Coherent synchrotron radiation instability in low-emittance electron storage rings

High-frequency longitudinal impedances, particularly at wavenumbers <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>k</a:mi><a:mo>≫</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:msub><a:mrow><a:mi>σ</a:mi></a:mrow><a:mrow><a:mi>z</a:mi></a:mrow></a:msub></a:mrow></a:math> (where <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>σ</c:mi><c:mi>z</c:mi></c:msub></c:math> 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:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>e</e:mi><e:mo>+</e:mo></e:msup><e:msup><e:mi>e</e:mi><e:mo>−</e:mo></e:msup></e:math> 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. Published by the American Physical Society 2024