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Landau damping : ウィキペディア英語版
Landau damping
In physics, Landau damping, named after its discoverer,〔Landau, L. "On the vibration of the electronic plasma". ''J. Phys. USSR'' 10 (1946), 25. English translation in ''JETP'' 16, 574. Reproduced in Collected papers of L.D. Landau, edited and with an introduction by D. ter Haar, Pergamon Press, 1965, pp. 445–460; and in Men of Physics: L.D. Landau, Vol. 2, Pergamon Press, D. ter Haar, ed. (1965).〕 the eminent Soviet physicist Lev Landau (1908-68), is the effect of damping (exponential decrease as a function of time) of longitudinal space charge waves in plasma or a similar environment.〔Chen, Francis F. ''Introduction to Plasma Physics and Controlled Fusion''. Second Ed., 1984 Plenum Press, New York.〕 This phenomenon prevents an instability from developing, and creates a region of stability in the parameter space. It was later argued by Donald Lynden-Bell that a similar phenomenon was occurring in galactic dynamics,〔Lynden-Bell, D. (1962), "The stability and vibrations of a gas of stars". ''Mon. Not. R. Astr. Soc.'' 124(4) 279–296.〕 where the gas of electrons interacting by electro-static forces is replaced by a "gas of stars" interacting by gravitation forces.〔Binney, J., and Tremaine, S. ''Galactic Dynamics'', second ed. Princeton Series in Astrophysics. Princeton University Press, 2008.〕 Landau damping can be manipulated exactly in numerical simulations such as particle-in-cell simulation. 〔Chang Woo Myung, Jae Koo Lee "Finite Amplitude Effects on Landau Damping and Diminished Transportation of Trapped Electrons" ''JPSJ'' 83 074502 (2014)〕
== Wave-particle interactions〔Tsurutani, B., and Lakhina, G. ( "Some basic concepts of wave–particle interactions in collisionless plasmas" ). ''Reviews of Geophysics'' 35(4), pp. 491–502〕 ==

Landau damping occurs because of the energy exchange between an electromagnetic wave with phase velocity v_ and particles in the plasma with velocity approximately equal to v_, which can interact strongly with the wave. Those particles having velocities slightly less than v_ will be accelerated by the wave electric field to move with the wave phase velocity, while those particles with velocities slightly greater than v_ will be decelerated by the wave electric field, losing energy to the wave.
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In a collisionless plasma the particle velocities are often taken to be approximately a Maxwellian distribution function.
If the slope of the function is negative, the number of particles with velocities slightly less than the wave phase velocity is greater than the number of particles with velocities slightly greater. Hence, there are more particles gaining energy from the wave than losing to the wave, which leads to wave damping.
If, however, the slope of the function is positive, the number of particles with velocities slightly less than the wave phase velocity is smaller than the number of particles with velocities slightly greater. Hence, there are more particles losing energy to the wave than gaining from the wave, which leads to a resultant increase in the wave energy.

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