Revisiting the validity of quasilinear theory

Abstract

The weak turbulence theory of Langmuir waves in a one-dimensional, one-species plasma is discussed. Analytic calculations using the theory of two-point correlations show that in the weak turbulence regime, τac≪min(τtr,γ−1k) (where τac is the field autocorrelation time and τtr is the particle decorrelation time), the nonlinear enhancement of the mode growth rate γk beyond the linear, Landau growth rate γkL is small, additive, and higher order in the weak turbulence expansion parameter. This result thus supports the validity of the quasilinear theory for Langmuir wave turbulence, and disagrees with the predictions of Adam, Laval, and Pesme [Phys. Rev. Lett. 43, 1671 (1979)], which indicate a non-negligible, multiplicative enhancement in the regime τac≪τtr≪γ−1k. Analysis shows that their result comes from the use of an invalid source term for the fluctuations.