Band structure of the growth rate of the twostream instability of an electron beam propagating in a bounded plasma
Our paper presents a study of the twostream instability of an electron beam propagating in a finitesize 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)ω _{pe}(n _{b}/n _{p})(Lω _{pe}/v _{b})ln(Lω _{pe}/v _{b})[10.18 cos (Lω _{pe}/v _{b}+π/2)], where ωpe is the electron plasma frequency, n _{b} and n _{p} are the beam and the plasma densities, respectively, v _{b} 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:

^{[1]};
^{[2]}
 Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.
 Univ. of Alberta, Edmonton, AB (Canada)
 Publication Date:
 Grant/Contract Number:
 AC0209CH11466
 Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: 11; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
 OSTI Identifier:
 1338610
 Alternate Identifier(s):
 OSTI ID: 1332763
Kaganovich, I. D., and Sydorenko, D.. Band structure of the growth rate of the twostream instability of an electron beam propagating in a bounded plasma. United States: N. p.,
Web. doi:10.1063/1.4967858.
Kaganovich, I. D., & Sydorenko, D.. Band structure of the growth rate of the twostream instability of an electron beam propagating in a bounded plasma. United States. doi:10.1063/1.4967858.
Kaganovich, I. D., and Sydorenko, D.. 2016.
"Band structure of the growth rate of the twostream instability of an electron beam propagating in a bounded plasma". United States.
doi:10.1063/1.4967858. https://www.osti.gov/servlets/purl/1338610.
@article{osti_1338610,
title = {Band structure of the growth rate of the twostream 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 twostream instability of an electron beam propagating in a finitesize 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)[10.18 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 = {2016},
month = {11}
}