Tracking simulations remain the essential tool for evaluating how multipolar imperfections in ring magnets restrict the domain of stable phase-space motion. In the Large Hadron Collider (LHC) at CERN, particles circulate at the injection energy, when multipole errors are most significant, for more than ${10}^7$ turns, but systematic tracking studies are limited to a small fraction of this total time—even on modern computers. A considerable speedup is expected by replacing element-by-element tracking with the use of a symplectified one-turn map. We have applied this method to the realistic LHC lattice, version 6, and report here our results for various map orders, with special emphasis on precision and speed.

A calorimeter, WAMPAC, operating at room temperature has been designed and installed into the SPS to measure directly the electron cloud induced heat load due to the Large Hadron Collider (LHC)-type proton beam. Theoretical behavior, calibrations, measurement protocols, preliminary results, and simulation benchmarking are presented. Scaling of the results to the LHC indicated a linear heating power in a LHC dipole of about $500\mathrm{mW}{\mathrm{m}}^{-1}$ for $5\times {10}^{10}\mathrm{\text{protons}}/{\mathrm{\text{bunch}}}^{-1}$ for a copper surface which is not fully conditioned (maximum of secondary electron yield $\sim 1.9$).

Conventional metal-wall waveguides support waveguide modes with phase velocities exceeding the speed of light. However, for infrared frequencies and guide dimensions of a fraction of a millimeter, one of the waveguide modes can have a phase velocity equal to or less than the speed of light. Such a metal microchannel then acts as a slow-wave structure. Furthermore, if it is a transverse magnetic mode, the electric field has a component along the direction of propagation. Therefore, a strong exchange of energy can occur between a beam of charged particles and this slow-waveguide mode. Moreover, the energy exchange can be sustained over a distance limited only by the natural damping of the wave. This makes the microchannel metal waveguide an attractive possibility for high-gradient electron laser acceleration because the wave can be directly energized by a long-wavelength laser. Indeed the frequency of ${\mathrm{CO}}_2$ lasers lies at a fortuitous wavelength that produces a strong laser-particle interaction in a channel of reasonable macroscopic size (e.g., $\sim 0.6\mathrm{mm}$). The dispersion properties including phase velocity and damping for the slow wave are developed. The performance and other issues related to laser accelerator applications are discussed.

For simulations of plasma wakefield acceleration (PWFA) and similar problems, we developed two-dimensional fully electromagnetic fully relativistic hybrid code LCODE. The code is very fast due to explicit use of several simplifying assumptions (quasistatic approximation, ultrarelativistic beam, and the symmetry). With LCODE, we make high-resolution simulations of the blowout regime of PWFA and study the temperature effect on the amplitude of the accelerating field spike.

Future linear colliders may require a nonzero crossing angle between the two beams at the interaction point (IP). This requirement in turn implies that the beams will pass through the strong interaction region solenoid with an angle, and thus that the component of the solenoidal field perpendicular to the beam trajectory is nonzero. The interaction of the beam and the solenoidal field in the presence of a crossing angle will cause optical effects not observed for beams passing through the solenoid on axis; these effects include dispersion, deflection of the beam, and synchrotron radiation effects. For a purely solenoidal field, the optical effects which are relevant to luminosity exactly cancel at the IP when the influence of the solenoid’s fringe field is taken into account. Beam size growth due to synchrotron radiation in the solenoid is proportional to the fifth power of the product of the solenoidal field, the length of the solenoid, and the crossing angle. Examples based on proposed linear collider detector solenoid configurations are presented.

The linear one-turn map of a storage ring contains coupling information on which a correction algorithm can be based. In principal, the one-turn matrix can be fitted from turn-by-turn data of beam position monitors. However, the signal-to-noise ratio of the coupling information can be greatly enhanced by fitting maps for larger turn numbers $N$. Furthermore, by using a number of beam position monitors in a region with only small coupling sources, the determination of the $N$-turn map can be made robust against failures of individual beam position monitors, and the signal-to-noise ratio of the coupling information is further enhanced. With the so obtained $N$-turn maps an automated global coupling correction is possible without the need for a tune change. This is demonstrated for the Brookhaven Relativistic Heavy Ion Collider where the implementation of the algorithm allows a global coupling correction within a few seconds at injection.

Preservation of the femtosecond (fs) microbunches, created during laser acceleration, is a crucial step to enable staging of the laser acceleration process. This paper focuses on the optimization of the beam dynamics of fs microbunches transported through the staged electron laser acceleration (STELLA-II) experiment being carried out at the Brookhaven National Laboratory Accelerator Test Facility. STELLA-II consists of an inverse free electron laser (IFEL) untapered undulator, which acts as an electron beam energy modulator; a magnetic chicane, which acts as a buncher; a second IFEL tapered undulator, which acts as an accelerator; and a dipole, which serves as an energy spectrometer. When the energy-modulated macrobunch traverses through the chicane and a short drift space, microbunches of order fs in duration (i.e., $\sim 3\mathrm{fs}$ FWHM) are formed. The 3-fs microbunches are accelerated by interacting with a high-power ${\mathrm{CO}}_2$ laser beam in the following tapered undulator. These extremely short microbunches may experience significant space charge and coherent synchrotron radiation effects when traversing the STELLA-II transport line. These effects are analyzed and the safe operating conditions are determined. With less than 0.5-pC microbunch charge, both microbunch debunching and emittance growth are negligible, and the energy-spread increase is less than 5%. These results are also useful for the laser electron acceleration project at SLAC and in possible future programs where the fs microbunches are employed for other purposes.

The correlation between the horizontal beam size versus the cavity temperature, observed at the Taiwan Light Source, is explained by the combined effects of (i) the cavity resonance frequency shift resulting from temperature change, (ii) the cavity voltage and synchronous phase angle change resulting from uncompensated beam loading in the low-level rf-feedback system, (iii) the synchrotron frequency shift due to the cavity voltage, and (iv) the rf cavity voltage modulation for alleviating the coupled-bunch instability. We find that the effect of higher-order parasitic-mode losses on the change of the horizontal beam size is small. This experimental method can be used to evaluate the intrinsic resolution of the low-level rf-feedback system.

Multibunch instabilities of a storage ring electron beam occur due to coherent particle oscillations generated through a bunch to bunch coupling via the impedances, deteriorating the beam quality. One cure for multibunch instabilities is Landau damping, i.e., introducing a spread in the oscillation frequencies among the particles of the individual bunches in order to destroy the coherence of the coupled multibunch oscillation. Measurements at ELETTRA have shown that the harmonic sextupole provides Landau damping capable of suppressing transverse multibunch instabilities. The damping is induced by the nonlinear tune spread with amplitude among the electrons within the individual bunches.

Beam-bunch arrival time has been measured for the first time by operating superconducting cavities, normally part of the linac accelerator array, in a bunch-detecting mode. The very high $Q$ of the superconducting cavities provides high sensitivity and allows for phase-detecting low-current beams. In detecting mode, the resonator is operated at a very low field level comparable to the field induced by the bunched beam. Because of this, the rf field in the cavity is a superposition of a “pure” (or reference) rf and the beam-induced signal. A new method of circular phase rotation (CPR), allowing extraction of the beam phase information from the composite rf field was developed. Arrival time phase determination with CPR is better than 1° (at 48 MHz) for a beam current of 100 nA. The electronics design is described and experimental data are presented.

Electron effects in the High Current Experiment (HCX) are studied via computer simulation. An approximate expression for the secondary electron yield for a potassium ion striking stainless steel is derived and compared with experimental results. This approximate expression has a peak of roughly 55 electrons at normal incidence at an ion energy of 60 MeV. Using an empirical angular dependence, the secondary electron yield is combined with a numerical simulation of the HCX ion beam dynamics to obtain an estimate for the number of secondary electrons expected per ion-wall collision in the HCX. This estimate is that approximately 150–200 electrons per ion collision may result in the HCX.

A longitudinal quadrupole ($q$-pole) instability was limiting the maximum stable current in the DA$\Phi$NE $e^{-}$ ring at a level of $\sim 700–800\mathrm{mA}$. In order to investigate the phenomenon, the instability threshold has been measured as a function of various machine parameters as radio frequency voltage ($V_{\mathrm{rf}}$), momentum compaction (${\alpha }_c$), number of bunches, fill pattern, etc. An unexpected interaction with the longitudinal feedback system, built to control the dipole motion, has been found and a proper feedback tuning has allowed increasing the threshold. The maximum stable beam current has now exceeded 1.80 A and it is no longer limited by the quadrupole instability.

This paper presents a scheme for three-step laser-based stripping of an ${\mathrm{H}}^{-}$ beam for charge exchange injection into a high-intensity proton ring. First, ${\mathrm{H}}^{-}$ atoms are converted to ${\mathrm{H}}^0$ by Lorentz stripping in a strong magnetic field, then neutral hydrogen atoms are excited from the ground state to upper levels by a laser, and the remaining electron, now more weakly bound, is stripped in a strong magnetic field. The energy spread of the beam particles gives rise to a Doppler broadened absorption linewidth, which makes for an inefficient population of the upper state by a narrow-band laser. We propose to overcome this limitation with a “frequency sweeping” arrangement, which populates the upper state with almost 100% efficiency. We present estimates of peak laser power and describe a method to reduce the power by tailoring the dispersion function at the laser-particle beam interaction point. We present a scheme for reducing the average power requirements by using an optical ring resonator. Finally, we discuss an experimental setup to demonstrate this approach in a proof-of-principle experiment.

The narrow band chaotic output of the self-amplified spontaneous-emission free-electron laser exhibits intensity spikes. In the linear regime before saturation, we use an approach developed by Rice to determine probability distributions for the peak values of intensity in both the time and frequency domains. We also find the average number of spikes per unit time or frequency. In addition, we derive joint probabilities for the intensity in the output pulse to have values $I_1$ and $I_2$ at times $t_1$ and $t_2$, and for the spectral intensity to have values ${\tilde{I}}_1$ and ${\tilde{I}}_2$ at frequencies ${\omega }_1$ and ${\omega }_2$.

We present a statistical analysis of the temporal and spectral properties of self-amplified spontaneous emission from an energy-chirped electron beam passing through a long undulator. It is found that the coherence time is independent of the chirp, while the range of spectral coherence is linearly proportional to it. We consider the use of a monochromator to pick out a small temporal slice of the radiation output. For the filtered radiation pulse, we determine the pulse duration, the number of modes, and the energy fluctuation. We apply our analysis to schemes proposed to generate short x-ray pulses at the Linac Coherent Light Source.

The upgraded Accelerator Test Facility (ATF) ${\mathrm{CO}}_2$ laser located at Brookhaven National Laboratory offers a unique opportunity to investigate laser wakefield acceleration (LWFA) with a $10.6\mathrm{\text{−}}\mu \mathrm{m}$ laser, a wavelength where little experimental work exists. While long laser wavelengths have certain advantages over short wavelengths, our modeling analysis has uncovered another important effect. The upgraded ATF ${\mathrm{CO}}_2$ laser will have a pulse length as short as 2 ps. At a nominal plasma density of $\sim {10}^{16}{\mathrm{cm}}^{-3}$, this pulse length would normally be considered too long for resonant LWFA, but too short for self-modulated LWFA. However, our model simulations indicate that a well-formed wakefield is nevertheless generated with electric field gradients of $E_z\gtrsim 2\mathrm{GV}/\mathrm{m}$ assuming 2.5 TW laser peak power. The model indicates pulse steepening is occurring due to various nonlinear effects. It is possible that this intermediate laser pulse length mode of operation may permit the creation of well-formed, regular-shaped wakefields, which would be needed for staging the LWFA process. Discussed in this paper are the model, its predictions for an LWFA experiment at the ATF, and the pulse steepening effect.

A self-amplified spontaneous emission free-electron laser (SASE FEL) is a device which is based on the creation of a very intense, relativistic electron beam which has very little temperature in all three phase planes. The beam in this system is described as having “high brightness,” and when it is bent repetitively in a magnetic undulator, undergoes a radiation-mediated microbunching instability. This instability can amplify the original radiation amplitude at a particular, resonant wavelength by many orders of magnitude. In order to obtain high brightness beams, it is necessary to compress them to obtain higher currents than available from the electron source. Compression is accomplished by the use of magnetic chicanes, which are quite similar to, if much longer than, a single period of the undulator. It should not be surprising that such chicanes also support a radiation-mediated microbunching interaction, which has recently been investigated, and has been termed coherent synchrotron radiation (CSR) instability. The purpose of this paper is to compare and contrast the characteristics of the closely related FEL and CSR microbunching instabilities. We show that a high-gain regime of the CSR instability exists which is formally similar to the FEL instability.

A novel superconducting (sc) structure is proposed, to accelerate a high intensity proton beam within the energy range of 5–20 MeV. The comparison with different sc structures from the point of view of both rf efficiency and technological aspects of manufacture looks promising. Results of M.A.F.I.A. simulations are given.

This paper makes use of the Vlasov-Maxwell equations to investigate collective excitations in an intense sheet beam, infinite in the $y$ and $z$ directions, propagating in the $z$ direction with directed kinetic energy $({\gamma }_b-1)m_b{c}^2$. The beam is confined in the $x$ direction by the smooth-focusing force ${\overrightarrow{F}}_{\mathrm{foc}}=-{\gamma }_b{m}_b{\omega }_{\beta \perp }^{2}x{\overrightarrow{e}}_x$, and perfectly conducting walls are located at $x=\pm x_w$. A self-consistent water bag equilibrium $f_b^0$ satisfying the steady-state $(\partial /\partial t=0)$ Vlasov-Maxwell equations is shown to be exactly solvable for the beam density $n_b^0(x)$ and electrostatic potential ${\phi }^0(x)$. A closed Schrödinger-like eigenvalue equation is derived, assuming small-amplitude perturbations $(\delta f_b,\delta \phi )$ about the self-consistent water bag equilibrium, and the eigenfrequency spectrum is shown to be purely real. The WKB approximation is employed to determine the eigenfrequency spectrum as a function of the normalized beam intensity $s_b={\widehat{\omega }}_{pb}^2/{\gamma }_b^2{\omega }_{\beta \perp }^2$, where ${\widehat{\omega }}_{pb}^2=4\pi {\widehat{n}}_b{e}_b^2/{\gamma }_b{m}_b$ and ${\widehat{n}}_b=n_b(x=0)$ is the on-axis number density of beam particles.