Longitudinal Stability of Short Bunches in Storage Rings with Strong Longitudinal Focusing*

In the BESSY VSR project, the variable bunch length storage ring, two high gradient accelerating structures at 1.5 and 1.75 GHz will be phased such that long and short bunches can be stored simultaneously. The longitudinal stability of the short bunches is investigated taking into account the shielded CSRand a purely inductive impedance. Multi particle tracking studies and numerical solutions of the Vlasov-Fokker-Planck equation show that threshold currents for short bunches do not follow the simple scaling law which was found for long bunches. The inductive impedance can even lower the thresholds for the instability. With an 80 times increased accelerating gradient and reasonable assumptions on the inductive impedance for shorter bunches stable operation can be expected with bunches 1.8 ps long (RMS-value) and 0.8 mA current. According to the calculations and operating in a dedicated low-α mode will produce stable 40 A bunches with 400 fs length.