Equilibrium ion distribution in the presence of clearing electrodes and its influence on electron dynamics

TL;DR

This paper models the equilibrium ion distribution caused by electron beams with clearing electrodes, analyzing its nonlinear effects on beam dynamics and proposing efficient simulation algorithms, with applications to high-current energy recovery linacs.

Contribution

It introduces a fast algorithm leveraging adiabatic invariants to simulate ion distributions and their impact on electron beams in linacs, considering nonlinear forces and clearing electrode placement.

Findings

Ion density peaks at the beam center, causing nonlinear forces.

Proper placement of clearing electrodes is crucial for effective ion removal.

The developed algorithms enable efficient simulation of ion-electron interactions.

Abstract

Here we compute the ion distribution produced by an electron beam when ion-clearing electrodes are installed. This ion density is established as an equilibrium between gas ionization and ion clearing. The transverse ion distributions are shown to strongly peak in the beam's center, producing very nonlinear forces on the electron beam. We will analyze perturbations to the beam properties by these nonlinear fields. To obtain reasonable simulation speeds, we develop fast algorithms that take advantage of adiabatic invariants and scaling properties of Maxwell's equations and the Lorentz force. Our results are very relevant for high current Energy Recovery Linacs, where ions are produced relatively quickly, and where clearing gaps in the electron beam cannot easily be used for ion elimination. The examples in this paper therefore use parameters of the Cornell Energy Recovery Linac project. For simplicity we only consider the case of a circular electron beam of changing diameter. However, we parameterize this model to approximate non-round beams well. We find suitable places for clearing electrodes and compute the equilibrium ion density and its effect on electron-emittance growth and halo development. We find that it is not sufficient to place clearing electrodes only at the minimum of the electron beam potential where ions are accumulated.