Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma
Abstract
Our 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. Furthermore, 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. Finally, 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.
- Authors:
-
- Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.
- Univ. of Alberta, Edmonton, AB (Canada)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1338610
- Alternate Identifier(s):
- OSTI ID: 1332763
- Grant/Contract Number:
- AC02-09CH11466
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 11; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Kaganovich, I. D., and Sydorenko, D. Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma. United States: N. p., 2016.
Web. doi:10.1063/1.4967858.
Kaganovich, I. D., & Sydorenko, D. Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma. United States. https://doi.org/10.1063/1.4967858
Kaganovich, I. D., and Sydorenko, D. Fri .
"Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma". United States. https://doi.org/10.1063/1.4967858. https://www.osti.gov/servlets/purl/1338610.
@article{osti_1338610,
title = {Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma},
author = {Kaganovich, I. D. and Sydorenko, D.},
abstractNote = {Our 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. Furthermore, 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. Finally, 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.},
doi = {10.1063/1.4967858},
journal = {Physics of Plasmas},
number = 11,
volume = 23,
place = {United States},
year = {Fri Nov 18 00:00:00 EST 2016},
month = {Fri Nov 18 00:00:00 EST 2016}
}
Web of Science
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journal, December 2016
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- Physics of Plasmas, Vol. 23, Issue 12