Landau Damping and Kinetic Instabilities

Landau’s method works out waves and damping in collisionless plasmas, and in particular his prescription for dealing with the singularities in the integrals. The physical consequences resulting from Landau damping are illustrate with restriction to high frequency oscillations, i.e. that only the electrons respond to the wave. Thus, around the wave-particle resonance , the particles just lagging behind the wave receive energy from the wave and those just overtaking it give up energy to wave. This process is therefore intrinsically of kinetic nature.