Growth time of the longitudinal coupled bunch mode beam instability at the Duke FEL facility

To determine the required power of an amplifier for the longitudinal feedback (LFB) system, the growth time of the strongest longitudinal coupled bunch mode instability (CBMI) in the Duke storage ring should be measured in advance. In 2005, we measured strength of the strongest longitudinal beam instability in the Duke storage ring with four and eight symmetrically filled buckets. By analyzing measured data, the growth time of the strongest dipole mode of the longitudinal CBMI in the Duke storage ring can be estimated. At a beam energy of 274 MeV, the growth time is about 0.365 ms for a total stored beam current of 160 mA. From the measured growth time, we estimated the required power of the amplifier for the LFB system. To damp all harmful longitudinal CBMIs with an energy deviation of 0.1 % (rms) within its growth time of 0.365 ms, we have to supply about HOW (rms) to an LFB kicker whose a central frequency is 937.3875 MHz. In this paper, we describe the growth time of the longitudinal CBMI at the Duke storage ring and the estimation of the required power for the LFB system to damp all CBMIs within 0.365 ms.