Improving Touschek lifetime and synchrotron frequency spread by passive harmonic cavity in the storage ring of SSRF

Beam lifetime of a synchrotron is dominated by Touschek scattering. In the beamline Phase II project of Shanghai synchrotron radiation facility, a passive third harmonic cavity is to be installed for bunch lengthening and instability suppressing. In this paper, the beam dynamics of the cavity is investigated. The parameters of passive operation are optimized to cancel the slope of RF voltage and lengthen the bunches. The Touschek lifetime increases are estimated for optimum and non-optimum voltage flattening. A tolerance of the operation is studied in case that there is a shift on detuning angle. The effect caused by reduction in harmonic voltage generated by lengthened bunch distribution is also estimated using iteration method. An increase in synchrotron frequency spread due to nonlinearity of the voltage giving to the bunch is found by using tracking simulation. This spread can help in damping coupled bunch instability through Landau damping.