Landau damping: New aspects of an old story

We reinvestigate the dispersion relation for longitudinal plasma waves in a collisionless electron plasma. We show that even at finite temperature there exists a critical wave number k_cr below which Landau damping is absent. Furthermore, the magnitude of damping deviates from Landau's formula also well above k_cr. We propose to extend existing experiments to wave numbers k ～ k_cr.