Existence of non-Landau solutions for Langmuir waves

The propagation of linear one dimensional (1D) Langmuir waves is reinvestigated using numerical simulations of a new type with very low noise. The dependence of the result on the initial conditions is shown. New solutions are exhibited, with properties different from Landau's, even in the asymptotic behavior, in particular with regard to the damping rate. These solutions are shown to demand a special preparation of the initial plasma perturbation, but in a way which is quite physical, without any singularity in the electron distribution function, contrary to the classical van Kampen's solutions. Using an original theoretical calculation, a simple analytical form is derived for the perturbed distribution function, which allows interpreting both the Landau and non-Landau solutions observed numerically. The numerical results presented and their interpretations are potentially important in several respects: 1) They outline that Landau solutions, for the 1D electrostatic problem in collisionless plasmas, are only a few among an infinite amount of others; even if the non-Landau solutions are much less probable, their existence provides a different view on the concept of kinetic damping and may suggest interpretations different from usual for the subsequent nonlinear effects; 2) they show that the shape of the initial perturbation delta f(v), and not only its amplitude, is important for the long time wave properties, both linear and nonlinear; 3) the existence of non-Landau solutions makes clear that the classical energy arguments cannot be fully universal as long as they allow deriving the Landau damping rate independently of the initial conditions; 4) the particle signature of Landau damping, different from the usual guess, should imply a change in our understanding of the role of the resonant particles. (c) 2008 American Institute of Physics.