PLASMA DYNAMICS AT THE IONIZATION FRONT OF HIGH PRESSURE DISCHARGES USING ELECTRON MONTE

PLASMA DYNAMICS AT THE IONIZATION FRONT OF HIGH PRESSURE DISCHARGES USING ELECTRON MONTE

CARLO SIMULATIONS ON AN ADAPTIVE MESH*

Ananth N. Bhoja) and Mark J. Kushnerb)

a)Department of Chemical and Biomolecular Engineering

University of Illinois, Urbana, IL, USA.Email: [email protected]

b)Department of Electrical and Computer EngineeringIowa State University, Ames, IA, USA.

Email: [email protected]

http://uigelz.ece.iastate.edu

Gaseous Electronics Conference, October 2006

* Work supported by the National Science Foundation.

OUTLINE

GEC06_agenda

Introduction: High Pressure Discharges

Plasma Hydrodynamics Model

Kinetic Model – eMCS on Adaptive Mesh

Plasma Dynamics at the Ionization Front

100s Torr - Corona Discharges

10s Torr - Breakdown in cold HID lamps

Summary

Iowa State UniversityOptical and Discharge Physics

PLASMA DYNAMICS AT THE IONIZATION FRONT

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The ionization front during breakdown at high pressure (10s Torr to 1 atm) is a region of high E/N (100s Td) having steep gradients.


Large “confined” E/N produces large Te and ionization rates.

Though high pressure discharges are collisional, these gradients may be so severe (few Td/m) that electron transport can be non-local.

MODELING OF PLASMA DYNAMICS AT THE IONIZATION FRONT

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Non-local transport in ionization fronts can be expected when

For these conditions both high spatial resolution and kinetic transport of electrons are required.

Two-dimensional (2D) plasma hydrodynamics models employing fluid techniques typically do not capture non-local effects.

To address these conditions, a 2D kinetic electron Monte-Carlo simulation (eMCS) module within a fluid model was developed to track and resolve electron dynamics at the ionization front.


ee

NENE

t

NENE

,1

Iowa State University

Optical and Discharge Physics

2-D PLASMA MODELING PLATFORM

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Fully implicit solution of Poisson’s equation.

Continuity: Multi-fluid charged species equations using modified Scharfetter-Gummel fluxes.

Surface charge on dielectric surfaces.

2-d unstructured mesh, finite volume methods, Newton integration.


ELECTROSTATICS, CHARGED PARTICLE TRANSPORT

iiis tNqt-t )()(

iii St

N

iEiii

S jqt

1

)exp(1

)exp(

ij

ijijij x

xnnD

D

xqq

ij

ij

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ELECTRON, NEUTRAL TRANSPORT, REACTION KINETICS

Electron energy transport of bulk electrons:

Neutral species updated in a time-spliced manner between updates

to charged species.

Reaction Kinetics include sources due to electron impact and heavy particle reactions, photoionization and contributions from secondary emission.

eeeeeee TTkTTLTStkTn

2

5/

2

3

2

3

4

exp)()(

)(rr

rdrr

rNrN

rSjiji

Pi

jjijSi jjS ,

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iii St

N

iii ND

POSITIVE CORONA DISCHARGE

Corona discharge as used for polymer surface treatment with a powered electrode (V0) 2 mm from a grounded plane.

Air at 760 Torr, V0 = 15 kV

Species:

e, N2, N2*, N2

+, N2**, N4

+, N, N+, O2, O2+, O-, O2

*, O2*(1S), O*, O(1S), H, OH.

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POSITIVE CORONA BREAKDOWN

15 kV, 760 Torr, N2/O2/H2O=79/20/1, 5 ns

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E/N is enhanced at the ionization front to 500-1000 Td.

The enhanced E/N increases Te which rises at the front to 6 - 7 eV.

In the ionized channel, E/N falls below 50 Td with Te = 0.5 -1 eV.

[e] of 1013 cm-3 in channel.

MIN MAX

[e] cm-3 E/N (Td) Te (eV)

150 m

5x1012 - 5x1015 30-3000 0 - 10

Iowa State UniversityOptical and Discharge PhysicsAnimation Slide-AVI



NON-LOCAL ELECTRON TRANSPORT - eMCS

Electron transport may become “non-local” due to large E/N (500-1000 Td) and severe gradients (1000s Td/mm).

Kinetic approaches are required to obtain the electron energy distribution (EED), f(r,,t) in position and time to compute electron transport and reaction rates.

Calculating f(r,,t) over the entire domain is computationally prohibitive.

Our kinetic approach uses an electron Monte-Carlo simulation on smaller “regions of non-equilibrium” identified during the avalanche using “sensors”.

Outside these regions, calculations proceed as before using the hydrodynamics equations.

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Sensors identify regions on the unstructured mesh.

Te, ionization rates E/N (E/N) [e]

Combination of sensor outputs identify “non-equilibrium.”


ADAPTIVE eMCS – SENSORS AND MESH

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Boundary of non-equilibrium region with superimposed rectilinear mesh

For example, the non-equilibrium region in a positive corona can be tracked using

[e] 1011 cm-3 (E/N) 0.01 (E/N)max

A rectilinear mesh is superimposed over non-equilibrium region upon which eMCS is performed.



ADAPTIVE eMCS – PARTICLE LAUNCHING

Pseudoparticles weighted by electron flux moving into the region are launched from edges to obtain f(r,,t) inside the region.

Velocity of launched particles is the vector sum VT of vthermal at a randomly selected angle and the drift velocity vd.

)exp(1

)exp(

ij

ijijdirectedij x

xnnD

randomthermalii

thermalij vn ,

4

1

)1log(28 ,, rm

kTv

e

ierandomthermali

Edges of MCS mesh

i

j

directedij

directedi nv

,

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r = random numberVT

Trajectories of particles are integrated in time on the rectilinear mesh using interpolated electric fields to obtain f(r,,t).

Using f(r,,t), electron energy and electron impact sources are calculated on the rectilinear mesh and interpolated back to unstructured mesh nodes for use in the hydrodynamic model.

The Adaptive eMCS Module is called frequently enough to track the dynamics of the non-equilibrium region.


ADAPTIVE eMCS COUPLED TO HYDRODYNAMICS

df )(

dNkfr kji

k ),()(,

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POSITIVE CORONA: TRACKING THE FRONT

15 kV, 760 Torr, N2/O2/H2O=79/20/1, 5 ns

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eMCS mesh tracks regions of high (E/N).

[e] > 1011 cm-3

(E/N) > 1% of max.

Particles are launched from nodes on edges with a net influx of electrons to the region.

eMCS called every 100 ps.

1 30

150 m

Iowa State UniversityOptical and Discharge PhysicsAnimation Slide-AVI

(E/N) eMCS region103 (Td/mm)

Particle launch nodes

(E/N) 103 Td/mm

POSITIVE CORONA: Te

15 kV, 760 Torr, N2/O2/H2O=79/20/1

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At the ionization front, eMCS produce peak values of Te of 6 – 7 eV as it traverses the gap, about 1 eV higher than fluid model.

0 12150 m

eMCS


Animation Slide-AVI

Te (eV)

15 kV, 760 Torr, N2/O2/H2O=79/20/1

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Maxima in electron impact ionization sources with eMCS are smaller than with fluid model.

The higher Te and lower ionization sources indicate non-equilibrium in the EED at the front (cut-off tail).

1021 1025


Ionization Sources (cm-3s-1)

150 m

Animation Slide-AVI

POSITIVE CORONA: IONIZATION SOURCES

eMCS

15 kV, 760 Torr, N2/O2/H2O=79/20/1

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[e] density in the ionized channel 2 – 3 times lower with eMCS due to lower ionization sources.

Width of channel is narrower and more in-tune with experimental observations.

5x1012 5x1015


[e] (cm-3)

150 m

Animation Slide-AVI

POSITIVE CORONA: ELECTRON DENSITY

eMCS

BREAKDOWN IN COLD HID LAMPS : 10s Torr Investigations into breakdown in a cylindrically symmetric lamp

based on the experimental lamp geometry.

Dielectric

Groundedhousing

Air

Groundedelectrode

Poweredelectrode

Quartz tube

Plasma

Cylindrical center line

Dielectric

CL

0.5cm

0.5 cmRADIUS (cm)

HE

IGH

T

(cm

)

EL

EC

TR

OD

E G

AP

= 1

.6 c

m

Ar, 10s Torr, V0= 2000 V

Species: e, Ar, Ar*, Ar**, Ar+, Ar2*, Ar2

+. Iowa State UniversityOptical and Discharge PhysicsANANTH_GEC06_16

TRACKING THE IONIZATION FRONT


Ionization front with steep gradients in [e] and ionization sources moves across the gap.

eMCS sensors are the ratios

A second fixed eMCS mesh tracks secondary electrons emitted from the cathode due to photons, ion bombardment.

MIN MAX

[e]

1013 cm-3

[Sources]

1020 cm-3s-1

Te

10 eV MCS

Ar, 30 Torr, 2000 V, 400 ns

Animation Slide-AVIANANTH_GEC06_17

%01.][

][

max

e

e%1

][

][

max

ionization

ionization

S

S

EFFECT OF PRESSURE : Te


Ar, 2000 V

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0 10Animation Slide-AVI

Te at the front decreases with increasing pressure due to lower E/N.

Te from eMCS is 1.5 eV higher at 30 Torr, and 1 eV higher at 90 Torr.Te (eV)

30 Torr 50 Torr 90 Torr355 ns eMCS, 400 ns 540 ns eMCS, 700 ns 1245 ns eMCS, 1585 ns

5.5 6.47.7*6.2 5.0 6.1

* Typical values at locations midway across the gap as avalanche passes by.



Ar, 2000 V

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1017 1020Animation Slide-AVI

EFFECT OF PRESSURE : IONIZATION SOURCES

eMCS sources are also lower, indicating some non-equilibrium in the EED, but is comparable to fluid model values at higher pressures.

eMCS eMCS eMCS

[Sources] cm-3s-1

30 Torr 50 Torr 90 Torr

2.5 x 1019 1.1 x 10191 x 1019*4.5 x 1019 1.4 x 1019 1.1 x 1019




Ar, 2000 V

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109 1013

Animation Slide-AVI

EFFECT OF PRESSURE : ELECTRON DENSITY

[e] density increases with pressure, but is lower with eMCS since ionization sources are lower.

eMCS eMCS eMCS30 Torr 50 Torr 90 Torr

[e] cm-3

2.3 x 1011 1.0 x 10111.0 x 1011*2.2 x 1011 3.8 x 1011 2.5 x 1011


SUMMARY

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An eMCS was developed on adaptive meshes that track the ionization front of high pressure discharges using sensors.

In corona discharges at 100s Torr, the kinetic approach using eMCS yields Te 1 – 2 eV higher at the front.

eMCS calculated electron impact ionization sources have peak values lower by 3 – 5 times at the front, indicating non-equilibrium in the cut-off tail of the EED at these locations.

Electron density in the channel behind the ionization front is lower with eMCS, but the channel is also narrower in extent.

During breakdown in cold Ar-filled HID lamps at 10s Torr, Te at the

front using eMCS are greater than fluid Te values but this difference diminishes as pressure increases.

At constant pressure, ionization sources and electron density are lower by 2 – 3 with eMCS than fluid values.


The Adaptive eMCS is called at time intervals frequent enough to track the dynamic ionization front.


ADAPTIVE eMCS ALGORITHM FLOWCHART

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PLASMA DYNAMICS AT THE IONIZATION FRONT OF HIGH PRESSURE DISCHARGES USING ELECTRON MONTE

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