Effects of axial momentum spread on the electron–ion two-stream instability in high-intensity ion beams

Abstract

Use is made of the Vlasov–Maxwell equations to describe the electron–ion two-stream instability driven by the directed axial motion of a high-intensity ion beam propagating through a stationary population of (unwanted) background electrons. The ion beam is treated as continuous in the z-direction, and the electrons are electrostatically confined in the transverse direction by the space-charge potential produced by the excess ion charge. The analysis is carried out for arbitrary beam intensity, consistent with transverse confinement of the beam particles, and arbitrary fractional charge neutralization by the background electrons. For the case of overlapping step-function ion and electron density profiles, corresponding to monoenergetic electrons and ions in the transverse direction, detailed stability properties are calculated, including the important effects of an axial momentum spread, over a wide range of system parameters for dipole perturbations with azimuthal mode number ℓ=1. The two-stream instability growth rate is found to increase with increasing beam intensity, increasing fractional charge neutralization, and decreasing proximity of the conducting wall. It is shown that Landau damping associated with a modest axial momentum spread of the beam ions and background electrons has a strong stabilizing influence on the instability.