By numerically solving the relativistic equations of motion of a single electron in laser fields modeled by those of a Gaussian beam, we demonstrate electron capture by, reflection from, and transmission through the beam. In modeling the fields, terms of order up to ${ϵ}^5$, where $ϵ$ is the diffraction angle, are retained. All cases of capture are accompanied by energy gain that may reach a few GeV, from fields of present-day intensities. Reflection and transmission, on the other hand, result sometimes in no gain or even in a loss of energy. It is shown that a laboratory static magnetic field may be used to eject a captured electron, a process that sometimes results in even more energy gain. For example, a 2.5 T uniform magnetic field suffices to eject a 3.633 MeV electron injected at $6°$ to the axis of a linearly polarized beam of a 10 PW power output and aimed at a point near the focus. Such an electron gains 1128 MeV from the laser field alone. However, it emerges with a 1230 MeV net energy gain under the additional action of the small magnetic field.

We are building an $S$-band photocathode rf gun as an injector to a 30 MeV electron linac for FEL applications. Here we discuss details of design simulations performed using superfish and gdfidl and compare with results of cold tests performed on prototype cells of the photocathode rf gun. We also discuss beam dynamics simulations performed using parmela and report results from simulations to achieve a normalized transverse rms emittance of about $1\pi \mathrm{mm}\mathrm{mrad}$ for a 10 ps pulse with 1 nC charge in the presence of a solenoid magnetic field used for emittance compensation.

Beginning with the Green function for a rod beam in a round beam pipe we derive the space charge induced average energy change and rms spread for relativistic beams that are slowly converging or diverging in round beam pipes, a result that tends to be much larger than the $1/{\gamma }^2$ dependence for parallel beams. Our results allow for beams with longitudinal-transverse correlation, and for slow variations in beam pipe radius. We calculate, in addition, the space charge component of energy change and spread in a chicane compressor. This component indicates source regions of coherent synchrotron radiation (CSR) energy change in systems with compression. We find that this component, at the end of example compressors, approximates the total induced voltage obtained by more detailed CSR calculations. Our results depend on beam pipe radius (although only weakly) whereas CSR calculations do not normally include this parameter, suggesting that results of such calculations, for systems with beam pipes, are not complete.

In conventional beam-based alignment (BBA) procedures, the relative alignment of a quadrupole to a nearby beam-position monitor is determined by finding a beam position in the quadrupole at which the closed orbit does not change when the quadrupole field is varied. The final focus magnets of the interaction regions (IR) of circular colliders often have some specialized properties that make it difficult to perform conventional beam-based alignment procedures. At the HERA interaction points, for example, these properties are the following: (a) the quadrupoles are quite strong and long. Therefore a thin lens approximation is quite imprecise. (b) The effects of angular magnet offsets become significant. (c) The possibilities to steer the beam are limited as long as the alignment is not within specifications. (d) The beam orbit has design offsets and design angles with respect to the axis of the low-beta quadrupoles. (e) Often quadrupoles do not have a beam-position monitor in their vicinity. Here we present a beam-based alignment procedure that determines the relative offset of the closed orbit from a quadrupole center without requiring large orbit changes or monitors next to the quadrupole. Taking into account the alignment angle allows us to reduce the sensitivity to optical errors by 1 to 2 orders of magnitude. We also show how the BBA measurements of all IR quadrupoles can be used to determine the global position of the magnets. The sensitivity to errors of this method is evaluated and its applicability to HERA is shown.

This manuscript corrects and supplements results of a previous paper which first appeared at the 1999 Particle Accelerator Conference. Since then, substantial data have been gathered in the design of the Accelerator Production of Tritium Linac and corrections have been made to the original formula. In order to design any accelerator one should know three values related to the coupling slots: $\Delta f$, $k$, and $kk$. The $\Delta f$ determines the no-slot cavity frequency, i.e., the cavity frequency will drop with the introduction of coupling slots. The value of $k$ represents the coupling between an on-axis (accelerating) cavity and its adjoining coupling cavity. The value of $kk$ represents the next nearest neighbor coupling, between two on-axis cavities that are separated by an intervening coupling cavity. Recent work at Los Alamos National Laboratory has employed a perturbation technique developed by Gao. Accurate values of $k$ are obtained from analytical expressions. It is the purpose of this paper to extend this type of analysis to include $kk$ in a side-coupled linac. The approach will be to calculate the dipole induced in the slot by the field in the accelerating cavities, calculate an interaction energy between the two dipoles, and finally employ the Slater perturbation technique. The calculated value of $kk$ is typically a little less than 1%, which will be verified with the measured data.

The aim of this article is to demonstrate the practical value of radioscopic differentiation of materials in the 1–10 MeV energy range to the work of customs services. The proposed method for achieving singling out and identifying four basic groups of materials according to an atomic number is complex. Atomic numbers are identified using high- and low-energy profiles obtained through the irradiation of materials on an alternate pulse-by-pulse basis. This is done using a bremsstrahlung beam with $8\mathrm{MeV}/4\mathrm{MeV}$ dual boundary energies and by using scintillating crystals coupled with silicon photodiodes as detecting elements. An image segmentation technique is then used to discern the distribution of an atomic number on any given image. The color visualization of integral absorption and a material’s atomic composition is carried out according to the intensity hue saturation (IHS) colorization scheme. The experiments were carried out on a full-scale prototype of an 8 MeV customs inspection system developed by the Efremov Research Institute.

The emittance of a high-brightness electron beam from a photoinjector is affected by the transverse and longitudinal distributions of the laser beam illuminating the cathode. A nonuniform laser beam generates a nonuniform electron-beam distribution that experiences emittance growth on a time scale of the plasma period. Experiments were performed at the Brookhaven Accelerator Test Facility to investigate the emittance growth due to transversely nonuniform laser beams. Laser masks were fabricated to generate various laser distributions. Significant emittance growth was observed as the laser distribution deviated strongly from a uniform distribution. For cylindrically symmetric, nonuniform distributions, experimental results agree with PARMELA simulations. The emittance dependence on the bunch charge is linear as a function of the bunch charge for both uniform and nonuniform beams. For a uniform beam, the emittance measurements agree well with the predictions from PARMELA simulations, but the analytical approach overestimates the results. For nonuniform beams, analytical estimates are about 70% of the measurements. For noncylindrically symmetric, nonuniform beams, we observed that the emittance is linearly proportional to the rms laser nonuniformity and the best emittance for a perfectly uniform beam is extrapolated to be $1.07\pm 0.13\mathrm{mm}\mathrm{mrad}$ at 0.5 nC.

The betatron tune and the synchronous phase of individual bunches were measured at KEKB, an asymmetric electron/positron circular collider. The measurement was performed under three conditions: a single bunch, and multibunches with and without collision. The coupling impedance of the rings can be estimated from the current dependence of the parameters of a single bunch. The betatron tune along a positron-bunch train indicates variations of the electron cloud density that cause electron cloud instability. Comparing the betatron tune between colliding and noncolliding bunches, the beam-beam tune shift was investigated in regular operation. The coherent beam-beam parameter was evaluated in the two-ring collider with unequal tunes. Transient beam-loading effects were experimentally demonstrated by a phase shift along a bunch train in both rings. A rapid advance in the beam phase was observed, which is considered to be due to the effects of longitudinal wakes.

The beam-induced electron cloud buildup is one of the major concerns for the SPS and the design of the future LHC. During the 2000 run, this effect has also been observed in the PS with the nominal LHC-type beam. The electron cloud induces a baseline distortion in electrostatic pickup signals, both during the last turns in the PS, when the full bunch length is reduced to less than 4 ns, and in the transfer line between the PS and the SPS rings. In the year 2001, modifications in the rf hardware allowed us to study the properties of the beam instability related with the electron cloud phenomenon for a total bunch length of about 10 ns. The complete set of experimental observations carried out in the PS machine is presented and discussed in detail.

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.