Loss of Landau Damping for Bunch Oscillations

Conditions for the existence, uniqueness and stability of self-consistent bunch steady states are considered. For the existence and uniqueness problems, simple algebraic criteria are derived for both the action and Hamiltonian domain distributions. For the stability problem, van Kampen theory is used. The onset of a discrete van Kampen mode means the emergence of a coherent mode without any Landau damping; thus, even a tiny couple-bunch or multi-turn wake is sufficient to drive the instability. The method presented here assumes an arbitrary impedance, RF shape, and beam distribution function. Available areas on the intensity-emittance plane are shown for resistive wall wake and single harmonic, bunch shortening and bunch lengthening RF configurations. Thresholds calculated for the Tevatron parameters and impedance model are in agreement with the observations. These thresholds are found to be extremely sensitive to the small-argument behaviour of the bunch distribution function. Accordingly, a method to increase the LLD threshold is suggested. This article summarizes and extends recent author's publications.Comment: 8 p

Circular Modes for Flat Beams in LHC

Typically x/y optical coupling is considered as unwanted and thus suppressed--particular exclusions are electron and ionization coolers. Could some special coupled modes be effectively applied for the LHC complex? Apparently, the answer is positive: use of the circular modes in the injectors with their transformation into planar modes in the LHC allows both the space charge and beam-beam luminosity limitations to be significantly reduced, if not practically eliminated.Comment: 3 p

Head-Tail Modes for Strong Space Charge

The head-tail modes are described for the space charge tune shift significantly exceeding the synchrotron tune. A general equation for the modes is derived. The spatial shapes of the modes, their frequencies, and coherent growth rates are explored. The Landau damping rates are also found. The suppression of the transverse mode coupling instability by the space charge is explained.Comment: 11 pages, 7 figures, submitted to Phys. Rev. ST-Accel. Beam

Bucket shaking stops bunch dancing in Tevatron

Bunches in Tevatron are known to be longitudinally unstable: their collective oscillations, also called "dancing bunches," persist without any signs of decay. Typically, a damper is used to stop these oscillations, but recently, it was theoretically predicted that the oscillations can be stabilized by means of small bucket shaking. Dedicated measurements in Tevatron have shown that this method does stop the dancing.Comment: 3 pp. Particle Accelerator, 24th Conference (PAC'11) 2011. 28 Mar - 1 Apr 2011. New York, US

Impedances of Laminated Vacuum Chambers

Longitudinal and transverse impedances are derived for round and flat laminated vacuum chambers.Comment: 12 p