Related papers: Linear Collisionless Landau Damping in Hilbert Spa…
We study the unphysical recurrence phenomenon arising in the numerical simulation of the transport equations using Hermite-spectral method. From a mathematical point of view, the suppression of this numerical artifact with filters is…
Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is applied to low-collision electron-ion plasmas. Taking into account Coulomb collisions…
The theory of plasma waves and Landau damping in Maxwellian plasmas, Landau's ``rule of pass around poles'' include doubtful statements, particularly related to an artificial ``constructing'' of the dispersion equation, what should allow…
A Landau fluid model for a collisionless electron-proton magnetized plasma, that accurately reproduces the dispersion relation and the Landau damping rate of all the magnetohydrodynamic waves, is presented. It is obtained by an accurate…
The classic problem of the dynamic evolution of Langmuir electron waves in a collisionless plasma and their Landau damping is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies.…
To address the problem of Landau damping in kinetic turbulence, the forcing of the linearized Vlasov equation by a stationary random source is considered. It is found that the time-asymptotic density response is dominated by resonant…
For the first time the kinetic description of Landau diamagnetism for degenerate collisional plasma is given. The correct expression for transverse electric conductivity of the quantum plasma, found by authors (see arXiv:1002.1017 [math-ph]…
Landau damping is the tendency of solutions to the Vlasov equation towards spatially homogeneous distribution functions. The distribution functions however approach the spatially homogeneous manifold only weakly, and Boltzmann entropy is…
Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is here applied to consider transversal oscillations and waves in low-collision…
The asymptotic behaviour of the Hartree equation is studied near translation-invariant steady states. For short-range interaction kernels satisfying a uniform Penrose stability condition, including the screened Coulomb interaction,…
In this work, we establish the existence and decay of {\em plasmons}, the quantum of Langmuir's oscillatory waves found in plasma physics, for the linearized Hartree equations describing an interacting gas of infinitely many fermions near…
It is well established that the Hilbert space for charged particles in a plane subject to a uniform magnetic field can be described by two mutually commuting ladder algebras. We propose a similar formalism for Landau level quantization…
In this work we obtain the exact solution for relativistic Landau problem plus oscillator potential in a complex symmetric gauge field in a non-commutative complex space, using the algebraic techniques of creation and annihilation…
This paper is the third of a series on Hamiltonian stationary Lagrangian surfaces. We present here the most general theory, valid for any Hermitian symmetric target space. Using well-chosen moving frame formalism, we show that the equations…
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-$2_-$,…
The Caldeira-Leggett Hamiltonian (Eq. (1) below) describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature…
Kinetic simulations of collisionless plasmas are computationally challenging due to phase space mixing and filamentation, resulting in fine-scale velocity structures. This study compares three methods developed to reduce artifacts related…
We prove Landau damping for the collisionless Vlasov equation with a class of $L^1$ interaction potentials (including the physical case of screened Coulomb interactions) on $\mathbb R^3_x \times \mathbb R^3_v$ for localized disturbances of…
Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of…
Landau damping is the mechanism of plasma and beam stabilization; it arises through energy transfer from collective modes to the incoherent motion of resonant particles. Normally this resonance requires the resonant particle's frequency to…