Coherent synchrotron radiation instability in low-emittance electron storage rings

Longitudinal impedances at high frequencies, which extend far beyond the width of the beam spectrum, can pose a threat to the performance of modern low-emittance electron storage rings, as they can establish a relatively low threshold for microwave instability. In such rings, coherent synchrotron radiation (CSR) emerges as a prominent contributor to these high-frequency impedances. This paper undertakes a systematic investigation into the effects of CSR on electron rings, utilizing Elettra 2.0, a ring of fourth-generation light sources, and the SuperKEKB low-energy ring, a ring of $e^+e^-$ circular colliders, as illustrative examples. Our work revisits theories of microwave instability driven by CSR impedance, extending the analysis to encompass other high-frequency impedances such as resistive wall and coherent wiggler radiation. Through instability analysis and numerical simulations conducted on the two aforementioned rings, the study explored the impact of high-frequency impedances and their interactions with broadband impedances from discontinuities in vacuum chambers.