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Two-stream instability : ウィキペディア英語版
Two-stream instability
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 ==

Consider a cold, uniform, and unmagnetized plasma, where ions are stationary and the electrons have velocity \mathbf_0, that is, the reference frame is moving with the ion stream. Let the electrostatic waves be of the form:

\mathbf_1 = \xi_1 \exp(- \omega t) ) \mathbf^2 \left(+ \frac \right ),

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

\omega_j = \omega_j^R + i\gamma_j

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

\mathbf = \xi \exp(- \omega t) ) \mathbf = \xi \exp(- \omega_j^R t) ) \exp(t ) \mathbf 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 (v > v_) 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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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