Theoretical formulation of multiturn collective dynamics in a laser cavity modulator with comparison to Robinson and high-gain free-electron laser instability

Abstract

The study of collective beam instabilities has long been an important and active research topic in particle accelerators. The collective effects are typically divided into two categories: the short-range single-bunch instabilities and the long-range multibunch or multiturn instabilities. Robinson instability can be the mostly encountered long-range multiturn instability. We recently explored a collective multiturn instability driven by the short-range coherent undulator radiation in the laser cavity modulator of a steady-state microbunching (SSMB) storage ring. In this paper, we formulate and compare such an instability with the Robinson instability. Considering the radiation slippage effect and the finite duration, the functional form of the radiation wakes is essentially different from that of the Robinson case. We also relate a special case of the newly explored instability to the high-gain free-electron laser process and find that a similar cubic dispersion equation can be obtained. The discussions and comparisons presented in this paper may shed light on the underlying physical mechanisms of the collective beam dynamics in the laser cavity modulator of an SSMB storage ring.