Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton ($e\mathrm{\text{−}}p$) two-stream instability observed in the Proton Storage Ring (PSR) experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the $e\mathrm{\text{−}}p$ instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the $e\mathrm{\text{−}}p$ instability, is studied for self-consistent equilibrium populations of protons and electrons.

Longitudinal ballistic and collective beam echoes with diffusion effects are investigated theoretically. In the presence of the space-charge impedance, the collective echo amplitude is obtained as a closed form expression. In contrast to the ballistic case, the collective echo amplitude consists of one maximum at time $t_{\mathrm{echo}}$. The echo amplitude grows up and damps down with a rate proportional to the Landau damping rate of space-charge waves. The effect of weak diffusion is found to modify the ballistic and the collective echo amplitudes in the same manner. This effect of diffusion was confirmed using a “noiseless,” grid-based simulation code. As a first application the amount of numerical diffusion in our simulation code was determined using the echo effect.

This paper presents an analytical investigation of the transverse electron-proton ($e\mathrm{\text{−}}p$) two-stream instability in a proton bunch propagating through a stationary electron background. The equations of motion, including damping effects, are derived for the centroids of the proton beam and the electron cloud by considering Lorentzian and Gaussian frequency spreads for the particles. For a Lorentzian frequency distribution, we derive the asymptotic solution of the coupled linear centroid equations in the time domain and study the $e\mathrm{\text{−}}p$ instability in proton bunches with nonuniform line densities. Examples are given for both uniform and parabolic proton line densities.

Electron cloud instabilities in the Los Alamos Proton Storage Ring and those foreseen for the Oak Ridge Spallation Neutron Source are examined theoretically, numerically, and experimentally.

In preparation for the heavy ion program of the Large Hadron Collider at CERN, accumulation and cooling tests with lead ion beams have been performed in the Low Energy Antiproton Ring. These tests have revealed that due to the unexpected large outgassing of the vacuum system, the dynamic pressure of the ring could not be maintained low enough to reach the required beam intensities. To determine the actions necessary to lower the dynamic pressure rise, an experimental program has been initiated for measuring the molecular desorption yields of stainless steel vacuum chambers by the impact of $4.2\mathrm{MeV}/\mathrm{u}$ lead ions with the charge states $+27$ and $+53$. The test chambers were exposed either at grazing or at perpendicular incidence. Different surface treatments (glow discharges, nonevaporable getter coating) are reported in terms of the molecular desorption yields for ${\mathrm{H}}_{\mathrm{2}}$, $\mathrm{C}{\mathrm{H}}_{\mathrm{4}}$, CO, Ar, and $\mathrm{C}{\mathrm{O}}_{\mathrm{2}}$. Unexpected large values of molecular yields per incident ion up to $2\times {10}^4$ $\mathrm{\text{molecules}}/\mathrm{\text{ion}}$ have been observed. The reduction of the ion-induced desorption yield due to continuous bombardment with lead ions (beam cleaning) has been investigated for five different stainless steel vacuum chambers. The implications of these results for the vacuum system of the future Low Energy Ion Ring and possible remedies to reduce the vacuum degradation are discussed.

In a number of papers an attractive method of laser polarization of electrons (positrons) at storage rings or linear colliders has been proposed. We show that these suggestions are incorrect and based on errors in the simulation of multiple Compton scattering and in the calculation of the Compton spin-flip cross sections. We argue that the equilibrium polarization in this method is zero.

A transformer model of ferrite kicker magnets is presented in this paper. Based on this model, an equivalent circuit is derived for which the elements can be obtained by bench measurements or by estimates from the magnet geometry. Improved formulas for the transverse coupling impedance of lumped and traveling wave kicker magnets are derived from the model and the equivalent circuit. The formulas differ from the corresponding handbook results in their dependence on the external termination or aperture aspect, respectively. The effect of ferrite properties on the transverse coupling impedance is analyzed. The model was confirmed by bench measurements with the twin-wire technique made on the full-size and half-size prototypes of the extraction kicker of the SNS accumulator ring. The application of this model to the design of the kickers allowed a significant reduction of the SNS transverse coupling impedance budget.

A helical quadrupole focusing channel has continuous field symmetry and a stronger focusing power compared with a conventional FODO focusing channel. The good field symmetry allowed us to construct an explicit transfer matrix under the paraxial approximation. In the present paper, we report the paraxial analysis of the helical quadrupole focusing channel and compare its characteristics with those of a conventional FODO focusing channel.

A multibeamlet approach to a high current ion injector, whereby a large number of beamlets are accelerated and then merged to form a single beam, offers a number of potential advantages over a monolithic single beam injector. These advantages include a smaller transverse footprint, more control over the shaping and aiming of the beam, and more flexibility in the choice of ion sources. A potential drawback, however, is a larger emittance. In this paper, we seek to understand the merging of the beamlets and how it determines the emittance. When the constraints imposed by beam propagation physics and practical engineering issues are included, the design is reduced to a few free parameters. We describe the physics design of a multibeamlet injector and produce a design for an example set of parameters. Extensive use of 2D and 3D particle simulations was made in understanding the injector. Design tolerances and sensitivities are discussed in general and in relation to the example.

Experimental observations on the electron cloud have been collected at the CERN Proton Synchrotron machine throughout the last two years. At the same time, an intense campaign of simulations has been carried out to understand the observed electron cloud buildup and the related instability. In this paper, the results of the numerical simulations are presented and discussed.

The root-mean-squared (rms) envelope equations are derived and analyzed for an unbunched intense charged-particle beam in an alternating-gradient focusing field and a cylindrical conducting pipe. All higher-order image-charge effects from the cylindrical pipe are expressed in terms of so-called multiple moment factors in the rms beam envelope equations, and the multiple moment factors are evaluated. Numerical results show that for vacuum phase advance ${\sigma }_v<{90}^{\circ }$, the image-charge effects on the matched and slightly mismatched beam envelopes are negligibly small, at all orders, for all beams with arbitrary beam density profiles (including hollow density profiles) as well as for arbitrary small apertures (including beams with large aspect ratios). However, the main unstable region for the envelope evolution with image-charge effects, which occurs for ${90}^{\circ }<{\sigma }_v<{270}^{\circ }$, depending on the value of the normalized beam intensity $SK/\epsilon$, is found to be narrower than its counterpart without image-charge effects.

We provide a detailed description of a model and its computational algorithm for the secondary electron emission process. The model is based on a broad phenomenological fit to data for the secondary-emission yield and the emitted-energy spectrum. We provide two sets of values for the parameters by fitting our model to two particular data sets, one for copper and the other one for stainless steel.

A vertical coupled-bunch instability was observed for a positron beam at the Beijing Electron Positron Collider (BEPC). The experimental results show that the instability has similar characteristics as that observed in the Photon Factory of KEK several years ago. The instability at BEPC can be explained by the effect of an electron cloud which is produced in the beam chamber by synchrotron light hitting the wall.

Two different parameters for the quantitative description of beam halo are discussed. Both are based on moments of the particle distribution and represent a convenient and model-independent method for quantifying the magnitude of beam halo observed in either spatial or phase-space projections. One parameter is a measure of spatial profile of the beam and has been defined by Wangler and Crandall previously. The current authors defined a new parameter using kinematic invariants to quantify halo formation in 2D phase space. Here we expand the development and present detailed numerical results. Although the spatial-profile parameter and the phase-space halo parameter both reduce to the same value when the distribution has the elliptical symmetry, in general these parameters are not equal. Halo in the 1D spatial profiles is relatively easily measured, but is variable as the beam distribution evolves and can hide as it rotates in phase space. The 2D phase-space halo is more difficult to measure, but it varies more smoothly as the halo evolves. It provides a more reliable characterization of the halo as an intrinsic property of the beam.

We describe in this paper a measurement of vertical emittance in the Accelerator Test Facility (ATF) damping ring at KEK with a laser wire beam profile monitor. This monitor is based on the Compton scattering process of electrons with a laser light target which is produced by injecting a cw laser beam into a Fabry-Perot optical cavity. We installed the monitor at a straight section of the damping ring and measured the vertical emittance with three different ring conditions. In all cases, the ATF ring was operated at 1.28 GeV in a single bunch mode. When the ring was tuned for ultralow emittance, the vertical emittance of ${\epsilon }_y=(1.18\pm 0.08)\times {10}^{-11}\mathrm{mrad}$ was achieved. This shows that the ATF damping ring has realized its target value also vertically.

We report macroparticle simulations for comparison with measured results from a proton beam halo experiment in a 52-quadrupole periodic-focusing channel. An important issue is that the input phase-space distribution is not experimentally known. Three different initial distributions with different shapes predict different beam profiles in the transport system. Simulations have been fairly successful in reproducing the core of the measured matched-beam profiles and the trend of emittance growth as a function of the mismatch factor, but underestimate the growth rate of halo and emittance for mismatched beams. In this study, we find that knowledge of the Courant-Snyder parameters and emittances of the input beam is not sufficient for reliable prediction of the halo. Input distributions with greater population in the tails produce larger rates of emittance growth, a result that is qualitatively consistent with the particle-core model of halo formation in mismatched beams.

HEADTAIL is a simulation program developed at CERN which is aimed at studying the single-bunch instability arising from the interaction on successive turns of a single bunch with the cloud generated by the previous bunches. The code includes chromaticity, space charge tune spread, broad-band impedance, and detuning with amplitude for more realistic simulation. Examples of application are shown. Transverse and longitudinal wake functions are also outputs of the HEADTAIL code.