Recent advances in solid-state switches have made it feasible to design programmable, high-repetition-rate pulsers for induction accelerators. These switches could lower the cost of recirculating induction accelerators, such as the “small recirculator” at Lawrence Livermore National Laboratory (LLNL), by substantially reducing the number of induction modules. Numerical work is reported here to determine what effects the use of fewer pulsers at higher voltage would have on the beam quality of the LLNL small recirculator. Lattices with different numbers of pulsers are examined using the fluid/envelope code CIRCE, and several schedules for acceleration and compression are compared for each configuration. For selected schedules, the phase-space dynamics is also studied using the particle-in-cell code WARP3d.

Harmonic cavities have been used in storage rings to lengthen bunches and increase beam lifetimes dominated by Touschek scattering. Transient beam loading in the harmonic cavities generated by asymmetries in the fill pattern causes significant variation of the bunch synchronous phase and bunch length along the bunch train when the longitudinal restoring force has been reduced. This results in a significant reduction in the mean bunch lengthening and potential lifetime increase. We describe how beam current modulations give rise to transient effects much larger than expected from the linear model of the beam cavity interaction. We also develop a tracking simulation to predict results and apply this simulation to an analysis of the beam loading transients for the case of passive and active normal and superconducting third harmonic rf systems using Advanced Light Source parameters.

A halo generation mechanism in the nonperiodic lattices such as the SNS (Spallation Neutron Source) linac MEBT [medium-energy beam transport between radio-frequency quadrupole and DTL (drift tube linac)] is reported. We find that the nonlinear space charge force resulting from large transverse beam eccentricity $\sim 2:1$ in the $\sim 1.6\mathrm{m}$-long MEBT chopper section is responsible for halo formation. As a result, the beam distribution, based on the front end emittance measurements and multiparticle simulation studies, develops halo that leads to beam loss and radioactivation of the SNS linac. Designing lattices with transverse beam eccentricity close to 1:1 suppresses this kind of halo generation. Modifying the MEBT optics and introducing adjustable collimators in the MEBT significantly reduced beam losses in the coupled cavity linac, which is a preferred scheme for mitigating halo. It turns out that the DTL collimation does not effectively remove halo and presents a risk of overheating drift tubes.

A modified Boris-like integration, in which the spatial coordinate is the independent variable, is derived. This spatial-Boris integration method is useful for beam simulations, in which the independent variable is often the distance along the beam. The new integration method is second order accurate, requires only one force calculation per particle per step, and preserves conserved quantities more accurately over long distances than a Runge-Kutta integration scheme. Results from the spatial-Boris integration method and a Runge-Kutta scheme are compared for two simulations: (i) a particle in a uniform solenoid field and (ii) a particle in a sinusoidally varying solenoid field. In the uniform solenoid case, the spatial-Boris scheme is shown to perfectly conserve for any step size quantities such as the gyroradius and the perpendicular momentum. The Runge-Kutta integrator produces damping in these conserved quantities. In the sinusoidally varying case, the conserved quantity of canonical angular momentum is used to measure the accuracy of the two schemes. For the sinusoidally varying field simulations, error analysis is used to determine the integration distance beyond which the spatial-Boris integration method is more efficient than a fourth-order Runge-Kutta scheme. For beam physics applications where statistical quantities such as beam emittance are important, these results imply the spatial-Boris scheme is 3 times more efficient.

A scheme is proposed to exchange the transverse and longitudinal emittances of an electron bunch. A general analysis is presented and a specific beam line is used as an example where the emittance exchange is achieved by placing a transverse deflecting mode radio-frequency cavity in a magnetic chicane. In addition to reducing the transverse emittance, the bunch length is also simultaneously compressed. The scheme has the potential to introduce an added flexibility to the control of electron beams and to provide some contingency for the achievement of emittance and peak-current goals in free-electron lasers.

We derive a simple relation for estimating the relative emittance growth in $x$ and $y$ due to intrabeam scattering (IBS) in electron storage rings. We show that IBS calculations for the Accelerator Test Facility (ATF) damping ring, when using the formalism of Bjorken-Mtingwa, a modified formalism of Piwinski (where ${\eta }^2/\beta$ has been replaced by $H$), or a simple high-energy approximate formula all give results that agree well. Comparing theory, including the effect of potential well bunch lengthening, with a complete set of ATF steady-state beam size versus current measurements we find reasonably good agreement for energy spread and horizontal emittance. The measured vertical emittance, however, is larger than theory in both offset (zero current emittance) and slope (emittance change with current). Almost all the offset error can be accounted for by considering the expected projected vertical emittance due to machine errors rather than the real emittance. This result is consistent with the assumed Coulomb log factor being close to the correct one. The slope error indicates measurement error and/or additional current-dependent physics at the ATF.

The Vlasov-Maxwell equations are used to investigate the nonlinear evolution of an intense sheet beam with distribution function $f_b\backslash ({x,x}^{\prime },s\backslash )$ propagating through a periodic focusing lattice ${\kappa }_x\backslash (s+S\backslash )={\kappa }_x\backslash (s\backslash )$, where $S=\mathrm{const}$ is the lattice period. The analysis considers the special class of distribution functions with uniform phase-space density $f_b\backslash ({x,x}^{\prime },s\backslash )=A=\mathrm{const}$ inside of the simply connected boundary curves, $x_{+}^{\prime }\backslash (x,s\backslash )$ and $x_{-}^{\prime }\backslash (x,s\backslash )$, in the two-dimensional phase space $\backslash ({x,x}^{\prime }\backslash )$. Coupled nonlinear equations are derived describing the self-consistent evolution of the boundary curves, $x_{+}^{\prime }\backslash (x,s\backslash )$ and $x_{-}^{\prime }\backslash (x,s\backslash )$, and the self-field potential $\psi \backslash (x,s\backslash ){=e}_b\phi \backslash (x,s\backslash )/{\gamma }_b{m}_b{\beta }_b^2{c}^2$. The resulting model is shown to be exactly equivalent to a (truncated) warm-fluid description with zero heat flow and triple-adiabatic equation of state with scalar pressure $P_b\backslash (x,s\backslash )=\mathrm{const}[n_b\backslash (x,s\backslash ){]}^3$. Such a fluid model is amenable to direct analysis by transforming to Lagrangian variables following the motion of a fluid element. Specific examples of periodically focused beam equilibria are presented, ranging from a finite-emittance beam in which the boundary curves in phase space $\backslash ({x,x}^{\prime }\backslash )$ correspond to a pulsating parallelogram, to a cold beam in which the number density of beam particles, $n_b\backslash (x,s\backslash )$, exhibits large-amplitude periodic oscillations. For the case of a sheet beam with uniform phase-space density, the present analysis clearly demonstrates the existence of periodically focused beam equilibria without the undesirable feature of an inverted population in phase space that is characteristic of the Kapchinskij-Vladimirskij beam distribution.

Longitudinal phase space tomography has evolved into a powerful diagnostic tool in the particle accelerator domain. A computer code has been developed in order to visualize dynamic effects and measure machine parameters in longitudinal phase space. This code is capable of dealing with turn-by-turn parameter changes, for example, during rf rebucketing when the bunch is rotated in longitudinal phase space to minimize the bunch length. We describe the reconstruction code and show its application as a diagnostic tool for rebucketing in the Relativistic Heavy Ion Collider.

During the Relativistic Heavy Ion Collider commissioning in 2001 a fast transverse instability was observed on the ramp. In general this could be counteracted with increased chromaticity, resulting in Landau damping. However this method could not be applied around transition energy where chromaticities have to change sign. So octupoles were used near transition energy to create transverse Landau damping and avoid the transverse instability, emittance blowup, and beam loss. This paper describes the considerations that led to the present scheme, as well as experimental results.

The luminosity in flat-beam circular colliders is known to “saturate” at some “threshold” beam current above which (because the beam height grows) the luminosity varies (only) linearly with beam current, making both the specific luminosity (luminosity/current) and the beam-beam tune shift parameter ${\xi }_y$ independent of current. The purpose of this paper is to calculate ${\xi }_y$ analytically with the goal of maximizing the luminosity. A zero parameter application of the theory to 13 existing storage ring configurations yields theory/experiment equal to $1.26\pm 0.45$ for ${\xi }_{y,\max }$. Parameter values (especially tunes $Q_x$, $Q_y$, and $Q_s$) expected to maximize ${\xi }_y$ are given. The most favored tune combinations seem not to have been tried so far in colliding beam facilities. The vertical beam growth is ascribed to “parametric pumping” of the vertical betatron amplitude of each individual particle by its own (inexorable) horizontal and longitudinal oscillation. A unique determination of the distribution of all particles then follows from a saturation principle which asserts that the beam height adjusts itself to the value for which the least stable particle (of probable amplitude) is barely stable. The difference equation describing the pumping can be solved by numerical iteration or, because it is (almost) linear, it can be solved analytically, at least for amplitudes small enough that resonances remain isolated. Because of the aliasing (or undersampling) characteristic of accelerators, this equation exhibits an even richer spectrum of resonances than the Mathieu equation, which the present theory generalizes. Contrary to the lore of the field (which motivates the intentional increase of damping decrement ${\delta }_y$ using wigglers), the theory presented here predicts the dependence of luminosity on ${\delta }_y$ to be quite weak. This is not inconsistent with actual collider performance according to a survey by Rice [D. Rice, Cornell University Report No. CBN 01-09 (2001)] of colliding rings built thus far.

A mechanism for acceleration of protons is described, in which energy gain occurs near cyclotron resonance as protons drift through a sequence of rotating-mode ${\mathrm{TE}}_{111}$ cylindrical cavities in a strong nearly uniform axial magnetic field. Cavity resonance frequencies decrease in sequence from one another with a fixed frequency interval $\Delta f$ between cavities, so that synchronism can be maintained between the rf fields and proton bunches injected at intervals of $1/\Delta f$. An example is presented in which a 122 mA, 1 MeV proton beam is accelerated to 961 MeV using a cascade of eight cavities in an 8.1 T magnetic field, with the first cavity resonant at 120 MHz and with $\Delta f=8\mathrm{}\mathrm{MHz}$. Average acceleration gradient exceeds 40 MV/m, average effective shunt impedance is $223\mathrm{M}\Omega /\mathrm{m}$, but maximum surface field in the cavities does not exceed 7.2 MV/m. These features occur because protons make many orbital turns in each cavity and thus experience acceleration from each cavity field many times. Longitudinal and transverse stability appear to be intrinsic properties of the acceleration mechanism, and an example to illustrate this is presented. This acceleration concept could be developed into a proton accelerator for a high-power neutron spallation source, such as that required for transmutation of nuclear waste or driving a subcritical fission burner, provided a number of significant practical issues can be addressed.

Induction core alloys are evaluated that are appropriate for heavy-ion induction accelerators to drive heavy-ion inertial fusion (HIF) power plants. Parameters evaluated include the usable flux swing and the energy loss over a range of magnetization rates of $\sim {10}^5–{10}^7\mathrm{T}/\mathrm{s}$, corresponding to pulse durations of $\sim 20$ to $0.2\mu \mathrm{s}$, respectively. The usable flux swing, for minimum core losses, extends from near the reversed remanent field to about 80% of the saturation field. The usable flux swing is enhanced, with little increase in losses, by annealing the core after winding. Maintaining low energy loss at high magnetization rates requires insulation to block interlaminar eddy currents. To obtain annealed cores with a high ratio of remanent to saturation magnetic field, the insulation must withstand annealing temperatures and apply minimum mechanical stress to the core during cooldown. We find that commercially available insulating coatings for amorphous metals either break down near ${10}^6\mathrm{T}/\mathrm{s}$ (a factor of 10 below the requirement), or do not achieve the maximum remanent field and hence the usable flux swing after annealing. More satisfactory coatings are available for silicon steel and nanocrystalline alloys, which could have applications in HIF. Amorphous alloys are capable of meeting most HIF needs, especially with improved coatings.

On-line monitoring of beam quality for high brightness beams is possible only by using noninvasive instruments. For matching measurements, very few such instruments are available. One candidate is a quadrupole pickup. Therefore, a new type of quadrupole pickup has been developed for the 26 GeV Proton Synchrotron at CERN, and a measurement system consisting of two such pickups is now installed in this accelerator. Using the information from these pickups, it is possible to determine both injection matching and emittance in the horizontal and vertical planes, for each bunch separately. This paper presents the measurement method and some of the results from the first year of use, as well as comparisons with other measurement methods.

We discuss the underlying reasoning behind and the details of the numerical algorithm used in the GINGER free-electron laser simulation code to load the initial shot noise microbunching on the electron beam. In particular, we point out that there are some additional subtleties which must be followed for multidimensional codes which are not necessary for one-dimensional formulations. Moreover, requiring that the higher harmonics of the microbunching also be properly initialized with the correct statistics leads to additional complexities. We present some numerical results including the predicted incoherent, spontaneous emission as tests of the shot noise algorithm’s correctness.

Coherent enhancement of the Smith-Purcell radiation produced from the interaction of a 1.8 MeV electron beam with a grating has been observed. The emitted radiation has been measured at angles in the 40° to 120° range, which correspond to wavelengths from 0.65 to 4 mm, approximately. The radiated power was 320 mW at 90°. Its angular distribution agrees well with the description of the process in terms of induced surface currents and has been used to infer the longitudinal profile of the electron bunch. It is concluded that the bunch has an approximately triangular profile, with 85% of the bunch particles contained within 14 ps. The possibilities of the technique as a bunch-shape diagnostic tool are also discussed.

There are several advantages in using a crystal for stripping of the ${\mathrm{H}}^{-}$ ion to obtain efficient injection of protons into a circular accelerator. First, the stripping efficiency of a crystal is at least as large as for an amorphous foil of the same substance and thickness. Second, the emittance increase imposed by the multiple Coulomb scattering of the protons on subsequent turns is drastically lower by a factor of up to $\simeq 7$. Third, the restricted energy loss of the protons is lower by a factor of up to $\simeq 1.5$—this, combined with the fact that the thermal conductivity of a single crystal of diamond is much higher than that of the amorphous material, will reduce the effect of heating of the stripping material. In high-power schemes based on amorphous foils heating of the electron stripping material is a limiting factor. Fourth, the reduced total energy loss is accompanied by a smaller energy loss straggling implying a smaller longitudinal emittance. Last, the so-called random orientation of the crystal can provide the option of stripping the ${\mathrm{H}}^{-}$ ions as in an amorphous foil while preserving the advantage of a high thermal conductivity, simply by changing the orientation of the crystal. A simulation using realistic parameters is presented, which reflects the efficient conservation of emittance using a diamond crystal. The phenomenon should in fact be applicable in general for the stripping of ${\mathrm{H}}^{-}$, although the advantages depend on parameters such as the energy. A reasonable figure of merit is the ratio of the total transverse emittance increase of crystalline and amorphous foils in one turn and in the presented case this is as high as a factor 3.9.

Weak-strong tracking simulations for the Large Hadron Collider have shown that long-range beam-beam collisions give rise to a well-defined diffusive aperture beyond which particles are lost quickly. In order to derive analytical estimates of this stability boundary, we use leading order perturbation theory and the Chirikov resonance overlap criterion applied to a simplified model with a 2-dimensional transverse phase space. In addition, a Fokker-Plank–type diffusion coefficient is calculated through the nonlinear action kicks imparted by the long-range beam-beam force. The analytical results are compared with the tracking data.

A microbunching instability driven by coherent synchrotron radiation (CSR) in a bunch compressor chicane is studied using an iterative solution of the integral equation that governs this process. By including both one-stage and two-stage amplifications, we obtain analytical expressions for CSR microbunching that are valid in both low-gain and high-gain regimes. These formulas can be used to explore the dependence of CSR microbunching on compressed beam current, energy spread, and emittance, and to design stable bunch compressors required for an x-ray free-electron laser.