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).[l] Beyond a threshold bunch population of 3 x 10” 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 lO%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 x 10”.[2] When the bunch is very long in the ring it becomes difficult or impossible to properly compress it after extraction. We want 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.[3] According to previous calculations the impedance of the SLC damping rings is dominated by the many small discontinuities that are located in the socalled QD and QF vacuum chamber segments-elements such as transitions, masks, bellows-that are inductive to the beam.[4] Since these earlier calculations were performed the bellows of the QD segments have been sleeved, yielding a factor of 2 increase in the instability threshold.[l] In this paper we begin by discussing the gains that might be achieved if we can reduce the impedance of the rings even further. Then we estimate the effect on the total impedance of the actual design changes that are being proposed. Three important elements-the bend-to-quad transitions, the distributed ion pump slots, and the beam position monitor (BPM) electrodes are fully 3-dimensional and will be studied using T3 of the MAFIA computer programs.[5]