Using field matching techniques, closed form analytic expressions for the transverse impedance and for the shielding effectiveness of a smooth cylindrical beam pipe of arbitrary thickness are presented. In the limit of thick and thin beam pipes the well-known expressions are reproduced. The transverse transmission coefficient is compared with the longitudinal one that has been obtained in our previous work [A. M. Al-Khateeb, O. Boine-Frankenheim, R. W. Hasse, and I. Hofmann, Phys. Rev. E 71, 026501 (2005).]. The results are applied to the heavy ion synchrotron SIS 18 and to the planned SIS 100 at GSI. In both machines the stainless steel beam pipe in the dipole sections is much thinner than the skin depths at the revolution frequency and, therefore, the impedance value and the transmission are of concern.

Collective effects with strong coupling between the longitudinal and transverse dynamics are of fundamental importance for applications of high-intensity bunched beams. The self-consistent Vlasov-Maxwell equations are applied to high-intensity finite-length charge bunches, and a generalized particle simulation algorithm is developed for bunched beams with or without energy anisotropy. The nonlinear method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. Systematic studies are carried out under conditions corresponding to strong 3D nonlinear space-charge forces in the beam frame. For charge bunches with isotropic energy, finite bunch-length effects are clearly evident by the fact that the spectra for an infinitely long coasting beam and a nearly spherical charge bunch have strong similarities, whereas the spectra have distinctly different features when the bunch length is varied between these two limiting cases. For bunched beams with anisotropic energy, there exists no exact kinetic equilibrium because the particle dynamics do not conserve transverse energy and longitudinal energy separately. A reference state in approximate dynamic equilibrium has been constructed theoretically, and a quasi-steady state has been established in the simulations for the anisotropic case. Collective excitations relative to the reference state have been simulated using the generalized algorithm. In particular, the electrostatic Harris instability driven by strong energy anisotropy is investigated for a finite-length charge bunch. The observed growth rates are larger than those obtained for infinitely long coasting beams. However, the growth rate decreases for increasing bunch length to a value similar to the case of a long coasting beam. For long bunches, the instability is axially localized symmetrically relative to the beam center, and the characteristic wavelength in the longitudinal direction is comparable to the transverse dimension of the beam.

A theoretical methodology promising improved design of vacuum insulation in high-voltage pulsed-power systems is described. It consists of shaping the electromagnetic fields within the system in such a way that charged particles which can in principle initiate vacuum surface breakdown are deflected away from the insulator surface, and secondary electrons, if emitted, are prevented from restriking the surface. Thus, vacuum surface breakdown is prevented before it is able to develop. Our methodology is presented here by a set of case studies.

The extraordinary ability of space-charge waves in plasmas to accelerate charged particles at gradients that are orders of magnitude greater than in current accelerators has been well documented. We develop a phenomenological framework for laser wakefield acceleration (LWFA) in the 3D nonlinear regime, in which the plasma electrons are expelled by the radiation pressure of a short pulse laser, leading to nearly complete blowout. Our theory provides a recipe for designing a LWFA for given laser and plasma parameters and estimates the number and the energy of the accelerated electrons whether self-injected or externally injected. These formulas apply for self-guided as well as externally guided pulses (e.g. by plasma channels). We demonstrate our results by presenting a sample particle-in-cell (PIC) simulation of a $30\mathrm{fs}$, 200 TW laser interacting with a 0.75 cm long plasma with density $1.5\times {10}^{18}{\mathrm{cm}}^{-3}$ to produce an ultrashort (10 fs) monoenergetic bunch of self-injected electrons at 1.5 GeV with 0.3 nC of charge. For future higher-energy accelerator applications, we propose a parameter space, which is distinct from that described by Gordienko and Pukhov [Phys. Plasmas 12, 043109 (2005)] in that it involves lower plasma densities and wider spot sizes while keeping the intensity relatively constant. We find that this helps increase the output electron beam energy while keeping the efficiency high.

A possible scenario for the luminosity upgrade of the Large Hadron Collider is based on large aperture quadrupoles to lower ${\beta }^{*}$ in the interaction regions. Here we analyze the measurements relative to the field quality of the RHIC and LHC superconducting quadrupoles to find out the dependence of field errors on the size of the magnet aperture. Data are interpreted in the framework of a Monte Carlo analysis giving the reproducibility in the coil positioning reached in each production. We show that this precision is likely to be independent of the magnet aperture. Using this result, we can carry out an estimate of the impact of the field quality on the beam dynamics for the collision optics.

The wakefields of a relativistic electron beam passing through a waveguide loaded with an active medium with weak resonant dispersion are considered. For the calculations in this paper, the parameters of the medium are those of a solution of fullerene (${\mathrm{C}}_{60}$) in a nematic liquid crystal that exhibits activity in the X-band. It is shown that several of the $\mathrm{TM}$ accelerating modes can be amplified for the geometries under consideration; structures in which higher order modes are amplified exhibit essential advantages as PASERs. In particular, the amplification of the highest mode occurs in a structure loaded with a rather thick active medium layer that maximizes the energy stored by the active medium.

A major expense and design challenge in carbon/proton cancer therapy machines are the isocentric gantries. The transport elements of the carbon/proton gantry are presently made of standard conducting dipoles. Because of their large weight, of the order of $\sim 100\mathrm{\text{tons}}$, the total weight of the gantry with support structure is $\sim 600\mathrm{\text{tons}}$. The novel gantry design that is described here is made of fixed field superconducting magnets, thus dramatically reducing magnet size and weight compared to conventional magnets. In addition, the magnetic field is constant throughout the whole energy region required for tumor treatment. Particles make very small orbit offsets, passing through the beam line. The beam line is built of combined-function dipoles such as a nonscaling fixed field alternating gradient (NS-FFAG) structure. The very large momentum acceptance NS-FFAG comes from very strong focusing and very small dispersion. The NS-FFAG small magnets almost completely filled the beam line. They first make a quarter (or close to a quarter) of an arc bending upward and an additional half of a circle beam line finishing so that the beam is pointed towards the patient. At the end of the gantry, additional magnets with a fast response are required to allow radial scanning and to provide the required position and spot size. The fixed field combined-function magnets for the carbon gantry could be made of superconducting magnets by using low temperature superconducting cable or by using high temperature superconductors.

Coherent synchrobetatron resonances can present a serious limit for low-energy synchrotrons. An excitation of a dipole transverse mode is considered at resonance condition. As an example, the growth rate for the Fermilab Booster is estimated.

Nonscaling fixed field alternating gradient (FFAG) rings for cancer hadron therapy offer reduced physical aperture and large dynamic aperture as compared to scaling FFAGs. The variation of tune with energy implies the crossing of resonances during acceleration. Our design avoids intrinsic resonances, although imperfection resonances must be crossed. We consider a system of three nonscaling FFAG rings for cancer therapy with 250 MeV protons and $400\mathrm{MeV}/u$ carbon ions. Hadrons are accelerated in a common radio frequency quadrupole and linear accelerator, and injected into the FFAG rings at $v/c=0.1294$. ${\mathrm{H}}^{+}/{\mathrm{C}}^{6+}$ ions are accelerated in the two smaller/larger rings to 31 and $250\mathrm{MeV}/68.8$ and $400\mathrm{MeV}/u$ kinetic energy, respectively. The lattices consist of doublet cells with a straight section for rf cavities. The gantry with triplet cells accepts the whole required momentum range at fixed field. This unique design uses either high-temperature superconductors or superconducting magnets reducing gantry magnet size and weight. Elements with a variable field at the beginning and at the end set the extracted beam at the correct position for a range of energies.

We present a theoretical formulation for calculating the electromagnetic space-charge fields within a simplified electron source geometry using time-dependent Green’s function methods. The source geometry is assumed to be comprised of a flat cathode along with a pipe of arbitrary but uniform cross section. Under the assumption that the beam currents are parallel to the pipe axis, we derive exact solutions for the electromagnetic potentials in the Lorentz gauge. In addition, for the special case of a pipe with rectangular cross section, we present the exact solutions of the electromagnetic potentials for arbitrary beam currents. Finally, we show the results of an analytical benchmark study in which the electromagnetic fields that are solved using the Green’s function method are in excellent agreement ($<1\%$ error) with the benchmark fields.

Even at a continuous wave facility such as CEBAF at Jefferson Lab, an electron beam with long time intervals (tens of ns) between individual bunches can be useful, for example, to isolate sources of background via time of flight detection or to measure the energy of neutral particles that cannot be separated with a magnetic field. This paper describes a demonstrated method to quickly and easily deliver bunches with repetition rates of 20 to 100 MHz corresponding to time intervals between 50 and 10 ns (respectively). This is accomplished by changing the ON/OFF frequency of the photogun drive laser by a small amount ($\Delta f/f<20\%$), resulting in a bunch frequency equal to the beat frequency between the radio frequencies of the drive laser and the photoinjector chopper system.

One possible way to demonstrate both the efficiency and beam quality in a plasma wakefield accelerator is to prepare matched drive and accelerated beams by removing a central slice from a single high-quality electron bunch (parent beam). For parameters of the parent beam given, the question arises how to maximize the number and energy of accelerated particles and minimize their energy spread and emittance. This question is addressed by numerical simulations. The optimum shape of the beams, required plasma length, achievable energy gain, and energy spread are found as functions of the plasma density and parent beam characteristics. The required control accuracy of adjustable beam and plasma parameters is determined.

Direct numerical methods for solving the Vlasov equation offer some advantages over macroparticle simulations, as they do not suffer from the consequences of the statistical fluctuations inherent in using a number of macroparticles smaller than the bunch population. Unfortunately, these methods are more time consuming and generally considered impractical in a full 6D phase space. However, in a lower-dimension phase space they may become attractive if the beam dynamics is sensitive to the presence of small charge-density fluctuations and a high resolution is needed. In this paper we present a 2D Vlasov solver for studying the longitudinal beam dynamics in single-pass systems of interest for x-ray FELs, where characterization of the microbunching instability stemming from self-field amplified noise is of particular relevance.

A new technique for the simulation of coherent synchrotron radiation (CSR) and space-charge fields from a single electron bunch in straight or toroidal rectangular waveguide sections has been developed. It is based on the integration of the paraxial approximation to the wave equations, using the perturbation technique where the bending radius is large compared to the dimension of the waveguide. We have implemented an unconditionally stable integration method in the time domain with transparent boundary conditions that allows the use of a minimally sized computational domain about the bunch. This technique explicitly enforces the causality condition so that no portion of the fields can propagate faster than the speed of light, can be used with arbitrary three-dimensional charge distributions, and contains corrections for finite energy. We have also developed a method for the calculation of the transverse forces within the bunch including space-charge. This method has been developed for incorporation with a particle-in-cell code so that we may self-consistently model CSR and space-charge in combinations of bending sections with a fully dynamic electron bunch in an efficient manner. In this paper we describe the model and methods for calculation of the fields in detail and compare results to theory wherever possible.

In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually equivalent to the approximation of geometric optics in electromagnetic theory. Using this approximation, we derive equations for the longitudinal impedance for arbitrary offsets, with respect to a reference orbit, of source and test particles. With the help of the Panofsky-Wenzel theorem, we also obtain expressions for the transverse impedance (also for arbitrary offsets). We further simplify these expressions for the case of the small offsets that are typical for practical applications. Our final expressions for the impedance, in the general case, involve two-dimensional integrals over various cross sections of the transition. We further demonstrate, for several known axisymmetric examples, how our method is applied to the calculation of impedances. Finally, we discuss the accuracy of the optical approximation and its relation to the diffraction regime in the theory of impedance.

Fast proportional rf control is used as the basis for rf field regulation in actual linear accelerator projects like the international linear collider (ILC) and the European x-ray free electron laser (XFEL) based on TESLA technology. Additional control loops improve the field regulation by treating repetitive effects and compensating the beam loading. Nevertheless, the ability for high gain operation of the fast loops is desirable for the strong suppression of nonpredictive and nonrepetitive disturbances. TESLA cavities host nine fundamental modes (FMs) where only one is used for beam acceleration. The unwanted FMs have a significant influence on the proportional rf control loop stability at high gains. Within this paper, the stability of proportional rf control loops taking the FMs and digitalization effects into account will be discussed in detail together with measures enabling a significant increase of the gain values.

The longitudinal wake is considered for a bunch of electrons that are suddenly accelerated to an ultrarelativistic velocity. This wake describes the wake of forward transition radiation, and it approximates the edge-radiation wake of a bunch exiting a bending magnet. The wake is large within the radiation formation zone, where it provides resistive impedance. A comparison with the computed wake downstream of a bending magnet yields good agreement, indicating that our wake expressions may be used to approximate the wake without numerical computation. For schemes in which a bunch produced by laser-plasma acceleration exits the plasma and then drives a free electron laser (FEL), the transition-radiation wake causes energy losses of many MeV that may affect the FEL process.

Thin carbon foils are used as strippers for charge exchange injection into high intensity proton rings. However, the stripping foils become radioactive and produce uncontrolled beam loss, which is one of the main factors limiting beam power in high intensity proton rings. Recently, we presented a scheme for laser stripping an ${\mathrm{H}}^{-}$ beam for the Spallation Neutron Source (SNS) ring. First, ${\mathrm{H}}^{-}$ atoms are converted to ${\mathrm{H}}^0$ by a magnetic field, then ${\mathrm{H}}^0$ atoms are excited from the ground state to the upper levels by a laser, and the excited states are converted to protons by a magnetic field. In this paper we report on the proof-of-principle demonstration of this scheme to give high efficiency (around 90%) conversion of ${\mathrm{H}}^{-}$ beam into protons at SNS in Oak Ridge. The experimental setup is described, and comparison of the experimental data with simulations is presented.

Integrated multipoles may perturb the beam dynamics in accelerators. In particular in periodic magnets, as undulators and wigglers, only the odd orders in the U.S. notation have to be considered, because the other ones compensate themselves in each period of the magnet. In the past, several methods have been considered to reduce them, but, if their effects on the beam are very strong, because of the small particles energy and mass, and in long period magnets, a different solution has to be explored. The method proposed in this article consists in compensating the contribution to the integral of the region between the poles with the one of the pole regions in each semiperiod of the magnet. It will be shown that this condition can be achieved by displacing the magnetic axis in each semiperiod of the magnet. To demonstrate the validity of this approach, it has been applied and optimized on a real wiggler.

We describe the improvements of a Fresnel zone plate (FZP) beam-profile monitor, which is being developed at the KEK-ATF damping ring to measure ultralow emittance electron-beam profiles. This monitor, which is designed to have a submicrometer spatial resolution, is based on x-ray imaging optics composed of two FZPs. Various improvements were performed to the old setup. First, a new crystal monochromator was introduced to suppress the beam image drift. Second, the two FZP folders were improved in order to realize a precise beam-based alignment during x-ray imaging. Third, a fast mechanical shutter was installed to achieve a shorter time resolution, and an x-ray mask system was also installed to obstruct direct synchrotron radiation through the FZPs. These improvements could make beam-profile measurements more precise and reliable. The beam profiles with less than $50\mu \mathrm{m}$ horizontal beam size and less than $6\mu \mathrm{m}$ vertical beam size could be measured within a 1 ms time duration. Furthermore, measurements of the damping time and the coupling dependence of the ATF damping ring were successfully carried out with this upgraded FZP monitor.