Longitudinal single-bunch instabilities driven by coherent undulator radiation in the cavity modulator of a steady-state microbunching storage ring

TL;DR

This paper investigates a new instability mechanism caused by coherent undulator radiation in a steady-state microbunching storage ring, providing theoretical analysis and numerical validation to understand its impact on longitudinal beam stability.

Contribution

It introduces a novel multi-turn instability mechanism driven by coherent undulator radiation and formulates its dynamics within the steady-state microbunching storage ring context.

Findings

Predicted instability growth rates align with numerical simulations.

Identified differences from Robinson instability in RF-based storage rings.

Provided insights into the impact of undulator radiation on beam stability.

Abstract

Recently a mechanism of storage ring operation based on the steady-state microbunching has been proposed and investigated, which contains a laser cavity modulator providing the longitudinal focusing for the circulating microbunches. In this paper we analyze the impact of the coherent undulator radiation on the longitudinal single-bunch multi-turn collective dynamics, exploring a new possible instability mechanism. We formulate the multi-turn equations of motion for the single microbunch as two sets of difference equations in the modulator and in the remaining storage ring. The dispersion equation can then be obtained by introduction of the undulator-averaged phase space coordinates. The predicted instability growth rate shows reasonable agreement with the numerical turn-by-turn tracking simulations provided validity of the underlying assumptions. The analysis shall provide some insights for the coherent undulator radiation driven multi-turn instability in the cavity modulator. Differences between such a new instability mechanism and the Robinson instability in a conventional radio-frequency-based storage ring are also discussed.