Analysis of Transverse Coherent Instability in KEK Booster

Coherent transverse instability observed in KEK booster was analyzed with a free string model, taking into account of the chromaticity of the, bunched beam. The build-up time of the instability is represented by an eigen value of a matrix equation. The results of the calculation explain quite well experimental observations. The instability is induced by the interaction of the beam with ferrite loaded kicker magnet. The interaction is represented experimentally and theoretically with a mutual inductance. Using an equivalent circuit of the magnet, the induced field and the buildup time of the instability were calculated. So far many theoretical studies have been made but satisfactory agreement is not yet obtained partly because of the difficulty of a correct estimation of the source of the interaction. The analysis of the kicker magnet is rather easy when the current terminator is removed. This leads to a thorough description of the instability and gives a good agreement with the observations.