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

摘要

For linear Langmuir waves, it is well known that the energy exchanges generally lead to acontinuous dissipation, on average, from the electric form to the kinetic one. Many papers haveestimated these exchanges and indeed shown that the classical Landau value γ_L,characterizing theelectric field damping, can be derived from this estimation. The paper comes back to thisdemonstration and its implicit assumption of "forgetting the initial conditions." The limits of theusual energy calculations have become much apparent recently when non-Landau solutions,decreasing with damping rates smaller than γ_L,have been evidenced [Belmontet al.,Phys. Plasmas15, 052310 (2008)]. Taking advantage of the explicit form provided in this paper for the perturbeddistribution function, the dissipation process is revisited here in a more general way. It is shown thatthe energy calculations, when complete (i.e., when the role of the initial conditions is not excludedby the very hypotheses of the calculations), are indeed in full agreement with the existence ofnon-Landau solutions; Landau damping, by the way, appears as a particular mode of dissipation, inwhich the ballistic transport of the initial plasma perturbation leads to negligible effects. Twoapproaches are presented for this demonstration, Eulerian and Lagrangian, the first one starting fromthe Vlasov equation and the second from the dynamics of the individual particles. The specific roleof the so-called resonant particles is investigated in both formalisms, which providescomplementary pictures of the microphysics involved in the energy transfers between field andparticles for Landau as well as for non-Landau solutions.