Related papers: Basic microscopic plasma physics from N-body mecha…
Debye shielding, collisional transport, Landau damping of Langmuir waves, and spontaneous emission of these waves are introduced, in typical plasma physics textbooks, in different chapters. This paper provides a compact unified introduction…
The derivation of Debye shielding and Landau damping from the $N$-body description of plasmas requires many pages of heavy kinetic calculations in classical textbooks and is done in distinct, unrelated chapters. Using Newton's second law…
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…
We discuss the self-consistent dynamics of plasmas by means of hamiltonian formalism for a system of $N$ near-resonant electrons interacting with a single Langmuir wave. The connection with the Vlasov description is revisited through the…
In this paper, we establish nonlinear Landau damping below survival threshold for collisionless charged particles following the meanfield Vlasov theory near general radial equilibria. In absence of collisions, the long-range Coulomb pair…
Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data…
This paper brings further insight into the recently published N-body description of Debye shielding and Landau damping [Escande D F, Elskens Y and Doveil F 2014 Plasma Phys. Control. Fusion 57 025017]. Its fundamental equation for the…
We focus our attention on some relevant aspects of the beam-plasma instability in order to refine some features of the linear and non-linear dynamics. After a re-analysis of the Poisson equation and of the assumption dealing with the…
Difficulties in founding microscopically the Vlasov equation for Coulomb-interacting particles are recalled for both the statistical approach (BBGKY hierarchy and Liouville equation on phase space) and the dynamical approach (single…
In this paper, we establish the large time asymptotic behavior of solutions to the linearized Vlasov-Poisson system near general spatially homogenous equilibria $\mu(\frac12|v|^2)$ with connected support on the torus $\mathbb{T}^3_x \times…
Landau damping/growing at boundary condition of excitation of a harmonic wave in collisionless ion-electron-neutrals plasma contradicts to the law of energy conservation of a wave damping/growing in space. There is also no criterion of a…
Our last three papers provide an occasion to make some brief notes on ideology of waves in plasmas and to rehabilitate Vlasov prescription to calculate relevant logarithmically divergent integrals in the principal value sense. In this…
Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes…
The evolution of an initial perturbation in Vlasov plasma is studied in the intrinsically nonlinear long-time limit dominated by the effects of particle trapping. After the possible transient linear exponential Landau damping, the evolution…
The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet…
In this paper, we study the Vlasov-Poisson-Landau Equations on $\mathbb{T}^3\times \mathbb{R}^3$ with small collision frequency $\nu\ll 1$. We prove that for $\nu$-independent perturbations of the global Maxwellians in Gevrey-$2_-$,…
We consider a homogeneous plasma composed of $N$ particles of the same electric charge which interact through a Coulomb potential. In the large plasma parameter limit, classical kinetic theories justify that the empirical density is the…
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…
A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming that the electric field decays with sufficient rapidity as $t \to\infty$, we show that the velocity characteristics and spatial averages of the particle…
It is shown that partial incoherence, in the form of stochastic phase noise, of a Langmuir wave in an unmagnetized plasma gives rise to a Landau-type damping. Starting from the Zakharov equations, which describe the nonlinear interaction…