In the proximity of a nonlinear resonance $\nu \approx \frac{m}{n}$, the beam distribution in a storage ring is distorted depending on how close is the resonance and how strong is the resonance strength. In the 1-dimensional case, it is well known that the particle motion near the resonance can be described in a smooth approximation by a Hamiltonian of the form $(\nu -\frac{m}{n})J+D_{\nu }(J)+f_1(\phi ,J)$, where $(\phi ,J)$ are the phase space angle and action variables, $D_{\nu }$ is the detuning function, and $f_1$ is an oscillating resonance term. In a proton storage ring, the equilibrium beam distribution is readily solved to be any function exclusively of the Hamiltonian. For an electron beam, this is not true and the equilibrium distribution is more complicated. This paper solves the Fokker-Planck equation near a single resonance for an electron beam in a storage ring. The result is then applied to obtain the quantum lifetime of an electron beam in the presence of this resonance. Resonances due to multipole fields and due to the beam-beam force are considered as examples.

Transverse beam combining is a cost-saving option employed in many designs for heavy ion fusion drivers. However, the resultant transverse phase space dilution must be minimized so as not to sacrifice focusability at the target. A prototype combining experiment has been completed employing four 3-mA ${\mathrm{Cs}}^{+}$ beams injected at 160 keV. The focusing elements upstream of the merge consist of four quadrupoles and a final combined-function element (quadrupole and dipole). Following the merge, the resultant single beam is transported in a single alternating gradient channel where the subsequent evolution of the distribution function is diagnosed. The results are in fair agreement with particle-in-cell simulations. They indicate that for some heavy ion fusion driver designs, the phase space dilution from merging is acceptable.

Based on the requirements from a conceptual design of a polarized positron beam for future linear colliders, we constructed a special collision system with a short focal length of 150 mm of the laser beams so as to produce $\gamma$ rays through inverse Compton scattering. In order to achieve efficient laser-electron collisions, we created a special optics to produce very small $e^{-}$-beam sizes of ${\sigma }_{e_{x0}}=7.6\mu \mathrm{m}$ and ${\sigma }_{e_{y0}}=5.4\mu \mathrm{m}$ in the horizontal and vertical directions at the collision point. Using laser light with a wavelength of 532 nm and an $e^{-}$ beam of 1.28 GeV, provided from the ATF-damping ring at KEK, we generated $2\times {10}^5$ $\gamma$ rays with a time duration of 26 ps in rms, leading to a peak brightness of $1.7\times {10}^{18}/({\mathrm{mrad}}^2{\mathrm{mm}}^{2}0.1\%\mathrm{bandwidth}\mathrm{s}$) near to the maximum energy of 56 MeV.

We explore the rf characteristics of pipe cooled superconducting cavities versus bath cooled ones, using different pipe configurations and different liquid helium temperatures. Pipe cooled cavities can perform nearly as well as bath cooled ones, provided a suitable pipe configuration and cavity wall thickness is chosen. Pure thermal estimates and fits with experimental data show that pipe cooling is a viable solution for future cavities.

An analytical formalism for the solution of cumulative beam breakup in linear accelerators with arbitrary time dependence of beam current is presented, and a closed-form expression for the time and position dependence of the transverse displacement is obtained. It is applied to the behavior of a single bunch and to the steady-state and transient behavior of dc beams and beams composed of pointlike and finite-length bunches. This formalism is also applied to the problem of cumulative beam breakup in the presence of random displacement of cavities and focusing elements, and a general solution is presented.

The applicability of superconducting TEM-class spoke cavities to high-energy ion linacs is discussed, and detailed designs for two TEM-class, triple-spoke-loaded superconducting niobium resonant cavities are presented. The 345 MHz cavities have a velocity range of $0.4<\beta <0.75$ and a beam aperture of 4 cm. Spoke-loaded cavities offer several advantages compared with the higher-frequency elliptical-cell cavities that are currently being developed for this range of particle velocities. The proposed triple-spoke cavities can provide broader velocity acceptance, more accelerating voltage per cavity, reduced heat-load operation at 4.2 K, and increased longitudinal acceptance through the high-energy section. Application to the proposed U.S. rare-isotope accelerator driver linac is discussed in detail.

The interaction between a low-density electron cloud in a circular particle accelerator with a circulating charged particle beam is considered. The particle beam’s space charge attracts the cloud, enhancing the cloud density near the beam axis. It is shown that this enhanced charge and the image charges associated with the cloud charge and the conducting wall of the accelerator may have important consequences for the dynamics of the beam propagation. The tune shift due to the electron cloud is obtained analytically and compared to a new numerical model (QuickPIC) that is described here. Sample numerical results are presented and their significance for current and planned experiments is discussed.

In plasmas with strongly anisotropic distribution functions $(T_{\parallel b}/T_{\perp b}\ll 1)$ a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9, 3138 (2002)] of the stability properties of intense non-neutral charged particle beams with large temperature anisotropy $(T_{\perp b}\gg T_{\parallel b})$ to allow for nonaxisymmetric perturbations with $\partial /\partial \theta \ne 0$. The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined. The simulation results clearly show that moderately intense beams with $s_b={\widehat{\omega }}_{pb}^2/2{\gamma }_b^2{\omega }_{\beta \perp }^2\gtrsim 0.5$ are linearly unstable to short-wavelength perturbations with $k_z^2{r}_b^2\gtrsim 1$, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ${\widehat{\omega }}_{pb}^2=4\pi {\widehat{n}}_b{e}_b^2/{\gamma }_b{m}_b$ is the relativistic plasma frequency squared, and ${\omega }_{\beta \perp }$ is the betatron frequency associated with the applied smooth-focusing field. A theoretical model is developed based on the Vlasov-Maxwell equations which describes the essential features of the linear stages of instability. Both the simulations and the analytical theory predict that the dipole mode (azimuthal mode number $m=1$) is the most unstable mode. In the nonlinear stage, tails develop in the longitudinal momentum distribution function, and the kinetic instability saturates due to resonant wave-particle interactions.

We describe the status of our effort to realize a first neutrino factory and the progress made in understanding the problems associated with the collection and cooling of muons towards that end. We summarize the physics that can be done with neutrino factories as well as with intense cold beams of muons. The physics potential of muon colliders is reviewed, both as Higgs factories and compact high-energy lepton colliders. The status and time scale of our research and development effort is reviewed as well as the latest designs in cooling channels including the promise of ring coolers in achieving longitudinal and transverse cooling simultaneously. We detail the efforts being made to mount an international cooling experiment to demonstrate the ionization cooling of muons.

The coherent synchrotron radiation instability may be driven at the shielding threshold by a single mode excited in the beam pipe. Such a problem may have general interest for other one-mode dominated problems arising in plasma, free-electron laser theory, and microwave instability. The problem may have practical interest if the steady state exists but requires the study of the nonlinear regime of instability. The results of the study, both analytic and numerical, are presented in the coasting beam approximation and for a bunched beam.

Photocathodes for free electron lasers (FELs) are required to produce nano-Coulomb pulses in picosecond time scales with demonstrable reliability, lifetime, and efficiency. Dispenser cathodes, traditionally a rugged and long-lived thermionic source, are under investigation to determine their utility as a photocathode and have shown promise. The present study describes theoretical models under development to analyze experimental data from dispenser cathodes and to create predictive time-dependent models to predict their performance as an FEL source. Here, a steady-state model of a dispenser cathode with partial coverage of a low work function coating and surface nonuniformity is developed. Quantitative agreement is found for experimental data, especially with regard to temperature, field, laser intensity, and quantum efficiency versus laser wavelength dependence. In particular, for long wavelength incident lasers of sufficient intensity, the majority of the absorbed energy heats the electron gas and background lattice, and photoemission from the heated electron distribution constitutes the emitted current.

We present studies of space-charge-induced beam profile broadening at high intensities in the Proton Storage Ring (PSR) at Los Alamos National Laboratory. We investigate the profile broadening through detailed particle-in-cell simulations of several experiments and obtain results in good agreement with the measurements. We interpret these results within the framework of coherent resonance theory. With increasing intensity, our simulations show strong evidence for the presence of a quadrupole-mode resonance of the beam envelope with the lattice in the vertical plane. Specifically, we observe incoherent tunes crossing integer values, and large amplitude, nearly periodic envelope oscillations. At the highest operating intensities, we observe a continuing relaxation of the beam through space charge forces leading to emittance growth. The increase of emittance commences when the beam parameters encounter an envelope stop band. Once the stop band is reached, the emittance growth balances the intensity increase to maintain the beam near the stop band edge. Additionally, we investigate the potential benefit of a stop band correction to the high intensity PSR beam.

We present measurements of dark currents and x rays in a six cell 805 MHz cavity, taken as part of an rf development program for muon cooling, which requires high power, high stored energy, low frequency cavities operating in a strong magnetic field. We have done the first systematic study of the behavior of high power rf in a strong (2.5–4 T) magnetic field. Our measurements extend over a very large dynamic range in current and provide good fits to the Fowler-Nordheim field emission model assuming mechanical structures produce field enhancements at the surface. The locally enhanced field intensities we derive at the tips of these emitters are very large, (), and should produce tensile stresses comparable to the tensile strength of the copper cavity walls and should be capable of causing breakdown events. We also compare our data with estimates of tensile stresses from a variety of accelerating structures. Preliminary studies of the internal surface of the cavity and window are presented, which show splashes of copper with many sharp cone shaped protrusions and wires which can explain the experimentally measured field enhancements. We discuss a “cold copper” breakdown mechanism and briefly review alternatives. We also discuss a number of effects due to the 2.5 T solenoidal fields on the cavity such as altered field emission due to mechanical deformation of emitters, and dark current ring beams, which are produced from the irises by drifts during the nonrelativistic part of the acceleration process.

A numerical algorithm for simulating electron beam shot noise in free electron lasers (FELs) is presented. Shot noise is a source of spontaneous emission that may be amplified in the self-amplified spontaneous emission regime of operation. This regime is of great importance to XUV and x-ray FELs where the spontaneous emission is currently the only effective source available for amplification. The algorithm uses a quasiuniform phase-space distribution of appropriately charge weighted macroparticles. The statistical properties of the macroparticles are derived directly from the temporal Poisson statistical properties of the real electron distribution. Unlike previous algorithms, ours does not rely upon any averaging over a resonant radiation period time scale and so more correctly describes the underlying physics. The algorithm also allows shot noise to be modeled self-consistently in unaveraged FEL models which are able to describe subwavelength phenomena such as coherent spontaneous emission (CSE). The algorithm is used in the unaveraged 1D FEL numerical simulation code FemFel and demonstrates spontaneous emission due to shot noise and CSE in both rectangular and Gaussian electron pulse current profiles. The preliminary results show good qualitative and quantitative agreement with theory.

Experimental observations obtained on an electron-cyclotron-resonance ion source with electron injection by a ferroelectric cathode are presented. The results are in reasonable agreement with the proposed qualitative plasma model based on the Fokker-Planck equation. A procedure for the optimized operation of an ion source with electron injection is presented on the base of the experimental observations.

A high-harmonic rf system is going to be installed in both rings of the $\mathrm{DA}\Phi \mathrm{NE}$ $\Phi$-Factory collider to improve the Touschek lifetime. The main goal of this paper is to study the impact of the 3rd harmonic cavity on beam dynamics making a special emphasis on the dynamics of a bunch train with a gap. The shift of the coherent synchrotron frequencies of the coupled-bunch modes has been estimated. In the following we investigated the effect of magnification of the synchrotron phase spread and beam spectrum variation due to the gap. Besides we simulated the bunch lengthening for different bunches along the unevenly filled train and evaluated the Touschek lifetime enhancement taking into account the obtained bunch distributions. Finally, the “cavity parking” option is discussed. It can be considered as a reliable backup procedure consisting of tuning the cavity away from the 3rd harmonic frequency and in between two revolution harmonics. It allows recovering, approximately, the same operating conditions as were before the harmonic cavity installation.

Transverse hose instability may disrupt the propagation of a charged-particle beam in a channel of oppositely charged particles. A theoretical model predicts stabilization of this two-stream instability when the instability wavelength becomes smaller than the beam’s transverse size in a frame of reference where the instability’s phase velocity is nonrelativistic. Suppression of short-wavelength instability is also predicted when a proton beam propagates through a channel consisting of electrons and positive ions, consistent with previous experimental results.

The microwave instability driven by the coherent synchrotron radiation (CSR) has been previously studied [S. Heifets and G. V. Stupakov, Phys. Rev. ST Accel. Beams 5, 054402 (2002)] neglecting effect of the shielding caused by the finite beam pipe aperture. In practice, the unstable mode can be close to the shielding threshold where the spectrum of the radiation in a toroidal beam pipe is discrete. In this paper, the CSR instability is studied in the case when it is driven by a single synchronous mode. A system of equations for the beam-wave interaction is derived and its similarity to the 1D free-electron laser theory is demonstrated. In the linear regime, the growth rate of the instability is obtained and a transition to the case of continuous spectrum is discussed. The nonlinear evolution of the single-mode instability, both with and without synchrotron damping and quantum diffusion, is also studied.