We examine the use of sextupole magnets to correct nonlinearities in the longitudinal phase space transformation of a relativistic beam of charged particles in a dispersionless translating section, or dogleg. Through heuristic analytical arguments and examples derived from recent experimental efforts, augmented by simulations using the particle tracking codes PARMELA and ELEGANT, sextupole corrections are found to be effective in optimizing the use of such structures for beam compression or for shaping the current profile of the beam, by manipulation of the second-order longitudinal dispersion. Recent experimental evidence of the use of sextupoles to manipulate second-order horizontal and longitudinal dispersion of the beam is presented. The theoretical and experimental results indicate that these manipulations can be used to create an electron bunch with a current profile having a long ramp followed by a sharp cutoff, which is optimal for driving large-amplitude wake fields in a plasma wake field accelerator.

We examine the effect of the collective force due to coherent synchrotron radiation (CSR) in an electron storage ring with small bending radius. In a computation based on time-domain integration of the nonlinear Vlasov equation, we find the threshold current for a longitudinal microwave instability induced by CSR alone. The model accounts for suppression of radiation at long wavelengths due to shielding by the vacuum chamber. In a calculation just above threshold, small ripples in the charge distribution build up over a fraction of a synchrotron period, but then die out to yield a relatively smooth but altered distribution with eventual oscillations in bunch length. The instability evolves from small noise on an initial smooth bunch of rms length much greater than the shielding cutoff.

We are concerned with coherent longitudinal motion in a storage ring, especially with situations in which coherent synchrotron radiation (CSR) can influence stability of the beam. The collective force from CSR is usually described by an impedance or a wake function in such a way that the force depends only on the charge distribution at the present time. This description is exact only for a rigid bunch, since causality demands that the force depend on the prior history of the bunch. We show how to treat a deforming bunch by applying the “complete impedance” $Z(n,\omega )$, a function of wave number and frequency. We derive this impedance and study its analytic properties for a special model: radiation from circular orbits shielded by parallel plates representing the metallic vacuum chamber. We analyze the corresponding collective force, obtaining the usual formula as a first approximation, plus easily computed corrections that depend on present and prior values of the time derivative of the charge density. In related papers we have applied these results in numerical simulations of instabilities induced by CSR.

A method of organizing electron-wave interaction at the multiplied frequency of the signal wave is proposed. This type of electron-wave interaction provides multiplied-frequency electron bunching, which leads to formation of an intense harmonic of the electron current at a selected multiplied frequency of the signal wave. This effect is attractive for the use in klystron-type cyclotron masers with frequency multiplication as a way to increase the output frequency and improve the selectivity.

High current and low emittance are principal requirements for heavy-ion injection into a linac driver for inertial fusion energy. An electrostatic quadrupole injector is capable of providing these high charge density and low emittance beams. We have modified the existing 2-MV injector to reduce beam emittance and to double the pulse length. We characterize the beam delivered by the modified injector to the High Current Transport Experiment and the effects of finite rise time of the extraction voltage pulse in the diode on the beam head. We demonstrate techniques for mitigating aberrations and reducing beam emittance growth in the injector.

Velocity bunching has been recently proposed as a tool for compressing electron beam pulses in modern high brightness photoinjector sources. This tool is familiar from earlier schemes implemented for bunching dc electron sources, but presents peculiar challenges when applied to high current, low emittance beams from photoinjectors. The main difficulty foreseen is control of emittance oscillations in the beam in this scheme, which can be naturally considered as an extension of the emittance compensation process at moderate energies. This paper presents two scenarios in which velocity bunching, combined with emittance control, is to play a role in nascent projects. The first is termed ballistic bunching, where the changing of relative particle velocities and positions occur in distinct regions, a short high gradient linac, and a drift length. This scenario is discussed in the context of the proposed ORION photoinjector. Simulations are used to explore the relationship between the degree of bunching, and the emittance compensation process. Experimental measurements performed at the UCLA Neptune Laboratory of the surprisingly robust bunching process, as well as accompanying deleterious transverse effects, are presented. An unanticipated mechanism for emittance growth in bends for highly momentum chirped beam was identified and studied in these experiments. The second scenario may be designated as phase space rotation, and corresponds closely to the recent proposal of Ferrario and Serafini. Its implementation for the compression of the electron beam pulse length in the PLEIADES inverse Compton scattering (ICS) experiment at LLNL is discussed. It is shown in simulations that optimum compression may be obtained by manipulation of the phases in low gradient traveling wave accelerator sections. Measurements of the bunching and emittance control achieved in such an implementation at PLEIADES, as well as aspects of the use of velocity-bunched beam directly in ICS experiments, are presented.

Measurement of the residual betatron coupling with skew quadrupole modulation is a new diagnostics technique. It was developed and tested at the Relativistic Heavy Ion Collider (RHIC) as a promising method for measuring coupling on the ramp. By modulating the strengths of skew quadrupole families, the two tunes' responses are precisely measured with the phase lock loop system. The projection ratio of the residual coupling coefficient onto the coupling modulation direction can be determined. In this article, the analytical solution to the skew quadrupole modulation is given. Dedicated beam studies were carried out in RHIC Run'04 and the results are presented. The ability to measure coupling on the ramp opens the possibility of continuously correcting coupling during acceleration.

Commissioning of two large coherent light facilities (XFELs) at SLAC and DESY should begin in 2008 and 2011, respectively. In this paper we look further into the future, hoping to answer, in a very preliminary way, two questions. First: What will the next generation of XFEL facilities look like? Believing that superconducting technology offers advantages such as high quality beams with highly populated bunches, the possibility of energy recovery and higher overall efficiency than warm technology, we focus this preliminary study on the superconducting option. From this belief the second question arises: What modifications in superconducting technology and in the machine design are needed, as compared to the present DESY XFEL, and what kind of research and development program should be proposed to arrive in the next few years at a technically feasible solution with even higher brilliance and increased overall conversion of ac power to photon beam power? In this paper we will very often refer to and profit from the DESY XFEL design, acknowledging its many technically innovative solutions.

A theory of nonrelativistic, laminar, elliptic-beam formation is presented. The beam is shown to have the one-dimensional Child-Langmuir flow form. An analytic expression for the electrostatic potential outside the beam is derived. Equipotentials corresponding to electrode surfaces are computed numerically. The effectiveness of the electric field formed by the electrodes in focusing and preserving the elliptic, 1D Child-Langmuir flow beam is verified via 3D ray-tracing simulations.

For magnetic alloy (MA) loaded rf accelerating cavity, we have developed an indirect cooling system, which is effective for retaining its shunt impedance by cooling only one side of the MA cores. Because of its low-$Q$ high-permeability property, MA cores are suitable for constructing untuned broadband accelerating systems. Since these same cores are made of wound thin tape, the key to establishing an untuned broadband cavity with effective indirect cooling method is to suppress the reduction of core impedance when attaching metallic cooling plates to the core and keeping a good thermal contact between them. We have employed indium bonding to thermally connect both cores and cooling plates. Both cooling and endurance tests have demonstrated its successful results.

Using a simple field evaporation model and molecular dynamics simulations of nanoscale copper tip evolution in a high electric field gradient typical for linacs, we have studied a new mechanism for rf-field evaporation. The mechanism consists of simultaneous (collective) field evaporation of a large group of tip atoms in high-gradient fields. Thus, evaporation of large clusters is energetically more favorable when compared with the conventional, “one-by-one” mechanism. The studied mechanism could also be considered a new mechanism for the triggering of rf-vacuum breakdown. This paper discusses the mechanism and the experimental data available for electric field evaporation of field-emission microscopy tips.

Various projects under study require an angular-momentum-dominated electron beam generated by a photoinjector. Some of the proposals directly use the angular-momentum-dominated beams (e.g., electron cooling of heavy ions), while others require the beam to be transformed into a flat beam (e.g., possible electron injectors for light sources and linear colliders). In this paper we report our experimental study of an angular-momentum-dominated beam produced in a photoinjector, addressing the dependencies of angular momentum on initial conditions. We also briefly discuss the removal of angular momentum. The results of the experiment, carried out at the Fermilab/NICADD Photoinjector Laboratory, are found to be in good agreement with theoretical and numerical models.

Electrons generated and accumulated inside the beam-pipe form an “electron cloud” that interacts with a charged particle beam. If the number of electrons is sizable, this beam-cloud interaction can give rise to a two-stream instability, resulting in beam loss or emittance growth. The instability can occur within a single bunch, e.g., passing through the cloud on successive turns in a storage ring, or it can be a multibunch instability, where the motion of successive bunches is coupled via the electron cloud. In this paper, I review the experimental evidence for, simulation approaches to, and analytical treatments of single-bunch two-stream instabilities caused by an electron cloud. Depending on the parameter regime, this type of instability may resemble a coasting-beam instability, classical beam breakup, or transverse mode coupling. It can also cause long-term emittance growth. Despite the apparent similarities, a few fundamental differences distinguish the two-stream instability from a conventional impedance-driven instability, and limit the applicability of established accelerator-physics concepts, like “wakefield.” On the other hand, if, in addition to the electron cloud, space-charge forces, conventional impedance, or beam-beam interaction are also present, these can conspire so as to enhance the growth rate.

Accelerating polarized proton beams and storing them for many turns can lead to a loss of polarization when accelerating through energies where a spin rotation frequency is in resonance with orbit oscillation frequencies. First-order resonance effects can be avoided by installing Siberian snakes in the ring, devices which rotate the spin by $180°$ around the snake axis while not changing the beam’s orbit significantly. For large rings, several Siberian snakes are required. Here a criterion will be derived that allows one to find an optimal choice for the orientation of the snake axes. Rings with superperiod four are analyzed in detail, and the HERA proton ring is used as an example for approximate fourfold symmetry. The proposed arrangement of Siberian snakes matches their effects so that all spin-orbit coupling integrals vanish at all energies and therefore there is no first-order spin-orbit coupling at all for this choice, which I call snake matching. It will be shown that in general at least eight Siberian snakes are needed and that there are exactly four possibilities to arrange their axes. When the betatron phase advance between snakes is chosen suitably, four Siberian snakes can be sufficient. Since the spin motion depends on a particle’s trajectory, protons at different phase space positions generally have different spin directions. The time averaged polarization at each phase space point is parallel to the invariant spin field, and the spread of this spin field limits the polarization that can be stored. By the here presented choice of Siberian snakes this limit is completely eliminated up to first order in the transverse phase space coordinates. The invariant spin field and the amplitude-dependent spin tune are also computed without linearization to show the advantages of this choice of snakes. Ultimately, the goal of snake matching is to reduce the loss of polarization during the acceleration of the beam. To show that a favorable choice of snakes has been found, polarized protons are tracked for part of HERA-$p$’s acceleration cycle which shows that polarization is preserved best for the here proposed arrangement of Siberian snakes.

We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters, and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchrobetatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case, too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchrobetatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g., where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to “measure” spin tune during computer simulations of spin motion on synchrobetatron orbits.

A possible method to realize a dispersion-free storage ring is described. The simultaneous use of a magnetic field $\mathbf{B}$ and an electric field $\mathbf{E}$ in bending regions, where the two fields are set perpendicular to each other, enables us to control the effect of momentum dispersion. When the relation $(1+1/{\gamma }_0^2)\mathbf{E}(\rho )=-{\mathbf{v}}_0\times \mathbf{B}$ is satisfied for a beam with the velocity $v_0$, the linear dispersion can be completely eliminated all around the ring. It is shown that the acceleration and deceleration induced by the electrostatic deflector counteracts the heating mechanism due to the shearing force from dipole magnets. The dispersion-free system is thus beneficial to producing ultracold beams. It looks probable that the technique will allow one to achieve three-dimensional crystalline beams. At ICR Kyoto University, an ion cooler storage ring S-LSR oriented for various beam physics purposes is now under construction. The application of the present idea to S-LSR is discussed and the actual design of the dispersionless bend is given.

Stray electrons can arise in positive-ion accelerators for heavy-ion fusion or other applications as a result of ionization of ambient gas or gas released from walls due to halo-ion impact, or as a result of secondary-electron emission. We summarize the distinguishing features of electron-cloud issues in heavy-ion-fusion accelerators and a plan for developing a self-consistent simulation capability for heavy-ion beams and electron clouds (also applicable to other accelerators). We also present results from several ingredients in this capability. (1) We calculate the electron cloud produced by electron desorption from computed beam-ion loss, which illustrates the importance of retaining ion reflection at the walls. (2) We simulate the effect of specified electron-cloud distributions on ion beam dynamics. We consider here electron distributions with axially varying density, centroid location, or radial shape, and examine both random and sinusoidally varying perturbations. We find that amplitude variations are most effective in spoiling ion beam quality, though for sinusoidal variations which match the natural ion beam centroid oscillation or breathing-mode frequencies, the centroid and shape perturbations can also have significant impact. We identify an instability associated with a resonance between the beam-envelope “breathing” mode and the electron perturbation. We estimate its growth rate, which is moderate (compared to the reciprocal of a typical pulse duration). One conclusion from this study is that heavy-ion beams are surprisingly robust to electron clouds, compared to a priori expectations. (3) We report first results from a long-time-step algorithm for electron dynamics, which holds promise for efficient simultaneous solution of electron and ion dynamics.

The linear coupling's parameterization in the uncoupled action-angle frame is introduced, where the two eigenmodes' phases at one point and the phase advances between two points in the ring are well defined. The general expressions of the coordinates $(x,x^{\prime },y,y^{\prime })$ are also given. The transfer matrix $\mathbf{P}$ from the action-angle frame to the laboratory frame can be obtained from the eigenvectors of the one-turn transfer map $\mathbf{T}$ or from Twiss and coupling parameters defined in Edwards-Teng parameterization. Matrix $\mathbf{P}$ can also be constructed from turn-by-turn beam position monitor (BPM) data. The phase ellipses and beam sizes in different projection planes are calculated through the action-angle parameterization. The two eigenmodes' Twiss and coupling parameters at point $s_2$ are described in terms of the section transfer map ${\mathbf{T}}_{1\to 2}$ and parameters at point $s_1$. The linear coupling's action-angle parameterization is useful for the analytical calculations and turn-by-turn BPM data interpretations.

Recently a new electron-bunch injection scheme for the laser wakefield accelerator has been proposed [JETP Lett. 74, 371 (2001); Phys. Rev. E 65, 046504 (2002)]. In this scheme, a low energy electron bunch, sent in a plasma channel just before a high-intensity laser pulse, is trapped in the laser wakefield, considerably compressed and accelerated to an ultrarelativistic energy. In this paper we show the possibility of the generation of an extremely short (on the order of $1\mu \mathrm{m}$ long or a few femtoseconds in duration) relativistic-electron-bunch by this mechanism. The initial electron bunch, which can be generated, for example, by a laser-driven photocathode rf gun, should have an energy of a few hundred keVs to a few MeVs, a duration in the picosecond range or less and a relatively low concentration. The trapping conditions and parameters of an accelerated bunch are investigated. The laser pulse dynamics as well as a possible experimental setup for the demonstration of the injection scheme are also considered.

The exact analytical expression for the longitudinal impedance of two-layer cylindrical tube with finite wall thickness is obtained. The numerical results for the copper-NEG, stainless steel-copper, and ceramic-copper laminated vacuum chamber impedances are given.