HYBRID GLOBAL MODEL SIMULATIONS OF He/N2 AND He/H2O ...lieber/LiebGEC141024crop.pdf · University...
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University of California, Berkeley PLASMA
HYBRID GLOBAL MODEL SIMULATIONSOF He/N2 AND He/H2O ATMOSPHERIC PRESSURE
CAPACITIVE DISCHARGES
M.A. Lieberman
Department of Electrical Engineering and Computer SciencesUniversity of California
Berkeley, CA 94720
Collaborators:E. Kawamura, A.J. Lichtenberg, UC BerkeleyKe Ding, Donghua University, Shanghai, ChinaC. Lazzaroni, University Paris 13, FranceP. Chabert, Ecole Polytechnique, France
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OUTLINE
• He/0.1%N2 discharge with simplified chemistry
— Particle-in-cell (PIC) simulations (hours to days)
— Use PIC to develop fast hybrid global model(two electron temperatures + sheaths)
— Hybrid global model simulations (30 seconds)
— Electron multiplication in sheaths ⇒ α-to-γ transition
• He/H2O bounded discharge with complex chemistry
— Depletion of H2O, reaction product diffusion
— Hybrid model simulations (two minutes)
— α-to-γ transition including depletion/diffusion effects
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He/N2 DISCHARGE
(Kawamura et al, PSST 23, 035014, 2014)
• Helium with 1000 ppm nitrogen at 760 Torr
• 1D plane-parallel geometry with 1 mm gap
• Current driven at 13.56–40.68 MHz, J = 400–6000 A/m2
• Simplified reaction set with fixed He and N2 densities:
e + He → e + He, Elastic Scatteringe + N2 → e + e + N+
2, Ionization
e + N+
2→ N + N, Recombination (N is not followed in the PIC)
N+
2+ He → N+
2+ He, Ion Elastic Scattering
e + He → e + He∗, Metastable ExcitationHe∗ + 2He → He∗
2+ He, Loss of He∗ (He∗
2is not followed in the PIC)
He∗ + N2 → e + N+
2+ He, Penning Ionization by He∗
He∗ + He → He∗ + He, He∗ Elastic Scattering
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PIC RESULTS (27.12 MHz, 1 mm gap, 1000 ppm N2)α-mode γ-mode
0 0.0002 0.0004 0.0006 0.0008 0.001
x (m)
0
5e+16
1e+17
1.5e+17
Density (m )
He*
N2+e-
-3
400 A/m 2
0 0.0002 0.0004 0.0006 0.0008 0.001
x (m)
0
2e+18
4e+18
6e+18
8e+18
1e+19Density (m )
He*
N2+
e-
-3
2000 A/m 2
0 0.0002 0.0004 0.0006 0.0008 0.001
x (m)
0.001
0.01
0.1
1
Temperature (V)
e-
N2+
He*
0 0.0002 0.0004 0.0006 0.0008 0.001
x (m)
0.001
0.01
0.1
1
Temperature (V)
e-
N2+
He*
Sheath SheathHe* insheath
He* insheath
Hot ThHot Th
Bulk Te
Bulk Te
e-i recomb
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PIC RESULTS (cont’d)
α-mode
γ-mode
400 A/m2
2000 A/m2
400 A/m2
2000 A/m2
• Half of Penning ionization in high-field sheath region in γ-modeLiebermanGEC14 5
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He/N2 HYBRID MODEL ASSUMPTIONS
• Homogeneous discharge model for E(z, t) and s(t) (analytic)
• Electron power balance in bulk determines warm Te(t) (analytic)(ohmic power J · E ≈ e-He elastic scattering power loss)
• E/nHe in sheaths determines hot Th(t) (analytic, BOLSIG+)
• Time-average over oscillating temperatures gives warm and hotelectron rate coefficients (analytic, BOLSIG+)
• Uniform or triangular ion source profile within Child law sheathdetermines the mobility-driven ion wall losses (analytic)
• Secondary and Penning multiplication factors (numerical)
• Particle balance relations (numerical, using MATLAB ode15s)
⇒ Fast solution of discharge equilibrium
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HYBRID MODEL – PIC COMPARISON
27.12 MHz
13.56 MHz
0 1000 2000 3000 4000 5000 6000
J (A/m )
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
PICUni SourceTri SourceTri Src, no Mult
Average T (V)
2
e
400 1000 6000
J (A/m )
1e+17
1e+18
1e+19PICUni SourceTri SourceTri Src, no Mult
Average n (m )-3
2
i
0 500 1000 1500 2000 2500 3000
J (A/m )
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
PICUni SourceTri SourceTri Src, no Mult
Average T (V)
2
e
400 1000 3000
J (A/m )
1e+17
1e+18
1e+19PICUni SourceTri SourceTri Src, no Mult
Average n (m )-3
2
i
Collapse ofwarm Te
n ∝ J/√Te
Collapse ofwarm Te
n ∝ J/√Te
• Field at wall Ew = J/ωǫ0 ≈ 106 V/m at α-to-γ transitionLiebermanGEC14 7
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He/H2O MODELING
• In an experiment, a 1 cm radius 0.5 mm gap discharge was embeddedin a large chamber with fixed H2O concentration
(P. Bruggeman et al, JPD 43, 012003, 2010)
nHe+ next,H2O
(fixed)
Discharge
• In a global model (46 species, 577 reactions), particle and energybalance were solved to determine the discharge equilibrium
(D.X. Liu et al, PSST 19, 025018, 2010)
• Discharge depletes external H2O density, reaction products diffuseto axial and radial walls, sheaths cause α-to-γ transition
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He/H2O ADDITIONAL HYBRID MODEL PHYSICS
(Ke Ding et al, JPD 47, 305203, 2014)
• Diffusive flow of H2O into discharge region (analytic)
• Diffusive flow of reaction products to walls (analytic)
• Multiple Penning processes and positive ion wall losses (numerical)
• 203 reactions, 43 species (includes clusters up to H19O+9 )
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VARIATIONS WITH J AND H2O CONCENTRATION
• Radius 1 cm, gap 0.5 mm, 13.56 MHz, secondary emission = 0.25
No α-modeat 10000 ppm(sheaths fill gap)
Collapse ofwarm Te
γ
Secondary multiplication Mγdominates Penning multiplication MP
Penning ionizationdominates α-mode
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DENSITY VARIATIONS WITH J AT 1000 ppm H2O
• Radius 1 cm, gap 0.5 mm, 13.56 MHz, secondary emission = 0.25
ne ∝ J
nh ≈ const
HeH+
00010011E14
1E15
1E16
1E17
1E18
Density (
m-3
)
J (A/m2)
H2O3+
H3O+
H4O2+
H5O2+
H7O3+
H9O4+
H11O5+
H13O6+
H15O7+
ne
H11O5+ne ∝ J
• H11O+5 is the main ion in α-mode
• HeH+ is the main ion in the γ-mode
• The α-mode scalings ne ∝ J and nh ≈ const are seen
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PRINCIPAL REACTION PATHWAYS ANALYSIS
(Ke Ding et al, submitted to JPD, 2014)
• Open source software package PumpKin (www.pumpkin-tool.org)
(A. H. Markosyan, A. Luque, F. Gordillo-Vazquez, and U. Ebert,Comput. Phys. Commun. 185, 2697, 2014)
• Example of O2 formation from H2O
— The important intermediates are OH, HO2, and H2O2
— OH is produced from H2O via Penning ionization-initiatedcluster formation, and also by direct electron dissociation
— OH production is followed by
2 · (2 OH + He → H2O2 + He)
e + H2O2 → 2 OH + e
OH + H2O2 → HO2 + H2O
OH + HO2 → O2 + H2OLiebermanGEC14 12
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SUMMARY
• We used PIC simulations of a He/N2 atmospheric pressure rf capac-itive discharge, with simplified chemistry, to develop a hybrid globalmodel including sheaths and two electron temperatures.
• The hybrid model simulations of the discharge gave reasonable agree-ment with the PIC simulations, including the α-to-γ transition.
• We added trace gas depletion and reaction product diffusion to thehybrid model to simulate a chemically complex He/H2O boundeddischarge.
• We determined the H2O depletion, the reaction product diffusion,the α-to-γ transition, the suppression of the α-mode by the sheathsat high H2O concentrations, and the principal pathways for variousspecies.
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