Modeling of dust formation in a DC discharge A.Michaua*, G. Lombardia, C. Arnasb, X. Bonnina and K. Hassounia aLaboratoire
d'Ingénierie des Matériaux et des Hautes Pressions (LIMHP), UPR 1311 CNRS, Université Paris 13, F-93430 Villetaneuse, France. de Physique des Interactions Ioniques et Moléculaires (PIIM), UMR 6633 CNRS-Université de Provence, F-13397 Marseille, France.
bLaboratoire
In tokamaks with carbon plasma-facing components, one can observe the presence of nano-sized dust particulates. Understanding such dust particle formation is a prerequisite to any attempt to limit or avoid this dust that may be responsible for tritium retention and pollution of the plasma. We report on coupled modelling of carbon chemistry and dust particle nucleation, growth, and transport in a plasma discharge. The results are compared to experimental measurements made at LPIIM from low-pressure argon DC discharges with a graphite cathode, serving as a proxy for the tokamak plasma edge. The time evolution of the “large” dust particles consists of a nucleation phase followed by a coagulation phase. These reach a dust grain size of 40 nm on a timescale comparable to the observations inside the LPIIM device (minutes to hours). The dependencies of cluster size distribution and growth speed on plasma parameters and details of the chemical model are analyzed. The experimentally observed particle population is the net result of this complex chemistry, transport and aerosol dynamics mechanism.
Model
DustDust-free DC discharge module A low particle density allows us to use a dust-free discharge model • 3 electron population : energetic, passing, trapped • Monte-Carlo simulation combined with analytic model 2 V0/dc
Cluster module
Particle module
Neutral and negative cluster time-evolution governed by a drift-diffusion equation
Growth and transport of particles resulting from the nucleation process
• Sputtering of C, C2, C3 i +i Eb (∆G'i +∆G' j ) .exp − .exp −γ i. j kT RT
kij = Vthσij
Energetic electrons (γ) Passing electrons (j) Trapped electrons (ne) and negative ions
E eφ
NG
• Charge transfer
PC
x R
x1
• Trapped electron density • Electric field profile (field reversal)
(
Eai − Eaj i +i .exp − ζ i. j kT
Tij = Vthσij
E0 sheath d x0 c
C n− + C x → C n−+ x
Cn + C x − > C n + x
Averaged mass : • Cluster mass addition by nucleation and sticking on the particles • Transport by electric field and diffusion
• Electron attachment/detachment
~C15
Simulation parameters : DC discharge
• Te=0.1eV (this value was chosen from Tsendin) • Tg = 373.15K • ζ = 0.1 • Sputtering yield at the cathode of 10-4. • Parametric study of aggregation activation energy Eb = 0.2 -0.225 -.23eV Results are given at 600 s
Ar -
+
2.5 nm
See C. Arnas,et al., PSI-16, JNM 337-339 (2005), 69. Carbon is emitted by sputtering of the graphite cathode: - Argon ions undergoing sheath acceleration - Energetic neutrals from CX reactions Carbon forms clusters than aggregate into dust particulates
Ar+
1
1.0x10
• Short discharge : no PC or FDS
e=0.1eV E
1E11
0.0
• Maximum electron density of 1011cm-3 decreasing to 1010cm-3
0
-5.0x10
1
-1.0x10
1E10
• Existence of an electric field reversal - > trapping of negatively charged species
Numerical chemical model
1E9
0
2
4
6
8
5x10
8
4x10
8
3x10
8
2x10
8
1x10
Eb=0.2 Eb=0.225 Eb=0.23
• Existence of magic number distribution correctly reproduced • Neutral cluster densities are much smaller than negatively charged ones
• Growth of particles in the field reversal region
• Loss of neutral clusters to the electrodes and walls
• Maximum electron density of 109cm-3 with an averaged diameter of 20 nm consistent with experimental value and model assumption
8
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
carbon number
• Existence of particles near the sheath in the field reversal region due to the trapping of charged species
• Small Eb : aggregation easier compared with others cluster processes
22
Eb=0.2 Eb=0.225 Eb=0.23
18
7
10
2
10
10
2
-6
10
1
2
3
4
5
6
7
8
9
10 11
carbon number
LIMHP Université Paris 13, CNRS Institut Galilée, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, FRANCE Fax : 01 49 40 34 14
12
13
14
15
7
10
6
5
10
4
10
3
10
2
0
2
4
6
8
10
12
14
x (cm)
8
4
-4
8
10 10
Eb=0.2 Eb=0.225 Eb=0.23
9
10
0
1
2
3
12
x (cm)
Corresponding authors : Armelle Michau –
[email protected] +33-(0)1.49.40.34.10 Khaled Hassouni –
[email protected] +33-0(1).49.40.34.11 http://www-limhp.univ-paris13.fr
14
5
-2x10
5
-3x10
5
-4x10
5
-5x10
5
Anode
x (cm)
10
10
-1x10
14
Faster aggregation -> more small particles
12
10
-2
12
14
6
10
10
16
0
10
• Nucleation of negative particles by C15-
8
• Competition between aggregation and sticking of clusters
Eb=0.2 Eb=0.225 Eb=0.23
20
dust diameter (nm)
• Cluster growth by attachment on small neutral clusters and aggregation of large negative cluster with C, C2, C3
neutral cluster density (cm-3)
9
10
10
dust density (cm-3)
negative cluster density (cm-3)
Cathode
6x10
0
5.0x10
Slower aggregation -> more C, C2, C3 stick on the particles
E (V/cm)
P = 0.6 mbar VDC = - 550 V Tg=375 K I=8x10-2 A
-3
Biasing : 550 V Inter-electrode distance: 14 cm Electrode diameter : 10 cm Current: 8x10-2 A
ne (cm )
LPIIM Reactor
