Fast beam-ion instability. I. Linear theory and simulations

The interaction of an electron beam with residual gas ions results in mutually driven transverse oscillations. This effect arises during the passage of a single train of bunches. An equivalent instability mechanism is encountered in positron beams where ionization electrons oscillate within a single bunch. In either case, the oscillations grow exponentially with an exponent proportional to ${\mathit{t}}^{1/2}$. In this report, the rise time of the instability is calculated analytically by a perturbation series approach and is compared with computer simulations. Growth rates are evaluated for several existing or proposed storage rings and linear accelerators; the effect considered could be a significant limitation in many of the future designs.