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

TLDR

The interaction of an electron beam with residual gas ions produces mutually driven transverse oscillations that grow exponentially with a \(t^{1/2}\) exponent during a single train of bunches, a mechanism also seen in positron beams with ionization electrons. The authors aim to calculate the rise time of this beam‑ion instability analytically and compare it with computer simulations. They employ a perturbation‑series approach to derive the rise time and validate the results against simulations. Growth rates computed for existing and proposed storage rings and linear accelerators indicate that the instability could significantly limit many future designs.

Abstract

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.