Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma
Abstract
This paper presents a study of the two-stream instability of an electron beam propagating in a finite-size plasma placed between two electrodes. It is shown that the growth rate in such a system is much smaller than that of an infinite plasma or a finite size plasma with periodic boundary conditions. Even if the width of the plasma matches the resonance condition for a standing wave, a spatially growing wave is excited instead with the growth rate small compared to that of the standing wave in a periodic system. The approximate expression for this growth rate is γ≈(1/13)ωpe(nb/np)(Lωpe/vb)ln(Lωpe/vb)[1−0.18 cos (Lωpe/vb+π/2)], where ωpe is the electron plasma frequency, nb and np are the beam and the plasma densities, respectively, vb is the beam velocity, and L is the plasma width. The frequency, wave number, and the spatial and temporal growth rates, as functions of the plasma size, exhibit band structure. The amplitude of saturation of the instability depends on the system length, not on the beam current. For short systems, the amplitude may exceed values predicted for infinite plasmas by more than an order of magnitude.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Nov 01, 2016
- Source ID
- 10.1063/1.4967858
Entities
People
- Dmytro Sydorenko
- I. D. Kaganovich
Organizations
- Air Force Office of Scientific Research
- Princeton University
- United States Department of Energy
- University of Alberta