Recent theoretical and experimental studies have shown that the self-amplified spontaneous emission free-electron laser (SASE FEL) with a planar undulator holds a potential for generation of relatively strong coherent radiation at the third harmonic of the fundamental frequency. Here we present a detailed study of the nonlinear harmonic generation in the SASE FEL obtained with a time-dependent FEL simulation code. Using similarity techniques we present universal dependencies for temporal, spectral, and statistical properties of the odd harmonics of the radiation from SASE FEL. In particular, we derived universal formulas for radiation power of the odd harmonics at saturation. It was also found that coherence time at saturation falls inversely proportional to the harmonic number, and relative spectrum bandwidth remains constant with the harmonic number.

The analytical expressions for the multipole longitudinal and transverse impedances of two-layer laminated vacuum chamber are obtained in ultrarelativistic limit. A number of special cases are derived that coincide with the well-known solutions. A numerical example for the impedance of stainless steel–copper laminated vacuum chamber is given.

We revisit the estimation of the power deposited by the electron cloud (EC) in the arc dipoles of the Large Haydron Collider, by means of simulations. We adopt, as simulation input, a set of electron-related parameters closely resembling those used in recent simulations at CERN [F. Zimmermann, in LTC Meeting No. 40, CERN, 2005]. We explore values for the bunch population $N_b$ in the range $0.4\times {10}^{11}\le N_b\le 1.6\times {10}^{11}$, peak secondary electron yield ${\delta }_{\max }$ in the range $1.0\le {\delta }_{\max }\le 2.0$, and bunch spacing $t_b$ either 25 or 75 ns. For $t_b=25\mathrm{ns}$ we find that the EC average power deposition per unit length of beam pipe, $d\overline{P}/dz$, will exceed the available cooling capacity, which we take to be $1.7\mathrm{W}/\mathrm{m}$ at nominal $N_b$ [F. Zimmermann, in LHC MAC Meeting No. 17, 2005], if ${\delta }_{\max }$ exceeds $\sim 1.3$, but $d\overline{P}/dz$ will be comfortably within the cooling capacity if ${\delta }_{\max }\le 1.2$. For $t_b=75\mathrm{ns}$ $d\overline{P}/dz$ exceeds the cooling capacity only when ${\delta }_{\max }>2$ and $N_b>1.5\times {10}^{11}$ taken in combination. The rediffused component of the secondary electron emission spectrum plays a significant role: if we artificially suppress this component while keeping ${\delta }_{\max }$ fixed, $d\overline{P}/dz$ is roughly cut in half for most values of $N_b$ explored here, and in this case we find good agreement with earlier results [F. Zimmermann, in LTC Meeting No. 40, CERN, 2005], as expected. We provide a fairly detailed explanation of the mechanism responsible for such a relatively large effect. We assess the sensitivity of our results to numerical simulation parameters, and to physical parameters such as the photoelectric yield, bunch train length, etc. Owing to the lack of detailed knowledge of the electron emission spectrum, the sensitivity of $d\overline{P}/dz$ to the rediffused component appears to be the most significant source of uncertainty in our results. Nevertheless, taking our results as a whole, the condition ${\delta }_{\max }\le 1.2$ seems to be a conservative requirement for the cooling capacity not to be exceeded.

Linear nonscaling FFAGs (fixed-field alternating gradient accelerators) are machines that use linear magnets to achieve an extremely large energy acceptance (generally a factor of 2 or more). This paper examines the longitudinal dynamics in such a machine, focusing on the longitudinal acceptance, the phase space area that is transmitted without excessive distortion. The paper shows how to compute the distortion in two ways: computing the emittance growth, and computing the distortion of an initial ellipse from an elliptical shape. The paper will describe a model for the longitudinal dynamics in a linear nonscaling FFAG, show how to compute the longitudinal distortion in such a machine using a Dragt-Finn factorization, examine the accuracy of the calculation, and describe how longitudinal acceptance can interact with other performance criteria for an FFAG.

The transverse compression and dynamics of an intense beam propagating through an alternating-gradient quadrupole lattice, plays an important role in many accelerator physics applications. Typically, the compression can be achieved by means of increasing the focusing strength of the lattice along the beam propagation direction. However, beam propagation through the lattice transition region inevitably leads to a certain level of beam mismatch and halo formation. In this work we present a detailed analysis of these phenomena using the envelope equations in the smooth-focusing approximation, which describe the average effects of an alternating-gradient lattice, and full particle-in-cell numerical simulations using the WARP code, taking into account the effects of the alternating-gradient quadrupole field. Simulations are presented for both space-charge–dominated beams, and beams with a moderate space-charge strength.

Capillary channels of $\approx 3\mathrm{cm}$ in length and with plasma densities $\approx {10}^{18}{\mathrm{cm}}^{-3}$ are a promising alternative to the much shorter, higher-density gas jets for GeV-scale laser wakefield acceleration of electrons. However, the large discrepancy between length scales of the plasma and the laser presents a major computational challenge for particle-in-cell (PIC) simulations. Methods are therefore sought that relax the need to concurrently resolve both length scales. For example, the commonly used “moving window” algorithm enables a reduction of the computational domain to a few plasma wavelengths, which is orders of magnitude smaller than the full length of the laser-plasma interaction. In addition, ponderomotive guiding center methods enable relaxation of the constraint to resolve the laser wavelength. These averaging methods split the laser-induced current into a rapidly varying part and a slowly varying envelope. The average over fast time scales is performed in a semianalytic way, leaving the evolution of the laser envelope and the plasma response to be modeled numerically. Here, we present a ponderomotive guiding center algorithm and demonstrate its applicability to model capillary channels by comparing it with fully kinetic PIC simulations.

A formal eigenmode method to solve for electromagnetic fields in a longitudinally translationally invariant multizone dielectric-lined waveguide is presented. The method is specialized to the development of wakefield theory for rectangular dielectric-lined structures which have an arbitrary number of dielectric layers. It is shown that the fields excited by a drive particle moving through the vacuum beam channel in such a structure can simultaneously include both propagating and decaying modes. The decaying modes characterize the short-range self-fields that move together with the particle, while the propagating modes characterize the long-range radiation fields or wakefields that carry energy away from the particle. It is also shown that the formal solution obtained in rectangular structures is applicable to all translationally invariant dielectric-lined waveguides, for example, cylindrical structures. Two important identities which the method relies upon are computationally confirmed for rectangular two-zone dielectric-lined structures. This theory may be employed for calculations of space charge effects, particularly for low or moderate-energy beams where self-field effects cannot be neglected.

The low-level rf control system currently commissioned throughout the Spallation Neutron Source (SNS) LINAC evolved from three design iterations over 1 yr intensive research and development. Its digital hardware implementation is efficient, and has succeeded in achieving a minimum latency of less than 150 ns which is the key for accomplishing an all-digital feedback control for the full bandwidth. The control bandwidth is analyzed in frequency domain and characterized by testing its transient response. The hardware implementation also includes the provision of a time-shared input channel for a superior phase differential measurement between the cavity field and the reference. A companion cosimulation system for the digital hardware was developed to ensure a reliable long-term supportability. A large effort has also been made in the operation software development for the practical issues such as the process automations, cavity filling, beam loading compensation, and the cavity mechanical resonance suppression.

It has been shown that the maintenance condition for a crystalline beam requires that there be no resonance between the crystal’s phonon frequencies, and the frequency associated with a beam moving through a lattice of $N_{\mathrm{sp}}$ periods. This resonance can be avoided provided that the phonon frequencies all are below half the lattice frequency. Here, we study in detail the phonon modes of several crystalline beams. The analytic results obtained in the smooth approximation are compared with numerical evaluations employing Fourier transform of the molecular dynamics (MD) modes. The stability of various crystalline structures is examined through systematic MD simulations based on several different lattice designs. The maintenance condition, when combined with either the simple analytic theory or the numerical evaluation of phonon modes, exhibits excellent agreement with the MD calculations of crystal stability. A confirmed maintenance condition, derived from linear-resonance criteria, is that the lattice frequency must not equal the sum of any two phonon frequencies.

Linear dynamics in a storage ring can be described by the one-turn map matrix. In the case of a resonance where two of the eigenvalues of this matrix are degenerate, a coupling perturbation causes a mixing of the uncoupled eigenvectors. A perturbation formalism is developed to find eigenvalues and eigenvectors of the one-turn map near such a linear resonance. Damping and diffusion due to synchrotron radiation can be obtained by integrating their effects over one turn, and the coupled eigenvectors can be used to find the coupled damping and diffusion coefficients. Expressions for the coupled equilibrium emittances and beam distribution moments are then derived. In addition to the conventional instabilities at the sum, integer, and half-integer resonances, it is found that the coupling can cause an instability through antidamping near a sum resonance even when the symplectic dynamics are stable. As one application of this formalism, the case of linear synchrobetatron coupling is analyzed where the coupling is caused by dispersion in the rf cavity, or by a crab cavity. Explicit closed-form expressions for the sum/difference resonances are given along with the integer/half-integer resonances. The integer and half-integer resonances caused by coupling require particular care. We find an example of this with the case of a crab cavity for the integer resonance of the synchrotron tune. Whether or not there is an instability is determined by the value of the horizontal betatron tune, a unique feature of these coupling-caused integer or half-integer resonances. Finally, the coupled damping and diffusion coefficients along with the equilibrium invariants and projected emittances are plotted as a function of the betatron and synchrotron tunes for an example storage ring based on PEP-II.

The generation of a flat electron beam directly from a photoinjector is an attractive alternative to the electron damping ring as envisioned for linear colliders. It also has potential applications to light sources such as the generation of ultrashort x-ray pulses or Smith-Purcell free electron lasers. In this paper, we report on the experimental generation of a flat beam with a measured transverse emittance ratio of $100\pm 20$ for a bunch charge of $\sim 0.5\mathrm{nC}$; the smaller measured normalized root-mean-square emittance is $\sim 0.4\mu \mathrm{m}$ and is limited by the resolution of our experimental setup. The experimental data, obtained at the Fermilab/NICADD Photoinjector Laboratory, are compared with numerical simulations and the expected scaling laws.

This paper deals with two topics: the generation of incoherent pairs in two beam-beam simulation programs, GUINEA-PIG and CAIN, and the influence of the International Linear Collider (ILC) beam parameter choices on the background in the micro–vertex detector (VD) induced by direct hits. One of the processes involved in incoherent pair creation (IPC) is equivalent to a four fermions interaction and its cross section can be calculated exactly with a dedicated generator, BDK. A comparison of GUINEA-PIG and CAIN results with BDK allows to identify and quantify the uncertainties on IPC background predictions and to benchmark the GUINEA-PIG calculation. Based on this simulation and different VD designs, the five currently suggested ILC beam parameter sets have been compared regarding IPC background induced in the VD by direct IPC hits. We emphasize that the high luminosity set, as it is currently defined, would constrain both the choices of magnetic field and VD inner layer radius.

We propose a novel alignment technique utilizing the x-ray beam of an undulator in conjunction with pinholes and position-sensitive detectors for positioning components of the accelerator, undulator, and beam line in an x-ray free-electron laser. Two retractable pinholes at each end of the undulator define a stable and reproducible x-ray beam axis (XBA). Targets are precisely positioned on the XBA using a pinhole camera technique. Position-sensitive detectors responding to both x-ray and electron beams enable direct transfer of the position setting from the XBA to the electron beam. This system has the potential to deliver superior alignment accuracy ($1–3\mu \mathrm{m}$) for target pinholes in the transverse directions over a long distance (200 m or longer). It can be used to define the beam axis of the electron-beam–based alignment, enabling high reproducibility of the latter. This x-ray–based concept should complement the electron-beam–based alignment and the existing survey methods to raise the alignment accuracy of long accelerators to an unprecedented level. Further improvement of the transverse accuracy using x-ray zone plates will be discussed. We also propose a concurrent measurement scheme during accelerator operation to allow real-time feedback for transverse position correction.

It is shown that there exists an exact paraxial cold-fluid equilibrium of a high-intensity, space-charge-dominated charged-particle beam with a periodically twisted elliptic cross section in a nonaxisymmetric periodic magnetic field. Generalized envelope equations, which determine the beam envelopes, ellipse orientation, density, and internal flow velocity profiles, are derived. Nonrelativistic and relativistic examples of such beam equilibria are presented. The equilibrium and stability of such beams are demonstrated by self-consistent particle-in-cell (PIC) simulations.

We report the use of coherent Smith-Purcell radiation to measure the bunch length of femtosecond-scale, 15 MeV electron bunches produced by a 17 GHz rf accelerator. The Smith-Purcell radiation was produced by passing a train of electron bunches above a metal grating. The radiation was verified as Smith-Purcell radiation by measuring the resonance condition, dependence on beam current, and dependence on beam height above the grating. Measurements of the intensity of the radiation vs emission angle were analyzed to obtain the bunch length. The accelerator was operated in two different modes, producing bunches that were determined to have bunch lengths of 600 and $1000\pm 200\mathrm{fs}$. These nondestructive bunch length measurements were found to agree well with an independent, but destructive, measurement using a microwave deflecting cavity.

We describe capabilities of an integrated software suite to simulate pinched-electron-beam diodes for pulsed radiography. In contrast to other reported work using particle-in-cell methods, we employ a ray-tracing code (Trak) with advanced capabilities for modeling beam-generated magnetic fields. Ray tracing is a direct approach to a steady-state solution and involves less work than a particle-in-cell calculation. The second software component, GamBet, is a new Monte Carlo code for radiation transport that incorporates effects of the complex electric and magnetic fields at the radiation target. The ray-tracing approach exhibits good convergence in calculations for the diode geometry of the compact radiography (CRAD) program at Lawrence Livermore National Laboratory. With a 1.5 MV, 30 ns driver, we predict that the diode can produce a beam with axial length $\sim 1\mathrm{mm}$ that generates isotropic bremsstrahlung radiation exceeding 1 rad at 1 m. The ray-tracing procedure encounters convergence problems when applied to the rod-pinch geometry, a configuration used in several pulsed radiographic machines. We observe a fundamental difference in the nature of electron orbits in the two diodes. There is an increased chance for particle-orbit feedback in the rod pinch, so that equilibrium solutions are sensitive to small changes in emission characteristics.

Frequency-locked Smith-Purcell radiation (FL-SPR), generated by a train of electron bunches traveling above a grating, is characterized by a broad range of frequencies which are locked to the train frequency in a discrete comb and are spatially dispersed in space. We report absolute-scale power measurement of FL-SPR in the millimeter wave range. A 50 ns long train of $170\mu \mathrm{m}$ electron bunches was produced by a 15 MeV, 17 GHz accelerator with 80 mA of average current. The grating had 20 periods spaced by 2.54 mm. The experimental results were compared, on an absolute scale, with the electric-field integral equation model which takes into consideration the finite length of the grating. Very good agreement was obtained. The present results should be useful in planning SPR applications such as diagnostics of electron bunch length on the femtosecond scale and coherent THz radiation sources.

The Twiss parameters provide a convenient description of beam optics in uncoupled linear beam lines. For coupled beam lines, a variety of approaches are possible for describing the linear optics; here, we propose an approach and notation that naturally generalizes the familiar Twiss parameters to the coupled case in 3 degrees of freedom. Our approach is based on an eigensystem analysis of the matrix of second-order beam moments, or alternatively (in the case of a storage ring) on an eigensystem analysis of the linear single-turn map. The lattice functions that emerge from this approach have an interpretation that is conceptually very simple: in particular, the lattice functions directly relate the beam distribution in phase-space to the invariant emittances. To emphasize the physical significance of the coupled lattice functions, we develop the theory from first principles, using only the assumption of linear symplectic transport. We also give some examples of the application of this approach, demonstrating its advantages of conceptual and notational simplicity.