Related papers: Mathematical aspects of the cold plasma model
We report the observation of plasma oscillations in an ultracold neutral plasma. With this collective mode we probe the electron density distribution and study the expansion of the plasma as a function of time. For classical plasma…
The boundary sheath of a low temperature plasma comprises typically only a small fraction of its volume but is responsible for many aspects of the macroscopic behavior. A thorough understanding of the sheath dynamics is therefore of…
We give a survey at an introductory level of old and recent results in the study of critical points of solutions of elliptic and parabolic partial differential equations. To keep the presentation simple, we mainly consider four exemplary…
The linear intensity profile of multiply scattered light in a slab geometry extrapolates to zero at a certain distance beyond the boundary. The diffusion equation with this "extrapolated boundary condition" has been used in the literature…
A new quasi-neutral model describing the Weibel instability of a high-current relativistic beam propagating through a resistive plasma is developed. It treats beam electrons as kinetic particles, and ambient plasma as a non-relativistic…
A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing…
We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations, the following alternative holds: either the shape…
One-dimensional steady-state plasma-field structures in overdense plasma are studied assuming that the electron temperature is uniform over plasma bulk and the ions are stationary. It is shown that there may exist solutions for electron…
In this paper, we use a probabilistic approach to show that there exists a unique, bounded continuous solution to the Dirichlet boundary value problem for a general class of second order non-symmetric elliptic operators $L$ with singular…
We present a derivation of the dispersion relation for electrostatic oscillations (ESOs) in a zero temperature quantum plasma. In the latter, degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the…
We study the Schr\"odinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. This model has been proposed in…
The ion-electron coupling properties for a ion impurity in an electron gas and for a two component plasma are carried out on the basis of a regularized electron-ion potential removing the short-range Coulomb divergence. This work is largely…
Polarizability tensor of a strongly magnetized plasma and the polarization vectors and opacities of normal electromagnetic waves are studied for the conditions typical of neutron star atmospheres, taking account of partial ionization…
This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma…
In this paper, we deal with the initial value problem for a class of fully nonlinear parabolic equations with a singular Dirichlet boundary condition in one space dimension. The interior equation includes, for example, a fully nonlinear…
Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions.…
We present a new model of warm dense matter that represents an intermediate approach between the relative simplicity of ''one-ion'' average atom models and the more realistic but computationally expensive ab initio simulation methods.…
We present the results of direct simulation of the expansionof a two-component ultracold plasmafor various numbers of particles, densities, and electron temperatures. A description of the expansionprocess common to all plasma parameters is…
The aim of this paper is to give an account of some applications of pseudodifferential calculus for solving linear wave equations in the limit of high frequency/short wavelength waves. More specifically, on using as a benchmark the case of…
We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for…