Analytical Solution for Space-Charge Waves in a Two-Stream Cylindrical Electron Beam

We present an analytical method to compute the wavenumbers and electric fields of space-charge-wave eigenmodes supported by a two-stream electron beam, consisting solid inner cylindrical stream coaxial outer annular stream, both contained within metallic tunnel.We extend model developed Ramo case two streams. The accounts for interaction between streams with presence beam-tunnel wall; it can be used complex associated instability plasma frequency reduction effects in vacuum electronic amplifiers other devices.