(Science: radiobiology) damping of a wave propagating in a hot plasma, due to the interaction of the wave with particles whose velocity is close to the phase velocity of the wave. Depends on the shape of the velocity-space distribution function at the phase velocity of the wave.
The phenomenon is very similar to surfing on water waves at the beach. If a particles speed is just slightly lower than the wave, then the particle can catch the wave and surf along at the wave speed. In so doing, the particle will gain some energy, which will be at the expense of the wave. This is called landau damping, since the loss of energy tends to damp the wave. At the same time, if a particle moves just slightly faster than the wave, then it will also be caught on the wave. However, in this case, it will slow down, giving the wave some extra energy. In this case particles transfer energy to the wave, this is called inverse landau damping. Which effect dominates depends on whether there are more particles moving faster than the wave or more particles moving slower. Thus it depends on the derivative of the distribution function with respect to velocity, evaluated at the waves phase velocity. Landau dmaping can lead to the decay of waves. Inverse landau damping can be a mechanism for some kinetic instabilities.