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This paper presents a study of the two-stream instability of an electron beampropagating in a finite-size plasma placed between two electrodes. It is shownthat the growth rate in such a system is much smaller than that of an infiniteplasma or a finite size plasma with periodic boundary conditions. Even if thewidth of the plasma matches the resonance condition for a standing wave, aspatially growing wave is excited instead with the growth rate small comparedto that of the standing wave in a periodic system. The approximate expressionfor this growth rate is $\gamma \approx(1/13)\omega_{pe}(n_{b}/n_{p})(L\omega_{pe}/v_{b})\ln (L\omega_{pe}/v_{b})[1-0.18\cos ( L\omega_{pe}/v_{b}+{\pi }/{2}) ]$, where $\omega_{pe}$ is theelectron plasma frequency, $n_{b}$ and $n_{p}$ are the beam and the plasmadensities, respectively, $v_{b}$ is the beam velocity, and $L$ is the plasmawidth. The frequency, wave number and the spatial and temporal growth rates asfunctions of the plasma size exhibit band structure. The amplitude ofsaturation of the instability depends on the system length, not on the beamcurrent. For short systems, the amplitude may exceed values predicted forinfinite plasmas by more than an order of magnitude.

Band Structure of the Growth Rate of the Two-Stream Instability of an Electron Beam Propagating in a Bounded Plasma