Stability of Bounded Electron Beams Neutralized by Co-Moving Ions

It has been claimed that bounded ion beams neutralized by co-moving electrons are inherently unstable for currents above the threshold for the Pierce instability. In this paper, it is noted that the Pierce instability can be suppressed for certain conditions satisfied by the Occidental neutralized light ion beam driver for inertial confinement fusion. A model is presented for the analysis of guided wave propagation and instability along a cylindrical waveguide that is partially filled with a cold drifting electron beam. The beam is assumed to be fully neutralized by a positive ion background of infinite mass that is drifting at the same velocity as the electron beam -- thereby removing streaming instabilities from consideration. Under these conditions, the electron-ion beam is found to be stable for both zero and infinite applied longitudinal magnetic fields, except for ¿ = 0 waves satisfying certain axial boundary conditions first derived by Pierce in 1944. It is demonstrated for pulsed beams, whose downstream boundary is just the beam head, that the excited waves never catch the beam head and hence cannot induce the Pierce instability. It is also shown for zero applied magnetic field that the guided waves are excited within a boundary layer on the beam surface whose skin depth becomes negligible for sufficiently high current density beams of a given acceleration voltage.