Longitudinal Stability of Flat Bunches with Space-Charge or Inductive Impedance
We study the loss of Landau damping for the longitudinal plane via the “Sacherer formalism”. Stability limits are calculated for several longitudinal beam distributions, in particular for two types of flat bunches, which could be of interest to the LHC upgrade. The resulting stability diagrams are computed and displayed for different azimuthal modes. A general recipe is given for calculating the threshold intensity in the case of a capacitive impedance below transition or, equivalently, for a purely inductive impedance above transition. The formalism was applied to the case of the PS Booster, as an example of space-charge impedance below transition, and to the SPS, as an example of inductive impedance above transition. Contribution to the EPAC’08 Conference, Genoa (Italy), 23-27 June 2008 Work supported by the European Community-Research Infrastructure Activity under the FP6 “Structuring the European Research Area” programme (CARE, contract number RII3-CT2003-506395) Longitudinal Stability of Flat Bunches with Space-Charge or Inductive Impedance I. Santiago Gonzalez ∗, F. Zimmermann, CERN, Geneva, Switzerland
Stability diagrams for Landau damping
Coherent modes which are present when there is no incoherent tune spread may be absent when such a spread exists. Such modes are "Landau damped". There is instead an incoherent spectrum, a continuum of an infinite number of frequencies, which will decohere (filament), thus not leading to collective instabilities. A stability diagram indicates when Landau damping will be effective. It divides the effective impedance plane, or equivalently the plane of coherent frequency in the absence of tune spread, into regions. The region which contains +i/spl infin/ corresponds to instability. Thus, one can substitute a simpler computation (finding discrete eigenvalues) for a more complex computation (solving an eigenvalue system with both a discrete and a continuous eigenvalue spectrum). We present stability diagrams assuming a linear tune shift with amplitude, allowing tune spread in two transverse planes or in the longitudinal plane alone. When there is longitudinal tune spread, this can not be done exactly, and we describe approximations which make the computation tractable.
Parameters for low energy operation of CESR
We present a detailed design for operation of the Cornell Electron Storage Ring, CESR, in the energy range covering the /spl psi/ resonances and the Charm and Tau thresholds, as well as reaching to the upper Y resonances near 11 GeV. The addition of 18 m of super-ferric wiggler magnets will partially restore low energy beam emittance and damping times. Installation of superconducting quadrupoles in the interaction region and the addition of high performance superconducting RF cavities will enhance performance at all energies. Studies of optics, beam dynamics, wiggler and vacuum system performance, beam stability, and beam-beam effects confirm operation with a luminosity of 3/spl times/ 10/sup 32/ CM/sup -2/ sec/sup -1/ at 1.88 GeV.