An energy variable ion linac consisting of multigap, constant-$\beta$ cavities was developed. The effect of phase sliding, unavoidable in any constant-$\beta$ section, is leading to a coherent rf phase motion, which fits well to the H-type structures with their long $\pi$-mode sections and separated lenses. The exact periodicity of the cell lengths within each cavity results in technical advantages, such as higher calculation accuracy when only one single period can be simulated, simpler manufacturing, and tuning. This is most important in the case of superconducting cavities. By using this concept, an improved design for a 217 MHz cw superconducting heavy ion linac with energy variation has been worked out. The small output energy spread of $\pm 3\mathrm{AkeV}$ is provided over the whole range of energy variation from 3.5 to 7.3 AMeV. These capabilities would allow for a competitive research in the field of radiochemistry and for a production of super heavy elements (SHE), especially. A first 19-cell cavity of that type was designed, built, and rf tested successfully at the Institute for Applied Physics (IAP) Frankfurt. A 325.224 MHz, seven-cell cavity with constant $\beta =0.16$ is under development and will be operated in a frequency controlled mode. It will be equipped with a power coupler and beam tests with Unilac beams at GSI are foreseen.

The effect of space charge and image currents on the transverse Schottky spectrum for bunched beams has been investigated using simulations combined with an analytic model. We found a good agreement between the shifts of synchrotron satellites observed in the simulation noise spectrum and a simplified model for head-tail modes with space charge and image currents.

Self-consistent Vlasov-Poisson simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel—both in terms of low-order rms (envelope) properties as well as the higher-order phase-space structure. Here, we first review broad classes of kinetic distributions commonly in use as initial Vlasov distributions in simulations of unbunched or weakly bunched beams with intense space-charge fields including the following: the Kapchinskij-Vladimirskij (KV) equilibrium, continuous-focusing equilibria with specific detailed examples, and various nonequilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of standard accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial kinetic distributions are constructed using transformations that preserve linear focusing, single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for noncontinuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulations that more precisely probe intrinsic stability properties and machine performance.

The flat voltage of the main pulse on the load of intense electron-beam accelerators (IEBA) is one of the important factors which affect the quality and characteristic of the output beam current of IEBA. In this paper, the effect of the transition section between the Blumlein pulse forming line (BPFL) and load on the output voltage of IEBA is analyzed in theory. Based on the telegraph equations of the BPFL, a formula which is used to calculate the output voltage of IEBA is obtained, and the factor which affects the output voltage is analyzed. It is found from the theoretical analysis that the wave impedance and transmission time of the transition section influence considerably the fluctuation of the main pulse voltage waveform at the load. In order to get a well-shaped square waveform at load and to improve the electron-beam quality of such an accelerator, there should be a proper wave impedance of the transition section, and the transmission time of the transition section should be designed as short as possible. At last, some experiments are performed on IEBA, and the experimental results show reasonable agreement with theoretical analysis.

Recent measurement of voltage $V$ and current $I$ of the electron gun of a relativistic klystron amplifier revealed that the resulting current-voltage relationship appeared to differ from the usual Child-Langmuir law ($I\propto V^{3/2}$) especially during the initial period of voltage increase. This paper attempts to explain this deviation by examining the emission mechanism using particle-in-cell simulation. The emission area in the cathode increased stepwise as the applied voltage increased and within each step the current and voltage followed the Child-Langmuir law. The electron emission began when the voltage reached a threshold, and the perveance increased with the emission area. Furthermore, an apparent virtual cathode was formed which was larger than the cathode tip. This occurs because, above a certain voltage, the emission from the edge and the side of the cathode surface dominates the emission from the front-end surface.

A new scheme for the compression of electron bunches is proposed. This scheme uses a plasma wave generated by a high intensity laser pulse to compress an electron bunch produced by a typical rf photogun. In the scheme, the electron bunch is injected into a plasma channel in front of the high intensity laser pulse. The laser pulse generates a plasma wave which “sweeps up” the electron bunch resulting in both compression and acceleration. The electron bunch will eventually overtake the laser pulse so that, afterwards, the electrons travel in front of the plasma wave. The scheme differs from previous schemes using a plasma wave to accelerate and compress electron bunches by sacrificing part of the acceleration to get a lower final energy spread and decrease the sensitivity to jitter in the synchronization between laser and electrons. Using a hybrid model, combining particle tracking for the electrons and a relativistic fluid model for the plasma, the scheme is investigated. The model is used to study the effects of the size of the injected bunches, the initial energy spread, and jitter in the laser-bunch synchronization. Also, one of the ways to vary the compression ratio of the scheme is explored by varying the plasma density. From these simulations, it can be concluded that the proposed scheme can compress bunches from an initial size of picoseconds to below one hundred femtoseconds with an energy spread below 0.2%. The scheme can also be adjusted to still produce these bunches in the presence of synchronization jitter up to 1 ps (for the parameters chosen).

We analyze ${\mu }^{+}{\mu }^{-}$ pair production generated by high-energy electrons emerging from a laser-wakefield accelerator. The ${\mu }^{+}{\mu }^{-}$ pairs are created in a solid thick high-$Z$ target, following the electron accelerating plasma region. Numerical estimates are presented for 1 to 10 GeV electron beams which are expected to be reliable in the nearest future. Reactions induced by the secondary bremsstrahlung photons dominate the dimuon production. According to our estimates, a 20 pC electron bunch with energy of 1 (10) GeV may create about 100 (5000) muon pairs. The produced ${\mu }^{\pm }$ can be used in studying various aspects of muon-related physics in tabletop installations. This may be considered as an important step towards the investigation of more complicated elementary processes induced by laser-driven electrons.

An algorithm for optimization of the multicell cavity cells is proposed. Inner cells are optimized for minimal losses or minimal magnetic field, when the aperture diameter, $E_{pk}/E_{\mathrm{acc}}$—the ratio of peak electric field to the accelerating field, and the wall slope angle are given. Optimization of the end cells is done for minimal losses or maximal acceleration in them. Two shapes of the end cells—with and without the end irises—are analyzed. This approach facilitates further optimization for higher order modes extraction because it permits keeping the achieved optimal values nearly the same while changing some dimensions of the cells. Comparison of the proposed cavity geometry with the TESLA cavity geometry illustrates the traits of the presented approach. It is also shown that lower values of the wall slope angle, which lead to the reentrant shape for the inner cells, are also beneficial for the end cells. For the Cornell Energy Recovery Linac most dangerous are dipole modes causing the beam breakup (BBU). Minimization of power of higher order modes (HOMs) in a multicell cavity was done using derivatives of the BBU parameter with respect to geometric parameters of the cavity cells. As a starting point of optimization, the shape with minimal losses at the fundamental mode was taken. Further changing the shape for better propagation of HOMs was done with degradation of the fundamental mode loss parameter $G·R_{\mathrm{sh}}/Q$ within 1% while decrease of the BBU parameter was nearly 3 orders of magnitude. The BBU threshold current tends to be inversely proportional to this parameter.

A few years ago a new theory for producing coherent Smith-Purcell (SP) radiation from an initially continuous beam was proposed. This experiment confirms that two-dimensional theory. The beam was typically 10 cm wide, a few mm thick, with a peak current of 200 A and beam energy of 85 keV. The 10 cm-wide grating had twenty 2-cm periods, and radiation was produced at the fundamental frequency near 4.5 GHz. Second and third harmonics were observed at the expected angles. Beam bunching was measured using a B-dot probe placed at the end of a groove. Generally good agreement between this experiment and the 2D theory is found.

A coaxial-type water load was used to measure the voltage output from a Marx generator for a high power microwave source. This output had a rise time of 20 ns, a pulse duration of a few hundred ns, and an amplitude up to 500 kV. The design of the coaxial water load showed that it is an ideal resistive divider and can also accurately measure a short pulse. Experiments were performed to test the performance of the Marx generator with the calibrated coaxial water load.

The grazing function $g$ is introduced—a synchrobetatron optical quantity that is analogous (and closely connected) to the Twiss and dispersion functions $\beta$, $\alpha$, $\eta$, and ${\eta }^{\prime }$. It parametrizes the rate of change of total angle with respect to synchrotron amplitude for grazing particles, which just touch the surface of an aperture when their synchrotron and betatron oscillations are simultaneously (in time) at their extreme displacements. The grazing function can be important at collimators with limited acceptance angles. For example, it is important in both modes of crystal collimation operation—in channeling and in volume reflection. The grazing function is independent of the collimator type—crystal or amorphous—but can depend strongly on its azimuthal location. The rigorous synchrobetatron condition $g=0$ is solved, by invoking the close connection between the grazing function and the slope of the normalized dispersion. Propagation of the grazing function is described, through drifts, dipoles, and quadrupoles. Analytic expressions are developed for $g$ in perfectly matched periodic FODO cells, and in the presence of $\beta$ or $\eta$ error waves. These analytic approximations are shown to be, in general, in good agreement with realistic numerical examples. The grazing function is shown to scale linearly with FODO cell bend angle, but to be independent of FODO cell length. The ideal value is $g=0$ at the collimator, but finite nonzero values are acceptable. Practically achievable grazing functions are described and evaluated, for both amorphous and crystal primary collimators, at RHIC, the SPS (UA9), the Tevatron (T-980), and the LHC.

We study an impedance due to coherent synchrotron radiation (CSR) generated by a short bunch of charged particles passing through a dipole magnet of finite length in a vacuum chamber of a given cross section. In our method we decompose the electromagnetic field of the beam over the eigenmodes of the toroidal chamber and derive a system of equations for the expansion coefficients in the series. The general method is further specialized for a toroidal vacuum chamber of a rectangular cross section where the eigenmodes can be computed analytically. We also develop a computer code that calculates the CSR impedance for a toroid of rectangular cross section. Numerical results obtained with the code are presented in the paper.

The Large Hadron Collider (LHC) at CERN is equipped with a feed-forward control system known as the field description for the LHC (FiDeL) which is designed to predict the magnetic field and its multipoles, hence reducing the burden on beam based feedback. FiDeL consists of a physical and empirical parametric field model based on magnetic measurements at warm and in cryogenic conditions. It is particularly critical during beam injection when the field decays and at the beginning of acceleration when the field snaps back. It is known that the decay amplitude is largely affected by the powering history of the magnet, particularly by the precycle flattop current and duration and the preinjection preparation duration. Recently, we have collected data that quantify the dependence of the decay amplitude on the precycle ramp rate. This paper presents the results of the measurements performed to investigate this effect, and the method included in FiDeL to model the precycle dependence. With this complete picture of dynamic changes, we finally discuss the effect on the data taken at nominally constant field, along the magnet loadline. We show that a correction for dynamic changes is required for adequate magnet characterization.

The rapid cycling synchrotron of the intense pulsed neutron source at Argonne National Laboratory normally operates at an average beam current of 14 to $15\mu \mathrm{A}$, accelerating protons from 50 to 450 MeV 30 times per second. The beam current is limited by a single-bunch vertical instability that occurs in the later part of the 14 ms acceleration cycle. By analyzing turn-by-turn beam position monitor data, two cases of vertical beam centroid oscillations were discovered. The oscillations start from the tail of the bunch, build up, and develop toward the head of the bunch. The development stops near the bunch center and oscillations remain localized in the tail for a relatively long time (2–4 ms, $1–2\times {10}^4$ turns). This vertical instability is identified as the cause of the beam loss. We compared this instability with a head-tail instability that was purposely induced by switching off sextupole magnets. It appears that the observed vertical instability is different from the classical head-tail instability.

We propose a dielectric photonic structure for ultrafast deflection and focusing of relativistic charged particle beams. The structure is designed to transform a free-space laser beam into a deflection force that acts on the free particles with the same optical phase over a distance of travel that is much greater than the laser wavelength. The proposed structure has a two-dimensional geometry and is compatible with existing nanofabrication methods. Deflection fields of $\mathrm{GV}/\mathrm{m}$ magnitude and subfemtosecond switching speeds are expected to be possible from these dielectric structures. With these elements a submeter scale extreme ultraviolet synchrotron source seems feasible.

A new local field quantity is presented which gives the high gradient performance limit of accelerating structures due to vacuum rf breakdown. The new field quantity, a modified Poynting vector $S_c$, is derived from a model of the breakdown trigger in which field emission currents from potential breakdown sites cause local pulsed heating. The field quantity $S_c$ takes into account both active and reactive power flow on the structure surface. This new quantity has been evaluated for many X-band and 30 GHz rf tests, both traveling wave and standing wave, and the value of $S_c$ achieved in the experiments agrees well with analytical estimates.

Laser-plasma accelerators are expected to deliver electron bunches with high space charge fields. Several recent publications have addressed the impact of space charge effects on such bunches after the extraction into vacuum. Artifacts due to the approximation of retardation effects are addressed, which are typically either neglected or approximated. We discuss a much more appropriate calculation for the case of laser wakefield acceleration with negligible retardation artifacts due to the calculation performed in the mean rest frame. This presented calculation approach also aims at a validation of other simulation approaches.

A form is given of the retarded electric field and magnetic induction generated by the motion of a charged particle that expresses these fields as integrals of the retarded charge density only, with kernels depending on the charge velocity and acceleration fields. In the case of a single pointlike charge, the usual Liénard-Wiechert fields follow very easily. The set of equations for the dynamics of particles in assigned electromagnetic fields with the self-consistent field is written and integrated. The code Retar for the dynamics of charged particles in external and self-consistent fields is described and a few examples of benchmark are proposed. As a physical application, the case of an electron beam moving in a bending magnetic dipole is examined, and the radiation produced analyzed, in order to characterize a therahertz radiation source.