Coherent synchrotron radiation and stability of a short bunch in a compact storage ring

It should be possible to observe coherent synchrotron radiation at millimeter wavelengths in a compact electron storage ring, provided that the bunch can be made sufficiently short. On the other hand, for a short bunch the radiation reaction is so strong that it could cause a longitudinal instability if the current exceeded some threshold. This might cause bunch lengthening, and cut off or reduce the coherent radiation. Using wake fields from simple models of the vacuum chamber, the authors estimate the threshold current for a proposed upgrade of the Brookhaven small x-ray light source, SXLS-Phase 1