Analytic and numerical studies of resistive beam instabilities

We have used a variety of analytic and numerical techniques to study the resistive beam instabilities. We present a tractable model of the resistive hose instability which preserves the exact Vlasov resonance and analytic properties. We show that the sausage mode, unstable for a highly current neutralized beam in a prepared plasma channel, is stable for a beam propagating in and collisionally ionizing a neutral gas.