Optics parameters such as betatron tunes, beta functions, and dispersions depend on momentum deviation. Such dependence is characterized by general chromaticity. General chromaticity can induce emittance growth and luminosity degradation in colliders. To investigate the influence of general chromaticity on beam dynamics, a symplectic map for chromaticity was implemented in the beam-beam codes and used in simulations at KEKB. A systematic investigation revealed that chromatic $X\mathrm{\text{−}}Y$ couplings can deteriorate the machine luminosity in the order of 10% with head-on colliding beams. The results of this study triggered the installation of skew sextupoles to KEKB rings for the purpose of correcting the chromatic $X\mathrm{\text{−}}Y$ couplings. Beam commissioning with skew-sextupole tuning knobs at KEKB has proved to be very successful; a new world’s record luminosity of $2.1\times {10}^{34}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$ was achieved with Belle taking data in June, 2009. In this paper, we discuss the approach of general chromaticity and present the results of simulations at KEKB.

This discussion revisits two articles on synchrotron radiation damping published in 1958, one by this author and Evgeny K. Tarasov [Zh. Eksp. Teor. Fiz. 34, 651 (1958); Sov. Phys. JETP 34, 449 (1958)], and one by Kenneth W. Robinson [Phys. Rev. 111, 373 (1958)]. The latter is the source of what is known as “Robinson’s sum rule.” Both present the familiar rule, but with very different proofs and calculations of concrete damping decrements. Comparative analysis of these differences reveals serious flaws in Robinson’s proof and calculations.

A three-dimensional, fully electromagnetic model of the principal pulsed-power components of the 26-MA ZR accelerator [D. H. McDaniel et al., in Proceedings of the 5th International Conference on Dense $Z$-Pinches (AIP, New York, 2002), p. 23] has been developed. This large-scale simulation model tracks the evolution of electromagnetic waves through the accelerator’s intermediate-storage capacitors, laser-triggered gas switches, pulse-forming lines, water switches, triplate transmission lines, and water convolute to the vacuum insulator stack. The insulator-stack electrodes are coupled to a transmission-line circuit model of the four-level magnetically insulated vacuum-transmission-line section and double-post-hole convolute. The vacuum-section circuit model is terminated by a one-dimensional self-consistent dynamic model of an imploding $z$-pinch load. The simulation results are compared with electrical measurements made throughout the ZR accelerator, and are in good agreement with the data, especially for times until peak load power. This modeling effort demonstrates that 3D electromagnetic models of large-scale, multiple-module, pulsed-power accelerators are now computationally tractable. This, in turn, presents new opportunities for simulating the operation of existing pulsed-power systems used in a variety of high-energy-density-physics and radiographic applications, as well as even higher-power next-generation accelerators before they are constructed.

A new dc high voltage spin-polarized photoelectron gun has been constructed that employs a compact inverted-geometry ceramic insulator. Photogun performance at 100 kV bias voltage is summarized.

We investigate the operation of a load current multiplier (LCM) on a pulse-forming-line nanosecond pulse-power generator. Potential benefits of using the LCM technique on such generators are studied analytically for a simplified case. A concrete LCM design on the Zebra accelerator (1.9 Ohm, $\sim 1\mathrm{MA}$, 100 ns) is described. This design is demonstrated experimentally with high-voltage power pulses having a rise time of dozens of nanoseconds. Higher currents and magnetic energies were observed in constant-inductance solid-state loads when a better generator-to-load energy coupling was achieved. The load current on Zebra was increased from the nominal 0.8–0.9 MA up to about 1.6 MA. This result was obtained without modifying the generator energetics or architecture and it is in good agreement with the presented numerical simulations. Validation of the LCM technique at a nanosecond time scale is of importance for the high-energy-density physics research.

The coupling impedance of beam tubes is a long-standing important topic for particle accelerators that many authors have addressed. The present study was initiated in view of a specific problem, but its novel approach is broadly applicable to the longitudinal and transverse coupling impedances of coated beam tubes or multilayer tubes. The matrix method presented here derives the wall impedance by treating the radial wave propagation of the beam-excited electromagnetic fields in full analogy to longitudinal transmission lines. Starting from the Maxwell equations, the radially transverse magnetic field components are described for monopole and dipole modes by a $2\times 2$ matrix. Assuming isotropic material properties within one layer, the transverse field components at the inner boundary of a layer uniquely are determined by matrix transfer of the field components at its outer boundary. By imposing power-flow constraints on the matrix, wave impedance mapping and field matching between layers is enforced and replaced by matrix multiplication. The longitudinal and transverse coupling impedances are derived from the wall impedance at the innermost boundary, and the different procedures for its determination are discussed. The matrix method is demonstrated via selected yet representative examples of the well-documented cases of a stainless-steel tube, and of a graphite collimator.

The aim of this paper is to investigate the effect of the magnetic bunch length compression on the development of the microbunching instability. It will be shown that, after removing the linear energy chirp required for the compression, an additional and properly tuned $R_{\mathbf{56}}$ transport matrix element is able to dilute the initial energy modulation and to suppress the current spikes created by the microbunching instability without affecting the bunch length. A by-product of the study is the observation that a single compressor is more effective than the two-compressors scheme in reducing the unwanted modulations caused by the microbunching instability. The study is based on analytical calculations and on the simulation code elegant.

Circular machines are plagued by coupled bunch instabilities (CBI), driven by impedance peaks, where then all cavity higher order modes (HOMs) are possible drivers. Limiting the CBI growth rate is the fundamental reason that all superconducting rf cavities in circular machines are equipped with HOM dampers. The question arises if for similar reasons HOM damping would not be imperative also in high current superconducting rf proton linacs. Therefore we have simulated the longitudinal bunched beam dynamics in such machines, also including charge and position noise on the injected bunches. Simulations were executed for a generic linac with properties close to the planned SPL at CERN, SNS, or Project X at FNAL. It was found that with strong bunch noise and monopole HOMs with high $Q_{\mathrm{ext}}$ large beam scatter, possibly exceeding the admittance of a receiving machine, cannot be excluded. A transverse simulation shows similar requirements. Therefore including initial bunch noise in any beam dynamic study on superconducting rf cavities in high current proton linacs is advisable before envisaging to omit all HOM dampers.

A technique is proposed to generate electron beam with ultralow transverse emittance through laser assisted transverse-to-longitudinal emittance exchange. In the scheme a laser operating in the TEM10 mode is used to interact with the electron beam in a dispersive region and to initiate the emittance exchange. It is shown that with the proposed technique one can significantly downsize an x-ray free electron laser (FEL), which may greatly extend the availability of these light sources. A hard x-ray FEL operating at 1.5 Å with a saturation length within 30 meters using a 3.8 GeV electron beam is shown to be practically feasible.

The CLIC study is exploring the scheme for an electron-positron collider with a center-of-mass energy of 3 TeV in order to make the multi-TeV range accessible for lepton physics. The current goal of the project is to demonstrate the feasibility of the technology by the year 2010. Recently, important progress has been made concerning the high-gradient accelerating structure tests and the experiments with beam in the CLIC test facility, CTF3. Several important aspects of the project are dealt with through international collaborations, which has considerably boosted the CLIC study.

Future ampere-class energy recovery linacs (ERLs) based on superconducting technology demand efficient damping of the higher-order modes in the superconducting radio-frequency (SRF) accelerating structures to achieve stable beam operation in multipass, multibeam ERLs. We propose a new and novel SRF structure that is extremely efficient in damping the higher-order modes of SRF structures for ERLs. Initial simulation results indicate extremely good and efficient damping of the dipole and the quadrupole modes that determine the beam breakup threshold of the superconducting structures. The proposed new structure has the added benefit of having simpler fabrication steps with potential fabrication cost savings.

The edge-focusing (EF) wiggler, which produces the strong field gradient for transverse focusing incorporated with the normal wiggler field, has been fabricated to evaluate its performance rigorously with the magnetic field measurement. It is a five-period planar wiggler with an edge angle of 2° and a period length of 60 mm. The magnetic field in the wiggler is measured using Hall probes at four different wiggler gaps. It is experimentally confirmed that a high field gradient of $1.0\mathrm{T}/\mathrm{m}$ is realized, as designed, along the beam axis in the EF wiggler. The magnetic field gradient of the EF wiggler is derived as a function of the magnetic gap. The field gradient decreases with increasing magnet gap more slowly than the peak magnetic field does for the present experimental model. An analytic formula for the field gradient of the EF wiggler is derived and it is shown that the slope of the field gradient with the magnet gap can be changed by varying the magnet width of the EF wiggler.

We report on an experimental study of space-charge effects in a radio-frequency (rf) photoinjector. A 5 MeV electron bunch, consisting of a number of beamlets separated transversely, was generated in an rf photocathode gun and propagated in the succeeding drift space. The collective interaction of these beamlets was studied for different experimental conditions. The experiment allowed the exploration of space-charge effects and its comparison with 3D particle-in-cell simulations. Our observations also suggest the possible use of a multibeam configuration to tailor the transverse distribution of an electron beam.

Wakefield excitation has been experimentally studied in a three-cell X-band standing wave photonic band gap (PBG) accelerating structure. Major monopole (${\mathrm{TM}}_{01}$- and ${\mathrm{TM}}_{02}$-like) and dipole (${\mathrm{TM}}_{11}$- and ${\mathrm{TM}}_{12}$-like) modes were identified and characterized by precisely controlling the position of beam injection. The quality factor $Q$ of the dipole modes was measured to be $\sim 10\mathrm{times}$ smaller than that of the accelerating mode. A charge sweep, up to 80 nC, has been performed, equivalent to $\sim 30\mathrm{MV}/\mathrm{m}$ accelerating field on axis. A variable delay low charge witness bunch following a high charge drive bunch was used to calibrate the gradient in the PBG structure by measuring its maximum energy gain and loss. Experimental results agree well with numerical simulations.

A new technique of undulator field correction for cryogenic permanent magnet undulators (CPMUs) is proposed to correct the phase error induced by temperature gradient. This technique takes advantage of two important instruments: one is the in-vacuum self-aligned field analyzer with laser instrumentation system to precisely measure the distribution of the magnetic field generated by the permanent magnet arrays placed in vacuum, and the other is the differential adjuster to correct the local variation of the magnet gap. The details of the two instruments are described together with the method of how to analyze the field measurement data and deduce the gap variation along the undulator axis. The correction technique was applied to the CPMU with a length of 1.7 m and a magnetic period of 14 mm. It was found that the phase error induced during the cooling process was attributable to local gap variations of around $30\mu \mathrm{m}$, which were then corrected by the differential adjuster.

Transverse coherent oscillations of a bunched beam in a ring accelerator are considered with space charge dominated impedance, taking into account linear synchrotron oscillations. A general equation of the bunch eigenmodes is derived, its exact analytical solution is presented for boxcar bunch, and numerical solutions are found for several realistic models. Both low and high synchrotron frequency approximations are considered and compared, fields of their applicability are determined, and some estimations are developed in the intermediate region. It is shown that most of the bunch eigenmodes are stabilized by Landau damping due to the space charge produced tune spread.

Trapping by resonances or scattering off resonances induced by space charge (SC) or electron cloud (EC) in conjunction with synchrotron motion can explain observations of slow beam loss and emittance growth, which are often accompanied by changes in the longitudinal beam profile. In this paper we review the recent progress in understanding and modeling of the underlying mechanisms, highlight the differences and similarities between space charge and electron cloud, and discuss simulation results in the light of experimental observations, e.g., at GSI, CERN, and BNL. In particular, we address the role of the pinched electrons and describe in detail the complexity of the electron pinch formation. We present simulation results within a dipole or in a field-free region of the beam pipe, which reveal the morphology and main features of this phenomenon, explain the physical origin of the complex electron structures like stripe in either field configuration, and discuss the dependence on some key parameters.

Two-dimensional particle-in cell simulation shows that protons in a small target located in an underdense high-mass plasma can be accelerated by the radiation pressure of a short circularly polarized laser pulse as well as by the wake bubble field of the laser in the background plasma. The radiation-pressure preaccelerated protons are easily trapped and accelerated stably in front of the bubble for a relatively long distance. It is found that a quasimonoenergetic proton beam of 38 GeV peak energy and 12.6% energy spread as well as small divergence angle can be obtained with a ${10}^{23}\mathrm{W}/{\mathrm{cm}}^2$ 18.26 kJ laser pulse in a tritium plasma of density $5.2\times {10}^{20}{\mathrm{cm}}^{-3}$.

We describe herein a system of self-magnetically insulated vacuum transmission lines (MITLs) that operated successfully at 20 MA, 3 MV, and 55 TW. The system delivered the electromagnetic-power pulse generated by the $Z$ accelerator to a physics-package load on over 1700 $Z$ shots. The system included four levels that were electrically in parallel. Each level consisted of a water flare, vacuum-insulator stack, vacuum flare, and 1.3-m-radius conical outer MITL. The outputs of the four outer MITLs were connected in parallel by a 7.6-cm-radius 12-post double-post-hole vacuum convolute. The convolute added the currents of the four outer MITLs, and delivered the combined current to a single 6-cm-long inner MITL. The inner MITL delivered the current to the load. The total initial inductance of the stack-MITL system was 11 nH. A 300-element transmission-line-circuit model of the system has been developed using the tl code. The model accounts for the following: (i) impedance and electrical length of each of the 300 circuit elements, (ii) electron emission from MITL-cathode surfaces wherever the electric field has previously exceeded a constant threshold value, (iii) Child-Langmuir electron loss in the MITLs before magnetic insulation is established, (iv) MITL-flow-electron loss after insulation, assuming either collisionless or collisional electron flow, (v) MITL-gap closure, (vi) energy loss to MITL conductors operated at high lineal current densities, (vii) time-dependent self-consistent inductance of an imploding $z$-pinch load, and (viii) load resistance, which is assumed to be constant. Simulations performed with the tl model demonstrate that the nominal geometric outer-MITL-system impedance that optimizes overall performance is a factor of $\sim 3$ greater than the convolute-load impedance, which is consistent with an analytic model of an idealized MITL-load system. Power-flow measurements demonstrate that, until peak current, the $Z$ stack-MITL system performed as expected. tl calculations of the peak electromagnetic power at the stack, stack energy, stack voltage, outer-MITL current, and load current, as well as the pinch-implosion time, agree with measurements to within 5%. After peak current, tl calculations and measurements diverge, which appears to be due in part to the idealized pinch model assumed by tl. The results presented suggest that the design of the $Z$ accelerator’s stack-MITL system, and the tl model, can serve as starting points for the design of stack-MITL systems of future superpower accelerators.

MAX IV will be Sweden’s next-generation high-performance synchrotron radiation source. The project has recently been granted funding and construction is scheduled to begin in 2010. User operation for a broad and international user community should commence in 2015. The facility is comprised of two storage rings optimized for different wavelength ranges, a linac-based short-pulse facility and a free-electron laser for the production of coherent radiation. The main radiation source of MAX IV will be a 528 m ultralow emittance storage ring operated at 3 GeV for the generation of high-brightness hard x rays. This storage ring was designed to meet the requirements of state-of-the-art insertion devices which will be installed in nineteen 5 m long dispersion-free straight sections. The storage ring is based on a novel multibend achromat design delivering an unprecedented horizontal bare lattice emittance of 0.33 nm rad and a vertical emittance below the 8 pm rad diffraction limit for 1 Å radiation. In this paper we present the beam dynamics considerations behind this storage-ring design and detail its expected unique performance.