Coherent synchrotron radiation instability in low-emittance electron storage rings

High-frequency longitudinal impedances, particularly at wavenumbers k >> 1/ sigma z (where sigma z is the bunch length), can drive microwave instability and potentially limit the performance of modern low-emittance electron storage rings. In such rings, the 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 the fourth-generation storage ring light source Elettra 2.0 and the low-energy ring of the SuperKEKB e & thorn;e- circular collider 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 combined effects with broadband impedances caused by discontinuities in vacuum chambers.