Direct path from microscopic mechanics to Debye shielding, Landau damping and wave-particle interaction
The derivation of Debye shielding and Landau damping from the N-body description of plasmas is performed directly by using Newton’s second law for the N-body system. This is done in a few steps with elementary calculations using standard tools of calculus and no probabilistic setting. Unexpectedly, Debye shielding is encountered together with Landau damping. This approach is shown to be justified in the one-dimensional case when the number of particles in a Debye sphere becomes large. The theory is extended to accommodate a correct description of trapping and chaos due to Langmuir waves. On top of their well-known production of collisional transport, the repulsive deflections of electrons are shown to produce shielding, in such a way that each particle is shielded by all other ones, while keeping in uninterrupted motion.
Features of the Debye Mode in an Electron Plasma at Various Degrees of the Electron Gas Degeneracy
We have considered the response of an electron plasma with an arbitrary degree of degeneration to an alternating electromagnetic field directed perpendicularly to the boundary of the plasma layer. The plasma screening of the electric field is determined by the Debye mode. The analysis of the behavior of this mode has been carried out depending on the parameters of the problem. For the first time, it has been shown that, ar sufficiently high degrees of the electron gas degeneracy, the range of the Debye mode existence has a substantially nontrivial character, in which the ranges of existence and absence of this mode alternate with increasing electric field frequency.
Large time behavior and asymptotic stability of the 2D Euler and linearized Euler equations
Abstract We study the asymptotic behavior and the asymptotic stability of the 2D Euler equations and of the 2D linearized Euler equations close to parallel flows. We focus on flows with spectrally stable profiles U ( y ) and with stationary streamlines y = y 0 (such that U ′ ( y 0 ) = 0 ), a case that has not been studied previously. We describe a new dynamical phenomenon: the depletion of the vorticity at the stationary streamlines. An unexpected consequence is that the velocity decays for large times with power laws, similarly to what happens in the case of the Orr mechanism for base flows without stationary streamlines. The asymptotic behaviors of velocity and the asymptotic profiles of vorticity are theoretically predicted and compared with direct numerical simulations. We argue on the asymptotic stability of this ensemble of flow profiles even in the absence of any dissipative mechanisms.