Landau and non-Landau linear damping: Physics of the dissipation

For linear Langmuir waves, it is well known that the energy exchanges generally lead to a continuous dissipation, on average, from the electric form to the kinetic one. Many papers have estimated these exchanges and indeed shown that the classical Landau value γ _L, characterizing the electric field damping, can be derived from this estimation. The paper comes back to this demonstration and its implicit assumption of "forgetting the initial conditions." The limits of the usual energy calculations have become much apparent recently when non-Landau solutions, decreasing with damping rates smaller than γ _L, have been evidenced [Belmont, Phys. Plasmas 15, 052310 (2008)]. Taking advantage of the explicit form provided in this paper for the perturbed distribution function, the dissipation process is revisited here in a more general way. It is shown that the energy calculations, when complete (i.e., when the role of the initial conditions is not excluded by the very hypotheses of the calculations), are indeed in full agreement with the existence of non-Landau solutions; Landau damping, by the way, appears as a particular mode of dissipation, in which the ballistic transport of the initial plasma perturbation leads to negligible effects. Two approaches are presented for this demonstration, Eulerian and Lagrangian, the first one starting from the Vlasov equation and the second from the dynamics of the individual particles. The specific role of the so-called resonant particles is investigated in both formalisms, which provides complementary pictures of the microphysics involved in the energy transfers between field and particles for Landau as well as for non-Landau solutions.