The ion-hose (or fast-ion) instability sets limits on the allowable vacuum ina long-pulse, high current accelerator. Beam-induced ionization of thebackground gas leads to the formation of an ion channel which couples to thetransverse motion of the beam. The instability is studied analytically andnumerically for several ion frequency distributions. The effects of beamenvelope oscillations on the growth of the instability will be discussed. Thesaturated non-linear growth of the instability is derived analytically andnumerically for two different ion frequency distributions.
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