Damping 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 mechanisms of the damping scheme are rotation of the head-tail phase such that the instability does not occur, and Landau damping due to the incoherent betatron tune spread generated by the varying chromaticity. [S0031-9007(97)03326-7]