Trapped ions and beam coherent instability

In accelerators with negatively charged beams, ions generated from the residual gas molecules may be trapped by the beam. Trapped ions may interact resonantly with the beam and cause a beam-ion coherent instability. This coherent instability bears many similarities to the resistive wall instability and can present important limitations to those machines´ operation. A description of this effect requires a treatment of the beam coherent instability including both the normal machine wake field and the interaction with ions. We present a linear approach incorporating contributions from the machine impedance as well as ion forces. It also includes spreads in beam and ion frequencies and thus Landau damping. The analysis results in a modified stability diagram which will be used together with physical arguments to explain experimental observations in the Fermilab antiproton accumulator