# 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 …