In this paper, we discuss the electromagnetic interaction between a point charge travelling inside a waveguide of elliptical cross section, and the waveguide itself. By using a convenient expansion of the Mathieu functions, useful in particular for treating a variety of problems in applied mathematics and physics with elliptic geometry, we first obtain the longitudinal electromagnetic field of a point charge (Green’s function) in free space in terms of elliptical coordinates. This expression allows, then, to calculate the scattered field due to the boundary conditions in our geometry. By summing the contribution of the direct or primary field and the indirect field scattered by the boundary, after a careful choice of some expansion expressions, we derive a novel formula of the longitudinal electric field, in any transverse position of the elliptical cross section, generated by the charge moving along the longitudinal axis of the waveguide. The obtained expression is represented in a closed form, it can be differentiated and integrated, it can be used to fully describe the radiation process of a particle beam travelling inside a waveguide of elliptical cross section, and it is valid for any elliptic geometry. The equations are used to evaluate the coupling impedance due to indirect space charge in case of elliptical geometry. In addition, they are useful as preliminary studies for the determination of the coupling impedance in different cases involving elliptic vacuum chambers, as, for example, the effect of the finite conductivity of the beam pipe wall or the geometrical variation of the vacuum chamber due to elliptic step transitions existing in some accelerators.

The RadiaBeam/SLAC dechirper, a structure consisting of pairs of flat, metallic, corrugated plates, has been installed just upstream of the undulators in the Linac Coherent Light Source (LCLS). As a dechirper, with the beam passing between the plates on axis, longitudinal wakefields are induced that can remove unwanted energy chirp in the beam. However, with the beam passing off axis, strong transverse wakes are also induced. This mode of operation has already been used for the production of intense, multicolor photon beams using the fresh-slice technique, and is being used to develop a diagnostic for attosecond bunch length measurements. Here we measure, as a function of offset, the strength of the transverse wakefields that are excited between the two plates, and also for the case of the beam passing near to a single plate. We compare with analytical formulas from the literature, and find good agreement. This report presents the first systematic measurements of the transverse wake strength in a dechirper, one that has been excited by a bunch with the short pulse duration and high energy found in an x-ray free electron laser.

We propose a novel method to align accelerating structures such as those used in the Compact Linear Collider (CLIC) by exploiting a mode that copropagates with the normal accelerating mode. This mode has an octupolar dependence in the transverse direction and is caused by radial waveguides intended to damp higher-order modes. The nonlinear dependence of the octupolar mode makes it possible to determine the center of the structure from the nonlinear dependence of the transverse kick, observed on a downstream beam position monitor, while changing the transverse position of the beam with respect to the accelerating structures. We discuss the method, its tolerances and disentangling the individual misalignments of two adjacent accelerating structures that are powered from a single source.

NORMA is a design for a normal-conducting racetrack fixed-field alternating-gradient accelerator for protons from 50 to 350 MeV. In this article we show the development from an idealized lattice to a design implemented with field maps from rigorous two-dimensional (2D) and three-dimensional (3D) FEM magnet modeling. We show that whilst the fields from a 2D model may reproduce the idealized field to a close approximation, adjustments must be made to the lattice to account for differences brought about by the 3D model and fringe fields and full 3D models. Implementing these lattice corrections we recover the required properties of small tune shift with energy and a sufficiently large dynamic aperture. The main result is an iterative design method to produce the first realistic design for a proton therapy accelerator that can rapidly deliver protons for both treatment and for imaging at up to 350 MeV. The first iteration is performed explicitly and described in detail in the text.

The problem of planar channeling of high-energy negatively charged particles in a bent crystal was considered on the basis of analytical calculation and numerical simulation. We show the existence of an optimal radius of crystal curvature for planar channeling, corresponding to the maximum deflection of the particle beam. The analytical calculation was carried out in the parabolic planar potential approximation, and in the numerical simulation the Doyle-Turner approximation was used.

A radio frequency (rf) quadrupole has been considered as a potential alternative device for Landau damping in circular hadron colliders. The objective of this study is to benchmark and confirm its stabilizing effect predicted by stability diagram theory by means of numerical tracking simulations. To that end, two complementary models of the device are implemented in pyheadtail, a 6D macroparticle tracking code designed to study the formation and mitigation of collective instabilities. The rf quadrupole model is applied to a slow head-tail instability observed experimentally in the Large Hadron Collider to show that such a device can in principle provide beam stability similarly to magnetic octupoles. Thereafter, alternative usage schemes of rf quadrupoles also in combination with magnetic octupoles are proposed, discussed, and benchmarked with simulations.

A gigawatt-class nonlinear transmission line based electron beam driver is experimentally demonstrated. Four experimental series, each with a different Marx bank charge voltage (15, 20, 25, and 30 kV), were completed. Within each experimental series, shots at peak frequencies ranging from 950 MHz to 1.45 GHz were performed. Peak amplitude modulations of the NLTL output voltage signal were found to range between 18% and 35% for the lowest frequency shots and between 5% and 20% for the highest frequency shots (higher modulation at higher Marx charge voltage). Peak amplitude modulations of the electron beam current were found to range between 10% and 20% for the lowest frequency shots and between 2% and 7% for the highest frequency shots (higher modulation at higher Marx charge voltage).

FLASH and the European XFEL are SASE-FEL user facilities, at which superconducting TESLA cavities are operated in a pulsed mode to accelerate long bunch-trains. Several cavities are powered by one klystron. While the low-level rf system is able to stabilize the vector sum of the accelerating gradient of one rf station sufficiently, the rf parameters of individual cavities vary within the bunch-train. In correlation with misalignments, intrabunch-train trajectory variations are induced. An efficient model is developed to describe the effect at low beam energy, using numerically adjusted transfer matrices and discrete coupler kick coefficients, respectively. Comparison with start-to-end tracking and dedicated experiments at the FLASH injector will be shown. The short computation time of the derived model allows for comprehensive numerical studies on the impact of misalignments and variable rf parameters on the transverse intra-bunch-train beam stability at the injector module. Results from both, statistical multibunch performance studies and the deduction of misalignments from multibunch experiments are presented.

The Large Hadron Collider (LHC) radio frequency (rf) and low-level rf (LLRF) systems are currently configured for constant rf voltage to minimize transient beam loading effects. The present scheme cannot be extended beyond nominal LHC beam current (0.55 A dc) and cannot be sustained for the high-luminosity (HL-LHC) beam current (1.1 A dc), since the demanded power would exceed the peak klystron power. A new scheme has therefore been proposed: for beam currents above nominal (and possibly earlier), the voltage reference will reproduce the modulation driven by the beam (transient beam loading), but the strong rf feedback and one-turn delay feedback will still be active for loop and beam stability. To achieve this, the voltage reference will be adapted for each bunch. This paper includes a theoretical derivation of the optimal cavity modulation, introduces the implemented algorithm, summarizes simulation runs that tested the algorithm performance, and presents results from a short LHC physics fill with the proposed implementation.

Radiofrequency cavities based on superconducting technology are widely used in particle accelerators for various applications. The cavities usually have high quality factors and hence narrow bandwidths, so the field stability is sensitive to detuning from the Lorentz force and external loads, including vibrations and helium pressure variations. If not properly controlled, the detuning can result in a serious performance degradation of a superconducting accelerator, so an understanding of the underlying detuning mechanisms can be very helpful. Recent advances in the simulation suite ace3p have enabled realistic multiphysics characterization of such complex accelerator systems on supercomputers. In this paper, we present the new capabilities in ace3p for large-scale 3D multiphysics modeling of superconducting cavities, in particular, a parallel eigensolver for determining mechanical resonances, a parallel harmonic response solver to calculate the response of a cavity to external vibrations, and a numerical procedure to decompose mechanical loads, such as from the Lorentz force or piezoactuators, into the corresponding mechanical modes. These capabilities have been used to do an extensive rf-mechanical analysis of dressed TESLA-type superconducting cavities. The simulation results and their implications for the operational stability of the Linac Coherent Light Source-II are discussed.

High average current, transportable energy recovery linacs (ERLs) can be very attractive tools for a number of applications including next generation high-luminosity, compact light sources. Conventional ERLs are based on an electron beam circulating through the same set of rf cavity cells. This leads to an accumulation of high-order modes inside the cavity cells, resulting in the development of a beam breakup (BBU) instability, unless the beam current is kept below the BBU start current. This limits the maximum current which can be transported through the ERL and hence the intensity of the photon beam generated. It has recently been proposed that splitting the accelerating and decelerating stages, tuning them separately and coupling them via a resonance coupler can increase the BBU start current. The paper presents the first experimental rf studies of a dual axis 7-cell asymmetric cavity and confirms the properties predicted by the theoretical model. The field structures of the symmetric and asymmetric modes are measured and good agreement with the numerical predictions is demonstrated. The operating mode field flatness was also measured and discussed. A novel approach based on the coupled mode (Fano-like) model has been developed for the description of the cavity eigenmode spectrum and good agreement between analytical theory, numerical predictions and experimental data is shown. Numerical and experimental results observed are analyzed, discussed and a good agreement between theory and experiment is demonstrated.

Recently, relations were established between the coefficients of free and forced amplitude detuning polynomial expansions. The forced oscillations were considered only in a single plane. In this paper we extend and generalize previous results by developing analytical equations that transform the free amplitude detuning function into the amplitude detuning involving forced oscillations in both transverse planes. These are used to obtain closed approximated formulas for the beam-beam amplitude detuning with forced oscillations. Formulas are compared to single and multiparticle simulations.

New developments relating to compact X-band, SLED-I type pulse compressors being developed at CERN for testing high gradient structures are described. Pulse compressors of interest take rf pulses from one or more high power klystrons with duration typically $>1.5\mu \mathrm{s}$ and deliver up to 5 times the input power for a shorter duration $<250\mathrm{ns}$. Time domain models for pulse compressor operation with low level rf (LLRF) control have been developed. Input drive amplitude and phase for each pulse is evolved with a control algorithm from the pulse compressor output for previous pulses. The goal is to deliver precise amplitude for pulses to test stands and precise amplitude and phase for pulses to accelerator systems. Control algorithms have been developed and validated experimentally.

The interest in producing ultrashort electron bunches has risen sharply among scientists working on the design of high-gradient wakefield accelerators. One attractive approach generating electron bunches is to illuminate a photocathode with a train of femtosecond laser pulses. In this paper we describe the design and testing of a laser system for an rf gun based on a commercial titanium-sapphire laser technology. The technology allows the production of four femtosecond laser pulses with a continuously variable pulse delay. We also use the designed system to demonstrate the experimental generation of an electron microbunch train obtained by illuminating a cesium-telluride semiconductor photocathode. We use conventional diagnostics to characterize the electron microbunches produced and confirm that it may be possible to control the main parameter of an electron microbunch train.

The effect of double frequency heating on the performance of the CERN GTS-LHC 14.5 GHz Electron Cyclotron Resonance (ECR) ion source in afterglow mode is reported. The source of the secondary microwave frequency was operated both in pulsed and continuous wave (CW) modes within the range of 12–18 GHz. The results demonstrate that the addition of the secondary frequency can significantly impact the extracted beam currents and the temporal stability of the beam during the afterglow discharge. For example, up to a factor of 2.6 increase was achieved for ${{}^{208}\mathrm{Pb}}^{35+}$ and a factor of 3.1 for ${{}^{208}\mathrm{Pb}}^{37+}$ compared to single frequency afterglow currents. It is shown that these effects are dependent on the choice of the secondary frequency with respect to the primary one and on the temporal synchronization between the two microwave sources. Overall, the results provide new insight into the afterglow discharge supporting the prevailing understanding of the physical processes behind the phenomenon.

Development of superconducting undulators continues at the Advanced Photon Source (APS). Two years after successful installation and commissioning of the first relatively short superconducting undulator “SCU0” in Sector 6 of the APS storage ring, the second 1.1-m-long superconducting undulator “SCU1” was installed in Sector 1 of the APS. The device has been in user operation since its commissioning in May 2015. This paper describes the magnetic and cryogenic design of the SCU1 together with the results of stand-alone cold tests. The SCU1’s magnetic and cryogenic performance as well as its operating experience in the APS storage ring are also presented.

The most frequently used radionuclide in diagnostic nuclear medicine, ${}^{99m}\mathrm{Tc}$, is generally obtained by the decay of its parent radionuclide, ${}^{99}\mathrm{Mo}$. Recently, concerns have been raised over shortages of ${}^{99}\mathrm{Mo}{/}^{99m}\mathrm{Tc}$, owing to aging of the research reactors which have been supplying practically all of the global demand for ${}^{99}\mathrm{Mo}$ in a centralized fashion. In an effort to prevent such ${}^{99}\mathrm{Mo}{/}^{99m}\mathrm{Tc}$ supply disruption and, furthermore, to ameliorate the underlying instability of the centralized ${}^{99}\mathrm{Mo}{/}^{99m}\mathrm{Tc}$ supply chain, we designed an $X$-band electron linear accelerator which can be distributed over multiple regions, whereby ${}^{99}\mathrm{Mo}{/}^{99m}\mathrm{Tc}$ can be supplied with improved accessibility. The electron beam energy was designed to be 35 MeV, at which an average beam power of 9.1 kW was calculated by the following beam dynamics analysis. Subsequent radioactivity modeling suggests that 11 of the designed electron linear accelerators can realize self-sufficiency of ${}^{99}\mathrm{Mo}{/}^{99m}\mathrm{Tc}$ in Japan.

Solenoid Siberian snakes have successfully maintained polarization in particle rings below 1 GeV, but never in multi-GeV rings, because the spin rotation by a solenoid is inversely proportional to the beam momentum. High energy rings, such as Brookhaven’s 255 GeV Relativistic Heavy Ion Collider (RHIC), use only odd multiples of pairs of transverse B-field Siberian snakes directly opposite each other. When it became impractical to use a pair of Siberian Snakes in Fermilab’s $120\mathrm{GeV}/\mathrm{c}$ Main Injector, we searched for a new type of single Siberian snake that could overcome all depolarizing resonances in the $8.9–120\mathrm{GeV}/\mathrm{c}$ range. We found that a snake made of one 4-twist helix and 2 dipoles could maintain the polarization. This snake design could solve the long-standing problem of significant polarization loss during acceleration of polarized protons from a few GeV to tens of GeV, such as in the AGS, before injecting them into multi-hundred GeV rings, such as RHIC.