrm{eV}$) of the diagnostic. (c) Comparison with other analyses and diagnostics.—The results of the histogram algorithm are compared with other analyses, including a test with data acquired by the DANTE filtered-XRD array at the NOVA laser facility. Overall, the histogram algorithm is found to be most useful for x-ray flux estimates, as opposed to spectral details. The following companion paper [D. L. Fehl et al., Phys. Rev. ST Accel. Beams 13, 120403 (2010)] considers (a) uncertainties in $S_{\mathrm{unfold}}$ and ${\mathcal{F}}_{\mathrm{unfold}}$ induced by both data noise and calibrational errors in the response functions; and (b) generalization of the algorithm to arbitrary spectra. These techniques apply to other diagnostics with analogous channel responses and supported by unfold algorithms of invertible matrix form.

A five-channel, filtered-x-ray-detector (XRD) array has been used to measure time-dependent, soft-x-ray flux emitted by $z$-pinch plasmas at the $Z$ pulsed-power accelerator (Sandia National Laboratories, Albuquerque, New Mexico, USA). The preceding, companion paper [D. L. Fehl et al., Phys. Rev. ST Accel. Beams 13, 120402 (2010)] describes an algorithm for spectral reconstructions (unfolds) and spectrally integrated flux estimates from data obtained by this instrument. The unfolded spectrum $S_{\mathrm{unfold}}(E,t)$ is based on ($N=5$) first-order B-splines (histograms) in contiguous unfold bins $j=1,\dots ,N$; the recovered x-ray flux ${\mathcal{F}}_{\mathrm{unfold}}(t)$ is estimated as $\int S_{\mathrm{unfold}}(E,t)dE$, where $E$ is x-ray energy and $t$ is time. This paper adds two major improvements to the preceding unfold analysis: (a) Error analysis.—Both data noise and response-function uncertainties are propagated into $S_{\mathrm{unfold}}(E,t)$ and ${\mathcal{F}}_{\mathrm{unfold}}(t)$. Noise factors $\nu$ are derived from simulations to quantify algorithm-induced changes in the noise-to-signal ratio (NSR) for $S_{\mathrm{unfold}}$ in each unfold bin $j$ and for ${\mathcal{F}}_{\mathrm{unfold}}$ ($\nu \equiv NS{R}_{\mathrm{output}}/NS{R}_{\mathrm{input}}$): for $S_{\mathrm{unfold}}$, $1\lesssim {\nu }_j\lesssim 30$, an outcome that is strongly spectrally dependent; for ${\mathcal{F}}_{\mathrm{unfold}}$, $0.6\lesssim {\nu }_{\mathcal{F}}\lesssim 1$, a result that is less spectrally sensitive and corroborated independently. For nominal $z$-pinch experiments, the combined uncertainty (noise and calibrations) in ${\mathcal{F}}_{\mathrm{unfold}}(t)$ at peak is estimated to be $\sim 15\%$. (b) Generalization of the unfold method.—Spectral sensitivities (called here passband functions) are constructed for $S_{\mathrm{unfold}}$ and ${\mathcal{F}}_{\mathrm{unfold}}$. Predicting how the unfold algorithm reconstructs arbitrary spectra is thereby reduced to quadratures. These tools allow one to understand and quantitatively predict algorithmic distortions (including negative artifacts), to identify potentially troublesome spectra, and to design more useful response functions.

We report the results of surface characterizations of niobium (Nb) samples electropolished together with a single cell superconducting radio-frequency accelerator cavity. These witness samples were located in three regions of the cavity, namely at the equator, the iris, and the beam pipe. Auger electron spectroscopy was utilized to probe the chemical composition of the topmost four atomic layers. Scanning electron microscopy with energy dispersive x ray for elemental analysis was used to observe the surface topography and chemical composition at the micrometer scale. A few atomic layers of sulfur (S) were found covering the samples nonuniformly. Niobium oxide granules with a sharp geometry were observed on every sample. Some Nb-O granules appeared to also contain sulfur.

Experimental data is presented that illustrates important displacement current phenomena in the magnetically insulated transmission lines (MITLs) of the refurbished $Z$ accelerator [D. V. Rose et al., Phys. Rev. ST Accel. Beams 13, 010402 (2010)]. Specifically, we show how displacement current in the MITLs causes significant differences between the accelerator current measured at the vacuum-insulator stack (at a radial position of about 1.6 m from the $Z$ axis of symmetry) and the accelerator current measured at the load (at a radial position of about 6 cm from the $Z$ axis of symmetry). The importance of accounting for these differences was first emphasized by Jennings et al. [C. A. Jennings et al., IEEE Trans. Plasma Sci. 38, 529 (2010)], who calculated them using a full transmission-line-equivalent model of the four-level MITL system. However, in the data presented by Jennings et al., many of the interesting displacement current phenomena were obscured by parasitic current losses that occurred between the vacuum-insulator stack and the load (e.g., electron flow across the anode-cathode gap). By contrast, the data presented herein contain very little parasitic current loss, and thus for these low-loss experiments we are able to demonstrate that the differences between the current measured at the stack and the current measured at the load are due primarily to the displacement current that results from the shunt capacitance of the MITLs (about 8.41 nF total). Demonstrating this is important because displacement current is an energy storage mechanism, where energy is stored in the MITL electric fields and can later be used by the system. Thus, even for higher-loss experiments, the differences between the current measured at the stack and the current measured at the load are often largely due to energy storage and subsequent release, as opposed to being due solely to some combination of measurement error and current loss in the MITLs and/or double post-hole convolute. Displacement current also explains why the current measured downstream of the MITLs (i.e., the load current) often exceeds the current measured upstream of the MITLs (i.e., the stack current) at various times in the power pulse (this particular phenomenon was initially thought to be due to timing and/or calibration errors). To facilitate a better understanding of these phenomena, we also introduce and analyze a simple $LC$ circuit model of the MITLs. This model is easily implemented as a simple drive circuit in simulation codes, which has now been done for the LASNEX code [G. B. Zimmerman and W. L. Kruer, Comments Plasma Phys. Controlled Fusion 2, 51 (1975)] at Sandia, as well as for simpler MATLAB®-based codes at Sandia. An example of this $LC$ model used as a drive circuit will also be presented.

Optics stability during all phases of operation is crucial for the LHC. Tools and procedures have been developed for rapid checks of beta beating, dispersion, and linear coupling, as well as for prompt optics corrections. Important optics errors during the different phases of the beam commissioning were observed and locally corrected using the segment-by-segment technique. The most relevant corrections at injection have been corroborated with dedicated magnetic measurements.

The temperature rise and induced stress due to Ohmic heating in the vicinity of microcracks on the walls of high-gradient accelerating structures are considered. The temperature rise and induced stress depend on the orientation of the crack with respect to the rf magnetic field, the shape of the crack, and the power and duration of the rf pulse. Under certain conditions the presence of cracks can double the temperature rise over that of a smooth surface. Stress at the bottom of the cracks can be several times larger than that of the case when there are no cracks. We study these effects both analytically and by computer simulation. It is shown that the stress in cracks is maximal when the crack depth is on the order of the thermal penetration depth.

The performance of superconducting radio-frequency (SRF) resonant cavities made of bulk niobium is limited by nonlinear localized effects. Surface analysis of regions of higher power dissipation is thus of intense interest. Such areas (referred to as “hotspots”) were identified in a large-grain single-cell cavity that had been buffered-chemical polished and dissected for examination by high resolution electron microscopy, electron backscattered diffraction microscopy (EBSD), and optical microscopy. Pits with clearly discernible crystal facets were observed in both “hotspot” and “coldspot” specimens. The pits were found in-grain, at bicrystal boundaries, and on tricrystal junctions. They are interpreted as etch pits induced by crystal defects (e.g. dislocations). All coldspots examined had a qualitatively lower density of etch pits or relatively smooth tricrystal boundary junctions. EBSD mapping revealed the crystal orientation surrounding the pits. Locations with high pit density are correlated with higher mean values of the local average misorientation angle distributions, indicating a higher geometrically necessary dislocation content. In addition, a survey of the samples by energy dispersive x-ray analysis did not show any significant contamination of the samples’ surface. The local magnetic field enhancement produced by the sharp-edge features observed on the samples is not sufficient to explain the observed degradation of the cavity quality factor, which starts at peak surface magnetic field as low as 20 mT.

A hollow-core photonic band-gap (PBG) lattice in a dielectric fiber has been proposed as a high-gradient low-cost particle accelerator operating in the optical regime where the accelerating mode confined to a defect in the PBG fiber can be excited by high-power lasers [X. Lin, Phys. Rev. ST Accel. Beams 4, 051301 (2001)]. Developing efficient methods of coupling laser power into these structures requires a thorough examination of the propagating mode and its near and far-field radiation. In this paper, we develop a simulation method using the parallel finite-element electromagnetic suite ACE3P to calculate the radiation of the propagating accelerator mode into free space at the end of the fiber. The far-field radiation will be calculated and the mechanism of coupling power from an experimental laser setup will be discussed.

A laser-wire transverse electron beam size measurement system has been constructed and operated at the Accelerator Test Facility (ATF) extraction line at KEK. The construction of the system is described in detail along with the environment of the ATF related to the laser wire. A special set of electron beam optics was developed to generate an approximately $1\mu \mathrm{m}$ vertical focus at the laser-wire location. The results of our operation at the ATF extraction line are presented, where a minimum rms electron beam size of $4.8\pm 0.3\mu \mathrm{m}$ was measured, and smaller electron beam sizes can be measured by developing the method further. The beam size at the laser-wire location was changed using quadrupoles and the resulting electron beam size measured, and vertical emittance extracted.

The best rf bulk niobium accelerating cavities have nearly reached their ultimate limits at rf equatorial magnetic field $H\approx 200\mathrm{mT}$ close to the thermodynamic critical field $H_c$. In 2006 Gurevich proposed to use nanoscale layers of superconducting materials with high values of $H_c>H_c{}^{\mathrm{Nb}}$ for magnetic shielding of bulk niobium to increase the breakdown magnetic field of superconducting rf cavities. Depositing good quality layers inside a whole cavity is rather difficult, so as a first step, characterization of single layer coating and multilayers was conducted on high quality sputtered samples by applying the technique used for the preparation of superconducting electronics circuits. The samples were characterized by x-ray reflectivity, dc resistivity (PPMS), and dc magnetization (SQUID) measurements. Dc magnetization curves of a 250 nm thick Nb film have been measured, with and without a magnetron sputtered coating of a single or multiple stack of 15 nm MgO and 25 nm NbN layers. The Nb samples with/without the coating exhibit different behaviors and clearly show an enhancement of the magnetic penetration field. Because SQUID measurements are influenced by edge and shape effects, we propose to develop a specific local magnetic measurement of $H_{C1}$ based on ac third harmonic analysis in order to reveal the true screening effect of multilayers.

Several future accelerator projects at Brookhaven for the Relativistic Heavy Ion Collider (RHIC) are based on energy recovery linacs (ERLs) with high-charge high-current electron beams. Their stable operation mandates effective higher-order-mode (HOM) damping. The development of HOM dampers for these projects is pursued actively at this laboratory. Strong HOM damping was experimentally demonstrated both at room and at superconducting (SC) temperatures in a prototype research and development (R&D) five-cell niobium superconducting rf (SRF) cavity with ferrite dampers. Two room-temperature mock-up five-cell copper cavities were used to study various damper configurations with emphasis on capacitive antenna dampers. An innovative type of ferrite damper over a ceramic break for an R&D SRF electron gun also was developed. For future SRF linacs longer cryomodules comprised of multiple superconducting cavities with reasonably short intercavity transitions are planned. In such a configuration, the dampers, located closer to the cavities, will be at cryogenic temperatures; this will impose additional constraints and complications. This paper presents the results of simulations and measurements of several damper configurations.

Longitudinal space-charge forces from density fluctuations generated by shot noise can be a major source of microbunching instability in relativistic high brightness electron beams. The gain in microbunching due to this effect is broadband, extending at least up to optical frequencies, where the induced structure on the beam distribution gives rise to effects such as coherent optical transition radiation. In the high-frequency regime, theoretical and computational analyses of microbunching formation require a full three-dimensional treatment. In this paper we address the problem of space-charge induced optical microbunching formation in the high-frequency limit when transverse thermal motion due to finite emittance is included for the first time. We derive an analytical description of this process based on the beam’s plasma dielectric function. We discuss the effect of transverse temperature on the angular distribution of microbunching gain and its connection to the physics of Landau damping in longitudinal plasma oscillations. Application of the theory to a relevant experimental scenario is discussed. The analytical results obtained are then compared to the predictions arising from high resolution three-dimensional molecular dynamics simulations.