Microwave instabilities in electron rings with negative momentum compaction factor

Bunch lengthening (or shortening) caused by the potential well distortion and the microwave instability in electron rings with negative momentum compaction factor is discussed in detail based on the resonator impedance model; further, a comparison with rings of positive momentum compaction factor is given. It was found that the bunch shape is less deformed and the current threshold of the microwave instability is higher in the rings with negative momentum compaction factor over a very wide range of the impedance parameters. The results also show that even within the range where the threshold for positive momentum compaction is higher than that for negative momentum compaction, the bunch lengthening is still less serious in most cases. Finally, an example of bunch lengthening in the case that α<0 with a real wake field of the SLC damping ring (old vacuum chamber) is given in contrast to the case in which α>0