Effect of Collisions on the Landau Damping of Plasma Oscillations

The effect of collisions on the Landau damping of a one-dimensional longitudinal plasma oscillation in the absence of a magnetic field is analyzed. It is found that in a steady state, collisions (no matter how few in number) affect the velocity distribution of the trapped electrons and thus play a major role in determining the Landau damping. When the damping is small (Im k « Re k), it is reduced from its collisionless value by a factor νc2/(νc2 + Ω2) where νc is the electron collision frequency for momentum transfer and Ω2 = eEk/m is the frequency of oscillation of a trapped electron in the approximately parabolic potential trough of the wave.