Search Results (14 total)

The effect of space charge and image currents on the transverse Schottky spectrum for bunched beams has been investigated using simulations combined with an analytic model. We found a good agreement between the shifts of synchrotron satellites observed in the simulation noise spectrum and a simplified model for head-tail modes with space charge and image currents.

The effect of moderate space charge on the transverse Schottky spectrum of a coasting beam is studied using measurements and simulations together with an analytic model. The measurements of transverse Schottky bands from heavy ion beams were performed in the SIS-18 synchrotron at GSI. In addition, we analyze the noise spectrum from a particle tracking code with self-consistent space charge. Both results are compared to an analytic model that is based on the dispersion relation for linear space charge forces and chromatic betatron tune spreads. The analytic model reproduces the characteristic deformation of Schottky bands with increasing space charge, observed in both measurement and simulation.

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.

The stability of longitudinal dipole oscillations in Gaussian bunches is studied for different rf wave forms and with nonlinear space charge. In a previous study [O. Boine-Frankenheim and T. Shukla, Phys. Rev. ST Accel. Beams 8, 034201 (2005)], the space charge induced loss of Landau damping and the bunch response to rf phase modulations was analyzed for elliptic distributions. The present study investigates Landau damping of dipole modes with nonlinear space charge in Gaussian bunches. The stability boundary resulting from a dispersion relation is compared with stability scans performed within a self-consistent simulation scheme. The results are compared with numerically obtained beam transfer functions.

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.

The interplay of nonlinear rf fields and space charge is studied using a particle simulation code together with analytic derivations. In the framework of the elliptic (“Hofmann-Pedersen”) distribution function the matched beam parameters are obtained. Using the simulation “Schottky” noise from matched bunches the coherent mode spectrum is analyzed and compared with analytic expression. The bunch response to a small rf phase modulation is studied over a large range of initial simulation parameters (modulation frequency, bunch intensity). These bunch response scans clearly show the location of the dipole mode frequency as well as the threshold for the loss of Landau damping due to space charge. In addition, bunch stability scans are performed in order to determine the stability boundaries for flattopped bunches in single and double rf wave forms. The results are related to previous work on beam transfer functions in single and double rf buckets and to experimental observations in the GSI synchrotron SIS.

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.

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.

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.

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.

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.