Beam instability excited by space charge effect is investigated by particle simulations during final beam bunching in heavy ion inertial fusion. The beam current is continuously increased along the beam transport line with longitudinal bunch compression. A transverse particle-in-cell simulation is carried out with a simple model of beam current increase. The multiparticle simulation shows emittance growth accompanied by the restructuring of charge distribution in the interior of the beam. An analytical stability criterion for the high-current beam transport predicts the growth of density fluctuation by the space charge effect. Although results indicate that an abrupt emittance growth is induced by the space charge oscillation at critical tune depression in the final buncher, the increase of emittance can be estimated as high as 23% at the worst case during the bunching process.

In this paper, we report on the halo formation and emittance growth driven by a parametric resonance during beam-beam collisions with optically mismatched injection. In the regime of the weak-strong beam-beam interaction, if two beams have the same machine tunes, on-axis head-on collisions between a mismatched strong beam and a weak beam will not cause the formation of halo. However, if the two beams collide with an initial offset, the beam-beam force from the mismatched strong beam can cause halo formation and emittance growth in the weak beam. Meanwhile, if two beams have different machine tunes, for opposite charged colliding beams, when the machine tune of the weak beam is smaller than that of the strong beam, there is emittance growth in the weak beam. When the machine tune of the weak beam is larger than that of the strong beam, there is little emittance growth. In the regime of the strong-strong beam-beam interaction, halo is formed in both beams even when the two beams collide head-on on the axis with equal machine tunes. This puts a strong requirement for a good beam match during the injection to colliders in order to avoid emittance growth if there are no other mechanisms after the injection to decohere the mismatched envelope oscillation.

The cumulative beam breakup problem excited by the resistive-wall wake is formulated. An approximate analytic method of finding the asymptotic behavior for the transverse bunch displacement is developed and solved. Comparison between the asymptotic analytical expression and the direct numerical solution is presented. Good agreement is found. The criterion of using the asymptotic analytical expression is discussed.

Several modern applications of radiation processing require compact and self-contained electron accelerators. To match these requirements, a 5 MeV, 1 kW electron linac has been developed at the Dipartimento di Fisica (Università di Messina) and will be described in this paper. This standing wave accelerator, driven by a 3 GHz, 2.5 MW magnetron generator, has an autofocusing structure and will be used to study several applications of radiation processing.

The charge-exchange method is now one of the main techniques for ion injection into accelerators and storage rings. The disadvantages of conventional methods, based on the atom or ion stripping in a material target, are emittance growth, energy straggling, and production of ions in many charge states. Recently suggested stripping methods based on direct photoionization require employment of hard-UV lasers, which still do not exist and must obviously be very bulky and expensive. An alternative method, suggested for injection of proton beams, employs excitation of the atom to $3p$ intermediate state with subsequent Lorentz ionization in a magnetic field gradient. This technique applies rigid requirements to laser characteristic and is not free of growing of the beam divergence. In this paper a variant of the stripping technique based on the resonantly enhanced two-photon ionization (RETPI) is considered. The technique allows ionization of singly charged ions of the elements from helium to bismuth. A variant of the technique can be used for proton injection. RETPI can be applied for both ion injection and stacking, as well as for diagnostics of ion beam characteristics on the orbit. Stripping efficiency can be about 100% for the singly charged ions having the singlet ground state and decreases for the other ions. Special methods for “cleaning” unwanted atomic states in such ions, that can provide high stripping efficiency, are discussed. Excimer lasers with very moderate parameters can be employed for implementation of this technique for almost all elements. Numerical examples show that for most of the singly charged ions and for hydrogen atom necessary laser-beam energy density is merely $0.5–8\mathrm{J}/{\mathrm{cm}}^2$ for a 1 m interaction region, and is 10 times higher for several light ions.

Pulse compression systems for future linear colliders, such as NLC and JLC, involve hundreds of kilometers of waveguide runs. These waveguides are highly overmoded to reduce the rf losses. In this paper we present a novel idea for utilizing these waveguides several times by using different modes. This idea is suitable for reflective delay lines. All the modes being used have low-loss characteristics. We describe mechanically simple mode transducers that switch the propagation mode from one configuration to another with no observable dispersion. We apply this technique to a resonant delay line pulse compression system. We also present experimental results that verify these theoretical developments.

We describe a mechanism using clearing electrodes and solenoids to remove the electron cloud in the Spallation Neutron Source’s accumulator ring. Simulation indicates that strong multipacting could happen at median clearing fields. A similar phenomenon was reported in an experimental study at Los Alamos Laboratory’s Proton Storage Ring. A weak solenoid is proven to be a good remedy for suppressing multipacting by confining electrons near the chamber wall’s surfaces. We investigated the clearing mechanism using both electrodes and solenoids.

In the soft x-ray region, the demand for helicity switching of circularly polarized undulator radiation is increasing to study circular dichroism. The asymmetric figure-8 undulator is an insertion device to provide circularly polarized radiation (CPR) and a simple method of helicity switching which has been proposed and built at SPring-8. Because of its complicated magnetic structure, it is important to optimize the magnetic parameters for more effective utilization of CPR. Using an analytical method, the relation between the magnetic parameters to maximize the degree of circular polarization is obtained. The impact of the finite emittance of electron beams on the polarization performance is also investigated numerically.

Crystalline undulators with periodically deformed crystallographic planes offer coherent electromagnetic fields on the order of 1000 T and provide undulator period $L$ in submillimeter range. We present an idea for creation of a crystalline undulator and report its realization. One face of a silicon crystal was given periodic microscratches (grooves) by means of a diamond blade, with a period ranging from 0.1 to 0.5 mm in different samples. The x-ray tests of the crystal deformation have shown that a sinusoidal-like shape of crystalline planes goes through the bulk of the crystals. This opens up the possibility for experiments with high-energy particles channeled in the crystalline undulator, a new compact source of radiation. The first experiments on photon emission in the crystal undulator are in preparation at IHEP (Protvino) with 2–15 GeV positrons and at LNF (Frascati) with 500–800 MeV positrons, aiming to produce undulator photons in the range of 50–500 keV. The results of Monte Carlo simulations for the planned experiments are presented as well.

We recently studied spin flipping of a $1.94\mathrm{GeV}/c$ vertically polarized proton beam at COSY in Jülich, Germany. We swept an rf-dipole’s frequency through an rf-induced spin resonance to flip the beam’s polarization direction. After determining the resonance’s frequency, we varied the dipole’s strength, frequency range, and frequency ramp time. At the rf-dipole’s maximum strength, and optimum frequency range and ramp time, we measured a spin-flip efficiency of $99.3\%\pm 0.1\%$. This result indicates that an rf dipole may allow efficient spin flipping in high energy proton rings.

This paper describes a self-consistent kinetic model for the longitudinal dynamics of a long, coasting beam propagating in straight (linear) geometry in the $z$ direction in the smooth-focusing approximation. Starting with the three-dimensional Vlasov-Maxwell equations, and integrating over the phase-space $({\mathbf{x}}_{\perp },{\mathbf{p}}_{\perp })$ transverse to beam propagation, a closed system of equations is obtained for the nonlinear evolution of the longitudinal distribution function $F_b(z,p_z,t)$ and average axial electric field $⟨E_z^s⟩(z,t)$. The primary assumptions in the present analysis are that the dependence on axial momentum $p_z$ of the distribution function $f_b(\mathbf{x},\mathbf{p},t)$ is factorable, and that the transverse beam dynamics remains relatively quiescent (absence of transverse instability or beam mismatch). The analysis is carried out correct to order $k_z^2{r}_w^2$ assuming slow axial spatial variations with $k_z^2{r}_w^2\ll 1$, where $k_z\sim \partial /\partial z$ is the inverse length scale of axial variation in the line density ${\lambda }_b(z,t)=\int d{p}_z{F}_b(z,p_z,t)$, and $r_w$ is the radius of the conducting wall (assumed perfectly conducting). A closed expression for the average longitudinal electric field $⟨E_z^s⟩(z,t)$ in terms of geometric factors, the line density ${\lambda }_b$, and its derivatives $\partial {\lambda }_b/\partial z,\dots$ is obtained for the class of bell-shaped density profiles $n_b(r,z,t)=({\lambda }_b/\pi r_b^2)f(r/r_b)$, where the shape function $f(r/r_b)$ has the form specified by $f(r/r_b)=(n+1)(1-r^2/r_b^2{)}^n$ for $0\le r<r_b$, and $f(r/r_b)=0$ for $r_b<r\le r_w$, where $n=0,1,2,\dots$. The general kinetic formalism developed here is valid for the entire range of beam intensities (proportional to ${\lambda }_b$) ranging from low-intensity, emittance-dominated beams, to very-high-intensity, low-emittance beams.

We have augmented the code POSINST to include solenoid fields and used it to simulate the buildup of electron cloud due in the PEP-II positron ring. We find that the distribution of electrons is strongly affected by the resonances associated with the cyclotron period and bunch spacing. In addition, we discover a threshold beyond which the electron density grows exponentially until it reaches the space charge limit. The threshold does not depend on the bunch spacing but does depend on the positron bunch population.

This work is a three-dimensional stability study based on the modal analysis for a continuous beam with an axisymmetric Kapchinskij-Vladimirskij (KV) distribution. The analysis is carried out self-consistently within the context of linearized Vlasov-Maxwell equations and electrostatic approximation. The emphasis is on investigating the coupling between longitudinal and transverse perturbations in the high-intensity region. The interaction between the transverse modes supported by the KV distribution and the “usual transverse modes” is examined. We found two classes of “coupling modes” that would not exist if longitudinal and transverse perturbations are treated separately. We also found that some transverse modes can interact among themselves through longitudinal perturbation to cause instability. The effects of wall impedance on beam stability is also studied and numerical examples are presented.

The transverse evolution of the envelope of an intense, unbunched ion beam in a linear transport channel can be modeled for the approximation of linear self-fields by the Kapchinskij-Vladimirskij (KV) envelope equations. Here we employ the KV envelope equations to analyze the linear stability properties of so-called mismatch perturbations about the matched (i.e., periodic) beam envelope in continuous focusing, periodic solenoidal, and periodic quadrupole transport lattices for a coasting beam. The formulation is analyzed and explicit self-consistent KV distributions are derived for an elliptical beam envelope in a periodic solenoidal transport channel. This derivation extends previous work to identify emittance measures and Larmor-frame transformations to allow application of standard form envelope equations to solenoidal focusing channels. Perturbed envelope equations are derived that include driving sources of mismatch excitation resulting from focusing errors, particle loss, and beam emittance growth. These equations are solved analytically for continuous focusing and demonstrate a factor of 2 increase in maximum mismatch excursions resulting from sudden driving perturbations relative to adiabatic driving perturbations. Numerical and analytical studies are carried out to explore properties of normal mode envelope oscillations without driving excitations in periodic solenoidal and quadrupole focusing lattices. Previous work on this topic by Struckmeier and Reiser [Part. Accel. 14, 227 (1984)] is extended and clarified. Regions of parametric instability are mapped, new classes of envelope instabilities are found, parametric sensitivities are explored, general limits and mode invariants are derived, and analytically accessible limits are checked. Important, and previously unexplored, launching conditions are described for pure envelope modes in periodic quadrupole focusing channels.

When an electron beam collides with a high-intensity laser beam, the spectrum of the nonlinear Thomson scattering in the backward direction shows strong oscillations like those in the spectrum of an optical klystron. Laser gain on the backward Thomson scattering is estimated using the Madey theorem, and the results suggest that Thomson-backscatter free-electron lasers are possible at wavelengths extending to the far uv using a terawatt laser beam from a chirped-pulse amplifier and a high-brightness electron beam from a needle cathode.

Recently a novel approach has been proposed for performing multiturn extraction from a circular machine. Such a technique consists of splitting the beam by means of stable islands created in transverse phase space by magnetic elements creating nonlinear fields, such as sextupoles and octupoles. Provided a slow time variation of the linear tune is applied, adiabatic with respect to the betatron motion, the islands can be moved in phase space and eventually charged particles may be trapped inside the stable structures. This generates a certain number of well-separated beamlets. Originally, this principle was successfully tested using a fourth-order resonance. In this paper the approach is generalized by considering other types of resonances as well as the possibility of performing multiple multiturn extractions. The results of numerical simulations are presented and described in detail. Of course, by time reversal, the proposed approach could be used also for multiturn injection.

An alternative layout of the TESLA linear collider (Technical Design Report, DESY Report No. 2001-011, 2001), based on weakly coupled multicell superconducting structures (superstructures), significantly reduces the investment cost due to a simplification in the rf system of the main accelerator. In January 1999, preparation of the beam test of the superstructure began in order to prove the feasibility of this layout. Progress in the preparation was reported frequently in Proceedings of TESLA Collaboration Meetings. Last year, two superstructures were installed in the Tesla Test Facility linac at DESY to experimentally verify methods to balance the accelerating gradient in a weakly coupled system, the stability of the energy gain for the entire train of bunches in macropulses, and the damping of higher order modes. We present results of the first cold and beam test of these two Nb prototypes.

When accelerating gold ions in the Relativistic Heavy Ion Collider (RHIC) the transition energy must be crossed. For this purpose, RHIC uses a set of correction quadrupoles and special power supplies which can reverse polarity in less than 40 ms. These quadrupoles are used to produce dispersion bumps which increase the transition energy as the beam approaches transition. The change of polarity will then jump the transition energy across the beam energy. This paper describes the commissioning of the RHIC first-order matched transition crossing system.

We investigate the validity of the Vlasov-Poisson equations for calculating properties of systems of $N$ charged particles governed by time-independent Hamiltonians. Through numerical experiments we verify that there is a smooth convergence toward a continuum limit as $N\to \infty$ and the particle charge $q\to 0$ such that the system charge $Q=qN$ remains fixed. However, in real systems $N$ and $q$ are always finite, and the assumption of the continuum limit must be questioned. We demonstrate that Langevin simulations can be used to assess the importance of discreteness effects, i.e., granularity, in systems for which the physical particle number $\mathcal{N}$ is too large to enable orbit integrations based on direct summation of interparticle forces. We then consider a beam bunch in thermal equilibrium and apply Langevin techniques to assess whether the continuum limit can be safely applied to this system. In the process we show, especially for systems supporting a sizable population of chaotic orbits that roam globally through phase space, that for the continuum limit to be valid, $\mathcal{N}$ must sometimes be surprisingly large. Otherwise the influence of granularity on particle orbits cannot be ignored.