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

Download this talk:

http://www.eecs.berkeley.edu/∼lieber

LiebermanGEC14 1

University of California, Berkeley PLASMA

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

LiebermanGEC14 2

University of California, Berkeley PLASMA

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

LiebermanGEC14 3

University of California, Berkeley PLASMA

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

LiebermanGEC14 4

University of California, Berkeley PLASMA

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

University of California, Berkeley PLASMA

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

LiebermanGEC14 6

University of California, Berkeley PLASMA

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

University of California, Berkeley PLASMA

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

LiebermanGEC14 8

University of California, Berkeley PLASMA

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 )

LiebermanGEC14 9

University of California, Berkeley PLASMA

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

LiebermanGEC14 10

University of California, Berkeley PLASMA

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

LiebermanGEC14 11

University of California, Berkeley PLASMA

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

University of California, Berkeley PLASMA

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.

Download this talk:

http://www.eecs.berkeley.edu/∼lieber

LiebermanGEC14 13