Theory of Head - Tail Chromaticity Sharingr
نویسنده
چکیده
Chromaticity compensation (Q 0 x Q 0 y 0) is required to avoid the \head-tail" eeect in all high-energy accelerators. A potential advantage of the \MM obius" scheme, or any other strongly coupled lattice, is that, because of cooperation between damping in the two planes, a less-restrictive condition, Q 0 x ?Q 0 y , should be satisfactory. This \chromaticity sharing" concept has been tested at CESR and, with qualiication, been found valid. During these studies numerous fascinating features have emerged. This report contains theoretical calculations bearing on these phenomena, the most important of which are the innuence on the head-tail eeect of coupling, decoherence, and sympathetic damping. Most results are obtained independently by the Krylov and Bogoliubov method and by near-symplectic perturbation theory. In spite of the paper's considerable length and complexity , signiicant observational features are left qualitatively unexplained. 2
منابع مشابه
The Measurement of Q' and Q'' in the Cern-sps by Head-tail Phase Shift Analysis
A so-called "Head-Tail" chromaticity measurement system has recently been installed in the CERN-SPS, which allows the chromaticity (Q') to be calculated from several hundred turns of data after transverse excitation. The measurement relies on the periodic dephasing and rephasing that occurs between the head and tail of a single bunch for non-zero chromaticity. By measuring the turnby-turn posit...
متن کاملDamping of the Transverse Head-Tail Instability by Periodic Modulation of the Chromaticity
An analytical and numerical study of the suppression of the transverse head-tail instability by modulating the chromaticity over a synchrotron period is presented. We find that a threshold can be developed, and it can be increased to a value larger than the strong head-tail instability threshold. The stability criterion derived agrees very well with the simulations. The underlying physical mech...
متن کاملVarying chromaticity: A damping mechanism for the transverse head-tail instability
A detailed analytical and numerical study of the suppression of the transverse head-tail instability by modulating the chromaticity over a synchrotron period is presented. We find that a threshold can be developed, and it can be increased to a value larger than the strong head-tail instability threshold. The stability criterion derived agrees very well with the simulations. The underlying physi...
متن کاملStudy of Beam Decoherence in the Presence of Head-tail Instability Using a Two-particle Model∗
The decoherence behavior of a beam centroid motion after a kick is studied using a two-particle model. A simple theory based on averaging of the governing equation is developed. The effects of a finite chromaticity and synchrotron motion are taken into account. Increasing the tune spread in the beam, a transition from a head-tail instability to a stable decay of an initial kick is explicitly de...
متن کامل