On the theory of the nonlinear Landau damping

Abstract

An exact solution of the collisionless time-dependent Vlasov equation is found for the first time. By means of this solution the behavior of the Langmuir waves in the nonlinear stage is considered. The analysis is restricted by the consideration of the first nonlinear approximation keeping the second power of the electric strength. It is shown that in general the waves with finite amplitudes are not subject to damping. Only in the linear approximation, when the wave amplitude is very small, are the waves experiencing damping. It is shown that with the definite resonance conditions imposed, the waves become unstable.

Novel features of electromagnetic waves in an isotropic degenerate electron-ion plasma

“…Direct evidence of LD in a turbulent space plasma [31] suggests that it has played a significant role in the dissipation process, in which the energy can be transferred from the electric field to the electrons. The nonlinear stage of the Langmuir wave analysis [32] has also determined that Langmuir waves can carry a finite amplitude and oscillation frequency that are larger than the damping rate (found in the linear approximation) and one does not have a damping effect, while only showing a periodic structure. However, the efforts [33][34][35] cannot be ignored in studying the nonlinear LD in a degenerate Fermi gas.…”