Nonlinear Landau Damping Rate of a Driven Plasma Wave

In this Letter, we discuss the concept of the nonlinear Landau damping rate, nu, of a driven electron plasma wave, and provide a very simple, practical formula for nu, which agrees very well with results inferred from Vlasov simulations of stimulated Raman scattering. nu actually is more complicated an operator than a plain damping rate, and it may only be seen as such because it assumes almost constant values before abruptly dropping to 0. The decrease of nu to 0 is moreover shown to occur later when the wave amplitude varies in the direction transverse to its propagation.