The mathematical theory of Landau damping is somewhat involved see the section below.
2.
Villani received the Fields Medal for his work on Landau damping and the Boltzmann equation.
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A mechanical N-body approach provides together the derivation of electric-field screening and of Landau damping [, ].
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Since Landau damping occurs for waves with arbitrarily small amplitudes, this shows the most active particles in this damping are far from being trapped.
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His work " On Landau damping " with Villani ( published in 2011 ) was quoted in the Fields Medal laudation of Villani in 2010.
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In a recent paper the initial data issue is solved and Landau damping is mathematically established for the first time for the non-linear Vlasov equation.
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Considering Crab-like Pulsars it has been shown that by means of the Landau damping the centrifugally induced electrostatic waves efficiently lose energy transferring it to electrons.
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Vlasov Poisson equations are used to describe various phenomena in plasma, in particular Landau damping and the distributions in a Maxwellian, and therefore inaccessible to fluid models.
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Effects which are essentially kinetic and not captured by fluid models include double layers, Landau damping, a wide range of instabilities, chemical separation in space plasmas and electron runaway.
10.
Landau damping occurs because of the energy exchange between an electromagnetic wave with phase velocity v _ { ph } and particles in the plasma with velocity approximately equal to v _ { ph }, which can interact strongly with the wave.
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