Starting from the electric fields produced by a point charge and a dipole traveling inside a circular vacuum chamber, in this paper we derive a formalism for a complete set of equations that describe the electromagnetic fields and the longitudinal and transverse coupling impedances arising by the interaction of a beam with a perfectly conducting pipe in the case of elliptic geometry. The expressions, which are valid for any frequency and beam energy, are written in terms of expansions of Mathieu functions, allow to range from a circular geometry to the parallel plates, and show an interesting parallelism with the well-known expressions for a circular pipe. We also obtain that, under the approximation of low frequency, the formalism allows us to derive the Laslett coefficients for parallel plates, circular and elliptic beam pipe.

Active plasma lenses have the potential to enable broad-ranging applications of plasma-based accelerators owing to their compact design and radially symmetric kT/m-level focusing fields, facilitating beam-quality preservation and compact beam transport. We report on the direct measurement of magnetic field gradients in active plasma lenses and demonstrate their impact on the emittance of a charged particle beam. This is made possible by the use of a well-characterized electron beam with 1.4 mm mrad normalized emittance from a conventional accelerator. Field gradients of up to $823\mathrm{T}/\mathrm{m}$ are investigated. The observed emittance evolution is supported by numerical simulations, which suggests the potential for conservation of the core beam emittance in such a plasma lens setup.

The longitudinal charge density of an electron beam in its equilibrium state is given by the solution of the Haïssinski equation, which provides a stationary solution of the Vlasov-Fokker-Planck equation. The physical input is the longitudinal wake potential. We formulate the Haïssinski equation as a nonlinear integral equation with the normalization integral stated as a functional of the solution. This equation can be solved in a simple way by the matrix version of Newtons’s iteration, beginning with the Gaussian as a first guess. We illustrate for several quasirealistic wake potentials. Convergence is extremely robust, even at currents much higher than nominal for the storage rings considered. The method overcomes limitations of earlier procedures, and provides the convenience of automatic normalization of the solution.

Herein we present details of the design, simulation, and performance of a 100-GW linear transformer driver (LTD) cavity at Sandia National Laboratories. The cavity consists of 20 “bricks.” Each brick is comprised of two 80 nF, 100 kV capacitors connected electrically in series with a custom, 200 kV, three-electrode, field-distortion gas switch. The brick capacitors are bipolar charged to $\pm 100\mathrm{kV}$ for a total switch voltage of 200 kV. Typical brick circuit parameters are 40 nF capacitance (two 80 nF capacitors in series) and 160 nH inductance. The switch electrodes are fabricated from a $W\mathrm{Cu}$ alloy and are operated with breathable air. Over the course of 6,556 shots the cavity generated a peak electrical current and power of 1.03 MA ($\pm 1.8\%$) and 106 GW ($\pm 3.1\%$). Experimental results are consistent (to within uncertainties) with circuit simulations for normal operation, and expected failure modes including prefire and late-fire events. New features of this development that are reported here in detail include: (1) 100 ns, 1 MA, 100-GW output from a 2.2 m diameter LTD into a $0.1\mathrm{\Omega }$ load, (2) high-impedance solid charging resistors that are optimized for this application, and (3) evaluation of maintenance-free trigger circuits using capacitive coupling and inductive isolation.

We present a general method to derive the magnetic field dependence of the surface resistance of superconductors from the $Q$-curves obtained during the cryogenic tests of cavities. The results are applied to coaxial half-wave cavities, TM-like “elliptical” accelerating cavities, and cavities of more complicated geometries.

The phase error is an important parameter to represent the quality of an undulator, which makes it possible to quickly evaluate the reduction in photon intensity due to magnetic field errors without rigorous numerical calculations. Although the phase error has been used as a standard to evaluate the undulator field errors because of its simplicity, a couple of papers have reported that the phase error actually overestimates the intensity reduction under practical conditions, and thus its tolerance tends to be too tight. In other words, the applicability of the phase error defined in the conventional form is rather limited. To overcome this difficulty, we derive a set of formulas to quickly evaluate the undulator quality based on an analytical approach, which can be used in a more universal manner. Comparisons with rigorous numerical results under various conditions show the validity and universality of the derived formulas. Analytical methods to investigate the effects due to systematic errors in undulators are also presented as one of the important applications of these formulas.

The Future Circular Collider FCC-ee is a study toward a high luminosity electron-positron collider with a centre-of-mass energy from 91 GeV to 365 GeV. Due to the beam parameters and pipe dimensions, collective effects and electron cloud can be very critical aspects for the machine and can represent the main limitations to its performance. An estimation of the electron cloud build up in the main machine components and an impedance model are required to analyze the induced instabilities and to find solutions for their mitigation. Special attention has been given to the resistive wall impedance associated with a layer of nonevaporable getter (NEG) coating on the vacuum chamber required for electron cloud mitigation. The studies presented in this paper will show that minimizing the thickness of this coating layer is mandatory to increase the single bunch instability thresholds in the proposed lepton collider at 45.6 GeV. For this reason, NEG thin films with thicknesses below 250 nm have been investigated by means of numerical simulations to minimize the resistive wall impedance. In parallel, an extensive measurement campaign was performed at CERN to characterize these thin films, with the purpose of finding the minimum effective thickness satisfying vacuum and electron cloud requirements.

We have developed a parametrization of the linear optics in a theoretical minimum emittance cell with three quadrupoles. It consists of five independent parameters: two phase advances, a dimensionless horizontal beta function at the center of the dipole, and a bending angle $\varphi$ and a length $L$ of the dipole. For the zero chromaticity cell, we again find that the dynamic aperture in the normalized phase space is scaled according to, $\overline{A}\propto \varphi \sqrt{L}$. Moreover, we study nonlinear dynamics near the third-order coupled resonances in the framework of the resonance normal form. In particular, we derive the effective Hamiltonians using the Lie algebra method and show that the periodic orbits in tracking can be interpreted as solutions of the Hamilton’s equations. Surprisingly, we discover that the scheme is not only applicable to the single resonance but also to the double resonances.

We present a method for determining the characteristics of an intense laser pulse by probing it with a relativistic electron beam. After an initial burst of very high-energy $\gamma$-radiation the electrons proceed to emit a series of attosecond duration x-ray pulses as they leave the field. These flashes provide detailed information about the interaction, allowing us to determine properties of the laser pulse: something that is currently a challenge for ultrahigh intensity laser systems.

The Microbunched Electron Cooling (MBEC) proposed by D. Ratner is a promising cooling technique that can find applications in future hadron and electron-ion colliders. In this paper, we develop a new framework for the study of MBEC which is based on the analysis of the dynamics of microscopic 1D fluctuations in the electron and hadron beams during their interaction and propagation through the system. Within this framework, we derive an analytical formula for the longitudinal cooling rate and benchmark it against 1D computer simulations. We then calculate the expecting cooling time for a set of parameters of the proposed electron-ion collider eRHIC in a simple cooling system with one chicane in the electron channel. While the cooling rate in this system turns out to be insufficient to counteract the intrabeam scattering in the proton beam, we discuss how the electron signal can be amplified by two orders of magnitude through the use of plasma effects in the beam.

This paper extends the existing Vlasov theory for transverse coherent beam instabilities to account for nonlinear chromaticity. It confirms the hypothesis that nonlinear chromaticity has two effects on the beam dynamics: (i) it changes the effective impedance which results in a modification of the coherent frequencies of the head-tail modes, and (ii) it can introduce betatron detuning with longitudinal action and provide Landau damping of transverse modes. Based on the new formalism, these two mechanisms are identified and studied analytically with both an airbag and a Gaussian beam. To complete the study, the theory is successfully benchmarked against the circulant matrix solver BimBim as well as the PyHEADTAIL macroparticle tracking code.

We describe a method for symplectic tracking of charged particles through static electric and magnetic fields. The method can be applied to cases where the fields have a dependence on the longitudinal as well as transverse position and where the reference trajectory may have nonzero curvature. Application of the method requires analytical expressions for the scalar and vector potentials: We show how suitable expressions, in the form of series analogous to multipole expansions, can be constructed from numerical field data, allowing the method to be used in cases where only numerical field data are available.

Bunch compression achieved via a fast bunch rotation in longitudinal phase space is a well-accepted scheme to generate short, intense ion bunches for various applications. During bunch compression, coherent beam instabilities and incoherent single particle resonances can occur because of increasing space charge, resulting in an important limitation for the bunch intensity. We present an analysis of the relevant space charge driven beam instability and resonance phenomena during bunch compression. A coupled longitudinal-transverse envelope approach is compared with particle-in-cell (PIC) simulations. Two distinct cases of crossing are discussed and applied to the GSI SIS-18 heavy-ion synchrotron. It is shown that during bunch compression, the 90° condition of phase advance is associated with a fourth order single particle resonance and the 120° condition with the recently discovered dispersion-induced instability. The agreement between the envelope and PIC results indicates that the stop band is defined by the 120° dispersion instability, which should be avoided during bunch compression.

It has been well known that the resonant interaction of an ultrarelativistic electron beam and the radiation field in the single-pass high-gain free electron laser (FEL) amplifier leads to the optical gain guiding. The transverse Laplacian term of the slowly varying wave equation in the linear regime can be approximated as a constant detuning parameter, i.e., $|{\nabla }_{\perp }^2|\sim k_R/z_R$ where $k_R$ is the resonant wave number and $z_R$ is the Rayleigh range of the laser. In the post-saturation regime, the radiation power begins to oscillate about an equilibrium for the untapered case while continues to grow by undulator tapering. Moreover, in this regime the gain guiding decreases and the simple constant detune is no longer valid. In this paper we study the single-pass high-gain FEL performance in the post-saturation regime with inclusion of diffraction effect and undulator tapering. Our analysis relies upon two constants of motion, one from the energy conservation and the other from the adiabatic invariant of the action variable. By constructing a two-dimensional axisymmetric wave equation and the coupled one-dimensional electron dynamical equations, the performance of a tapered FEL in the postsaturation regime can be analyzed, including the fundamental mode profile, the power efficiency and the scaled energy spread. We begin the analytical investigation with two different axisymmetric electron beam profiles, the uniform and bounded parabolic ones. It is found that the tapered FEL power efficiency can be smaller but close to the taper ratio provided the resonant phase remains constant and the beam-wave is properly matched. Such a tapered efficiency is nearly independent of transverse electron beam size before significant electron detrapping occurs. This is essentially different from the untapered case, where the power extraction efficiency is around the essential FEL gain bandwidth (or $\rho$, the Pierce or FEL parameter) and depends on the beam size. It is also found that the power enhancement due to undulator tapering is attributed more by the field increase outside the transverse electron beam than that inside the transverse electron beam. Several scaling properties on the taper ratio and the transverse electron beam size are also discussed in this paper.

For an optimal exploitation of the benefits of proton therapy the most accurate dose delivery system should be used. The TERA Foundation has extensive experience in the field of high gradient high frequency linacs. This paper describes a particular design of a 3 GHz linac boosting the typical cyclotron beams for proton therapy of 230–250 MeV up to 350 MeV. Such an upgrade of a typical proton therapy facility enables performing proton radiography, as well as extending therapeutic capabilities with high energy proton therapy (HEPT). The recent studies and measurements in high-gradient linac technology demonstrated that average fields in the accelerating structures of up to $25–30\mathrm{MV}/\mathrm{m}$ can be achieved, which results in a total linac length of less than 7 m. To test several characteristics of such a linac as a booster of a cyclotron beam, a design has been made of a linac unit accelerating from 250 MeV to 275 MeV, which could be built and inserted for tests in an existing beam line at the PSI proton therapy facility. The feasibility considerations, along with the design of the linac booster and the issues related to a possible integration in an existing cyclotron beam line are detailed in this study.

A new experimental technique for the accurate measurements of wakefields is presented. Knowledge of wakefields is required for many applications ranging from the suppression of wakefields that arise from geometrical discontinuities to the enhancement of wakefields in structure and plasma based wakefield accelerators. In the past, direct measurements of wakefields were done with the drive-witness technique wherein the delay of a short witness beam trailing collinearly behind a high-charge drive beam is scanned over multiple shots and the wakefield is inferred from the energy spectrum of the witness beam. That technique is limited by shot-to-shot jitter, overlap of the drive and witness energy spectrum and the loss of all time-domain information. In this paper, we describe a new technique that overcomes these limitations by measuring the longitudinal phase space of a long witness beam and the drive beam in a single shot. We conclude by presenting experimental results to demonstrate its feasibility using a dielectric structure wakefield accelerator.

At the beginning of the 2016 run, an anomalous beam instability was systematically observed at the CERN Large Hadron Collider (LHC). Its main characteristic was that it spontaneously appeared after beams had been stored for several hours in collision at 6.5 TeV to provide data for the experiments, despite large chromaticity values and high strength of the Landau-damping octupole magnet. The instability exhibited several features characteristic of those induced by the electron cloud (EC). Indeed, when LHC operates with 25 ns bunch spacing, an EC builds up in a large fraction of the beam chambers, as revealed by several independent indicators. Numerical simulations have been carried out in order to investigate the role of the EC in the observed instabilities. It has been found that the beam intensity decay is unfavorable for the beam stability when LHC operates in a strong EC regime.

A prototype 11.994 GHz, traveling-wave accelerating structure for the Compact Linear Collider has been built, using the novel technique of assembling the structure from milled halves. The use of milled halves has many advantages when compared to a structure made from individual disks. These include the potential for a reduction in cost, because there are fewer parts, as well as a greater freedom in choice of joining technology because there are no rf currents across the halves’ joint. Here we present the rf design and fabrication of the prototype structure, followed by the results of the high-power test and post-test surface analysis. During high-power testing the structure reached an unloaded gradient of $100\mathrm{MV}/\mathrm{m}$ at a rf breakdown rate of less than $1.5\times {10}^{-5}\mathrm{breakdowns}/\mathrm{pulse}/\mathrm{m}$ with a 200 ns pulse. This structure has been designed for the CLIC testing program but construction from halves can be advantageous in a wide variety of applications.

A conceptual design and performance of a round beam lattice for synchrotron light sources based on the phase space exchange principle and the noninterleaved sextupole distribution is presented. Optics design is performed for an approximately 30 pm emittance 6 GeV machine of 2300 m circumference which combines cells with and without straight sections for the insertion devices.

Brightness is a key figure of merit for charged particle beams, and time-resolved brightness measurements can elucidate the processes involved in beam creation and manipulation. Here we report on a simple, robust, and widely applicable method for the measurement of beam brightness with temporal resolution by streaking one-dimensional pepperpots, and demonstrate the technique to characterize electron bunches produced from a cold-atom electron source. We demonstrate brightness measurements with 145 ps temporal resolution and a minimum resolvable emittance of 40 nm rad. This technique provides an efficient method of exploring source parameters and will prove useful for examining the efficacy of techniques to counter space-charge expansion, a critical hurdle to achieving single-shot imaging of atomic scale targets.