Impedance calculations for the improved SLC damping rings

A longitudinal, single bunch instability is observed in the damping rings of the Stanford Linear Collider (SLC). Beyond a threshold bunch population of 3×10¹⁰ particles the bunch energy spread increases and a “saw-tooth” variation in bunch length and synchronous phase as functions of time is observed. Although the relative amplitude of the saw-tooth variation is small-only on the order of 10% the resulting unpredictability of the beam properties in the rest of the SLC accelerator makes it difficult, if not impossible, to operate the machine above the threshold current. An additional problem at higher currents is that the bunch length is greatly increased: according to earlier measurements the RMS length is increased by 60% at 3×10 ¹⁰. When the bunch is very long in the ring it becomes difficult or impossible to properly compress it after extraction. The authors aim to solve both of these problems so that the SLC can run at higher currents to increase the luminosity. In order to solve these problems the vacuum chambers of both damping rings are being rebuilt with the aim of reducing their impedance