The ultrafast and ultracold electron source, based on near-threshold photoionization of a laser-cooled and trapped atomic gas, offers a unique combination of low transverse beam emittance and high bunch charge. Its use is however still limited because of the required cold-atom laser-cooling techniques. Here we present a compact ultracold electron source based on a grating magneto-optical trap (GMOT), which only requires one trapping laser beam that passes through a transparent accelerator module. This makes the technique more widely accessible and increases its applicability. We show the GMOT can be operated with a hole in the center of the grating and with large electric fields applied across the trapping region, which is required for extracting electron bunches. The calculated values of the applied electric field were found to agree well with measured Stark shifts of the laser cooling transition. The electron beams extracted from the GMOT have been characterized. Beam energies up to 10 keV were measured using a time-of-flight method. The normalized root-mean-squared transverse beam emittance was determined using a waist scan method, resulting in $\epsilon =1.9\mathrm{nm}\mathrm{rad}$. The root-mean-squared transverse size of the ionization volume is $30\mu \mathrm{m}$ or larger, implying an electron source temperature in the few-10 K range, 2–3 orders of magnitude lower than conventional electron sources, based on photoemission or thermionic emission from solid state surfaces.

A unit cell with one homogeneous bending magnet is commonly used in the design of multi-bend achromat (MBA) lattices for the new generation of diffraction limited storage rings. But significantly lower emittance at moderate focusing properties can be achieved by combining longitudinal gradient bends (LGB) and reverse bends (RB) in a periodic lattice unit cell. LGBs alone, however, are of rather limited gain. We investigate the emittance achievable for different unit cell classes as a function of the cell phase advance in a general framework, i.e., with a minimum of assumptions on the particular cell optics. Each case is illustrated with a practical example of a realistic lattice cell, eventually leading to the LGB/RB unit cell of the baseline lattice for the upgrade of the Swiss Light Source.

In a lepton storage ring of very high energy (e.g., in the $e^{+}{e}^{-}$ Higgs factory) synchrotron radiation from quadrupoles constrains transverse dynamic aperture even in the absence of any magnetic nonlinearities. This was observed in tracking for LEP and the Future Circular $e^{+}{e}^{-}$ Collider (FCC-ee). Here we describe a new mechanism of instability created by modulation of the particle energy at the double betatron frequency by synchrotron radiation in the quadrupoles. Energy modulation varies transverse focusing strength at the same frequency and creates a parametric resonance of the betatron oscillations with unusual properties. It occurs at arbitrary betatron frequency (the resonant detuning is always zero) and the magnitude of the parameter modulation of the betatron oscillation (strength of the resonance driving term) depends on the oscillation amplitude. Equilibrium between the radiation damping and the resonant excitation gives the boundary of the stable motion. Starting from 6d equations of motion we derive and solve the relevant differential equation describing the resonance, and show good agreement between analytical results and numerical simulation.

The design of machine protection systems for high-energy accelerators with high-intensity beams requires analyzing a large number of failures leading to beam loss. One of the most serious failures is an accidental impact of a large number of bunches at one location, for example, due to a deflection of the particle beams by the extraction kicker magnets with the wrong strength. The numerical assessment of such an event requires an iterative execution of an energy-deposition code and a hydrodynamic code, in case the hydrodynamic tunneling effect plays an important role in the beam-matter interactions. Such calculations have been performed for the CERN Large Hadron Collider (LHC), since the energy stored in the LHC beams exceeds previous accelerators by 2 orders of magnitude. This was done using the particle shower code fluka and the hydrodynamic code big2 [Tahir et al., Phys. Rev. ST Accel. Beams 15, (2012)]. Later, simulations for a number of cases for other accelerators at CERN and the Future Circular Collider (FCC) were performed [Tahir et al., Phys. Rev. Accel. Beams 19, (2016)]. These simulations showed that the penetration depth of the beam in copper or graphite could be an order of magnitude deeper when considering the hydrodynamic tunneling, compared to a static approximation. big2 is very efficient and used at GSI. It is always advantageous to cross-check the simulation results with different codes, because dedicated experiments are very complex or even impossible to carry out. For this purpose, it was decided to study the use of a commercial tool (Autodyn) for such calculations and to compare the results with previous work. This paper reports a benchmarking study against beam experiments performed at the HiRadMat (High-Radiation to Materials) facility using beams at 440 GeV from the Super Proton Synchrotron. Good agreement has been found between the simulation results and the experiments as well as previous simulations with fluka and big2 [Tahir et al., Phys. Rev. E 90, (2014)], particularly in terms of the penetration depth of the beam in copper. This makes the coupling of fluka and Autodyn an alternative solution to the simulation of the hydrodynamic tunneling, at least in the parameter range of this case study. Studies with other parameters are planned for FCC and other high-beam-power accelerators.

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.