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A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the "one-fluid"…

Analysis of PDEs · Mathematics 2017-05-24 Yu Deng , Alexandru D. Ionescu , Benoit Pausader

The dynamics of dilute plasma particles such as electrons and ions can be modeled by the fundamental two species Vlasov-Poisson-Boltzmann equations, which describes mutual interactions of plasma particles through collisions in the…

Analysis of PDEs · Mathematics 2025-04-01 Zaihong Jiang , Yong Wang , Hang Xiong

The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…

Materials Science · Physics 2007-05-23 A. Ya. Shul'man , D. V. Posvyanskii

This paper is concerned with the analysis of a mathematical model arising in plasma physics, more specifically in fusion research. It directly follows \cite{DHK1}, where the tri-dimensional analysis of a Vlasov-Poisson equation with finite…

Analysis of PDEs · Mathematics 2010-11-30 Daniel Han-Kwan

The interaction of partially ionized plasmas with an electromagnetic field is investigated using quantum statistical methods. A general statistical expression for the current density of a plasma in an electromagnetic field is presented and…

Statistical Mechanics · Physics 2009-11-11 Dietrich Kremp , Dirk Semkat , Thomas Bornath , Michael Bonitz , Manfred Schlanges , Paul Hilse

We have obtained the solutions of linearized Shr{\"o}dinger equation for spherically and axially symmetrical electrons density oscillations in plasma in the approximation of the self-consistent field. It was shown that in the center or on…

Plasma Physics · Physics 2007-05-23 M. Dvornikov , S. Dvornikov , G. Smirnov

This paper is concerned with the global-in-time convergence from bipolar Euler-Poisson system (BEP) to unipolar one (UEP) through the infinity-ion-mass limit by letting the ratio of the mass of ion $m_i$ over that of electron $m_e$ goes to…

Analysis of PDEs · Mathematics 2026-02-03 Yachun Li , Shihao Wang , Liang Zhao

We investigate the critical threshold phenomena in a large class of one dimensional pressureless Euler--Poisson (EP) equations, with non-vanishing background states. First, we establish local-in-time well-posedness in proper regularity…

Analysis of PDEs · Mathematics 2024-02-21 Young-Pil Choi , Dong-ha Kim , Dowan Koo , Eitan Tadmor

Plasma is a medium filled with free electrons and positive ions. Each particle acts as a conducting fluid with a single velocity and temperature when electromagnetic fields are present. This distinction between the roles played by electrons…

Plasma Physics · Physics 2024-10-01 Emily Kelting , J. Douglas Wright

In this paper, we establish the stability of the quasineutral limit for the ionic Vlasov-Poisson system under perturbations exponentially small in Wasserstein sense. Notably, we emphasize that exponential smallness is a necessary condition…

Analysis of PDEs · Mathematics 2024-03-08 Megan Griffin-Pickering , Mikaela Iacobelli

We provide a rigorous justification of the semiclassical quasi-neutral and the quantum many-body limits to the isothermal Euler equations. We consider the nonlinear Schr\"{o}dinger-Poisson-Boltzmann system under a quasi-neutral scaling and…

Analysis of PDEs · Mathematics 2025-04-01 Immanuel Ben Porat , Gui-Qiang G. Chen , Difan Yuan

We study the three dimensional many-particle quantum dynamics in mean-field setting. We forge together the hierarchy method and the modulated energy method. We prove rigorously that the compressible Euler equation is the limit as the…

Analysis of PDEs · Mathematics 2024-10-10 Xuwen Chen , Shunlin Shen , Jiahao Wu , Zhifei Zhang

The Euler-Poisson (EP) system models the dynamics of a variety of physical processes, including charge transport, collisional plasmas, and certain cosmological wave phenomena. In this work, we establish sharp critical threshold conditions…

Analysis of PDEs · Mathematics 2025-12-18 Manas Bhatnagar , Hailiang Liu

We present a linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. The resulting method is systematically improvable and well suited to large-scale quantum mechanical calculations in which…

Materials Science · Physics 2021-11-09 J. E. Pask , N. Sukumar , S. E. Mousavi

In this paper we consider the Euler-Poisson system (describing a plasma made of ions with a negligible ion temperature) on the Sobolev spaces $H^s(\R^3)$, $s > 5/2$. Using a geometric approach we show that for any time $T > 0$ the…

Analysis of PDEs · Mathematics 2018-06-14 Hasan Inci

Brown, Preston, and Singleton (BPS) produced an analytic calculation for energy exchange processes for a weakly to moderately coupled plasma: the electron-ion temperature equilibration rate and the charged particle stopping power. These…

Plasma Physics · Physics 2009-06-26 Lowell S. Brown , Robert L. Singleton

The one-dimensional Vlasov-Poisson system is considered and a particle method is developed to approximate solutions without compact support which tend to a fixed background of charge as $| x | \to \infty$. Such a system of equations can be…

Numerical Analysis · Mathematics 2014-01-03 Stephen Pankavich

We establish the existence of $1$-parameter families of $\epsilon$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq 1/3$,…

General Relativity and Quantum Cosmology · Physics 2018-06-21 Chao Liu , Todd A. Oliynyk

The Schr\"odinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As $\hbar/m\to 0$, $m$ being the boson mass, the equations have been postulated to approximate…

Cosmology and Nongalactic Astrophysics · Physics 2018-05-02 Philip Mocz , Lachlan Lancaster , Anastasia Fialkov , Fernando Becerra , Pierre-Henri Chavanis

The Vlasov-Poisson system with massless electrons (VPME) is widely used in plasma physics to model the evolution of ions in a plasma. It differs from the Vlasov-Poisson system (VP) for electrons in that the Poisson coupling has an…

Analysis of PDEs · Mathematics 2021-05-27 Megan Griffin-Pickering , Mikaela Iacobelli