Dependence of Phase Instabilities on Bunch Length at the CEA

Betatron and phase instabilities have been observed at the CEA during multicycle filling and dc storage. The betatron instabilities are caused by the head-tail effect and have been controlled with sextupoles which make the chromaticity zero or slightly positive. The phase instability at present limits the electron and positron current which can be accumulated. We have made measurements of the threshold currents required to observe the onset of phase instabilities. These measurements show: a. The threshold current required to observe the onset of this phase instability is independent of the number of bunches down even to one bunch. (Here and throughout this paper, current is defined as the current in one bunch averaged over one rf period, ie., 1 mA = 1.4 × 107/bunch.) b. The threshold current for the onset of this instability first decreases with increasing bunch length, goes through a minimum, then increases again for long bunch length. A cavity operating at the third harmonic of the main accelerating system frequency, thus providing increased nonlinearity of the total rf voltage waveform (hence increasing the Landau damping), increased the threshold current for the onset of these instabilities.