1 . 1 Single bunch instabilities induced by electron cloud in short positron / proton / ion bunches

1.1.1 Introduction For linear accelerators, a single bunch instability of a positron bunch due to electrons created by ionization of the residual gas was discussed in Ref. [1], where a coherent oscillation of both electrons and positrons grows from any small initial perturbation of the bunch distribution, e.g. from the statistical fluctuations due to the finite number of beam particles. This instability can be considered as a two stream instability of the same type as studied in plasma physics. A similar two stream instability may occur in storage rings operating with positively charged particles, due to the interaction with electrons primarily generated via photoemission, gas ionization or particle loss and then multiplied via secondary emission [2]. Such instabilities can be very fast, since in the new generation of high intensity rings operating with many closely spaced bunches, the density of electrons can become quickly large. Even machines operating with bunches spaced by hundreds of ns can actually suffer from electron cloud because of the long survival time of low energy electrons in the beam pipe due to elastic reflection [3]. Electron clouds can also cause multi-bunch dipole mode instabilities. The multi-bunch instability is different from the instability we discuss in this article, which is a single bunch phenomenon induced by a pinched electron cloud which turn by turn carries memory of the offset bunch head to the bunch tail. Although the effect we discuss is purely single bunch, it occurs, however, only in multi-bunch operation, since the electron cloud requires several bunch passages to build up. Note also that the head tail effect we discuss here is different from the electron-proton instability observed in some machines operating with long bunches (like the Los Alamos PSR). In that case, electrons inside the beam pipe perform many oscillations during the bunch passage, and their number can be amplified if they are produced on the falling edge of the bunch and gain energy as they cross the pipe section (so called " trailing-edge multipacting " [4]). The quick multiplication of the number of electrons on the falling edge of the bunch is then responsible for the destabilization of the bunch tail. In our case, electrons can only perform about 1 oscillation while the bunch is passing by, and the bunch interacts with a pre-established cloud, which has been produced by the preceding bunches and fills almost uniformly the beam pipe prior to the …