Boundary conditions for plasma fluid models at the magnetic presheath entrance J. Loizu, P. Ricci, F.D. Halpern, S. Jolliet, A. Mosetto ´ Ecole Polytecnique F´ ed´ erale de Lausanne Centre de Recherches en Physique des Plasmas Association Euratom-Conf´ ed´ eration Suisse CH-1015 Lausanne, Suisse
Marseille, December 19th, 2012
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Boundary conditions
The problem of fluid codes
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Quasi-neutrality ne ' ni is assumed I
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A drift ordering is usually adopted, d/dt ωci , leading to the 0 ion drift approximation : v⊥i = vExB + ωbci × ddt vExB I
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This is violated in the Debye sheath
This is violated in the Magnetic presheath
Need B.C. that supply the sheath physics to fluid codes I I
To describe the main plasma dynamics To predict the particle and energy fluxes at the solid surface
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Boundary conditions
Simulations of the plasma-wall transition with ODISEE (a)
4
CP
e φ / Te
3 2 1
Total potential drop
MP DS
0
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12
1D3V
14
16
18
20
22
20
22
(b) 2
B = B0
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Ti Te
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ρe . λD ρs λmfp < L
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Absorbing walls
vs / cs
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1.5 1
vsi
0.5 0
12
14
16
18 (c)
2 vx / cs
1.5
vIDA
1 0.5 0
vxi 12
14
16
18
22
(d)
2
v
1.5 vy / cs
20
IDA
1 0.5
v
yi
0
12
14
18
20
22
18
20
22
(e)
0.6 (ni−ne) / nse
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0.4 0.2 0 12
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16 s / ρs
Boundary conditions
A theory to describe the magnetic presheath entrance A theoretical framework has been developed, from which one can derive a complete set of B.C. at the MP entrance « 2φ 1 θTe − θφ 2 Te „ « 2φ v||e = cs ± exp (Λ − ηm ) − θφ + 2(θn + θTe ) Te « „ 1 ∂s φ = −cs ±1 + θn ± θTe ∂s v||i 2 „ « 1 n ±1 + θn ± θTe ∂s v||i ∂s n = − cs 2 „
v||i = cs
±1 + θn ∓
∂s Te = κT ∂s φ h i ω = − cos2 α (1 + θTe ) (∂s v||i )2 + cs (±1 + θn ± θTe /2) ∂s2 v||i
Effect of radial gradients ∂x n, ∂x φ, ∂x Te :
θA =
cs ∂x A 2 tan α A
[Loizu et al., Physics of Plasmas, 2012]
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Boundary conditions
SOL simulations with self-consistent boundary conditions at the magnetic presheath entrance
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Boundary conditions
Parallel currents are drawn by the limiter plates
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Boundary conditions
Currently studying
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Equilibrium profiles in the SOL
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Spontaneous toroidal plasma rotation driven by the sheath
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Effect of the limter position on the SOL width
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Code validation (TORPEX)
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Boundary conditions
