Search Results (29 total)

In a particle accelerator with a periodic structure beam space charge force may excite resonant beam emittance growth if the particle’s transverse phase advance approaches 90°. A recent simulation study with the PARMILA code [D. Jeon , Phys. Rev. ST Accel. Beams 12, 054204 (2009)] has shown the feasibility of measuring the stop band of this fourth order resonance in the GSI Universal Linear Accelerator UNILAC and proposed its experimental verification, which is reported here. Measurements of transverse phase space distributions behind a periodically focusing structure reveal a fourfold symmetry characteristic of fourth order resonances as well as a resonance stop band above σ₀=90° per focusing cell. These experimental findings agree with results from three different beam dynamics simulation codes, i.e., DYNAMION, PARMILA, and TRACEWIN.

Transverse emittance growth along the Alvarez drift tube linac (DTL) section is a major concern with respect to the preservation of beam quality of high current beams at the GSI UNILAC. In order to define measures to reduce this growth, appropriate tools to simulate the beam dynamics are indispensable. This paper is about the benchmarking of three beam dynamics simulation codes, i.e. DYNAMION, PARMILA, and PARTRAN against systematic measurements of beam emittances for different transverse phase advances along the DTL. Special emphasis is put on the modeling of the initial distribution for the simulations. The concept of rms equivalence is expanded from full intensity to fractions of less than 100% of the beam. The experimental setup, data reduction, preparation of the simulations, and the evaluation of the simulations are described. In the experiments and in the simulations, a minimum of the rms-emittance growth was observed at zero current phase advances of about 60°. In general, good agreement was found between simulations and experiment for the mean values of horizontal and vertical emittances at the DTL exit.

In this paper we present a method for measuring the nonlinear errors in a circular accelerator by taking advantage of the feed-down effect of high order multipoles when the closed orbit is globally deformed. We devise a nonlinear tune response matrix in which the response to a closed orbit deformation is obtained in terms of change of machine tune and correlated with the strength of the local multipoles. A numerical example and a proof of principle experiment to validate the theoretical methods are presented and discussed.

The influence of the nonlinear space-charge force, which causes an amplitude-dependent tune shift, on the transverse stability of a coasting beam with impedances is investigated. In particular, the interplay of nonlinear space charge with a cubic lattice nonlinearity (octupoles) and with linear chromatic effects is considered. For each case, the stability diagram obtained from a dispersion relation with two-dimensional tune spread is compared with results from a simulation scan. For the latter, a 3D particle tracking code is used, with self-consistent 2D space charge, coupling to transverse impedances, chromaticity, and nonlinear lattice effects. The validity of non-self-consistent space-charge models in analytical and in numerical approaches is examined. We reconfirm that, although nonlinear space charge does not provide Landau damping of its own, it modifies strongly the stability properties and must be taken into account in an analysis of Landau damping induced by external (octupole or chromaticity) effects. It is demonstrated that non-self-consistent approaches for space charge are not always applicable.

Using field matching techniques, closed form analytic expressions for the transverse impedance and for the shielding effectiveness of a smooth cylindrical beam pipe of arbitrary thickness are presented. In the limit of thick and thin beam pipes the well-known expressions are reproduced. The transverse transmission coefficient is compared with the longitudinal one that has been obtained in our previous work [A. M. Al-Khateeb, O. Boine-Frankenheim, R. W. Hasse, and I. Hofmann, Phys. Rev. E 71, 026501 (2005).]. The results are applied to the heavy ion synchrotron SIS 18 and to the planned SIS 100 at GSI. In both machines the stainless steel beam pipe in the dipole sections is much thinner than the skin depths at the revolution frequency and, therefore, the impedance value and the transmission are of concern.

In this paper we present a comprehensive analysis of the self-consistent, collective behavior associated with the space-charge-driven (Montague) coupling resonance near 2Q_x-2Q_y=0, including the effect of linear coupling. Based on analytical work and particle-in-cell simulation in the 2D coasting beam limit, we derive scaling laws for stop-band widths and growth rates, which may be applied to circular machines as well as to linear accelerators. For slow crossing of the stop bands, we find a strong directional dependence. In the case of crossing from below—assuming that the rising tune pertains to the direction, in which the initial emittance is the larger one—the emittance exchange is a smooth and fully reversible process. For crossing from above, we encounter a discontinuous behavior, which disappears largely, if an external linear coupling is applied.

We show that pronounced collective nonlinear behavior is present in a beam with linear coupling and space charge as described by the complete second order moment equations. The collective effects result in a shifted and broadened resonance condition as well as saturation effects in the emittance transfer. For slow stop-band crossing either the beam evolves along a skewed matched solution with full emittance exchange or the exchange is hindered by collective space charge effects, depending on the emittance ratio and direction of crossing.

The longitudinal coupling impedance of a cylindrical beam pipe for arbitrary relativistic γ₀ and mode frequency is obtained analytically for finite wall conductivity and finite wall thickness. Closed form expressions for the electromagnetic fields excited by a beam perturbation are derived analytically. General expressions for the resistive-wall impedance in the presence of a metallic shield and for the rf shielding effectiveness of the beam pipe have been obtained and then compared with approximate expressions. The results are applied to the GSI synchrotron SIS, where the thickness of the vacuum chamber in the dipole magnets is much smaller than the skin depth at injection energy.

We investigate the phenomenon of space-charge driven emittance growth in a three-dimensional mismatched anisotropic charged particle beam with relevance to high-intensity linear accelerators. The final emittance growth can be understood as a superposition of the contributions from the mismatch-induced halo formation and from the anisotropy-induced energy exchange. The averaged emittance growth per degree of freedom is bounded from above by the so-called “free energy limit” extended by the contributions from energy exchange. The partition of the growth into longitudinal or transverse is, however, a strong function of the tune ratio including the possibility that an initially equipartitioned beam is even driven substantially away from equipartition. The growth of the beam halo extent is dominated by the effect of mismatch, whereas anisotropy itself generates practically no halo.

We study the response of coasting beams in the presence of space charge to linear coupling as well as gradient errors, based on linearizing the self-consistent Vlasov-Poisson equation. We determine the coherent shift of the resonance conditions as well as the response on lattice errors in smooth approximation, but allowing for arbitrary tune and/or emittance ratios. A characteristic feature is cancellation between the external forces due to the lattice errors and the beam induced space-charge forces, if the resonance condition is satisfied for the (space-charge shifted) single-particle tunes. For the linear coupling mode and small tune split we also identify a parameter region, where spontaneous instability exists in addition to the resonance.

The combined effect of space charge and nonlinear resonance on beam loss and emittance was measured in a benchmarking experiment over a 1.2 s long flat bottom at 1.4 GeV kinetic energy in the presence of a single controllable octupole. By lowering the working point towards the resonance, a gradual transition from a loss-free core emittance blowup to a regime dominated by continuous loss was found. We compare the observation with 3D simulations based on a new analytical space charge model and obtain good agreement in the emittance blowup regime. Our explanation is in terms of the synchrotron oscillation, which causes a periodic tune modulation due to space charge, and leads to trapping and detrapping on the resonance islands. For working points very close to the resonance this induces a beam halo with large radius. The underlying dynamics is studied in detail, and it is claimed that the predicted halo in conjunction with a reduced dynamic aperture for the real machine lattice is the source of the loss observed in the experiment.

Resonance-driven collective instabilities of charged-particle beams were extensively studied in connection with high-current transport systems, leading to restrictions imposed on the zero-current phase advance. In this paper, we discuss application of such parametric instabilities to circular machines. This effect is directly related to the space-charge limit in rings and its understanding is of crucial importance. Its relation to the coherent resonance condition of an integer type is explained. Practical application of such resonant responses to both structural and imperfection driven harmonics is addressed.

A large-scale Vlasov simulation study of the microwave instability below transition energy in a beam confined between two barrier pulses is performed. Starting from a matched distribution function for the confined ion beam including the space charge impedance the stability threshold in the longitudinal impedance plane is obtained. A simple stability criterium is found to be in good agreement with the simulation results.

The theory and simulation of coherent resonant coupling due to space charge in coasting or bunched anisotropic equilibrium beams is presented. Our work confirms that analytical results on coherent oscillations and instabilities of anisotropic KV (Kapchinskij-Vladimirskij) distributions are a valid tool to interpret the findings from 2D and 3D self-consistent particle-in-cell simulations for both KV and waterbag distributions. With reference to rings we discuss space charge coherent tune shifts up to fourth order and introduce a coherent coupled mode coefficient, which enables us to resolve the issue of KV anomalies by relating them to negative energy modes. The second emphasis of this study is with reference to linacs and a detailed discussion of “stability charts” describing resonant regions where approach to equipartition may occur.

Longitudinal ballistic and collective beam echoes with diffusion effects are investigated theoretically. In the presence of the space-charge impedance, the collective echo amplitude is obtained as a closed form expression. In contrast to the ballistic case, the collective echo amplitude consists of one maximum at time t_echo. The echo amplitude grows up and damps down with a rate proportional to the Landau damping rate of space-charge waves. The effect of weak diffusion is found to modify the ballistic and the collective echo amplitudes in the same manner. This effect of diffusion was confirmed using a “noiseless,” grid-based simulation code. As a first application the amount of numerical diffusion in our simulation code was determined using the echo effect.

We study halo emittance growth in anisotropic beams and show that the rms emittance growth resulting from mismatch is highly anisotropic, depending on the tune ratio. We find that the free-energy limit calculated by Reiser [J. Appl. Phys. 70, 1919 (1991)] for an axisymmetric 1D halo can be extended to 2D if understood as an upper bound to the rms emittance growth averaged per degree of freedom. The thus-obtained “free-energy limit” of an ideal transport system is compared with the halo rms emittance growth in simulations of the Spallation Neutron Source linac.

A detailed study of the influence of space charge on the crossing of second-order resonances is presented and associated with the space-charge limit of high-intensity rings. Two-dimensional simulation studies are compared with envelope models, which agree in the finding of an increased intensity limit due to the coherent frequency shift. This result is also found for realistic bunched beams with multiturn injection painting. Characteristic features such as the influence of tune splitting, structure resonances, and the role of envelope instabilities are discussed in detail. The theoretical limits are found to be in good agreement with the performance of high-intensity proton machines.

A simple 1D model is proposed to explore the resonant extraction of intense beams from a synchrotron as performed in the SIS synchrotron in GSI (Darmstadt). The model Hamiltonian consists of a constant focusing, a thin sextupole, and a smooth space charge field. Hyperbolic normal forms are used to estimate the extraction times and the emittance of the extracted beam; the quality of the reconstruction is tested in absence of space charge. The effect of space charge on the dynamical behavior of the beam near the 1/3 betatron resonance is numerically investigated using the frequency map analysis and qualitatively explained with perturbation theory. A polynomial approximation to the one turn map is obtained by replacing the exact space charge force with a sequence of polynomial kicks, and the resonant normal forms reproduce quite accurately the nonlinear tunes and the fixed points position. At low order an analytical estimate of the area of the stable region is proposed to recover the self-consistency of the model.

Space charge can lead to emittance and/or energy exchange known as “equipartitioning issue” in linacs, or space-charge coupling in high-current synchrotrons. It is described here as an internal resonance driven by the self-consistent space-charge potential of coherent eigenmodes. By a detailed comparison of analytical theory with 2D particle-in-cell simulation for Kapchinskij-Vladimirskij (KV) and waterbag distributions, we discuss characteristic features of this resonance mechanism in the vicinity of the symmetric focusing resonance band—for practical purposes, the most important case—and discuss the applicability of the linearized KV theory.

Energy exchange between the longitudinal and transverse degrees of freedom of nonequipartitioned bunched beams (non-neutral plasmas) is investigated by means of 3D simulation. It is found that collective instability may lead to energy transfer in the direction of equipartition, without full progression to it, in certain bounded regions of parameter space where internal resonance conditions are satisfied, in good agreement with stability charts from an earlier derived 2D Vlasov analysis. Nonequipartitioned stable equilibria, however, exist in relatively wide regimes of parameter space. This provides evidence that such regimes may be safely used in the design of future high-intensity linacs.

The longitudinal space charge and resistive wall impedances have been investigated in a smooth cylindrical beam pipe. At any point from the beam axis, we obtained an expression for the total impedance, which at the beam surface r=a for infinite pipe wall conductivity gives the expression for the total impedance that was derived by Zotter and Kheifets in studying the impedance of uniform beams in concentric cylindrical wall chambers, when a single cylindrical chamber is considered [B. W. Zotter and S. A. Kheifets, Impedances and Wakes in High-Energy Particle Accelerators (World Scientific, Singapore, 1998), Chap. 6]. A fitting formula for the space-charge impedance at the beam surface (r=a), which is valid for arbitrary wavelengths, is given. Rather than calculating the impedance with the field on the axis [Joseph J. Bisognano, Fifth European Particle Accelerator Conference (EPAC96), edited by S. Myers, A. Pacheco, R. Pascual, Ch. Petit-Jean-Genaz, and J. Poole (Institute of Physics, Bristol, 1996), Vol. 1, p. 328], the fitting formula is obtained by averaging over the transverse beam distribution. We also give another approach for the calculation of the resistive wall impedance using the flux of the Poynting vector at the pipe wall and then compare it with the expression obtained from the volume integral over the beam distribution.

Advanced storage ring concepts for intense ion beams often require operation far outside the stability boundaries provided by Landau damping. Whether a machine can be operated in such a regime depends on the phase space dilution after saturation of the microwave instability. A Vlasov simulation model is employed to analyze the saturation mechanisms in space charge dominated coasting beams. The stabilizing effect of space charge [I. Hofmann, Laser Part. Beams 3, 1 (1985)] is addressed to fluidlike mode coupling effects.

It is shown that energy conservation in the longitudinal envelope equation can be used to derive analytic expressions to model fast bunch compression and the effect of space charge in terms of a dimensionless Coulomb parameter Σ (∝1/η, with η the slip factor). For small |η| (below transition, hence Σ≫1), the rf voltage required is nearly independent of η and dominated by space charge repulsion. The extra voltage generates the coherent momentum spread δ∝1/sqrt[|η|] required to compensate the increasing space charge force gradient during compression. This sets a clear limit to the useful approach to transition. An η jump scheme is discussed to minimize this effect. Particle-in-cell computer simulation confirms the validity of our results also for more realistic beam distributions. Noticeable tails in momentum space due to the nonlinear space charge force are found for Gaussian line density bunches and Σ≫1.

In the ESR heavy-ion cooler storage ring at GSI the exponential growth and the subsequent saturation phase of the longitudinal instability in space charge dominated ion beams can be monitored with high resolution. Kinetic simulations together with the experimental data lead to a new insight into the effects of space charge and electron cooling on the long-time evolution of the instability. In the simulations we observe the continuous excitation of long-lived collective modes generated by particle trapping in the self-excited potential, which suggest that previous “overshoot” concepts need revision.

Based on self-consistent Vlasov-Poisson equations, we derive coherent frequencies and stability properties of anisotropic or “nonequipartitioned” beams with different focusing constants and emittances in the two transverse directions. The thus obtained dispersion relations of transverse multipole oscillations with quadrupolar, sextupolar, and octupolar symmetries are solved numerically. We find that for sufficiently large energy anisotropy some of the eigenmodes become unstable in the space-charge-dominated regime. Applying our results to high-current linear accelerators, we find that “nonequipartitioned” beams may exist in relatively large regions of parameter space under stable conditions. It is only in beams with strongly space-charge-depressed betatron tunes that harmful instabilities leading to emittance exchange should be expected.