SSMB Longitudinal Dynamics

In this chapter, we study the single-particle longitudinal dynamics of SSMB. The motivation is to answer the question: how to realize the short bunch length and small longitudinal emittance in an electron storage ring, as required by SSMB? Note that the curvilinear (Frenet-Serret) coordinate system and the state vector \({\textbf {X}}=(x,x',y,'y',z,\delta )^{T}\) , with \(^{T}\) representing the transpose, are used throughout this dissertation. For the longitudinal dynamics without coupling from the transverse dimension, what we can play are the momentum compaction and RF systems, for SSMB the laser modulators.