When do residual gas electrons destabilize an ion beam?

The stability of coasting ion beams against residual gas electrons accumulating in the beam potential is studied. We analyze the instability threshold intensities for ion beams of different charge state and mass using the linear centroid theory. Numerical simulations are used to study the thresholds for realistic transverse beam distributions. The effect of Coulomb collisions between beam ions and electrons is analyzed analytically and numerically using the Langevin equations. We show that at low residual gas pressures Coulomb collisions limit the neutralization degree of the ion beam to values below the instability threshold.