doi:10.1016/j.cpc.2004.06.022
Copyright © 2004 Elsevier B.V. All rights reserved.
Study of the generation of a charge separation and electric field at a plasma edge using Eulerian Vlasov codes in cylindrical geometry
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M. Shoucri
,
, a, H. Gerhauserb and K. -H. Finkenb
a Institut de recherche d'Hydro-Québec, 1800, boul. Lionel-Boulet, Varennes, Québec, Canada J3X 1S1
b Institut für Plasmaphysik, Forschungszentrum Jülich GmbH, EURATOM Association, Trilateral Euregio Cluster, D-52425, Jülich, Germany
Available online 23 July 2004.
Abstract
A one-dimensional (1D) Eulerian Vlasov code in cylindrical geometry is used to study the problem of the formation of a charge separation at a plasma edge, together with the self-consistent electric field, in the presence of a density gradient. The code applies a method of fractional steps for the solution of the Vlasov equation. The electric field calculated along the gradient is compared with the macroscopic values calculated from the same kinetic code for the gradient of the ion pressure and the Lorentz force term. We find that these quantities balance the electric field fairly well along the gradient. The extension of this method to a two-dimensional (2D) problem will be presented, together with the corresponding results.
Author Keywords: Vlasov equation; Numerical simulation; Edge-plasma electric field
Fig. 3. Charge density (ni−ne).
Fig. 5. Temperature Tir, as defined in Eq. (12) (solid curve), niTir (broken curve), and density ni (which follows closely the curve niTir).
Fig. 6. Temperature Tiθ, as defined in Eq. (12) (solid curve), niTiθ (broken curve), and density ni (which follows closely the curve niTiθ).
Fig. 7. Electric field Er at θ=0 (full curve), θ=π/2 (broken curve), and θ=π (dash-dot curve), at t=500.
Fig. 8. Plot at θ=π of niEr (full curve),
pi (broken curve), and −0.1ni
vθ
/(1+0.2cosθ) (dash-dot curve). The curve −ni/12 is plotted for reference (dash-3 dots curve), t=500.
Fig. 9. Plot at θ=0 of niEr (full curve),
pi (broken curve), and −0.1ni
vθ
/(1+0.2cosθ) (dash-dot curve). The curve −ni/12 is plotted for reference (dash-3 dots curve), for θ=0, at t=500.
Fig. 10. Plot at θ=0 of Er (full curve),
pi/ni (broken curve), −0.1
vθ
/(1+0.2cosθ) (dash-dot curve). The curve −ni/2 is plotted for reference (dash-3 dots curve), t=500.
Fig. 11. Charge density at θ=0 (full curve), θ=π/2 (broken curve) and θ=π (dash-dot curve) t=500.
Fig. 12. Potential at θ=0 (full curve), θ=π/2 (broken curve) and θ=π (dash-dot curve), at t=480.
Fig. 13. Potential at θ=0 (full-curve), θ=π/2 (broken curve), and θ=π (dash-dot curve), at t=500.
Fig. 14. Temperature Tir at θ=0 (full curve), θ=π/2 (broken curve) and θ=π (dash-dot curve). The dash-3 dots curve is for niTir, which is essentially the same for all θ (t=500).
Fig. 15. Temperature Tiθ at θ=0 (full curve), θ=π/2 (broken curve) and θ=π (dash-dot curve). The dash-3 dots curve is for niTiθ, which is essentially the same for all θ (t=500).
Fig. 16. Plot of −Er(1+0.2cosθ)/0.1 for θ=0 (full curve), θ=π/2 (broken curve) and θ=π (dash-dot curve) (t=500).
Fig. 17. Plot of the total poloidal current (−niEr+
pi)/(1+0.2cosθ)/0.1 at θ=0 (full curve), θ=π/2 (broken curve) and θ=π (dash-dot curve) (t=500).
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