Linear Landau damping for pedestrians

It is considered a difficult task to explain Landau damping in physical terms. Why this is so there are two reasons. Landau recognized in his seminal paper of 1946 that no electrostatic eigenmodes exist in the strict sense, rather do longitudinal waves always show damping in the homogeneous collisionless plasma. Unfortunately, the elegant derivation Landau gave is mathematically stringent, however does not uncover the underlying physical principle. It was John Dawson to provide the first alternative deduction ten years later by basing Landau damping on energy conservation. Nevertheless many researchers may still prefer Landau’s formal proof to Dawson’s as the deficiency of the latter is its missing simplicity. To close the gap numerous attempts were subsequently undertaken by introducing the concept of “resonant particles” the usefulness of which is questionable if not confusing. Starting from a few general properties of linear waves in the present talk it is shown that particle motion in the self-consistent electric field of a wave leads automatically to loss of spatial coherence. This is because the path of the individual particle leads to a delay which is uniquely determined by its injection velocity into the given wave structure. At the very end the individual particle response manifests itself in collisionless wave, i.e., Landau damping. In concomitance with this characteristic behavior it becomes evident that Landau damping is a very universal phenomenon encountered in very different branches of physics. “Phase mixing”, “chaos” and onset of “turbulence” may be viewed as manifestations of one and the same principle. All phenomena have the property in common that periodic velocity modulations, for instance of cars on the road, or airplanes between Frankfurt and New York, cause delays. Time permitting the connection between Landau damping and the second law of thermodynamics (entropy) will be briefly touched.