In physics, Landau damping, named after its discoverer, Soviet physicist Lev Davidovich Landau (1908–68), is the effect of damping of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a region of stability in the parameter space. It was later argued by Donald Lynden-Bell that a similar phenomenon was occurring in galactic dynamics, where the gas of electrons interacting by electrostatic forces is replaced by a "gas of stars" interacting by gravitational forces. Landau damping can be manipulated exactly in numerical simulations such as particle-in-cell simulation. It was proved to exist experimentally by Malmberg and Wharton in 1964, almost two decades after its prediction by Landau in 1946.

Lev Davidovich Landau was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was also involved in the design of the Soviet atomic bomb.