Linear stability of the Vlasov–Poisson system with boundary conditions

Esentürk, Emre; Hwang, Hyung-Ju

doi:10.1016/j.na.2016.02.014

Cited by 5 publications

(3 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Batt-Morrison-Rein [5] showed the existence and linear stability of stationary solutions on a whole space. Furthermore, Esentürk-Hwang [11] discussed the existence and linear stability on a finite interval and half line with the inflow and specular reflection boundary conditions, respectively. The linear instability was discussed in [32].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Stability and Instability of Plasma Boundary Layers

Suzuki¹,

Takayama²,

Zhang³

2022

Preprint

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Nonlinear Stability and Instability of Plasma Boundary Layers

Suzuki¹,

Takayama²,

Zhang³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…As far as we know, in the presence of spatial boundaries and with inhomogeneous equilibria, there is no analogue to the Landau Damping. Nevertheless, spectral stability or Lyapunov type stability using the Energy Casimir method have been carried in [23,26,6,1,13,15]. We mention that in the use of the Energy Casimir method, very often a structural assumption on the equilibrium density is assumed.…”

Section: Introductionmentioning

confidence: 99%

“…As for the spectral analysis, a symmetric structure is needed to study the spectrum of the appropriate operator. Unfortunately, in the case of plasma sheath equilibria, we have not been able to use these tools in a satisfactory way, notably because the so called Bohm condition (13) prevents the non trivial equilibrium from being a decreasing function of the microscopic energy.…”

Section: Introductionmentioning

confidence: 99%

Linear electron stability for a bi-kinetic sheath model

Badsi

2017

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

Abstract. We establish the linear stability of an electron equilibrium for an electrostatic and 4 collisionless plasma in interaction with a wall. The equilibrium we focus on is called in plasma 5 physics a Debye sheath. Specifically, we consider a two species (ions and electrons) Vlasov-Poisson-6Ampère system in a bounded and one dimensional geometry. The interaction between the plasma 7 and the wall is modeled by original boundary conditions : On the one hand, ions are absorbed by 8 the wall while electrons are partially re-emited. On the other hand, the electric field at the wall is 9induced by the accumulation of charged particles at the wall. These boundary conditions ensure the 10 compatibility with the Maxwell-Ampère equation. A global existence, uniqueness and stability result 11 for the linearized system is proven. The main difficulty lies in the fact that (due to the absorbing 12 boundary conditions) the equilibrium is a discontinuous function of the particle energy, which results 13 in a linearized system that contains a degenerate transport equation at the border. 14 Key words. plasma wall interaction, Debye sheath, kinetic equations, Vlasov-Poisson-Ampère 15 system, linear stability, degenerate transport equations 16

show abstract

On the 3-D Vlasov–Poisson system with point charges: Global solutions with unbounded supports and propagation of velocity-spatial moments

Zhang

2017

Journal of Differential Equations

View full text Add to dashboard Cite

Linear stability of the Vlasov–Poisson system with boundary conditions

Cited by 5 publications

References 28 publications

Nonlinear Stability and Instability of Plasma Boundary Layers

Nonlinear Stability and Instability of Plasma Boundary Layers

Linear electron stability for a bi-kinetic sheath model

On the 3-D Vlasov–Poisson system with point charges: Global solutions with unbounded supports and propagation of velocity-spatial moments

Contact Info

Product

Resources

About