  High-brightness electron beams provided by modern accelerators require
several measures to preserve their high quality and to avoid instabilities. The
mitigation of the impact of residual ions is one of these measures. It is
particularly important if high bunch charges in combination with high
repetition rates are aimed for. This is because ions can be trapped in the
strong negative electrical potential of the electron beam causing emittance
blow-up, increased beam halo and longitudinal and transverse instabilities.
  Over the last decades three ion-clearing strategies have been applied to
counteract the degrading impact of the ions on the electron beam. These
strategies are installation of clearing electrodes, introduction of gaps in
filling pattern and beam shaking. Currently, their merit as clearing strategies
for the next generation of high brightness accelerators such as energy recovery
linacs (ERLs) are under intensive investigations by means of numerical and
experimental studies. Of particular interest in this context is the performance
of multi-purpose electrodes, which are designed such that they allow for a
simultaneous ion-clearing and beam-position monitoring. Such electrodes will be
installed in the bERLinPro facility.
  In this paper, we present numerical studies for the behavior of ions
generated by electron bunches while passing through the field of clearing
electrodes. The objective is to investigate the ion motion towards the
electrodes and to study under which circumstances and up to which ratio an
equilibrium between ion-generation and ion-clearing is established. Hereby,
several ion species and configurations of electrodes are considered in
combination with typical beam parameters of high-brightness electron
accelerators. Furthermore, we present detailed numerical studies of the
performance of multi-purpose clearing electrodes planned for bERLinPro.
