We have designed an “ultimate” storage ring for a future light source that would be resided in the positron-electron-project (PEP) tunnel and achieves the diffraction-limited emittances (at 1.5 Å) of 12 pm-rad in both horizontal and vertical planes with a 4.5-GeV electron beam. These emittances include the contribution of intrabeam scattering at a nominal current of 200 mA in 3300 bunches. This quality beam in conjunction with a conventional 4-m undulator in a straight section can generate synchrotron radiation having a spectral brightness above ${10}^{22}[\mathrm{photons}/\mathrm{s}/{\mathrm{mm}}^2/{\mathrm{mrad}}^2/0.1\%\mathrm{BW}]$ at a 10 keV photon energy. The high coherence at the diffraction limit makes this design competitive with 4th generation light sources based on an energy recovery linac. In addition, the beam lifetime is several hours and the dynamic aperture is large enough to allow off-axis injection. The alignment and stability tolerances, though challenging, are achievable. A ring with all these properties is only possible because of several major advances in mitigating the effects of nonlinear resonances.

Transverse instability of a bunched beam is investigated with synchrotron oscillations, space charge tune shift, and resistive wall wakefield taken into account. A boxcar model is used for a general analysis, and truncated Gaussian distribution is invoked for details. The beam spectrum, instability growth rate, and effects of chromaticity are studied in a wide range of parameters, both with head-tail and collective bunch interactions included. Influence of internal bunch oscillations on the collective instabilities is investigated thoroughly. Landau damping caused by the space charge tune spread is discussed, and the instability thresholds of different modes of truncated Gaussian bunch are estimated.

To compensate the beam-beam tune spread and beam-beam resonance driving terms in the polarized proton operation in the Relativistic Heavy Ion Collider (RHIC), we will introduce a low energy DC electron beam into each ring to collide head-on with the opposing proton beam. The device to provide the electron beam is called an electron lens. In this article, using a 6D weak-strong beam-beam interaction simulation model, we will investigate the effects of head-on beam-beam compensation with electron lenses on the proton beam dynamics for the RHIC 250 GeV polarized proton operation. Frequency maps, dynamic apertures, and proton beam loss rates are calculated for this study. Key beam parameters involved in this scheme are varied to search for the optimum compensation condition. The sensitivities of head-on beam-beam compensation to beam imperfections and beam offsets are also studied.

Proton bunches with energies up to 30 MeV have been measured at the PHELIX laser. Because of the laser-plasma interactions at a power density of about $4\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$, a total yield of $1.5\times {10}^{13}\mathrm{protons}$ was produced. For the reference energy of 10 MeV, the yield within $\pm 0.5\mathrm{MeV}$ was exceeding ${10}^{10}\mathrm{protons}$. The important topic for a further acceleration of the laser generated bunch is the matching into the acceptance of an rf accelerator stage. With respect to the high space charge forces and the transit energy range, only drift tube linacs seem adequate for this purpose. A crossbar $H$-type (CH) cavity was chosen as the linac structure. Optimum emittance values for the linac injection are compared with the available laser generated beam parameters. Options for beam matching into a CH structure by a pulsed magnetic solenoid and by using the simulation codes LASIN and LORASR are presented.

The accelerating field in superconducting cavities has to be stabilized in amplitude and phase by a radio-frequency (rf) control system. Because of their high loaded quality factor superconducting cavities are very susceptible for microphonics. To meet the increased requirements with respect to accuracy, availability, and diagnostics, the previous analog rf control system of the superconducting Darmstadt electron linear accelerator S-DALINAC has been replaced by a digital rf control system. The new hardware consists of two components: An rf module that converts the signal from the cavity down to the base-band and a field-programmable gate array board including a soft CPU that carries out the signal processing steps of the control algorithm. Different algorithms are used for normal-conducting and superconducting cavities. To improve the availability of the control system, techniques for automatic firmware and software deployment have been implemented. Extensive diagnostic features provide the operator with additional information. The architecture of the rf control system as well as the functionality of its components will be presented along with measurements that characterize the performance of the system, yielding, e.g., an amplitude stabilization down to $(\Delta A/A{)}_{\mathrm{rms}}=7\times {10}^{-5}$ and a phase stabilization of $(\Delta \varphi {)}_{\mathrm{rms}}=0.8°$ for superconducting cavities.

For the operation as an injector for the FAIR project, the heavy-ion synchrotron (SIS) has to deliver intense and high quality ion bunches with a high repetition rate. One requirement is that the initial momentum spread of the injected coasting beam should not exceed the limit set by the available SIS rf bucket area. Furthermore, the Schottky spectrum should be used to routinely measure the momentum spread and revolution frequency directly after injection in order to adjust the rf settings. During the transverse multiturn injection, the SIS is filled with microbunches from the UNILAC linac at 36 MHz. At low beam intensities, the microbunches debunch within a few turns and form a coasting beam with a Gaussian-like momentum distribution. With increasing intensity we observe persistent current fluctuations and an accompanying broadband, pseudo-Schottky spectrum. Analytical and numerical models indicate that the space charge induced multistream instability of the filaments formed after debunching is responsible for the observed turbulent current spectrum.

The aim of our study is the numerical computation of the wakefield and energy loss per unit length for relativistic, short ($<10\mathrm{ns}$) proton bunches interacting with an electron cloud inside the beam pipe. We present analytical expressions for the energy loss in the impulse kick approximation. For the simulation of the wakefields a 2D self-consistent, electrostatic particle-in-cell (PIC) code is employed. Results for the energy loss and for the wakefields are presented for the parameter scope of the CERN LHC and SPS. For selected parameters the results are compared to a three-dimensional (3D) electromagnetic PIC code.

We present the promise of generating gigawatt mode-locked multichromatic x rays in a seeded free-electron laser (FEL). We show that, by using a laser to imprint periodic modulation in electron beam phase space, a single-frequency coherent seed can be amplified and further translated to a mode-locked multichromatic output in an FEL. With this configuration the FEL output consists of a train of mode-locked ultrashort pulses which span a wide frequency gap with a series of equally spaced sharp lines. These gigawatt multichromatic x rays may potentially allow one to explore the structure and dynamics of a large number of atomic states simultaneously. The feasibility of generating mode-locked x rays ranging from carbon $K$ edge ($\sim 284\mathrm{eV}$) to copper $L_3$ edge ($\sim 931\mathrm{eV}$) is confirmed with numerical simulation using the realistic parameters of the linac coherent light source (LCLS) and LCLS-II. We anticipate that the mode-locked multichromatic x rays in FELs may open up new opportunities in x-ray spectroscopy (i.e. resonant inelastic x-ray scattering, time-resolved scattering and spectroscopy, etc.).

Free-electron lasers (FELs) can now generate temporally short, high power x-ray pulses of unprecedented brightness, even though their longitudinal coherence is relatively poor. The longitudinal coherence can be potentially improved by employing narrow bandwidth x-ray crystal optics, in which case one must also understand how the crystal affects the field profile in time and space. We frame the dynamical theory of x-ray diffraction as a set of coupled waves in order to derive analytic expressions for the spatiotemporal response of Bragg scattering from temporally short incident pulses. We compute the profiles of both the reflected and forward-scattered x-ray pulses, showing that the time delay of the wave $\tau$ is linked to its transverse spatial shift $\Delta x$ through the simple relationship $\Delta x=c\tau \cot \theta$, where $\theta$ is the grazing angle of incidence to the diffracting planes. Finally, we apply our findings to obtain an analytic description of Bragg forward scattering relevant to monochromatically seed hard x-ray FELs.

In particle accelerators a preferred direction, the direction of motion, is well defined. If in a numerical calculation the (numerical) dispersion in this direction is suppressed, a quite coarse mesh and moderate computational resources can be used to reach accurate results even for extremely short electron bunches. Several approaches have been proposed in the past decades to reduce the accumulated dispersion error in wakefield calculations for perfectly conducting structures. In this paper we extend the TE/TM splitting algorithm to a new hybrid scheme that allows for wakefield calculations in structures with walls of finite conductivity. The conductive boundary is modeled by one-dimensional wires connected to each boundary cell. A good agreement of the numerical simulations with analytical results and other numerical approaches is obtained.

The MAX IV facility presently under construction will include two storage rings for the production of synchrotron radiation. Both rings will be operated at a constant 500 mA of stored current with top-up shots supplied by the MAX IV linac acting as a full-energy injector. Until recently, injection into both storage rings was designed using a conventional approach: a closed four-kicker injection bump brings the stored beam to the septum blade where the injected bunches are captured in a single turn. This method, although commonly found in third generation light sources, has significant disadvantages. Therefore, an alternative injection into the storage rings using pulsed multipoles has been investigated. This type of injection does not require an injection bump and has the potential to make top-up injection fully transparent to users. Design studies have been successfully completed and as a consequence it has been decided to replace the originally foreseen conventional injection scheme with pulsed multipole injection in both MAX IV storage rings. This paper reports on these studies, presents pulsed sextupole injection schemes, and summarizes requirements for the pulsers, sextupole magnets, and vacuum chambers.

Full beam-based alignment of the LHC collimation system was a time-consuming procedure (up to 28 hours) as the collimators were set up manually. A yearly alignment campaign has been sufficient for now, although in the future due to tighter tolerances this may lead to a decrease in the cleaning efficiency if machine parameters such as the beam orbit drift over time. Automating the collimator setup procedure can reduce the beam time for collimator setup and allow for more frequent alignments, therefore reducing the risk of performance degradation. This article describes the design and testing of a semiautomatic algorithm as a first step towards a fully automatic setup procedure. The parameters used to measure the accuracy and performance of the alignment are defined and determined from experimental data. A comparison of these measured parameters at 450 GeV and 3.5 TeV with manual and semiautomatic alignment is provided.

The Large Hadron Collider (LHC) is designed to collide two proton beams with unprecedented particle energy of 7 TeV. Each beam comprises 2808 bunches and the separation between two neighboring bunches is 25 ns. The energy stored in each beam is 362 MJ, sufficient to melt 500 kg copper. Safety of operation is very important when working with such powerful beams. An accidental release of even a very small fraction of the beam energy can result in severe damage to the equipment. The machine protection system is essential to handle all types of possible accidental hazards; however, it is important to know about possible consequences of failures. One of the critical failure scenarios is when the entire beam is lost at a single point. In this paper we present detailed numerical simulations of the full impact of one LHC beam on a cylindrical solid carbon target. First, the energy deposition by the protons is calculated with the FLUKA code and this energy deposition is used in the BIG2 code to study the corresponding thermodynamic and the hydrodynamic response of the target that leads to a reduction in the density. The modified density distribution is used in FLUKA to calculate new energy loss distribution and the two codes are thus run iteratively. A suitable iteration step is considered to be the time interval during which the target density along the axis decreases by 15%–20%. Our simulations suggest that the full LHC proton beam penetrates up to 25 m in solid carbon whereas the range of the shower from a single proton in solid carbon is just about 3 m (hydrodynamic tunneling effect). It is planned to perform experiments at the experimental facility HiRadMat (High Radiation Materials) at CERN using the proton beam from the Super Proton Synchrotron (SPS), to compare experimental results with the theoretical predictions. Therefore simulations of the response of a solid copper cylindrical target hit by the SPS beam were performed. The particle energy in the SPS beam is 440 GeV while it has the same bunch structure as the LHC beam, except that it has only up to 288 bunches. Beam focal spot sizes of $\sigma =0.1$, 0.2, and 0.5 mm have been considered. The phenomenon of significant hydrodynamic tunneling due to the hydrodynamic effects is also expected for the experiments.

The heat load generated by an electron cloud in the cold arcs of the Large Hadron Collider (LHC) is a concern for operation near and beyond nominal beam current. We report the results of simulation studies, with updated secondary-emission models, which examine the severity of the electron heat load over a range of possible operation parameters, both for the nominal LHC and for various luminosity-upgrade scenarios, such as the so-called “full crab crossing” and “early separation” schemes, the “large Piwinski angle” scheme, and a variant of the latter providing “compatibility” with the (upgraded) LHCb experiment. The variable parameters considered are the maximum secondary-emission yield, the number of particles per bunch, and the spacing between bunches. In addition, the dependence of the heat load on the longitudinal bunch profile is investigated.

Beam-beam interaction constraints modify the basic plasma density scalings for a linear collider based on laser-plasma accelerators. In the quantum beamstrahlung regime, it is shown that operating at low plasma density increases beamstrahlung effects, owing to the higher bunch charge and longer bunch length. At high plasma density, the bunch charge is limited by beam loading, and the required power is proportional to the square root of the plasma density. At low plasma density, the bunch charge is limited by beamstrahlung, which, for fixed luminosity, requires operation at higher laser repetition rate and, hence, higher power requirements, or the use of multibunch trains. If round beams are used in a multibunch train format with fixed beam loading, and the collider is constrained by beamstrahlung, then the required collider power is independent of plasma density.

This paper uses the advanced light source (ALS) storage-ring lattice as an example to illustrate the strategies and techniques that we developed for lattice design and optimization. First, the theoretical minimum emittance (TME) theory is applied to optimize the ALS storage-ring lattice for its future upgrades. The study confirms the results found in earlier study using both global scan of all stable settings and multiobjective genetic algorithms (MOGA) techniques. It is shown that, using TME, the ALS natural emittance can be reduced to an even smaller value by introducing additional quadrupoles to the straight, which is unknown in previous studies. Then, the nonlinear properties of the lattice are optimized using MOGA. Instead of the conventionally used dynamic aperture area, the total diffusion rate of the lattice is used as an objective in the optimization, which leads to a superior performance in nonlinear beam dynamics. Finally, to find a best overall working lattice for ALS future upgrades, the linear and nonlinear properties of the lattice are optimized simultaneously using MOGA. Compared to the widely used dynamic aperture tune scan technique, MOGA not only allows us to rapidly find a best working point in a wide searching range, but also provides us trade-offs among the optimization objectives, such as the low emittance, small beta function, and large dynamic aperture. These trade-offs give us a guideline to choose a candidate lattice for ALS future upgrades. The strategies and techniques presented in this paper are not limited to the ALS, and can be adopted to other facilities.

The surface topography of samples after irradiation with heavy ions, protons, and helium ions based on accelerators is an important issue in the study of materials irradiation. We have coupled the separated function radio frequency quadrupole (SFRFQ) electrodes and the traditional RFQ electrodes into a single cavity that can provide a 0.8 MeV helium beam for our materials irradiation project. The higher accelerating efficiency has been verified by the successful commissioning of the prototype SFRFQ cavity. An energy modulated electron cyclotron resonance (ECR) ion source can achieve a well-bunched beam by loading a sine wave voltage onto the extracted electrodes. Bunching is achieved without the need for an external bunch cavity, which can substantially reduce the cost of the system and the length of the beam line. The coupled RFQ-SFRFQ with an energy modulated ECR ion source will lead to a more compact accelerator system. The conceptual design of this novel structure is presented in this paper.

The notion of brightness is efficiently conveyed in geometric optics as density of rays in phase space. Wigner has introduced his famous distribution in quantum mechanics as a quasiprobability density of a quantum system in phase space. Naturally, the same formalism can be used to represent light including all the wave phenomena as originally done by Walther and for synchrotron radiation by Kim. It provides a natural framework for radiation propagation and optics matching by transferring the familiar “baggage” of accelerator physics ($\beta$ function, emittance, phase-space transforms, etc.) to synchrotron radiation. More specifically, the use of Wigner distribution formalism allows a rigorous description of partially coherent non-Gaussian sources, which is generally the case for synchrotron radiation from an undulator with a high degree of transverse coherence. This paper reviews many of the properties of the Wigner distribution starting from quantum mechanics and provides examples of how its use enables physically insightful description of partially coherent synchrotron radiation in phase space. The concepts of diffraction limit and coherence are given an exact correspondence to their quantum mechanical counterparts. In particular, it is shown that the undulator radiation on resonance by a single electron is not diffraction limited though fully coherent. An extension of how to account for practically important cases of electron beams with nearly diffraction limited emittances is presented along with a discussion of appropriate figures of merit suitable for comparing future light sources.

Energy extraction efficiency of a free electron laser (FEL) can be greatly increased using a tapered undulator and self-seeding. However, the extraction rate is limited by various effects that eventually lead to saturation of the peak intensity and power. To better understand these effects, we develop a model extending the Kroll-Morton-Rosenbluth, one-dimensional theory to include the physics of diffraction, optical guiding, and radially resolved particle trapping. The predictions of the model agree well with that of the GENESIS single-frequency numerical simulations. In particular, we discuss the evolution of the electron-radiation interaction along the tapered undulator and show that the decreasing of refractive guiding is the major cause of the efficiency reduction, particle detrapping, and then saturation of the radiation power. With this understanding, we develop a multidimensional optimization scheme based on GENESIS simulations to increase the energy extraction efficiency via an improved taper profile and variation in electron beam radius. We present optimization results for hard x-ray tapered FELs, and the dependence of the maximum extractable radiation power on various parameters of the initial electron beam, radiation field, and the undulator system. We also study the effect of the sideband growth in a tapered FEL. Such growth induces increased particle detrapping and thus decreased refractive guiding that together strongly limit the overall energy extraction efficiency.

We propose a technique to extend noninvasive electro-optic detection of relativistic electron beams to bunch lengths of $\simeq 10\mathrm{fs}$. This is made possible by detecting the frequency mixing that occurs between the optical probe and the space charge fields of the beam, while simultaneously time resolving the resulting mixed frequency signal. The necessary formalism to describe this technique is developed and numerical solutions for various possible experimental conditions are made. These solutions are then compared to simulation results for consistency. Finally, the method to reconstruct the original bunch profile from the proposed diagnostic is discussed and an example showing a 15 fs test beam reconstructed to within an accuracy of 15% is given.