Impact of the wiggler coherent synchrotron radiation impedance on the beam instability and damping ring optimization

Coherent synchrotron radiation (CSR) can play an important role by not only increasing the energy spread and emittance of a beam, but also leading to a potential instability. Previous studies of the CSR induced longitudinal instability were carried out for the CSR impedance due to dipole magnets. However, many storage rings include long wigglers where a large fraction of the synchrotron radiation is emitted. This includes high-luminosity factories such as DAPHNE, PEP-II, KEK-B, and CESR-C as well as the damping rings of future linear colliders. In this paper, the instability due to the CSR impedance from a wiggler is studied assuming a large wiggler parameter K. The primary consideration is a low-frequency microwavelike instability, which arises near the pipe cutoff frequency. Detailed results are presented on the growth rate and threshold for the damping rings of several linear collider designs. The different scaling between the wiggler CSR impedance and the dipole CSR impedance suggests an optimization for the damping ring design.