Vlasov-Maxwell description of electron-ion two-stream instability in high-intensity linacs and storage rings

The Vlasov-Maxwell equations are used to investigate properties of the electron-ion two-stream instability for a continuous, high-intensity ion beam propagating in the z-direction with directed axial velocity V_b = β_bc through a background population of (stationary) electrons. 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. Detailed !Stability properties are calculated over a wide range of system parameters for dipole perturbations with azimuthal mode number ℓ = 1. The instability growth rate Imω is found to increase with increasing normalized beam intensity (ω̂²_pb/ω⁰²_Bb), increasing fractional charge neutralization (f = n̂_e/Z_bn̂_b), and decreasing proximity of the conducting wall (r_b/r_w).