Nonlinear Stability and Instability of Plasma Boundary Layers
@inproceedings{Suzuki2022NonlinearSA, title={Nonlinear Stability and Instability of Plasma Boundary Layers}, author={Masahiro Suzuki and Masahiro Takayama and Katherine Zhiyuan Zhang}, year={2022} }
We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov–Poisson system on a half-line with the completely absorbing boundary condition. In [54], the solvability of the stationary problem is studied. In this paper, we study the nonlinear stability and instability of these stationary solutions of the Vlasov–Poisson system.
References
SHOWING 1-10 OF 50 REFERENCES
Asymptotic stability of a boundary layer to the Euler--Poisson equations for a multicomponent plasma
- Mathematics
- 2016
The main concern of this paper is to analyze
a boundary layer called a sheath that
occurs on the surface of materials
when in contact with a multicomponent plasma.
For the formation of a sheath,…
A rigorous stability result for the Vlasov-Poisson system in three dimensions
- Mathematics
- 1993
It is proven that in a neutral two-component plasma with space homogeneous positively charged background, which is governed by the Vlasov-Poisson system and for which Poisson's equation is considered…
Existence of stationary, collisionless plasmas in bounded domains
- Physics, Mathematics
- 1992
We consider a collisionless plasma, which consists of electrons and positively charged ions and is confined to a bounded domain in ℝ3. The distribution functions of the particles are assumed to…
A Geometric Level-Set Formulation of a Plasma-Sheath Interface
- Physics, Mathematics
- 2005
In this paper, we present a new geometric level-set formulation of a plasma-sheath interface arising in plasma physics. We formally derive the explicit dynamics of the interface from the…
Asymptotic Stability of Boundary Layers to the Euler-Poisson Equations Arising in Plasma Physics
- MathematicsSIAM J. Math. Anal.
- 2012
The main concern of the present paper is to analyze the behavior of a boundary layer, called a sheath, which appears over a material in contact with a plasma, and proves the stability theorem exactly under the Bohm criterion in the spatial dimension up to three.
Nonlinear instability of periodic BGK waves for Vlasov‐Poisson system
- Mathematics
- 2005
We investigate the nonlinear instability of periodic Bernstein‐Greene‐Kruskal (BGK) waves. Starting from an exponentially growing mode to the linearized equation, we proved nonlinear instability in…
Instability of periodic BGK equilibria
- Mathematics
- 1995
A collisionless plasma is described by the Vlasov-Poisson equations. The BGK equilibria were proposed in 1957 as the simplest spatially-dependent equilibria. Since that time the question of their…
Quasi-neutral limit for the Euler-Poisson system in the presence of plasma sheaths with spherical symmetry
- Mathematics
- 2016
The purpose of this paper is to mathematically investigate the formation of a plasma sheath near the surface of a ball-shaped material immersed in a bulk plasma, and to obtain qualitative information…
Asymptotic stability of stationary solutions to the Euler-Poisson equationsarising in plasma physics
- Mathematics
- 2011
The main concern of the present paper
is to analyze a sheath formed
around a surface of a material with which plasma contacts.
Here, for a formation of the sheath,
the Bohm criterion requires …