JAEA/J-PARC, Tokai-Mura, Naka-Gun, Ibaraki-Ken
KEK, Ibaraki
We have developed a theory to calculate both longitudinal and transverse impedances of a resistive short (typically shorter than the chamber radius) insert with cylindrical symmetry, sandwiched by perfectly conductive chambers on both sides. It is found that unless the insert becomes extremely thin (typically a few nm for a metallic insert) the entire image current runs on the thin insert, even in the frequency range where the skin depth exceeds the insert thickness, and therefore the impedance increases drastically from the conventional resistive-wall impedance. In other words, the wake fields do not leak out of the insert unless it is extremely thin.
EPFL, Lausanne
CERN, Geneva
Two dimensional electromagnetic models (i.e. assuming an infinite length) for the vacuum chamber elements in a synchrotron are often quite useful to give a first estimate of the total beam-coupling impedance. In these models, classical approximations can fail under certain conditions of frequency or material properties. We present here two formalisms for flat and cylindrical geometries, enabling the computation of fields and impedances in the multilayer case without any assumption on the frequency, beam velocity or material properties (except linearity, isotropy and homogeneity).
Fermilab, Batavia
In 1955, van Kampen described a full set of eigenfunctions for collective oscillations in plasma. This formalism can be applied to the beams as well. As a result, a loss of Landau damping is seen as one of the main reasons for bunch instability. Bunch stability is seen to depend both on a shape of the distribution function and RF bucket. Available areas on intensity-emittance plane are shown for various RF shapes and wake functions. Results are compared with observations and simulations.
CERN, Geneva
The peak detected Schottky spectrum is used for beam observation in the CERN SPS and now already in the LHC. This tool was always believed, however without proof, to give a good picture of the particle distribution in synchrotron frequencies similar to the longitudinal Schottky spectrum of unbunched beam for revolution frequencies. The analysis shows that for an optimised experimental set-up the spectrum of the peak detected signal is very close to the synchrotron frequency distribution inside the bunch - much closer than that given by the traditional longitudinal bunched-beam Schottky spectrum. The limitations of the present experimental set-up in the SPS are discussed together with possible improvements.
GSI, Darmstadt
TEMF, TU Darmstadt, Darmstadt
A study of the transverse dynamics of coasting ion beams with moderate space charge is presented. An analytic model based on the dispersion relation with a linear space-charge force is used to describe the impact of space charge on transverse beam transfer functions (BTFs) and the stability limits of a beam. The dielectric function obtained in this way is employed to describe the transverse Schottky spectrum with linear space charge as well. The difference between space charge and impedance effects is highlighted. An experiment performed in the heavy ion synchrotron SIS-18 at GSI to detect space-charge effects at different beam intensities is explicated. The measured transverse Schottky spectra, BTFs and stability diagrams are compared with the analytic model. The space-charge parameters evaluated from the Schottky and BTF measurements are compared with estimations based on measured beam parameters. Furthermore, particle tracking simulations demonstrating the impact of collective effects on the Schottky and BTF diagnostics are presented. The simulation results are used to verify the space-charge model.
ORNL, Oak Ridge, Tennessee
The dependence of the e-p instability threshold on the 2nd harmonic voltage and on the longitudinal profile in general is observed in the SNS ring. Possible explanations of this phenomenon are discussed in the paper. The most optimal RF configuration to mitigate instabilities is presented.