Single-bunch instability estimates for the 1-nm APS storage ring upgrade with a smaller vacuum chamber

We recently studied a lattice achieving 1 -nm emittance at the APS storage ring [1]. The successful design required very strong sextupoles in order to tune the machine to the desired positive chromaticity. A preliminary design of such magnets indicated saturation in the poles unless the vacuum chamber gets smaller by a factor of two compared to the existing APS chamber. Since the resistive wall impedance scales as 1/b³, where b is the radius of the chamber, we questioned how much current we can store in a single bunch at the 1-nm storage ring. In order to answer this question quantitatively, we calculated all wake potentials of impedance elements of the existing APS storage ring with the transverse dimension properly scaled but with the longitudinal dimension kept unchanged. With the newly calculated impedance of a smaller chamber, we estimated the single- bunch current limit. It turned out that the ring with a smaller chamber would not diminish the single-bunch current limit substantially. We present both wake potentials of 1-nm and the existing rings followed by the simulation results carried out for determining the accumulation limit to the ring.