Modeling of fast Beam-Ion Instabilities

Beam-induced ionisation of residual gas in the vacuum chamber generates ions, which in an electron machine can accumulate around a passing bunch train. If the density of trapped ions becomes sufficiently high, a fast beam-ion in- stability will be excited. The development of the instability can be prevented by keeping the pressure of the residual gas below a certain value. This contribution describes the mod- eling of fast beam-ion instabilities and presents simulation studies of ion trapping and the evolution of the instability in the FCC-ee. Threshold ion densities for exciting the insta- bility are estimated in order to deduce acceptable vacuum pressures for operation.