SSMB Transverse-Longitudinal Coupling Dynamics

Abstract

After dedicated efforts devoted to the longitudinal dynamics to realize an ultrasmall longitudinal emittance and ultrashort bunch length for coherent radiation generation, we need to make sure that the coupling arising from transverse dynamics does not degrade or even destroy the longitudinal fine structures. Such an argument is based on the observation that the transverse beam size in an SSMB ring can be orders of magnitude larger than the desired microbunch length. This is the basic motivation for us to investigate the transverse-longitudinal coupling (TLC) dynamics. In this chapter, we start from the linear TLC and then investigate the nonlinear TLC dynamics. For the linear dynamics, first we analyze the passive bunch lengthening induced by bending magnets. We then emphasize the fact that TLC can actually be actively applied for efficient bunch compression and high harmonic generation when the transverse emittance is small. We present three theorems on the application of such TLC schemes, with their implications discussed. Further, we have analyzed the contribution of modulators to the vertical emittance from quantum excitation, to obtain a self-consistent evaluation of the required modulation laser power when applying these coupling schemes in a storage ring. The theorems and related analysis provide the theoretical basis for the application of TLC in SSMB to lower the requirement on the modulation laser power, by taking advantage of the fact that the vertical emittance in a planar ring is rather small. Based on the investigations, we have presented example parameters sets for the envisioned SSMB storage ring to generate high-power EUV and soft X-ray radiation at the end of this dissertation.