Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma

Kaganovich, I. D.; Sydorenko, D.

doi:10.1063/1.4967858

Title: 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)ω_pe(n_b/n_p)(Lω_pe/v_b)ln(Lω_pe/v_b)[1-0.18 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:

Kaganovich, I. D. ^[1]; Sydorenko, D. ^[2]

Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.
Univ. of Alberta, Edmonton, AB (Canada)

Publication Date:: Fri Nov 18 00:00:00 EST 2016

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.

Copy to clipboard


                    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

Copy to clipboard


                    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.

Copy to clipboard


                    
@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}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1063/1.4967858

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 21 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

On the LambertW function
journal, December 1996

Corless, R. M.; Gonnet, G. H.; Hare, D. E. G.
Advances in Computational Mathematics, Vol. 5, Issue 1
DOI: 10.1007/BF02124750

Self-Consistent Generation of Superthermal Electrons by Beam-Plasma Interaction
journal, November 2005

Yoon, Peter H.; Rhee, Tongnyeol; Ryu, Chang-Mo
Physical Review Letters, Vol. 95, Issue 21
DOI: 10.1103/PhysRevLett.95.215003

Unstable oscillatory Pierce modes of neutralized electron beams
journal, April 1982

Cary, John R.; Lemons, Don S.
Journal of Applied Physics, Vol. 53, Issue 4
DOI: 10.1063/1.330986

Generation of anomalously energetic suprathermal electrons by an electron beam interacting with a nonuniform plasma
journal, December 2015

Sydorenko, D.; Kaganovich, I. D.; Chen, L.
Physics of Plasmas, Vol. 22, Issue 12
DOI: 10.1063/1.4937785

Evolution of bounded beam–plasma interactions in a one‐dimensional particle simulation
journal, July 1989

Morey, I. J.; Boswell, R. W.
Physics of Fluids B: Plasma Physics, Vol. 1, Issue 7
DOI: 10.1063/1.858926

Sheath-Induced Instabilities in Plasmas with $E_{0} \times B_{0}$ Drift
journal, September 2013

Smolyakov, A. I.; Frias, W.; Kaganovich, I. D.
Physical Review Letters, Vol. 111, Issue 11
DOI: 10.1103/PhysRevLett.111.115002

On non-linear theory of instability of a mono-energetic electron beam in plasma
journal, June 1972

Matsiborko, N. G.; Onishchenko, I. N.; Shapiro, V. D.
Plasma Physics, Vol. 14, Issue 6
DOI: 10.1088/0032-1028/14/6/003

Limiting Stable Current in Electron Beams in the Presence of Ions
journal, October 1944

Pierce, J. R.
Journal of Applied Physics, Vol. 15, Issue 10
DOI: 10.1063/1.1707378

Collective Electron Instability in a Bounded Region
journal, January 1963

Rosenbluth, M. N.; Pearlstein, L. D.; Stuart, G. W.
Physics of Fluids, Vol. 6, Issue 9
DOI: 10.1063/1.1706897

Formation of Electric Field Spikes in Electron-Beam–Plasma Interaction
journal, December 1996

Gunell, H.; Verboncoeur, J. P.; Brenning, N.
Physical Review Letters, Vol. 77, Issue 25
DOI: 10.1103/PhysRevLett.77.5059

Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works
journal, January 1973

Boris, Jay P.; Book, David L.
Journal of Computational Physics, Vol. 11, Issue 1
DOI: 10.1016/0021-9991(73)90147-2

Interaction of a Highly Energetic Electron Beam with a Dense Plasma
journal, January 1972

Kainer, Selig
Physics of Fluids, Vol. 15, Issue 3
DOI: 10.1063/1.1693934

Effect of collisions on the two-stream instability in a finite length plasma
journal, December 2016

Sydorenko, D.; Kaganovich, I. D.; Ventzek, P. L. G.
Physics of Plasmas, Vol. 23, Issue 12
DOI: 10.1063/1.4972543

Works referencing / citing this record:

Photoemission driven electron two-stream instability (ETSI) and evolution of plasma sheath
journal, April 2019

Changmai, Suniti; Bora, Madhurjya P.
Physics of Plasmas, Vol. 26, Issue 4
DOI: 10.1063/1.5081928

Test cases for grid-based direct kinetic modeling of plasma flows
journal, June 2018

Hara, Kentaro; Hanquist, Kyle
Plasma Sources Science and Technology, Vol. 27, Issue 6
DOI: 10.1088/1361-6595/aac6b9

Improved understanding of the hot cathode current modes and mode transitions
journal, November 2017

Campanell, M. D.; Umansky, M. V.
Plasma Sources Science and Technology, Vol. 26, Issue 12
DOI: 10.1088/1361-6595/aa97a9

Effect of collisions on the two-stream instability in a finite length plasma
journal, December 2016

Sydorenko, D.; Kaganovich, I. D.; Ventzek, P. L. G.
Physics of Plasmas, Vol. 23, Issue 12
DOI: 10.1063/1.4972543

Similar Records in DOE PAGES and OSTI.GOV collections:

Dependence of electron beam instability growth rates on the beam-plasma system parameters

Journal Article Strangeway, R J - J. Geophys. Res.; (United States)

Electron beam instabilites are studied by using a simple model for an electron beam streaming through a cold plasma, the beam being of finite width perpendicular to the ambient magnetic field. Through considerations of finite geometry and the coldness of the beam and background plasma, an instability similar to the two stream instability is assumed to be the means for wave growth in the system. Having found the maximum growth rate for one set of beam-plasma system parameters, this maximum growth rate is traced as these parameters are varied. The parameters that describe the system are the beam velocity (v/submore »« less
https://doi.org/10.1029/JA087iA02p00833
Electrostatic and whistler instabilities excited by an electron beam

Journal Article An, Xin ; Bortnik, Jacob ; Van Compernolle, Bart ; ... - Physics of Plasmas

The electron beam-plasma system is ubiquitous in the space plasma environment. Here in this paper, using a Darwin particle-in-cell method, the excitation of electrostatic and whistler instabilities by a gyrating electron beam is studied in support of recent laboratory experiments. It is assumed that the total plasma frequency (ω_pe) is larger than the electron cyclotron frequency (Ω_e). The fast-growing electrostatic beam-mode waves saturate in a few plasma oscillations by slowing down and relaxing the electron beam parallel to the background magnetic field. Upon their saturation, the finite amplitude electrostatic beam-mode waves can resonate with the tail of the background thermalmore »« less
Cited by 23
https://doi.org/10.1063/1.4986511

Full Text Available
Linewidth limits in free-electron lasers caused by sidebands

Journal Article Riyopoulos, S - Physics of Plasmas; (United States)

Sideband excitation near the carrier determines the minimum spectral width for steady-state free-electron laser oscillators fed by continuous electron beams. A sideband separated by [delta][omega] from the carrier resonates with harmonics of the upshifted bounce frequency for trapped particles, [delta][omega]=[ital n]2[gamma][sup 2][sub [ital z]][Omega]. The analysis focuses on sidebands excited in the immediate vicinity of the carrier [delta][omega][r arrow]0, in resonance with particles trapped near the separatrix, [Omega][r arrow]0. For electrons distributed uniformly around their orbits, the growth tends to zero as [delta][omega], [Omega][r arrow]0, despite the infinite number of contributing harmonics. However, the distributions produced by injected electron beamsmore »« less
https://doi.org/10.1063/1.870499
Linear study of the beam-plasma interaction as a source mechanism for the broadband electrostatic emissions observed in the electron foreshock

Journal Article Canu, P - Journal of Geophysical Research; (USA)

Electron beams streaming back from the Earth's bow shock into the solar wind have been proposed as a possible source for the electron plasma waves observed by spacecraft in the electron foreshock. These waves often correspond to broadband electrostatic emissions extending both above and below the local electron plasma frequency. The linear beam-plasma interaction is studied numerically. We focus on the generation of emissions with upper cutoff frequency of the order of or above 1.5 times the electron plasma frequency ({omega}{sub {ital pe}}), which were reported from ISEE observations. Beam drift velocity, thermal spread and density are varied over amore »« less
https://doi.org/10.1029/JA094iA07p08793
Anomalous resistivity of current-driven isothermal plasmas due to phase space structuring

Journal Article Buechner, Joerg ; Elkina, Nina - Physics of Plasmas

The anomalous electric resistivity of collisionless plasmas is an important issue in the physics of hot plasmas, e.g., in the context of auroral particle acceleration and of reconnection in the solar corona. The linear stability theory of isothermal current driven space plasmas predicts an ion-acoustic instability if the relative drift velocity of the current carrying particles exceeds a certain threshold, which, generally, depends on the plasma parameters. The spectrum of waves, excited by a marginal instability, is very narrow. Hence, the wave power at saturation and the corresponding electric resistivity due to wave-particle interaction cannot be obtained by means ofmore »« less
https://doi.org/10.1063/1.2209611

Similar Records

Title: Band structure of the growth rate of the two-stream instability of an electron beam propagating in a bounded plasma

Abstract

Citation Formats

On the LambertW function journal, December 1996

Self-Consistent Generation of Superthermal Electrons by Beam-Plasma Interaction journal, November 2005

Unstable oscillatory Pierce modes of neutralized electron beams journal, April 1982

Generation of anomalously energetic suprathermal electrons by an electron beam interacting with a nonuniform plasma journal, December 2015

Evolution of bounded beam–plasma interactions in a one‐dimensional particle simulation journal, July 1989

Sheath-Induced Instabilities in Plasmas with E 0 × B 0 Drift journal, September 2013

On non-linear theory of instability of a mono-energetic electron beam in plasma journal, June 1972

Limiting Stable Current in Electron Beams in the Presence of Ions journal, October 1944

Collective Electron Instability in a Bounded Region journal, January 1963

Formation of Electric Field Spikes in Electron-Beam–Plasma Interaction journal, December 1996

Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works journal, January 1973

Interaction of a Highly Energetic Electron Beam with a Dense Plasma journal, January 1972

Effect of collisions on the two-stream instability in a finite length plasma journal, December 2016

Photoemission driven electron two-stream instability (ETSI) and evolution of plasma sheath journal, April 2019

Test cases for grid-based direct kinetic modeling of plasma flows journal, June 2018

Improved understanding of the hot cathode current modes and mode transitions journal, November 2017

Effect of collisions on the two-stream instability in a finite length plasma journal, December 2016

On the LambertW function
journal, December 1996

Self-Consistent Generation of Superthermal Electrons by Beam-Plasma Interaction
journal, November 2005

Unstable oscillatory Pierce modes of neutralized electron beams
journal, April 1982

Generation of anomalously energetic suprathermal electrons by an electron beam interacting with a nonuniform plasma
journal, December 2015

Evolution of bounded beam–plasma interactions in a one‐dimensional particle simulation
journal, July 1989

Sheath-Induced Instabilities in Plasmas with $E_{0} \times B_{0}$ Drift
journal, September 2013

On non-linear theory of instability of a mono-energetic electron beam in plasma
journal, June 1972

Limiting Stable Current in Electron Beams in the Presence of Ions
journal, October 1944

Collective Electron Instability in a Bounded Region
journal, January 1963

Formation of Electric Field Spikes in Electron-Beam–Plasma Interaction
journal, December 1996

Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works
journal, January 1973

Interaction of a Highly Energetic Electron Beam with a Dense Plasma
journal, January 1972

Effect of collisions on the two-stream instability in a finite length plasma
journal, December 2016

Photoemission driven electron two-stream instability (ETSI) and evolution of plasma sheath
journal, April 2019

Test cases for grid-based direct kinetic modeling of plasma flows
journal, June 2018

Improved understanding of the hot cathode current modes and mode transitions
journal, November 2017

Effect of collisions on the two-stream instability in a finite length plasma
journal, December 2016