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Mod-01 Lec-12 Two Stream Instability
Mod-01 Lec-12 Two Stream Instability
Published: 2013/04/25
Channel: nptelhrd
2e The two-stream instability
2e The two-stream instability
Published: 2015/09/15
Channel: Plasma Physics and Applications
Two Stream Instability Simulation
Two Stream Instability Simulation
Published: 2014/05/07
Channel: Frans Ebersohn
Phase space plot of two stream instability [best in HD or Original quality]
Phase space plot of two stream instability [best in HD or Original quality]
Published: 2011/03/08
Channel: stusearle
Two Stream Instability
Two Stream Instability
Published: 2009/04/22
Channel: kdusling
Two-Stream-Instability-Part-1
Two-Stream-Instability-Part-1
Published: 2013/01/08
Channel: Ross Burrows
Warm Two Stream Instability Simulation
Warm Two Stream Instability Simulation
Published: 2014/05/07
Channel: Frans Ebersohn
two stream instability
two stream instability
Published: 2015/01/21
Channel: me
Two-stream instability gone wrong(?)
Two-stream instability gone wrong(?)
Published: 2015/02/22
Channel: Knut Harald
Two stream instability
Two stream instability
Published: 2017/10/23
Channel: Gabriele Brambilla
Two Stream Instability
Two Stream Instability
Published: 2014/02/16
Channel: Sinéad Mannion
Two stream instability symulation
Two stream instability symulation
Published: 2014/07/09
Channel: Egor Seliunin
CUDAPIC - two stream instability
CUDAPIC - two stream instability
Published: 2016/06/12
Channel: Dominik Stańczak
Two-Stream-Instability-Part2
Two-Stream-Instability-Part2
Published: 2013/01/08
Channel: Ross Burrows
two stream instability
two stream instability
Published: 2015/01/16
Channel: Alberto Marocchino
1D Two Stream Instability
1D Two Stream Instability
Published: 2014/06/04
Channel: Sinéad Mannion
two stream instability
two stream instability
Published: 2017/02/22
Channel: Mohamad Shalaby
One Dimensional Two Stream Instability
One Dimensional Two Stream Instability
Published: 2012/02/24
Channel: numb7rs
Two Stream Instability
Two Stream Instability
Published: 2016/03/11
Channel: Andrew Myers
Two-Stream-Instability Electric-Field E_x = Ex_(x, t)
Two-Stream-Instability Electric-Field E_x = Ex_(x, t)
Published: 2013/01/11
Channel: Ross Burrows
relativistic particle acceleration - two stream instability
relativistic particle acceleration - two stream instability
Published: 2007/10/06
Channel: valsusa
two stream instability classical
two stream instability classical
Published: 2007/10/06
Channel: valsusa
Particle-in-Cell 1D Two Stream Instability
Particle-in-Cell 1D Two Stream Instability
Published: 2014/02/15
Channel: Sinéad Mannion
Mod-01 Lec-01 Instability and Transition of Fluid Flows
Mod-01 Lec-01 Instability and Transition of Fluid Flows
Published: 2012/06/26
Channel: nptelhrd
Two Stream Instability with Integer Lattice
Two Stream Instability with Integer Lattice
Published: 2016/09/23
Channel: Philip Mocz
ECE 5984 Course Project - #5 Counter-Stream Instability
ECE 5984 Course Project - #5 Counter-Stream Instability
Published: 2011/05/05
Channel: egthomas2010
Two Stream Instability
Two Stream Instability
Published: 2014/06/24
Channel: asdfuogh
Two Stream Instability (Electrons)
Two Stream Instability (Electrons)
Published: 2007/07/18
Channel: smarkidis
Relativistic Two-stream Instability with Parsek (Electron)
Relativistic Two-stream Instability with Parsek (Electron)
Published: 2007/07/17
Channel: smarkidis
Kelvin Helmholtz instability experiment vs. simulation
Kelvin Helmholtz instability experiment vs. simulation
Published: 2015/10/19
Channel: drahovcanka
Surface Tension: Plateau Rayleigh Instability
Surface Tension: Plateau Rayleigh Instability
Published: 2013/11/06
Channel: Vong yang chen
Shear instability (Andy Hogg)
Shear instability (Andy Hogg)
Published: 2014/07/25
Channel: CoE CSS
Farley - Buneman
Farley - Buneman
Published: 2008/04/27
Channel: Shahab Arabshahi
Andrew Murray Describes Plasma Instability Experiments for Radiant Energy Tech
Andrew Murray Describes Plasma Instability Experiments for Radiant Energy Tech
Published: 2014/12/04
Channel: PESNetwork
18A Plasma Instabilities | Introduction to Plasma Physics by J D Callen
18A Plasma Instabilities | Introduction to Plasma Physics by J D Callen
Published: 2015/12/24
Channel: Lucius Fox
Streaming Instability in the quasi-global protoplanetary disks - run AAu
Streaming Instability in the quasi-global protoplanetary disks - run AAu
Published: 2013/06/17
Channel: Kacper Kowalik
Dump-on-tail instability
Dump-on-tail instability
Published: 2007/12/26
Channel: zigen3rd
Cooking With Meteorology-Baroclinic Instability
Cooking With Meteorology-Baroclinic Instability
Published: 2016/11/21
Channel: Katherine McCuiston
Surface Tension: Plateau-Rayleigh Instability
Surface Tension: Plateau-Rayleigh Instability
Published: 2015/10/29
Channel: Kevin Hwang
Vlasov Simulation
Vlasov Simulation
Published: 2007/06/10
Channel: zigen3rd
Particle in cell plasma simulation
Particle in cell plasma simulation
Published: 2013/11/27
Channel: Kimi Tsai
Instability - Video Learning - WizScience.com
Instability - Video Learning - WizScience.com
Published: 2015/09/10
Channel: Wiz Science™
Mod-01 Lec-18 Weibel Instability
Mod-01 Lec-18 Weibel Instability
Published: 2013/04/25
Channel: nptelhrd
Space Developing Shear Layer with Weak Inflow Turbulence
Space Developing Shear Layer with Weak Inflow Turbulence
Published: 2017/11/14
Channel: APS Physics
Double tearing mode plus a shear instability.
Double tearing mode plus a shear instability.
Published: 2009/09/16
Channel: Brian Sullivan
Instability of a Rossby Wave in a baroclinically stable environment
Instability of a Rossby Wave in a baroclinically stable environment
Published: 2009/12/17
Channel: btnadiga
Plateau-Rayleigh Instability in Water Stream
Plateau-Rayleigh Instability in Water Stream
Published: 2014/05/06
Channel: wolframmathematica
Mali instability: Peace process under strain
Mali instability: Peace process under strain
Published: 2017/01/18
Channel: Al Jazeera English
two stream
two stream
Published: 2015/01/21
Channel: me
Buckling Instability of Crown Sealing
Buckling Instability of Crown Sealing
Published: 2014/11/25
Channel: APS Physics
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WIKIPEDIA ARTICLE

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The two-stream instability is a very common instability in plasma physics. It can be induced by an energetic particle stream injected in a plasma, or setting a current along the plasma so different species (ions and electrons) can have different drift velocities. The energy from the particles can lead to plasma wave excitation.

Dispersion relation[edit]

Consider a cold, uniform, and unmagnetized plasma, where ions are stationary and the electrons have velocity , that is, the reference frame is moving with the ion stream. Let the electrostatic waves be of the form:

Applying linearization techniques to the equation of motions for both species, to the equation of continuity, and Poisson's equation, and introducing the spatial and temporal harmonic operators , we can get the following expression:

which represents the dispersion relation for longitudinal waves, and represents a quartic equation in . The roots can be expressed in the form:

If the imaginary part () is zero, then the solutions represent all the possible modes, and there is no temporal wave growth or damping at all:

If , that is, any of the roots are complex, they will occur in complex conjugate pairs. Substituting in the expression for electrostatic waves leads to:

Because of the second exponential function at the right, the temporal dynamics of the wave amplitude depends strongly on the parameter ; if , then the waves will be exponentially damped; on the other hand, if , then the waves are unstable and will grow at an exponential rate.

Wave–particle interactions[edit]

Bump on tail dist.png

The two stream instability can be thought of as the inverse of Landau damping, where the existence of a greater number of particles that move slower than the wave phase velocity as compared with those that move faster, leads to an energy transfer from the wave to the particles. In the case of the two stream instability, when an electron stream is injected to the plasma, the particles' velocity distribution function has a "bump" on its "tail". If a wave has phase velocity in the region where the slope is positive, there is a greater number of faster particles () than slower particles, and so there is a greater amount of energy being transferred from the fast particles to the wave, giving rise to exponential wave growth.

Bibliography[edit]

  • Bittencourt, J. A. Fundamentals of Plasma Physics, Third Ed. 2004 Springer-Verlag, New York.
  • Chen, Francis F. Introduction to Plasma Physics and Controlled Fusion. Second Ed., 1984 Plenum Press, New York.
  • Nicholson, D. R. Introduction to Plasma Theory. 1983 John Wiley & Sons, New York.
  • Tsurutani, B., and Lakhina, G. Some basic concepts of wave–particle interactions in collisionless plasmas. Reviews of Geophysics 35(4), p.491-502

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