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In physics, Landau damping, named after its discoverer, the eminent Russian physicist Lev Davidovich Landau, is the effect of damping (exponential decrease as a function of time) of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a region of stability in the parameter space. Since antiquity, people have tried to understand the behavior of matter: why unsupported objects drop to the ground, why different materials have different properties, and so forth. ...
Lev Davidovich Landau (ЛеÌв ДавиÌдович ЛандаÌу) (January 22, 1908 – April 1, 1968) was a prominent Soviet physicist and winner of the Nobel Prize for Physics whose broad field of work included the theory of superconductivity and superfluidity, quantum electrodynamics, nuclear physics and particle physics. ...
Damping is any effect, either deliberately engendered or inherent to a system, that tends to reduce the amplitude of oscillations. ...
In physics, plasma oscillations, often referred to as Langmuir waves or plasma waves, are periodic oscillations of charge density in conducting media such as plasmas or metals. ...
The word plasma has a Greek root which means to be formed or molded (the word plastic shares this root). ...
Wave-Particle Interactions Landau damping occurs due to the energy exchange between a wave with phase velocity vph and particles in the plasma with approximately equal to vph, who can interact strongly with the wave. Those particles having velocities slightly less than vph will be accelerated by the wave electric field to move with the wave phase velocity, while those particles with velocities slightly greater than vph will be decelerated by the wave electric field, losing energy to the wave. A wave is a disturbance that propagates in a periodically repeating fashion, often transferring energy. ...
 In a collisionless plasma where the particle velocities have a Maxwellian distribution function, 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. Image File history File links Maxwell_dist_ress_partic_landau. ...
Physical Interpretation Mathematical proof of Landau damping is somewhat involved, requiring the use of contour integration. But there is an simple physical interpretation (although not strictly correct) that helps to visualize this phenomenon. It is possible to imagine Langmuir waves as waves in the sea, and the particles as surfers trying to catch the wave, all moving in the same direction. If the surfer is moving on the water surface at a velocity slightly less than the waves eventually will be caught and pushed along the wave (gaining energy), while a surfer moving slightly faster than a wave will be pushing on the wave as he moves uphill (losing energy to the wave). Image File history File links Phys_interp_landau_damp. ...
In physics, plasma oscillations, often referred to as Langmuir waves or plasma waves, are periodic oscillations of charge density in conducting media such as plasmas or metals. ...
It is worth to note that only the surfers are playing a important role in this energy interactions with the waves; a beachball floating on the water (zero velocity) will go up and down as the wave goes by, not gaining energy at all. Also, a boat that moves very fast (faster than the waves) does not exchange much energy with the wave.
Bibliography Chen, Francis F. Introduction to Plasma Physics and Controlled Fusion. Second Ed., 1984 Plenum Press, 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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