Two-Stream Problems in Accelerators

Electron beams are perturbed by positively charged ions in a similar way as proton and positron beams may be affected by electrons which are generated via gas ionization, photoemission, or multipacting. In particular, the ions or electrons can induce fast instabilities. These instabilities become more severe in accelerators operating with high current or close bunch spacing. They might even affect less intense muon beams during ionization cooling. Theories, simulations and observations of two-stream instabilities between a charged particle beam and either ions or electrons are reviewed.